1,-2,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c-c*sin(f*x+e))^(7/2)*(a+a*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*(-144*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(f*x+exp(1))/(16*f)^2-96*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(3*f*x+3*exp(1))/(96*f)^2+480*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(5*f*x+5*exp(1))/(160*f)^2-448*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(2*f*x+2*exp(1))/(64*f)^2-3328*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(4*f*x+4*exp(1))/(256*f)^2+384*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(6*f*x+6*exp(1))/(384*f)^2-1664*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(-2*f*x-2*exp(1))/(-128*f)^2+256*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(-4*f*x-4*exp(1))/(-256*f)^2)","F(-2)",0
2,-2,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c-c*sin(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*(-112*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(f*x+exp(1))/(16*f)^2-288*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(3*f*x+3*exp(1))/(96*f)^2+160*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(5*f*x+5*exp(1))/(160*f)^2-16*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(2*f*x+2*exp(1))/(16*f)^2-32*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(4*f*x+4*exp(1))/(32*f)^2-16*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(-2*f*x-2*exp(1))/(-16*f)^2)","F(-2)",0
3,-2,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c-c*sin(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*(-24*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(f*x+exp(1))/(8*f)^2-24*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(3*f*x+3*exp(1))/(24*f)^2-32*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(2*f*x+2*exp(1))/(32*f)^2-64*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(4*f*x+4*exp(1))/(64*f)^2-32*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(-2*f*x-2*exp(1))/(-32*f)^2)","F(-2)",0
4,-2,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(1/2)*(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*(-24*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(f*x+exp(1))/(8*f)^2-24*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(3*f*x+3*exp(1))/(24*f)^2)","F(-2)",0
5,-2,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)4*sqrt(2*a)*((sqrt(c*tan(1/2*exp(1))^2+c)*(-324259173170675712*tan(1/2*exp(1))^7+1188950301625810944*tan(1/2*exp(1))^5-684547143360315392*tan(1/2*exp(1))^3+108086391056891904*tan(1/2*exp(1)))+sqrt(c*tan(1/2*exp(1))^2+c)*(tan(1/2*(1/2*f*x+2*exp(1)))-1/tan(1/2*(1/2*f*x+2*exp(1))))^2*(40532396646334464*tan(1/2*exp(1))^8-81064793292668928*tan(1/2*exp(1))^7-378302368699121664*tan(1/2*exp(1))^6+297237575406452736*tan(1/2*exp(1))^5+567453553048682496*tan(1/2*exp(1))^4-171136785840078848*tan(1/2*exp(1))^3-162129586585337856*tan(1/2*exp(1))^2+27021597764222976*tan(1/2*exp(1))+4503599627370496)+sqrt(c*tan(1/2*exp(1))^2+c)*(tan(1/2*(1/2*f*x+2*exp(1)))-1/tan(1/2*(1/2*f*x+2*exp(1))))^3*(1125899906842624*tan(1/2*exp(1))^9-6755399441055744*tan(1/2*exp(1))^8-40532396646334464*tan(1/2*exp(1))^7+103582791429521408*tan(1/2*exp(1))^6+141863388262170624*tan(1/2*exp(1))^5-135107988821114880*tan(1/2*exp(1))^4-94575592174780416*tan(1/2*exp(1))^3+40532396646334464*tan(1/2*exp(1))^2+10133099161583616*tan(1/2*exp(1))-2251799813685248)+sqrt(c*tan(1/2*exp(1))^2+c)*(tan(1/2*(1/2*f*x+2*exp(1)))-1/tan(1/2*(1/2*f*x+2*exp(1))))*(-4503599627370496*tan(1/2*exp(1))^9-27021597764222976*tan(1/2*exp(1))^8+162129586585337856*tan(1/2*exp(1))^7+414331165718085632*tan(1/2*exp(1))^6-567453553048682496*tan(1/2*exp(1))^5-540431955284459520*tan(1/2*exp(1))^4+378302368699121664*tan(1/2*exp(1))^3+162129586585337856*tan(1/2*exp(1))^2-40532396646334464*tan(1/2*exp(1))-9007199254740992)+sqrt(c*tan(1/2*exp(1))^2+c)*(324259173170675712*tan(1/2*exp(1))^7-1188950301625810944*tan(1/2*exp(1))^5+684547143360315392*tan(1/2*exp(1))^3-108086391056891904*tan(1/2*exp(1)))*tan(1/4*exp(1))^6+sqrt(c*tan(1/2*exp(1))^2+c)*(-648518346341351424*tan(1/2*exp(1))^8+4107282860161892352*tan(1/2*exp(1))^6-7133701809754865664*tan(1/2*exp(1))^4+1945555039024054272*tan(1/2*exp(1))^2)*tan(1/4*exp(1))^5+sqrt(c*tan(1/2*exp(1))^2+c)*(2161727821137838080*tan(1/2*exp(1))^8-13690942867206307840*tan(1/2*exp(1))^6+23779006032516218880*tan(1/2*exp(1))^4-6485183463413514240*tan(1/2*exp(1))^2)*tan(1/4*exp(1))^3+sqrt(c*tan(1/2*exp(1))^2+c)*(4863887597560135680*tan(1/2*exp(1))^7-17834254524387164160*tan(1/2*exp(1))^5+10268207150404730880*tan(1/2*exp(1))^3-1621295865853378560*tan(1/2*exp(1)))*tan(1/4*exp(1))^2+sqrt(c*tan(1/2*exp(1))^2+c)*(-648518346341351424*tan(1/2*exp(1))^8+4107282860161892352*tan(1/2*exp(1))^6-7133701809754865664*tan(1/2*exp(1))^4+1945555039024054272*tan(1/2*exp(1))^2)*tan(1/4*exp(1))+sqrt(c*tan(1/2*exp(1))^2+c)*(-4863887597560135680*tan(1/2*exp(1))^7+17834254524387164160*tan(1/2*exp(1))^5-10268207150404730880*tan(1/2*exp(1))^3+1621295865853378560*tan(1/2*exp(1)))*tan(1/4*exp(1))^4+sqrt(c*tan(1/2*exp(1))^2+c)*(tan(1/2*(1/2*f*x+2*exp(1)))-1/tan(1/2*(1/2*f*x+2*exp(1))))^2*(90071992547409920*tan(1/2*exp(1))^9+540431955284459520*tan(1/2*exp(1))^8-3242591731706757120*tan(1/2*exp(1))^7-3422735716801576960*tan(1/2*exp(1))^6+11349071060973649920*tan(1/2*exp(1))^5+5944751508129054720*tan(1/2*exp(1))^4-7566047373982433280*tan(1/2*exp(1))^3-1621295865853378560*tan(1/2*exp(1))^2+810647932926689280*tan(1/2*exp(1)))*tan(1/4*exp(1))^3+sqrt(c*tan(1/2*exp(1))^2+c)*(tan(1/2*(1/2*f*x+2*exp(1)))-1/tan(1/2*(1/2*f*x+2*exp(1))))^2*(607985949695016960*tan(1/2*exp(1))^8-1215971899390033920*tan(1/2*exp(1))^7-5674535530486824960*tan(1/2*exp(1))^6+4458563631096791040*tan(1/2*exp(1))^5+8511803295730237440*tan(1/2*exp(1))^4-2567051787601182720*tan(1/2*exp(1))^3-2431943798780067840*tan(1/2*exp(1))^2+405323966463344640*tan(1/2*exp(1))+67553994410557440)*tan(1/4*exp(1))^4+sqrt(c*tan(1/2*exp(1))^2+c)*(tan(1/2*(1/2*f*x+2*exp(1)))-1/tan(1/2*(1/2*f*x+2*exp(1))))^2*(-27021597764222976*tan(1/2*exp(1))^9-162129586585337856*tan(1/2*exp(1))^8+972777519512027136*tan(1/2*exp(1))^7+1026820715040473088*tan(1/2*exp(1))^6-3404721318292094976*tan(1/2*exp(1))^5-1783425452438716416*tan(1/2*exp(1))^4+2269814212194729984*tan(1/2*exp(1))^3+486388759756013568*tan(1/2*exp(1))^2-243194379878006784*tan(1/2*exp(1)))*tan(1/4*exp(1))^5+sqrt(c*tan(1/2*exp(1))^2+c)*(tan(1/2*(1/2*f*x+2*exp(1)))-1/tan(1/2*(1/2*f*x+2*exp(1))))^2*(-27021597764222976*tan(1/2*exp(1))^9-162129586585337856*tan(1/2*exp(1))^8+972777519512027136*tan(1/2*exp(1))^7+1026820715040473088*tan(1/2*exp(1))^6-3404721318292094976*tan(1/2*exp(1))^5-1783425452438716416*tan(1/2*exp(1))^4+2269814212194729984*tan(1/2*exp(1))^3+486388759756013568*tan(1/2*exp(1))^2-243194379878006784*tan(1/2*exp(1)))*tan(1/4*exp(1))+sqrt(c*tan(1/2*exp(1))^2+c)*(tan(1/2*(1/2*f*x+2*exp(1)))-1/tan(1/2*(1/2*f*x+2*exp(1))))^2*(-40532396646334464*tan(1/2*exp(1))^8+81064793292668928*tan(1/2*exp(1))^7+378302368699121664*tan(1/2*exp(1))^6-297237575406452736*tan(1/2*exp(1))^5-567453553048682496*tan(1/2*exp(1))^4+171136785840078848*tan(1/2*exp(1))^3+162129586585337856*tan(1/2*exp(1))^2-27021597764222976*tan(1/2*exp(1))-4503599627370496)*tan(1/4*exp(1))^6+sqrt(c*tan(1/2*exp(1))^2+c)*(tan(1/2*(1/2*f*x+2*exp(1)))-1/tan(1/2*(1/2*f*x+2*exp(1))))^2*(-607985949695016960*tan(1/2*exp(1))^8+1215971899390033920*tan(1/2*exp(1))^7+5674535530486824960*tan(1/2*exp(1))^6-4458563631096791040*tan(1/2*exp(1))^5-8511803295730237440*tan(1/2*exp(1))^4+2567051787601182720*tan(1/2*exp(1))^3+2431943798780067840*tan(1/2*exp(1))^2-405323966463344640*tan(1/2*exp(1))-67553994410557440)*tan(1/4*exp(1))^2+sqrt(c*tan(1/2*exp(1))^2+c)*(tan(1/2*(1/2*f*x+2*exp(1)))-1/tan(1/2*(1/2*f*x+2*exp(1))))^3*(16888498602639360*tan(1/2*exp(1))^9-101330991615836160*tan(1/2*exp(1))^8-607985949695016960*tan(1/2*exp(1))^7+1553741871442821120*tan(1/2*exp(1))^6+2127950823932559360*tan(1/2*exp(1))^5-2026619832316723200*tan(1/2*exp(1))^4-1418633882621706240*tan(1/2*exp(1))^3+607985949695016960*tan(1/2*exp(1))^2+151996487423754240*tan(1/2*exp(1))-33776997205278720)*tan(1/4*exp(1))^4+sqrt(c*tan(1/2*exp(1))^2+c)*(tan(1/2*(1/2*f*x+2*exp(1)))-1/tan(1/2*(1/2*f*x+2*exp(1))))^3*(45035996273704960*tan(1/2*exp(1))^9-202661983231672320*tan(1/2*exp(1))^8-810647932926689280*tan(1/2*exp(1))^7+1891511843495608320*tan(1/2*exp(1))^6+2702159776422297600*tan(1/2*exp(1))^5-2837267765243412480*tan(1/2*exp(1))^4-2071655828590428160*tan(1/2*exp(1))^3+810647932926689280*tan(1/2*exp(1))^2+135107988821114880*tan(1/2*exp(1))-22517998136852480)*tan(1/4*exp(1))^3+sqrt(c*tan(1/2*exp(1))^2+c)*(tan(1/2*(1/2*f*x+2*exp(1)))-1/tan(1/2*(1/2*f*x+2*exp(1))))^3*(-1125899906842624*tan(1/2*exp(1))^9+6755399441055744*tan(1/2*exp(1))^8+40532396646334464*tan(1/2*exp(1))^7-103582791429521408*tan(1/2*exp(1))^6-141863388262170624*tan(1/2*exp(1))^5+135107988821114880*tan(1/2*exp(1))^4+94575592174780416*tan(1/2*exp(1))^3-40532396646334464*tan(1/2*exp(1))^2-10133099161583616*tan(1/2*exp(1))+2251799813685248)*tan(1/4*exp(1))^6+sqrt(c*tan(1/2*exp(1))^2+c)*(tan(1/2*(1/2*f*x+2*exp(1)))-1/tan(1/2*(1/2*f*x+2*exp(1))))^3*(-13510798882111488*tan(1/2*exp(1))^9+60798594969501696*tan(1/2*exp(1))^8+243194379878006784*tan(1/2*exp(1))^7-567453553048682496*tan(1/2*exp(1))^6-810647932926689280*tan(1/2*exp(1))^5+851180329573023744*tan(1/2*exp(1))^4+621496748577128448*tan(1/2*exp(1))^3-243194379878006784*tan(1/2*exp(1))^2-40532396646334464*tan(1/2*exp(1))+6755399441055744)*tan(1/4*exp(1))^5+sqrt(c*tan(1/2*exp(1))^2+c)*(tan(1/2*(1/2*f*x+2*exp(1)))-1/tan(1/2*(1/2*f*x+2*exp(1))))^3*(-13510798882111488*tan(1/2*exp(1))^9+60798594969501696*tan(1/2*exp(1))^8+243194379878006784*tan(1/2*exp(1))^7-567453553048682496*tan(1/2*exp(1))^6-810647932926689280*tan(1/2*exp(1))^5+851180329573023744*tan(1/2*exp(1))^4+621496748577128448*tan(1/2*exp(1))^3-243194379878006784*tan(1/2*exp(1))^2-40532396646334464*tan(1/2*exp(1))+6755399441055744)*tan(1/4*exp(1))+sqrt(c*tan(1/2*exp(1))^2+c)*(tan(1/2*(1/2*f*x+2*exp(1)))-1/tan(1/2*(1/2*f*x+2*exp(1))))^3*(-16888498602639360*tan(1/2*exp(1))^9+101330991615836160*tan(1/2*exp(1))^8+607985949695016960*tan(1/2*exp(1))^7-1553741871442821120*tan(1/2*exp(1))^6-2127950823932559360*tan(1/2*exp(1))^5+2026619832316723200*tan(1/2*exp(1))^4+1418633882621706240*tan(1/2*exp(1))^3-607985949695016960*tan(1/2*exp(1))^2-151996487423754240*tan(1/2*exp(1))+33776997205278720)*tan(1/4*exp(1))^2+sqrt(c*tan(1/2*exp(1))^2+c)*(tan(1/2*(1/2*f*x+2*exp(1)))-1/tan(1/2*(1/2*f*x+2*exp(1))))*(4503599627370496*tan(1/2*exp(1))^9+27021597764222976*tan(1/2*exp(1))^8-162129586585337856*tan(1/2*exp(1))^7-414331165718085632*tan(1/2*exp(1))^6+567453553048682496*tan(1/2*exp(1))^5+540431955284459520*tan(1/2*exp(1))^4-378302368699121664*tan(1/2*exp(1))^3-162129586585337856*tan(1/2*exp(1))^2+40532396646334464*tan(1/2*exp(1))+9007199254740992)*tan(1/4*exp(1))^6+sqrt(c*tan(1/2*exp(1))^2+c)*(tan(1/2*(1/2*f*x+2*exp(1)))-1/tan(1/2*(1/2*f*x+2*exp(1))))*(67553994410557440*tan(1/2*exp(1))^9+405323966463344640*tan(1/2*exp(1))^8-2431943798780067840*tan(1/2*exp(1))^7-6214967485771284480*tan(1/2*exp(1))^6+8511803295730237440*tan(1/2*exp(1))^5+8106479329266892800*tan(1/2*exp(1))^4-5674535530486824960*tan(1/2*exp(1))^3-2431943798780067840*tan(1/2*exp(1))^2+607985949695016960*tan(1/2*exp(1))+135107988821114880)*tan(1/4*exp(1))^2+sqrt(c*tan(1/2*exp(1))^2+c)*(tan(1/2*(1/2*f*x+2*exp(1)))-1/tan(1/2*(1/2*f*x+2*exp(1))))*(180143985094819840*tan(1/2*exp(1))^9+810647932926689280*tan(1/2*exp(1))^8-3242591731706757120*tan(1/2*exp(1))^7-7566047373982433280*tan(1/2*exp(1))^6+10808639105689190400*tan(1/2*exp(1))^5+11349071060973649920*tan(1/2*exp(1))^4-8286623314361712640*tan(1/2*exp(1))^3-3242591731706757120*tan(1/2*exp(1))^2+540431955284459520*tan(1/2*exp(1))+90071992547409920)*tan(1/4*exp(1))^3+sqrt(c*tan(1/2*exp(1))^2+c)*(tan(1/2*(1/2*f*x+2*exp(1)))-1/tan(1/2*(1/2*f*x+2*exp(1))))*(-54043195528445952*tan(1/2*exp(1))^9-243194379878006784*tan(1/2*exp(1))^8+972777519512027136*tan(1/2*exp(1))^7+2269814212194729984*tan(1/2*exp(1))^6-3242591731706757120*tan(1/2*exp(1))^5-3404721318292094976*tan(1/2*exp(1))^4+2485986994308513792*tan(1/2*exp(1))^3+972777519512027136*tan(1/2*exp(1))^2-162129586585337856*tan(1/2*exp(1))-27021597764222976)*tan(1/4*exp(1))^5+sqrt(c*tan(1/2*exp(1))^2+c)*(tan(1/2*(1/2*f*x+2*exp(1)))-1/tan(1/2*(1/2*f*x+2*exp(1))))*(-54043195528445952*tan(1/2*exp(1))^9-243194379878006784*tan(1/2*exp(1))^8+972777519512027136*tan(1/2*exp(1))^7+2269814212194729984*tan(1/2*exp(1))^6-3242591731706757120*tan(1/2*exp(1))^5-3404721318292094976*tan(1/2*exp(1))^4+2485986994308513792*tan(1/2*exp(1))^3+972777519512027136*tan(1/2*exp(1))^2-162129586585337856*tan(1/2*exp(1))-27021597764222976)*tan(1/4*exp(1))+sqrt(c*tan(1/2*exp(1))^2+c)*(tan(1/2*(1/2*f*x+2*exp(1)))-1/tan(1/2*(1/2*f*x+2*exp(1))))*(-67553994410557440*tan(1/2*exp(1))^9-405323966463344640*tan(1/2*exp(1))^8+2431943798780067840*tan(1/2*exp(1))^7+6214967485771284480*tan(1/2*exp(1))^6-8511803295730237440*tan(1/2*exp(1))^5-8106479329266892800*tan(1/2*exp(1))^4+5674535530486824960*tan(1/2*exp(1))^3+2431943798780067840*tan(1/2*exp(1))^2-607985949695016960*tan(1/2*exp(1))-135107988821114880)*tan(1/4*exp(1))^4)/(-(tan(1/2*(1/2*f*x+2*exp(1)))-1/tan(1/2*(1/2*f*x+2*exp(1))))^2-4)^2/((2251799813685248*sqrt(2)*c*tan(1/2*exp(1))^10+11258999068426240*sqrt(2)*c*tan(1/2*exp(1))^8+22517998136852480*sqrt(2)*c*tan(1/2*exp(1))^6+22517998136852480*sqrt(2)*c*tan(1/2*exp(1))^4+11258999068426240*sqrt(2)*c*tan(1/2*exp(1))^2+2251799813685248*sqrt(2)*c)*tan(1/4*exp(1))^6+(6755399441055744*sqrt(2)*c*tan(1/2*exp(1))^10+33776997205278720*sqrt(2)*c*tan(1/2*exp(1))^8+67553994410557440*sqrt(2)*c*tan(1/2*exp(1))^6+67553994410557440*sqrt(2)*c*tan(1/2*exp(1))^4+33776997205278720*sqrt(2)*c*tan(1/2*exp(1))^2+6755399441055744*sqrt(2)*c)*tan(1/4*exp(1))^4+(6755399441055744*sqrt(2)*c*tan(1/2*exp(1))^10+33776997205278720*sqrt(2)*c*tan(1/2*exp(1))^8+67553994410557440*sqrt(2)*c*tan(1/2*exp(1))^6+67553994410557440*sqrt(2)*c*tan(1/2*exp(1))^4+33776997205278720*sqrt(2)*c*tan(1/2*exp(1))^2+6755399441055744*sqrt(2)*c)*tan(1/4*exp(1))^2+2251799813685248*sqrt(2)*c*tan(1/2*exp(1))^10+11258999068426240*sqrt(2)*c*tan(1/2*exp(1))^8+22517998136852480*sqrt(2)*c*tan(1/2*exp(1))^6+22517998136852480*sqrt(2)*c*tan(1/2*exp(1))^4+11258999068426240*sqrt(2)*c*tan(1/2*exp(1))^2+2251799813685248*sqrt(2)*c)+1/4*(1/2*pi*sign(tan(1/2*(1/2*f*x+2*exp(1))))+atan(1/2*(tan(1/2*(1/2*f*x+2*exp(1)))^2-1)/tan(1/2*(1/2*f*x+2*exp(1)))))*(sqrt(c*tan(1/2*exp(1))^2+c)*(1073741824*sqrt(2)*tan(1/2*exp(1))^3-3221225472*sqrt(2)*tan(1/2*exp(1)))+sqrt(c*tan(1/2*exp(1))^2+c)*(16106127360*sqrt(2)*tan(1/2*exp(1))^3-48318382080*sqrt(2)*tan(1/2*exp(1)))*tan(1/4*exp(1))^4+sqrt(c*tan(1/2*exp(1))^2+c)*(-1073741824*sqrt(2)*tan(1/2*exp(1))^3+3221225472*sqrt(2)*tan(1/2*exp(1)))*tan(1/4*exp(1))^6+sqrt(c*tan(1/2*exp(1))^2+c)*(-19327352832*sqrt(2)*tan(1/2*exp(1))^2+6442450944*sqrt(2))*tan(1/4*exp(1))^5+sqrt(c*tan(1/2*exp(1))^2+c)*(64424509440*sqrt(2)*tan(1/2*exp(1))^2-21474836480*sqrt(2))*tan(1/4*exp(1))^3+sqrt(c*tan(1/2*exp(1))^2+c)*(-16106127360*sqrt(2)*tan(1/2*exp(1))^3+48318382080*sqrt(2)*tan(1/2*exp(1)))*tan(1/4*exp(1))^2+sqrt(c*tan(1/2*exp(1))^2+c)*(-19327352832*sqrt(2)*tan(1/2*exp(1))^2+6442450944*sqrt(2))*tan(1/4*exp(1)))/(-(2147483648*c*tan(1/2*exp(1))^4+4294967296*c*tan(1/2*exp(1))^2+2147483648*c)*tan(1/4*exp(1))^6-(6442450944*c*tan(1/2*exp(1))^4+12884901888*c*tan(1/2*exp(1))^2+6442450944*c)*tan(1/4*exp(1))^4-(6442450944*c*tan(1/2*exp(1))^4+12884901888*c*tan(1/2*exp(1))^2+6442450944*c)*tan(1/4*exp(1))^2-2147483648*c*tan(1/2*exp(1))^4-4294967296*c*tan(1/2*exp(1))^2-2147483648*c))/f","F(-2)",0
6,-1,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
7,-1,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
8,-1,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
9,-2,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(7/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*(-5760*a*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(f*x+exp(1))/(128*f)^2-7296*a*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(3*f*x+3*exp(1))/(384*f)^2-640*a*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(5*f*x+5*exp(1))/(640*f)^2+896*a*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(7*f*x+7*exp(1))/(896*f)^2-32*a*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(2*f*x+2*exp(1))/(32*f)^2-384*a*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(4*f*x+4*exp(1))/(128*f)^2-192*a*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(6*f*x+6*exp(1))/(192*f)^2-192*a*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(-2*f*x-2*exp(1))/(-64*f)^2-128*a*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(-4*f*x-4*exp(1))/(-128*f)^2)","F(-2)",0
10,-2,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*(-80*a*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(f*x+exp(1))/(16*f)^2-480*a*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(3*f*x+3*exp(1))/(96*f)^2-160*a*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(5*f*x+5*exp(1))/(160*f)^2-64*a*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(2*f*x+2*exp(1))/(64*f)^2-768*a*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(4*f*x+4*exp(1))/(256*f)^2-384*a*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(6*f*x+6*exp(1))/(384*f)^2-384*a*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(-2*f*x-2*exp(1))/(-128*f)^2-256*a*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(-4*f*x-4*exp(1))/(-256*f)^2)","F(-2)",0
11,-2,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*(-80*a*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(f*x+exp(1))/(16*f)^2-480*a*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(3*f*x+3*exp(1))/(96*f)^2-160*a*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(5*f*x+5*exp(1))/(160*f)^2)","F(-2)",0
12,-2,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*(-24*a*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(f*x+exp(1))/(8*f)^2-24*a*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(3*f*x+3*exp(1))/(24*f)^2+32*a*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(2*f*x+2*exp(1))/(32*f)^2+64*a*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(4*f*x+4*exp(1))/(64*f)^2+32*a*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(-2*f*x-2*exp(1))/(-32*f)^2)","F(-2)",0
13,-1,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
14,-1,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
15,-1,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
16,-1,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
17,-1,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
18,-1,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(11/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
19,-2,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(7/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*(-4480*a^2*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(f*x+exp(1))/(128*f)^2-8064*a^2*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(3*f*x+3*exp(1))/(384*f)^2-4480*a^2*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(5*f*x+5*exp(1))/(640*f)^2-896*a^2*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(7*f*x+7*exp(1))/(896*f)^2-2560*a^2*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(2*f*x+2*exp(1))/(512*f)^2-9216*a^2*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(4*f*x+4*exp(1))/(1024*f)^2-7680*a^2*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(6*f*x+6*exp(1))/(1536*f)^2-2048*a^2*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(8*f*x+8*exp(1))/(2048*f)^2-4608*a^2*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(-2*f*x-2*exp(1))/(-512*f)^2-5120*a^2*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(-4*f*x-4*exp(1))/(-1024*f)^2-1536*a^2*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(-6*f*x-6*exp(1))/(-1536*f)^2)","F(-2)",0
20,-2,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*(-4480*a^2*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(f*x+exp(1))/(128*f)^2-8064*a^2*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(3*f*x+3*exp(1))/(384*f)^2-4480*a^2*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(5*f*x+5*exp(1))/(640*f)^2-896*a^2*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(7*f*x+7*exp(1))/(896*f)^2)","F(-2)",0
21,-2,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*(-80*a^2*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(f*x+exp(1))/(16*f)^2-480*a^2*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(3*f*x+3*exp(1))/(96*f)^2-160*a^2*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(5*f*x+5*exp(1))/(160*f)^2+64*a^2*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(2*f*x+2*exp(1))/(64*f)^2+768*a^2*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(4*f*x+4*exp(1))/(256*f)^2+384*a^2*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(6*f*x+6*exp(1))/(384*f)^2+384*a^2*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(-2*f*x-2*exp(1))/(-128*f)^2+256*a^2*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(-4*f*x-4*exp(1))/(-256*f)^2)","F(-2)",0
22,-2,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*(-112*a^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(f*x+exp(1))/(16*f)^2-288*a^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(3*f*x+3*exp(1))/(96*f)^2+160*a^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(5*f*x+5*exp(1))/(160*f)^2+16*a^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(2*f*x+2*exp(1))/(16*f)^2+32*a^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(4*f*x+4*exp(1))/(32*f)^2+16*a^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(-2*f*x-2*exp(1))/(-16*f)^2)","F(-2)",0
23,-1,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
24,-1,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
25,-1,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
26,-1,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
27,-1,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
28,-1,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(11/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
29,-1,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(13/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
30,-2,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(9/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*(-16128*a^3*c^4*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(f*x+exp(1))/(256*f)^2-8064*a^3*c^4*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(3*f*x+3*exp(1))/(384*f)^2-5760*a^3*c^4*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(5*f*x+5*exp(1))/(640*f)^2-32256*a^3*c^4*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(7*f*x+7*exp(1))/(3584*f)^2-4608*a^3*c^4*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(9*f*x+9*exp(1))/(4608*f)^2-7168*a^3*c^4*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(2*f*x+2*exp(1))/(1024*f)^2-7168*a^3*c^4*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(4*f*x+4*exp(1))/(1024*f)^2-7680*a^3*c^4*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(6*f*x+6*exp(1))/(1536*f)^2-57344*a^3*c^4*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(8*f*x+8*exp(1))/(8192*f)^2-10240*a^3*c^4*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(10*f*x+10*exp(1))/(10240*f)^2-3584*a^3*c^4*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(-2*f*x-2*exp(1))/(-512*f)^2-5120*a^3*c^4*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(-4*f*x-4*exp(1))/(-1024*f)^2-43008*a^3*c^4*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(-6*f*x-6*exp(1))/(-6144*f)^2-8192*a^3*c^4*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(-8*f*x-8*exp(1))/(-8192*f)^2)","F(-2)",0
31,-2,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(7/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*(-16128*a^3*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(f*x+exp(1))/(256*f)^2-8064*a^3*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(3*f*x+3*exp(1))/(384*f)^2-5760*a^3*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(5*f*x+5*exp(1))/(640*f)^2-32256*a^3*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(7*f*x+7*exp(1))/(3584*f)^2-4608*a^3*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(9*f*x+9*exp(1))/(4608*f)^2)","F(-2)",0
32,-2,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*(-4480*a^3*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(f*x+exp(1))/(128*f)^2-8064*a^3*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(3*f*x+3*exp(1))/(384*f)^2-4480*a^3*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(5*f*x+5*exp(1))/(640*f)^2-896*a^3*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(7*f*x+7*exp(1))/(896*f)^2+2560*a^3*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(2*f*x+2*exp(1))/(512*f)^2+9216*a^3*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(4*f*x+4*exp(1))/(1024*f)^2+7680*a^3*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(6*f*x+6*exp(1))/(1536*f)^2+2048*a^3*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(8*f*x+8*exp(1))/(2048*f)^2+4608*a^3*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(-2*f*x-2*exp(1))/(-512*f)^2+5120*a^3*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(-4*f*x-4*exp(1))/(-1024*f)^2+1536*a^3*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(-6*f*x-6*exp(1))/(-1536*f)^2)","F(-2)",0
33,-2,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*(-5760*a^3*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(f*x+exp(1))/(128*f)^2-7296*a^3*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(3*f*x+3*exp(1))/(384*f)^2-640*a^3*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(5*f*x+5*exp(1))/(640*f)^2+896*a^3*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(7*f*x+7*exp(1))/(896*f)^2+32*a^3*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(2*f*x+2*exp(1))/(32*f)^2+384*a^3*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(4*f*x+4*exp(1))/(128*f)^2+192*a^3*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(6*f*x+6*exp(1))/(192*f)^2+192*a^3*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(-2*f*x-2*exp(1))/(-64*f)^2+128*a^3*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(-4*f*x-4*exp(1))/(-128*f)^2)","F(-2)",0
34,-2,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*(-144*a^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(f*x+exp(1))/(16*f)^2-96*a^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(3*f*x+3*exp(1))/(96*f)^2+480*a^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(5*f*x+5*exp(1))/(160*f)^2+448*a^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(2*f*x+2*exp(1))/(64*f)^2+3328*a^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(4*f*x+4*exp(1))/(256*f)^2-384*a^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(6*f*x+6*exp(1))/(384*f)^2+1664*a^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(-2*f*x-2*exp(1))/(-128*f)^2-256*a^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(-4*f*x-4*exp(1))/(-256*f)^2)","F(-2)",0
35,-1,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
36,-1,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
37,-1,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
38,-1,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
39,-1,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
40,-1,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(11/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
41,-1,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(13/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
42,-1,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(15/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
43,-1,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(17/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
44,-1,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
45,-1,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
46,-2,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)-32*sqrt(2*c)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^4/sqrt(2)/sqrt(a)/(tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^2+1)^4/f/sign(tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^4-1)","F(-2)",0
47,0,0,0,0.000000," ","integrate(cos(f*x+e)^2/(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\cos\left(f x + e\right)^{2}}{\sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(cos(f*x + e)^2/(sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)), x)","F",0
48,0,0,0,0.000000," ","integrate(cos(f*x+e)^2/(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\cos\left(f x + e\right)^{2}}{\sqrt{a \sin\left(f x + e\right) + a} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(f*x + e)^2/(sqrt(a*sin(f*x + e) + a)*(-c*sin(f*x + e) + c)^(3/2)), x)","F",0
49,0,0,0,0.000000," ","integrate(cos(f*x+e)^2/(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\cos\left(f x + e\right)^{2}}{\sqrt{a \sin\left(f x + e\right) + a} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(f*x + e)^2/(sqrt(a*sin(f*x + e) + a)*(-c*sin(f*x + e) + c)^(5/2)), x)","F",0
50,-1,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
51,-1,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
52,-1,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
53,-2,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)4*sqrt(2*c)*(1/2*(-tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^2-6-1/tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^2)/(tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^2+2+1/tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^2)/sign(-tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^2+1)+1/2*ln(tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^2+2+1/tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^2)/sign(-tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^2+1)-1/2*ln(tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^2-2+1/tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^2)/sign(-tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^2+1))*sign(sin(1/2*(f*x+exp(1))-1/4*pi))/sqrt(2)/sqrt(a)/a/f","F(-2)",0
54,0,0,0,0.000000," ","integrate(cos(f*x+e)^2/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\cos\left(f x + e\right)^{2}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} \sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(cos(f*x + e)^2/((a*sin(f*x + e) + a)^(3/2)*sqrt(-c*sin(f*x + e) + c)), x)","F",0
55,0,0,0,0.000000," ","integrate(cos(f*x+e)^2/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{\cos\left(f x + e\right)^{2}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(f*x + e)^2/((a*sin(f*x + e) + a)^(3/2)*(-c*sin(f*x + e) + c)^(3/2)), x)","F",0
56,0,0,0,0.000000," ","integrate(cos(f*x+e)^2/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{\cos\left(f x + e\right)^{2}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(f*x + e)^2/((a*sin(f*x + e) + a)^(3/2)*(-c*sin(f*x + e) + c)^(5/2)), x)","F",0
57,-1,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c-c*sin(f*x+e))^(9/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
58,-1,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
59,-1,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
60,-1,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
61,-1,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
62,0,0,0,0.000000," ","integrate(cos(f*x+e)^2/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\cos\left(f x + e\right)^{2}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} \sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(cos(f*x + e)^2/((a*sin(f*x + e) + a)^(5/2)*sqrt(-c*sin(f*x + e) + c)), x)","F",0
63,0,0,0,0.000000," ","integrate(cos(f*x+e)^2/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{\cos\left(f x + e\right)^{2}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(f*x + e)^2/((a*sin(f*x + e) + a)^(5/2)*(-c*sin(f*x + e) + c)^(3/2)), x)","F",0
64,0,0,0,0.000000," ","integrate(cos(f*x+e)^2/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{\cos\left(f x + e\right)^{2}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(f*x + e)^2/((a*sin(f*x + e) + a)^(5/2)*(-c*sin(f*x + e) + c)^(5/2)), x)","F",0
65,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^n*cos(f*x + e)^2, x)","F",0
66,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^3,x, algorithm=""giac"")","\int -{\left(c \sin\left(f x + e\right) - c\right)}^{3} {\left(a \sin\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate(-(c*sin(f*x + e) - c)^3*(a*sin(f*x + e) + a)^m*cos(f*x + e)^2, x)","F",0
67,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^2,x, algorithm=""giac"")","\int {\left(c \sin\left(f x + e\right) - c\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((c*sin(f*x + e) - c)^2*(a*sin(f*x + e) + a)^m*cos(f*x + e)^2, x)","F",0
68,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e)),x, algorithm=""giac"")","\int -{\left(c \sin\left(f x + e\right) - c\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate(-(c*sin(f*x + e) - c)*(a*sin(f*x + e) + a)^m*cos(f*x + e)^2, x)","F",0
69,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*cos(f*x + e)^2, x)","F",0
70,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e)),x, algorithm=""giac"")","\int -\frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)^{2}}{c \sin\left(f x + e\right) - c}\,{d x}"," ",0,"integrate(-(a*sin(f*x + e) + a)^m*cos(f*x + e)^2/(c*sin(f*x + e) - c), x)","F",0
71,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^2,x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)^{2}}{{\left(c \sin\left(f x + e\right) - c\right)}^{2}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*cos(f*x + e)^2/(c*sin(f*x + e) - c)^2, x)","F",0
72,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^3,x, algorithm=""giac"")","\int -\frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)^{2}}{{\left(c \sin\left(f x + e\right) - c\right)}^{3}}\,{d x}"," ",0,"integrate(-(a*sin(f*x + e) + a)^m*cos(f*x + e)^2/(c*sin(f*x + e) - c)^3, x)","F",0
73,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((-c*sin(f*x + e) + c)^(5/2)*(a*sin(f*x + e) + a)^m*cos(f*x + e)^2, x)","F",0
74,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((-c*sin(f*x + e) + c)^(3/2)*(a*sin(f*x + e) + a)^m*cos(f*x + e)^2, x)","F",0
75,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \sqrt{-c \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate(sqrt(-c*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m*cos(f*x + e)^2, x)","F",0
76,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)^{2}}{\sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*cos(f*x + e)^2/sqrt(-c*sin(f*x + e) + c), x)","F",0
77,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)^{2}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*cos(f*x + e)^2/(-c*sin(f*x + e) + c)^(3/2), x)","F",0
78,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)^{2}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*cos(f*x + e)^2/(-c*sin(f*x + e) + c)^(5/2), x)","F",0
79,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)^{2}}{\sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*cos(f*x + e)^2/sqrt(-c*sin(f*x + e) + c), x)","F",0
80,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c+c*sin(f*x+e))^m/(a-a*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(c \sin\left(f x + e\right) + c\right)}^{m} \cos\left(f x + e\right)^{2}}{\sqrt{-a \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((c*sin(f*x + e) + c)^m*cos(f*x + e)^2/sqrt(-a*sin(f*x + e) + a), x)","F",0
81,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-5-m),x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m - 5} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m - 5)*cos(f*x + e)^2, x)","F",0
82,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-4-m),x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m - 4} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m - 4)*cos(f*x + e)^2, x)","F",0
83,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-3-m),x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m - 3} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m - 3)*cos(f*x + e)^2, x)","F",0
84,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-2-m),x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m - 2} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m - 2)*cos(f*x + e)^2, x)","F",0
85,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-1-m),x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m - 1} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m - 1)*cos(f*x + e)^2, x)","F",0
86,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m/((c-c*sin(f*x+e))^m),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)^{2}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{m}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*cos(f*x + e)^2/(-c*sin(f*x + e) + c)^m, x)","F",0
87,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(1-m),x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m + 1} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m + 1)*cos(f*x + e)^2, x)","F",0
88,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(7/2)*(a+a*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} \sqrt{a \sin\left(f x + e\right) + a} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*sqrt(a*sin(f*x + e) + a)*(-c*sin(f*x + e) + c)^(7/2), x)","F",0
89,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} \sqrt{a \sin\left(f x + e\right) + a} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*sqrt(a*sin(f*x + e) + a)*(-c*sin(f*x + e) + c)^(5/2), x)","F",0
90,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} \sqrt{a \sin\left(f x + e\right) + a} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*sqrt(a*sin(f*x + e) + a)*(-c*sin(f*x + e) + c)^(3/2), x)","F",0
91,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(1/2)*(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c), x)","F",0
92,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
93,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
94,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
95,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
96,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
97,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
98,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^(3/2)*(-c*sin(f*x + e) + c)^(3/2), x)","F",0
99,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} \sqrt{-c \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^(3/2)*sqrt(-c*sin(f*x + e) + c), x)","F",0
100,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
101,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
102,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
103,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
104,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
105,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(11/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
106,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^(5/2)*(-c*sin(f*x + e) + c)^(5/2), x)","F",0
107,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^(5/2)*(-c*sin(f*x + e) + c)^(3/2), x)","F",0
108,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} \sqrt{-c \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^(5/2)*sqrt(-c*sin(f*x + e) + c), x)","F",0
109,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
110,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
111,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
112,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
113,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
114,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(11/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
115,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(13/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
116,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
117,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{7}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^(7/2)*(-c*sin(f*x + e) + c)^(3/2), x)","F",0
118,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{7}{2}} \sqrt{-c \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^(7/2)*sqrt(-c*sin(f*x + e) + c), x)","F",0
119,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
120,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
121,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
122,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
123,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
124,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(11/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
125,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(13/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
126,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(15/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
127,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
128,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
129,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
130,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}}}{\sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)/(sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)), x)","F",0
131,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}}}{\sqrt{a \sin\left(f x + e\right) + a} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)/(sqrt(a*sin(f*x + e) + a)*(-c*sin(f*x + e) + c)^(3/2)), x)","F",0
132,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}}}{\sqrt{a \sin\left(f x + e\right) + a} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)/(sqrt(a*sin(f*x + e) + a)*(-c*sin(f*x + e) + c)^(5/2)), x)","F",0
133,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}}}{\sqrt{a \sin\left(f x + e\right) + a} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)/(sqrt(a*sin(f*x + e) + a)*(-c*sin(f*x + e) + c)^(7/2)), x)","F",0
134,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
135,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
136,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
137,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
138,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} \sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)/((a*sin(f*x + e) + a)^(3/2)*sqrt(-c*sin(f*x + e) + c)), x)","F",0
139,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)/((a*sin(f*x + e) + a)^(3/2)*(-c*sin(f*x + e) + c)^(3/2)), x)","F",0
140,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)/((a*sin(f*x + e) + a)^(3/2)*(-c*sin(f*x + e) + c)^(5/2)), x)","F",0
141,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(7/2),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)/((a*sin(f*x + e) + a)^(3/2)*(-c*sin(f*x + e) + c)^(7/2)), x)","F",0
142,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(9/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
143,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
144,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
145,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
146,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
147,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} \sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)/((a*sin(f*x + e) + a)^(5/2)*sqrt(-c*sin(f*x + e) + c)), x)","F",0
148,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)/((a*sin(f*x + e) + a)^(5/2)*(-c*sin(f*x + e) + c)^(3/2)), x)","F",0
149,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)/((a*sin(f*x + e) + a)^(5/2)*(-c*sin(f*x + e) + c)^(5/2)), x)","F",0
150,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(7/2),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)/((a*sin(f*x + e) + a)^(5/2)*(-c*sin(f*x + e) + c)^(7/2)), x)","F",0
151,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x, algorithm=""giac"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^n, x)","F",0
152,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^3,x, algorithm=""giac"")","\int -\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(c \sin\left(f x + e\right) - c\right)}^{3} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate(-(g*cos(f*x + e))^(3/2)*(c*sin(f*x + e) - c)^3*(a*sin(f*x + e) + a)^m, x)","F",0
153,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^2,x, algorithm=""giac"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(c \sin\left(f x + e\right) - c\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(c*sin(f*x + e) - c)^2*(a*sin(f*x + e) + a)^m, x)","F",0
154,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e)),x, algorithm=""giac"")","\int -\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(c \sin\left(f x + e\right) - c\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate(-(g*cos(f*x + e))^(3/2)*(c*sin(f*x + e) - c)*(a*sin(f*x + e) + a)^m, x)","F",0
155,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m,x, algorithm=""giac"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^m, x)","F",0
156,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e)),x, algorithm=""giac"")","\int -\frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{c \sin\left(f x + e\right) - c}\,{d x}"," ",0,"integrate(-(g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^m/(c*sin(f*x + e) - c), x)","F",0
157,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^2,x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{{\left(c \sin\left(f x + e\right) - c\right)}^{2}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^m/(c*sin(f*x + e) - c)^2, x)","F",0
158,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^3,x, algorithm=""giac"")","\int -\frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{{\left(c \sin\left(f x + e\right) - c\right)}^{3}}\,{d x}"," ",0,"integrate(-(g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^m/(c*sin(f*x + e) - c)^3, x)","F",0
159,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(-c*sin(f*x + e) + c)^(5/2)*(a*sin(f*x + e) + a)^m, x)","F",0
160,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(-c*sin(f*x + e) + c)^(3/2)*(a*sin(f*x + e) + a)^m, x)","F",0
161,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} \sqrt{-c \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*sqrt(-c*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m, x)","F",0
162,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{\sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^m/sqrt(-c*sin(f*x + e) + c), x)","F",0
163,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^m/(-c*sin(f*x + e) + c)^(3/2), x)","F",0
164,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^m/(-c*sin(f*x + e) + c)^(5/2), x)","F",0
165,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{\sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^m/sqrt(-c*sin(f*x + e) + c), x)","F",0
166,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(c+c*sin(f*x+e))^m/(a-a*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(c \sin\left(f x + e\right) + c\right)}^{m}}{\sqrt{-a \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(c*sin(f*x + e) + c)^m/sqrt(-a*sin(f*x + e) + a), x)","F",0
167,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-3-m),x, algorithm=""giac"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m - 3}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m - 3), x)","F",0
168,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-2-m),x, algorithm=""giac"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m - 2}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m - 2), x)","F",0
169,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-1-m),x, algorithm=""giac"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m - 1}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m - 1), x)","F",0
170,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/((c-c*sin(f*x+e))^m),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{m}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^m/(-c*sin(f*x + e) + c)^m, x)","F",0
171,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(1-m),x, algorithm=""giac"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m + 1}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m + 1), x)","F",0
172,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(2-m),x, algorithm=""giac"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m + 2}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m + 2), x)","F",0
173,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^p*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x, algorithm=""giac"")","\int \left(g \cos\left(f x + e\right)\right)^{p} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^p*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^n, x)","F",0
174,-2,0,0,0.000000," ","integrate((g*cos(f*x+e))^(1-2*m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-1+m),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)(4*pi*exp(m*ln(abs(a))+m*ln(abs(c))-2*m*ln(abs(g))-ln(abs(c))+ln(abs(g)))*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)*tan((4*m*pi*floor(-(sign(a)-2)/4)+4*m*pi*floor(-(sign(c)-4)/4)+m*pi*sign(a)+m*pi*sign(c)-2*m*pi*sign(g)-4*pi*floor(-(sign(c)-4)/4)-pi*sign(c)+pi*sign(g)+pi)/4)^2-4*pi*exp(m*ln(abs(a))+m*ln(abs(c))-2*m*ln(abs(g))-ln(abs(c))+ln(abs(g)))*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)+4*pi*exp(m*ln(abs(a))+m*ln(abs(c))-2*m*ln(abs(g))-ln(abs(c))+ln(abs(g)))*floor((f*x+pi+exp(1))*1/2/pi)*tan((4*m*pi*floor(-(sign(a)-2)/4)+4*m*pi*floor(-(sign(c)-4)/4)+m*pi*sign(a)+m*pi*sign(c)-2*m*pi*sign(g)-4*pi*floor(-(sign(c)-4)/4)-pi*sign(c)+pi*sign(g)+pi)/4)^2-4*pi*exp(m*ln(abs(a))+m*ln(abs(c))-2*m*ln(abs(g))-ln(abs(c))+ln(abs(g)))*floor((f*x+pi+exp(1))*1/2/pi)+2*pi*exp(m*ln(abs(a))+m*ln(abs(c))-2*m*ln(abs(g))-ln(abs(c))+ln(abs(g)))*sign(tan((f*x+exp(1))/2)^2-1)*tan((4*m*pi*floor(-(sign(a)-2)/4)+4*m*pi*floor(-(sign(c)-4)/4)+m*pi*sign(a)+m*pi*sign(c)-2*m*pi*sign(g)-4*pi*floor(-(sign(c)-4)/4)-pi*sign(c)+pi*sign(g)+pi)/4)^2-2*pi*exp(m*ln(abs(a))+m*ln(abs(c))-2*m*ln(abs(g))-ln(abs(c))+ln(abs(g)))*sign(tan((f*x+exp(1))/2)^2-1)+3*pi*exp(m*ln(abs(a))+m*ln(abs(c))-2*m*ln(abs(g))-ln(abs(c))+ln(abs(g)))*tan((4*m*pi*floor(-(sign(a)-2)/4)+4*m*pi*floor(-(sign(c)-4)/4)+m*pi*sign(a)+m*pi*sign(c)-2*m*pi*sign(g)-4*pi*floor(-(sign(c)-4)/4)-pi*sign(c)+pi*sign(g)+pi)/4)^2-3*pi*exp(m*ln(abs(a))+m*ln(abs(c))-2*m*ln(abs(g))-ln(abs(c))+ln(abs(g)))-2*exp(1)*exp(m*ln(abs(a))+m*ln(abs(c))-2*m*ln(abs(g))-ln(abs(c))+ln(abs(g)))*tan((4*m*pi*floor(-(sign(a)-2)/4)+4*m*pi*floor(-(sign(c)-4)/4)+m*pi*sign(a)+m*pi*sign(c)-2*m*pi*sign(g)-4*pi*floor(-(sign(c)-4)/4)-pi*sign(c)+pi*sign(g)+pi)/4)^2+2*exp(1)*exp(m*ln(abs(a))+m*ln(abs(c))-2*m*ln(abs(g))-ln(abs(c))+ln(abs(g)))-4*exp(m*ln(abs(a))+m*ln(abs(c))-2*m*ln(abs(g))-ln(abs(c))+ln(abs(g)))*ln((2*tan((f*x+exp(1))/2)^2-4*tan((f*x+exp(1))/2)+2)/(tan((f*x+exp(1))/2)^2+1))*tan((4*m*pi*floor(-(sign(a)-2)/4)+4*m*pi*floor(-(sign(c)-4)/4)+m*pi*sign(a)+m*pi*sign(c)-2*m*pi*sign(g)-4*pi*floor(-(sign(c)-4)/4)-pi*sign(c)+pi*sign(g)+pi)/4))/(2*f*tan((4*m*pi*floor(-(sign(a)-2)/4)+4*m*pi*floor(-(sign(c)-4)/4)+m*pi*sign(a)+m*pi*sign(c)-2*m*pi*sign(g)-4*pi*floor(-(sign(c)-4)/4)-pi*sign(c)+pi*sign(g)+pi)/4)^2+2*f)","F(-2)",0
175,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^(5-2*m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
176,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3-2*m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
177,-2,0,0,0.000000," ","integrate((g*cos(f*x+e))^(1-2*m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)(-exp(m*ln(2)-2*m*ln(4*abs(tan((2*f*x-pi+2*exp(1))/8))/(tan((2*f*x-pi+2*exp(1))/8)^2+1))+m*ln(abs(a))-2*m*ln(abs(g))-n*ln(2)+2*n*ln(4*abs(tan((2*f*x-pi+2*exp(1))/8))/(tan((2*f*x-pi+2*exp(1))/8)^2+1))+n*ln(abs(c))-ln(2)+ln(4*abs(tan((2*f*x-pi+2*exp(1))/8))/(tan((2*f*x-pi+2*exp(1))/8)^2+1))+ln(abs(g)))*tan((2*f*x-8*m*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)-8*m*pi*floor((f*x+pi+exp(1))*1/2/pi)+8*m*pi*floor(-(sign(a)-2)/4)+2*m*pi*sign(a)-4*m*pi*sign(g)-4*m*pi*sign(tan((f*x+exp(1))/2)^2-1)-2*m*pi+8*n*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)+8*n*pi*floor((f*x+pi+exp(1))*1/2/pi)+8*n*pi*floor(-(sign(c)-4)/4)+2*n*pi*sign(c)+4*n*pi*sign(tan((f*x+exp(1))/2)^2-1)+2*n*pi+4*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)+4*pi*floor((f*x+pi+exp(1))*1/2/pi)+2*pi*sign(g)+2*pi*sign(tan((f*x+exp(1))/2)^2-1)+pi+2*exp(1))/8)^2*tan((f*x+exp(1))/2)^2+2*exp(m*ln(2)-2*m*ln(4*abs(tan((2*f*x-pi+2*exp(1))/8))/(tan((2*f*x-pi+2*exp(1))/8)^2+1))+m*ln(abs(a))-2*m*ln(abs(g))-n*ln(2)+2*n*ln(4*abs(tan((2*f*x-pi+2*exp(1))/8))/(tan((2*f*x-pi+2*exp(1))/8)^2+1))+n*ln(abs(c))-ln(2)+ln(4*abs(tan((2*f*x-pi+2*exp(1))/8))/(tan((2*f*x-pi+2*exp(1))/8)^2+1))+ln(abs(g)))*tan((2*f*x-8*m*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)-8*m*pi*floor((f*x+pi+exp(1))*1/2/pi)+8*m*pi*floor(-(sign(a)-2)/4)+2*m*pi*sign(a)-4*m*pi*sign(g)-4*m*pi*sign(tan((f*x+exp(1))/2)^2-1)-2*m*pi+8*n*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)+8*n*pi*floor((f*x+pi+exp(1))*1/2/pi)+8*n*pi*floor(-(sign(c)-4)/4)+2*n*pi*sign(c)+4*n*pi*sign(tan((f*x+exp(1))/2)^2-1)+2*n*pi+4*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)+4*pi*floor((f*x+pi+exp(1))*1/2/pi)+2*pi*sign(g)+2*pi*sign(tan((f*x+exp(1))/2)^2-1)+pi+2*exp(1))/8)^2*tan((f*x+exp(1))/2)-exp(m*ln(2)-2*m*ln(4*abs(tan((2*f*x-pi+2*exp(1))/8))/(tan((2*f*x-pi+2*exp(1))/8)^2+1))+m*ln(abs(a))-2*m*ln(abs(g))-n*ln(2)+2*n*ln(4*abs(tan((2*f*x-pi+2*exp(1))/8))/(tan((2*f*x-pi+2*exp(1))/8)^2+1))+n*ln(abs(c))-ln(2)+ln(4*abs(tan((2*f*x-pi+2*exp(1))/8))/(tan((2*f*x-pi+2*exp(1))/8)^2+1))+ln(abs(g)))*tan((2*f*x-8*m*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)-8*m*pi*floor((f*x+pi+exp(1))*1/2/pi)+8*m*pi*floor(-(sign(a)-2)/4)+2*m*pi*sign(a)-4*m*pi*sign(g)-4*m*pi*sign(tan((f*x+exp(1))/2)^2-1)-2*m*pi+8*n*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)+8*n*pi*floor((f*x+pi+exp(1))*1/2/pi)+8*n*pi*floor(-(sign(c)-4)/4)+2*n*pi*sign(c)+4*n*pi*sign(tan((f*x+exp(1))/2)^2-1)+2*n*pi+4*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)+4*pi*floor((f*x+pi+exp(1))*1/2/pi)+2*pi*sign(g)+2*pi*sign(tan((f*x+exp(1))/2)^2-1)+pi+2*exp(1))/8)^2-2*exp(m*ln(2)-2*m*ln(4*abs(tan((2*f*x-pi+2*exp(1))/8))/(tan((2*f*x-pi+2*exp(1))/8)^2+1))+m*ln(abs(a))-2*m*ln(abs(g))-n*ln(2)+2*n*ln(4*abs(tan((2*f*x-pi+2*exp(1))/8))/(tan((2*f*x-pi+2*exp(1))/8)^2+1))+n*ln(abs(c))-ln(2)+ln(4*abs(tan((2*f*x-pi+2*exp(1))/8))/(tan((2*f*x-pi+2*exp(1))/8)^2+1))+ln(abs(g)))*tan((2*f*x-8*m*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)-8*m*pi*floor((f*x+pi+exp(1))*1/2/pi)+8*m*pi*floor(-(sign(a)-2)/4)+2*m*pi*sign(a)-4*m*pi*sign(g)-4*m*pi*sign(tan((f*x+exp(1))/2)^2-1)-2*m*pi+8*n*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)+8*n*pi*floor((f*x+pi+exp(1))*1/2/pi)+8*n*pi*floor(-(sign(c)-4)/4)+2*n*pi*sign(c)+4*n*pi*sign(tan((f*x+exp(1))/2)^2-1)+2*n*pi+4*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)+4*pi*floor((f*x+pi+exp(1))*1/2/pi)+2*pi*sign(g)+2*pi*sign(tan((f*x+exp(1))/2)^2-1)+pi+2*exp(1))/8)*tan((f*x+exp(1))/2)^2+2*exp(m*ln(2)-2*m*ln(4*abs(tan((2*f*x-pi+2*exp(1))/8))/(tan((2*f*x-pi+2*exp(1))/8)^2+1))+m*ln(abs(a))-2*m*ln(abs(g))-n*ln(2)+2*n*ln(4*abs(tan((2*f*x-pi+2*exp(1))/8))/(tan((2*f*x-pi+2*exp(1))/8)^2+1))+n*ln(abs(c))-ln(2)+ln(4*abs(tan((2*f*x-pi+2*exp(1))/8))/(tan((2*f*x-pi+2*exp(1))/8)^2+1))+ln(abs(g)))*tan((2*f*x-8*m*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)-8*m*pi*floor((f*x+pi+exp(1))*1/2/pi)+8*m*pi*floor(-(sign(a)-2)/4)+2*m*pi*sign(a)-4*m*pi*sign(g)-4*m*pi*sign(tan((f*x+exp(1))/2)^2-1)-2*m*pi+8*n*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)+8*n*pi*floor((f*x+pi+exp(1))*1/2/pi)+8*n*pi*floor(-(sign(c)-4)/4)+2*n*pi*sign(c)+4*n*pi*sign(tan((f*x+exp(1))/2)^2-1)+2*n*pi+4*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)+4*pi*floor((f*x+pi+exp(1))*1/2/pi)+2*pi*sign(g)+2*pi*sign(tan((f*x+exp(1))/2)^2-1)+pi+2*exp(1))/8)+exp(m*ln(2)-2*m*ln(4*abs(tan((2*f*x-pi+2*exp(1))/8))/(tan((2*f*x-pi+2*exp(1))/8)^2+1))+m*ln(abs(a))-2*m*ln(abs(g))-n*ln(2)+2*n*ln(4*abs(tan((2*f*x-pi+2*exp(1))/8))/(tan((2*f*x-pi+2*exp(1))/8)^2+1))+n*ln(abs(c))-ln(2)+ln(4*abs(tan((2*f*x-pi+2*exp(1))/8))/(tan((2*f*x-pi+2*exp(1))/8)^2+1))+ln(abs(g)))*tan((f*x+exp(1))/2)^2-2*exp(m*ln(2)-2*m*ln(4*abs(tan((2*f*x-pi+2*exp(1))/8))/(tan((2*f*x-pi+2*exp(1))/8)^2+1))+m*ln(abs(a))-2*m*ln(abs(g))-n*ln(2)+2*n*ln(4*abs(tan((2*f*x-pi+2*exp(1))/8))/(tan((2*f*x-pi+2*exp(1))/8)^2+1))+n*ln(abs(c))-ln(2)+ln(4*abs(tan((2*f*x-pi+2*exp(1))/8))/(tan((2*f*x-pi+2*exp(1))/8)^2+1))+ln(abs(g)))*tan((f*x+exp(1))/2)+exp(m*ln(2)-2*m*ln(4*abs(tan((2*f*x-pi+2*exp(1))/8))/(tan((2*f*x-pi+2*exp(1))/8)^2+1))+m*ln(abs(a))-2*m*ln(abs(g))-n*ln(2)+2*n*ln(4*abs(tan((2*f*x-pi+2*exp(1))/8))/(tan((2*f*x-pi+2*exp(1))/8)^2+1))+n*ln(abs(c))-ln(2)+ln(4*abs(tan((2*f*x-pi+2*exp(1))/8))/(tan((2*f*x-pi+2*exp(1))/8)^2+1))+ln(abs(g))))/(f*m*tan((2*f*x-8*m*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)-8*m*pi*floor((f*x+pi+exp(1))*1/2/pi)+8*m*pi*floor(-(sign(a)-2)/4)+2*m*pi*sign(a)-4*m*pi*sign(g)-4*m*pi*sign(tan((f*x+exp(1))/2)^2-1)-2*m*pi+8*n*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)+8*n*pi*floor((f*x+pi+exp(1))*1/2/pi)+8*n*pi*floor(-(sign(c)-4)/4)+2*n*pi*sign(c)+4*n*pi*sign(tan((f*x+exp(1))/2)^2-1)+2*n*pi+4*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)+4*pi*floor((f*x+pi+exp(1))*1/2/pi)+2*pi*sign(g)+2*pi*sign(tan((f*x+exp(1))/2)^2-1)+pi+2*exp(1))/8)^2*tan((f*x+exp(1))/2)^2+f*m*tan((2*f*x-8*m*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)-8*m*pi*floor((f*x+pi+exp(1))*1/2/pi)+8*m*pi*floor(-(sign(a)-2)/4)+2*m*pi*sign(a)-4*m*pi*sign(g)-4*m*pi*sign(tan((f*x+exp(1))/2)^2-1)-2*m*pi+8*n*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)+8*n*pi*floor((f*x+pi+exp(1))*1/2/pi)+8*n*pi*floor(-(sign(c)-4)/4)+2*n*pi*sign(c)+4*n*pi*sign(tan((f*x+exp(1))/2)^2-1)+2*n*pi+4*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)+4*pi*floor((f*x+pi+exp(1))*1/2/pi)+2*pi*sign(g)+2*pi*sign(tan((f*x+exp(1))/2)^2-1)+pi+2*exp(1))/8)^2+f*m*tan((f*x+exp(1))/2)^2+f*m-f*n*tan((2*f*x-8*m*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)-8*m*pi*floor((f*x+pi+exp(1))*1/2/pi)+8*m*pi*floor(-(sign(a)-2)/4)+2*m*pi*sign(a)-4*m*pi*sign(g)-4*m*pi*sign(tan((f*x+exp(1))/2)^2-1)-2*m*pi+8*n*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)+8*n*pi*floor((f*x+pi+exp(1))*1/2/pi)+8*n*pi*floor(-(sign(c)-4)/4)+2*n*pi*sign(c)+4*n*pi*sign(tan((f*x+exp(1))/2)^2-1)+2*n*pi+4*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)+4*pi*floor((f*x+pi+exp(1))*1/2/pi)+2*pi*sign(g)+2*pi*sign(tan((f*x+exp(1))/2)^2-1)+pi+2*exp(1))/8)^2*tan((f*x+exp(1))/2)^2-f*n*tan((2*f*x-8*m*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)-8*m*pi*floor((f*x+pi+exp(1))*1/2/pi)+8*m*pi*floor(-(sign(a)-2)/4)+2*m*pi*sign(a)-4*m*pi*sign(g)-4*m*pi*sign(tan((f*x+exp(1))/2)^2-1)-2*m*pi+8*n*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)+8*n*pi*floor((f*x+pi+exp(1))*1/2/pi)+8*n*pi*floor(-(sign(c)-4)/4)+2*n*pi*sign(c)+4*n*pi*sign(tan((f*x+exp(1))/2)^2-1)+2*n*pi+4*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)+4*pi*floor((f*x+pi+exp(1))*1/2/pi)+2*pi*sign(g)+2*pi*sign(tan((f*x+exp(1))/2)^2-1)+pi+2*exp(1))/8)^2-f*n*tan((f*x+exp(1))/2)^2-f*n-f*tan((2*f*x-8*m*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)-8*m*pi*floor((f*x+pi+exp(1))*1/2/pi)+8*m*pi*floor(-(sign(a)-2)/4)+2*m*pi*sign(a)-4*m*pi*sign(g)-4*m*pi*sign(tan((f*x+exp(1))/2)^2-1)-2*m*pi+8*n*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)+8*n*pi*floor((f*x+pi+exp(1))*1/2/pi)+8*n*pi*floor(-(sign(c)-4)/4)+2*n*pi*sign(c)+4*n*pi*sign(tan((f*x+exp(1))/2)^2-1)+2*n*pi+4*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)+4*pi*floor((f*x+pi+exp(1))*1/2/pi)+2*pi*sign(g)+2*pi*sign(tan((f*x+exp(1))/2)^2-1)+pi+2*exp(1))/8)^2*tan((f*x+exp(1))/2)^2-f*tan((2*f*x-8*m*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)-8*m*pi*floor((f*x+pi+exp(1))*1/2/pi)+8*m*pi*floor(-(sign(a)-2)/4)+2*m*pi*sign(a)-4*m*pi*sign(g)-4*m*pi*sign(tan((f*x+exp(1))/2)^2-1)-2*m*pi+8*n*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)+8*n*pi*floor((f*x+pi+exp(1))*1/2/pi)+8*n*pi*floor(-(sign(c)-4)/4)+2*n*pi*sign(c)+4*n*pi*sign(tan((f*x+exp(1))/2)^2-1)+2*n*pi+4*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)+4*pi*floor((f*x+pi+exp(1))*1/2/pi)+2*pi*sign(g)+2*pi*sign(tan((f*x+exp(1))/2)^2-1)+pi+2*exp(1))/8)^2-f*tan((f*x+exp(1))/2)^2-f)","F(-2)",0
178,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(-1-2*m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x, algorithm=""giac"")","\int \left(g \cos\left(f x + e\right)\right)^{-2 \, m - 1} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(-2*m - 1)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^n, x)","F",0
179,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(-3-2*m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x, algorithm=""giac"")","\int \left(g \cos\left(f x + e\right)\right)^{-2 \, m - 3} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(-2*m - 3)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^n, x)","F",0
180,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(-5-2*m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x, algorithm=""giac"")","\int \left(g \cos\left(f x + e\right)\right)^{-2 \, m - 5} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(-2*m - 5)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^n, x)","F",0
181,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(-1-2*m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^m,x, algorithm=""giac"")","\int \left(g \cos\left(f x + e\right)\right)^{-2 \, m - 1} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{m}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(-2*m - 1)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^m, x)","F",0
182,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(-1-m-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(3+n),x, algorithm=""giac"")","\int \left(g \cos\left(f x + e\right)\right)^{-m - n - 1} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{n + 3}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(-m - n - 1)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(n + 3), x)","F",0
183,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(-1-m-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(2+n),x, algorithm=""giac"")","\int \left(g \cos\left(f x + e\right)\right)^{-m - n - 1} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{n + 2}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(-m - n - 1)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(n + 2), x)","F",0
184,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(-1-m-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(1+n),x, algorithm=""giac"")","\int \left(g \cos\left(f x + e\right)\right)^{-m - n - 1} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{n + 1}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(-m - n - 1)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(n + 1), x)","F",0
185,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(-1-m-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x, algorithm=""giac"")","\int \left(g \cos\left(f x + e\right)\right)^{-m - n - 1} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(-m - n - 1)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^n, x)","F",0
186,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(-1-m-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-1+n),x, algorithm=""giac"")","\int \left(g \cos\left(f x + e\right)\right)^{-m - n - 1} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{n - 1}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(-m - n - 1)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(n - 1), x)","F",0
187,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(-1-m-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-2+n),x, algorithm=""giac"")","\int \left(g \cos\left(f x + e\right)\right)^{-m - n - 1} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{n - 2}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(-m - n - 1)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(n - 2), x)","F",0
188,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(-1-m-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-3+n),x, algorithm=""giac"")","\int \left(g \cos\left(f x + e\right)\right)^{-m - n - 1} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{n - 3}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(-m - n - 1)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(n - 3), x)","F",0
189,0,0,0,0.000000," ","integrate((g*sec(f*x+e))^p*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x, algorithm=""giac"")","\int \left(g \sec\left(f x + e\right)\right)^{p} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((g*sec(f*x + e))^p*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^n, x)","F",0
190,1,28,0,0.132357," ","integrate(cos(d*x+c)*sin(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{3 \, a \sin\left(d x + c\right)^{4} + 4 \, a \sin\left(d x + c\right)^{3}}{12 \, d}"," ",0,"1/12*(3*a*sin(d*x + c)^4 + 4*a*sin(d*x + c)^3)/d","A",0
191,1,28,0,0.151563," ","integrate(cos(d*x+c)*sin(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{2 \, a \sin\left(d x + c\right)^{3} + 3 \, a \sin\left(d x + c\right)^{2}}{6 \, d}"," ",0,"1/6*(2*a*sin(d*x + c)^3 + 3*a*sin(d*x + c)^2)/d","A",0
192,1,23,0,0.130825," ","integrate(cos(d*x+c)*csc(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{a \log\left({\left| \sin\left(d x + c\right) \right|}\right) + a \sin\left(d x + c\right)}{d}"," ",0,"(a*log(abs(sin(d*x + c))) + a*sin(d*x + c))/d","A",0
193,1,26,0,0.131980," ","integrate(cos(d*x+c)*csc(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{a \log\left({\left| \sin\left(d x + c\right) \right|}\right) - \frac{a}{\sin\left(d x + c\right)}}{d}"," ",0,"(a*log(abs(sin(d*x + c))) - a/sin(d*x + c))/d","A",0
194,1,24,0,0.132776," ","integrate(cos(d*x+c)*csc(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{2 \, a \sin\left(d x + c\right) + a}{2 \, d \sin\left(d x + c\right)^{2}}"," ",0,"-1/2*(2*a*sin(d*x + c) + a)/(d*sin(d*x + c)^2)","A",0
195,1,26,0,0.149248," ","integrate(cos(d*x+c)*csc(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{3 \, a \sin\left(d x + c\right) + 2 \, a}{6 \, d \sin\left(d x + c\right)^{3}}"," ",0,"-1/6*(3*a*sin(d*x + c) + 2*a)/(d*sin(d*x + c)^3)","A",0
196,1,26,0,0.151753," ","integrate(cos(d*x+c)*csc(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{4 \, a \sin\left(d x + c\right) + 3 \, a}{12 \, d \sin\left(d x + c\right)^{4}}"," ",0,"-1/12*(4*a*sin(d*x + c) + 3*a)/(d*sin(d*x + c)^4)","A",0
197,1,45,0,0.164408," ","integrate(cos(d*x+c)*sin(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{6 \, a^{2} \sin\left(d x + c\right)^{5} + 15 \, a^{2} \sin\left(d x + c\right)^{4} + 10 \, a^{2} \sin\left(d x + c\right)^{3}}{30 \, d}"," ",0,"1/30*(6*a^2*sin(d*x + c)^5 + 15*a^2*sin(d*x + c)^4 + 10*a^2*sin(d*x + c)^3)/d","A",0
198,1,45,0,0.167494," ","integrate(cos(d*x+c)*sin(d*x+c)*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{3 \, a^{2} \sin\left(d x + c\right)^{4} + 8 \, a^{2} \sin\left(d x + c\right)^{3} + 6 \, a^{2} \sin\left(d x + c\right)^{2}}{12 \, d}"," ",0,"1/12*(3*a^2*sin(d*x + c)^4 + 8*a^2*sin(d*x + c)^3 + 6*a^2*sin(d*x + c)^2)/d","A",0
199,1,42,0,0.167626," ","integrate(cos(d*x+c)*csc(d*x+c)*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{a^{2} \sin\left(d x + c\right)^{2} + 2 \, a^{2} \log\left({\left| \sin\left(d x + c\right) \right|}\right) + 4 \, a^{2} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(a^2*sin(d*x + c)^2 + 2*a^2*log(abs(sin(d*x + c))) + 4*a^2*sin(d*x + c))/d","A",0
200,1,41,0,0.154764," ","integrate(cos(d*x+c)*csc(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{2 \, a^{2} \log\left({\left| \sin\left(d x + c\right) \right|}\right) + a^{2} \sin\left(d x + c\right) - \frac{a^{2}}{\sin\left(d x + c\right)}}{d}"," ",0,"(2*a^2*log(abs(sin(d*x + c))) + a^2*sin(d*x + c) - a^2/sin(d*x + c))/d","A",0
201,1,44,0,0.150079," ","integrate(cos(d*x+c)*csc(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{2 \, a^{2} \log\left({\left| \sin\left(d x + c\right) \right|}\right) - \frac{4 \, a^{2} \sin\left(d x + c\right) + a^{2}}{\sin\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"1/2*(2*a^2*log(abs(sin(d*x + c))) - (4*a^2*sin(d*x + c) + a^2)/sin(d*x + c)^2)/d","A",0
202,1,41,0,0.147712," ","integrate(cos(d*x+c)*csc(d*x+c)^4*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{3 \, a^{2} \sin\left(d x + c\right)^{2} + 3 \, a^{2} \sin\left(d x + c\right) + a^{2}}{3 \, d \sin\left(d x + c\right)^{3}}"," ",0,"-1/3*(3*a^2*sin(d*x + c)^2 + 3*a^2*sin(d*x + c) + a^2)/(d*sin(d*x + c)^3)","A",0
203,1,43,0,0.155370," ","integrate(cos(d*x+c)*csc(d*x+c)^5*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{6 \, a^{2} \sin\left(d x + c\right)^{2} + 8 \, a^{2} \sin\left(d x + c\right) + 3 \, a^{2}}{12 \, d \sin\left(d x + c\right)^{4}}"," ",0,"-1/12*(6*a^2*sin(d*x + c)^2 + 8*a^2*sin(d*x + c) + 3*a^2)/(d*sin(d*x + c)^4)","A",0
204,1,43,0,0.165960," ","integrate(cos(d*x+c)*csc(d*x+c)^6*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{10 \, a^{2} \sin\left(d x + c\right)^{2} + 15 \, a^{2} \sin\left(d x + c\right) + 6 \, a^{2}}{30 \, d \sin\left(d x + c\right)^{5}}"," ",0,"-1/30*(10*a^2*sin(d*x + c)^2 + 15*a^2*sin(d*x + c) + 6*a^2)/(d*sin(d*x + c)^5)","A",0
205,1,43,0,0.159132," ","integrate(cos(d*x+c)*csc(d*x+c)^7*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{15 \, a^{2} \sin\left(d x + c\right)^{2} + 24 \, a^{2} \sin\left(d x + c\right) + 10 \, a^{2}}{60 \, d \sin\left(d x + c\right)^{6}}"," ",0,"-1/60*(15*a^2*sin(d*x + c)^2 + 24*a^2*sin(d*x + c) + 10*a^2)/(d*sin(d*x + c)^6)","A",0
206,1,58,0,0.198323," ","integrate(cos(d*x+c)*sin(d*x+c)^3*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{20 \, a^{3} \sin\left(d x + c\right)^{7} + 70 \, a^{3} \sin\left(d x + c\right)^{6} + 84 \, a^{3} \sin\left(d x + c\right)^{5} + 35 \, a^{3} \sin\left(d x + c\right)^{4}}{140 \, d}"," ",0,"1/140*(20*a^3*sin(d*x + c)^7 + 70*a^3*sin(d*x + c)^6 + 84*a^3*sin(d*x + c)^5 + 35*a^3*sin(d*x + c)^4)/d","A",0
207,1,58,0,0.185419," ","integrate(cos(d*x+c)*sin(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{10 \, a^{3} \sin\left(d x + c\right)^{6} + 36 \, a^{3} \sin\left(d x + c\right)^{5} + 45 \, a^{3} \sin\left(d x + c\right)^{4} + 20 \, a^{3} \sin\left(d x + c\right)^{3}}{60 \, d}"," ",0,"1/60*(10*a^3*sin(d*x + c)^6 + 36*a^3*sin(d*x + c)^5 + 45*a^3*sin(d*x + c)^4 + 20*a^3*sin(d*x + c)^3)/d","A",0
208,1,58,0,0.155096," ","integrate(cos(d*x+c)*sin(d*x+c)*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{4 \, a^{3} \sin\left(d x + c\right)^{5} + 15 \, a^{3} \sin\left(d x + c\right)^{4} + 20 \, a^{3} \sin\left(d x + c\right)^{3} + 10 \, a^{3} \sin\left(d x + c\right)^{2}}{20 \, d}"," ",0,"1/20*(4*a^3*sin(d*x + c)^5 + 15*a^3*sin(d*x + c)^4 + 20*a^3*sin(d*x + c)^3 + 10*a^3*sin(d*x + c)^2)/d","A",0
209,1,56,0,0.182613," ","integrate(cos(d*x+c)*csc(d*x+c)*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{2 \, a^{3} \sin\left(d x + c\right)^{3} + 9 \, a^{3} \sin\left(d x + c\right)^{2} + 6 \, a^{3} \log\left({\left| \sin\left(d x + c\right) \right|}\right) + 18 \, a^{3} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(2*a^3*sin(d*x + c)^3 + 9*a^3*sin(d*x + c)^2 + 6*a^3*log(abs(sin(d*x + c))) + 18*a^3*sin(d*x + c))/d","A",0
210,1,55,0,0.193357," ","integrate(cos(d*x+c)*csc(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{a^{3} \sin\left(d x + c\right)^{2} + 6 \, a^{3} \log\left({\left| \sin\left(d x + c\right) \right|}\right) + 6 \, a^{3} \sin\left(d x + c\right) - \frac{2 \, a^{3}}{\sin\left(d x + c\right)}}{2 \, d}"," ",0,"1/2*(a^3*sin(d*x + c)^2 + 6*a^3*log(abs(sin(d*x + c))) + 6*a^3*sin(d*x + c) - 2*a^3/sin(d*x + c))/d","A",0
211,1,55,0,0.177115," ","integrate(cos(d*x+c)*csc(d*x+c)^3*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{6 \, a^{3} \log\left({\left| \sin\left(d x + c\right) \right|}\right) + 2 \, a^{3} \sin\left(d x + c\right) - \frac{6 \, a^{3} \sin\left(d x + c\right) + a^{3}}{\sin\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"1/2*(6*a^3*log(abs(sin(d*x + c))) + 2*a^3*sin(d*x + c) - (6*a^3*sin(d*x + c) + a^3)/sin(d*x + c)^2)/d","A",0
212,1,59,0,0.178853," ","integrate(cos(d*x+c)*csc(d*x+c)^4*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{6 \, a^{3} \log\left({\left| \sin\left(d x + c\right) \right|}\right) - \frac{18 \, a^{3} \sin\left(d x + c\right)^{2} + 9 \, a^{3} \sin\left(d x + c\right) + 2 \, a^{3}}{\sin\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(6*a^3*log(abs(sin(d*x + c))) - (18*a^3*sin(d*x + c)^2 + 9*a^3*sin(d*x + c) + 2*a^3)/sin(d*x + c)^3)/d","A",0
213,1,54,0,0.177776," ","integrate(cos(d*x+c)*csc(d*x+c)^5*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{4 \, a^{3} \sin\left(d x + c\right)^{3} + 6 \, a^{3} \sin\left(d x + c\right)^{2} + 4 \, a^{3} \sin\left(d x + c\right) + a^{3}}{4 \, d \sin\left(d x + c\right)^{4}}"," ",0,"-1/4*(4*a^3*sin(d*x + c)^3 + 6*a^3*sin(d*x + c)^2 + 4*a^3*sin(d*x + c) + a^3)/(d*sin(d*x + c)^4)","A",0
214,1,56,0,0.177214," ","integrate(cos(d*x+c)*csc(d*x+c)^6*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{10 \, a^{3} \sin\left(d x + c\right)^{3} + 20 \, a^{3} \sin\left(d x + c\right)^{2} + 15 \, a^{3} \sin\left(d x + c\right) + 4 \, a^{3}}{20 \, d \sin\left(d x + c\right)^{5}}"," ",0,"-1/20*(10*a^3*sin(d*x + c)^3 + 20*a^3*sin(d*x + c)^2 + 15*a^3*sin(d*x + c) + 4*a^3)/(d*sin(d*x + c)^5)","A",0
215,1,56,0,0.197667," ","integrate(cos(d*x+c)*csc(d*x+c)^7*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{20 \, a^{3} \sin\left(d x + c\right)^{3} + 45 \, a^{3} \sin\left(d x + c\right)^{2} + 36 \, a^{3} \sin\left(d x + c\right) + 10 \, a^{3}}{60 \, d \sin\left(d x + c\right)^{6}}"," ",0,"-1/60*(20*a^3*sin(d*x + c)^3 + 45*a^3*sin(d*x + c)^2 + 36*a^3*sin(d*x + c) + 10*a^3)/(d*sin(d*x + c)^6)","A",0
216,1,56,0,0.191711," ","integrate(cos(d*x+c)*csc(d*x+c)^8*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{35 \, a^{3} \sin\left(d x + c\right)^{3} + 84 \, a^{3} \sin\left(d x + c\right)^{2} + 70 \, a^{3} \sin\left(d x + c\right) + 20 \, a^{3}}{140 \, d \sin\left(d x + c\right)^{7}}"," ",0,"-1/140*(35*a^3*sin(d*x + c)^3 + 84*a^3*sin(d*x + c)^2 + 70*a^3*sin(d*x + c) + 20*a^3)/(d*sin(d*x + c)^7)","A",0
217,1,71,0,0.246571," ","integrate(cos(d*x+c)*sin(d*x+c)^4*(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{70 \, a^{4} \sin\left(d x + c\right)^{9} + 315 \, a^{4} \sin\left(d x + c\right)^{8} + 540 \, a^{4} \sin\left(d x + c\right)^{7} + 420 \, a^{4} \sin\left(d x + c\right)^{6} + 126 \, a^{4} \sin\left(d x + c\right)^{5}}{630 \, d}"," ",0,"1/630*(70*a^4*sin(d*x + c)^9 + 315*a^4*sin(d*x + c)^8 + 540*a^4*sin(d*x + c)^7 + 420*a^4*sin(d*x + c)^6 + 126*a^4*sin(d*x + c)^5)/d","A",0
218,1,71,0,0.222298," ","integrate(cos(d*x+c)*sin(d*x+c)^3*(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{35 \, a^{4} \sin\left(d x + c\right)^{8} + 160 \, a^{4} \sin\left(d x + c\right)^{7} + 280 \, a^{4} \sin\left(d x + c\right)^{6} + 224 \, a^{4} \sin\left(d x + c\right)^{5} + 70 \, a^{4} \sin\left(d x + c\right)^{4}}{280 \, d}"," ",0,"1/280*(35*a^4*sin(d*x + c)^8 + 160*a^4*sin(d*x + c)^7 + 280*a^4*sin(d*x + c)^6 + 224*a^4*sin(d*x + c)^5 + 70*a^4*sin(d*x + c)^4)/d","A",0
219,1,71,0,0.190594," ","integrate(cos(d*x+c)*sin(d*x+c)^2*(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{15 \, a^{4} \sin\left(d x + c\right)^{7} + 70 \, a^{4} \sin\left(d x + c\right)^{6} + 126 \, a^{4} \sin\left(d x + c\right)^{5} + 105 \, a^{4} \sin\left(d x + c\right)^{4} + 35 \, a^{4} \sin\left(d x + c\right)^{3}}{105 \, d}"," ",0,"1/105*(15*a^4*sin(d*x + c)^7 + 70*a^4*sin(d*x + c)^6 + 126*a^4*sin(d*x + c)^5 + 105*a^4*sin(d*x + c)^4 + 35*a^4*sin(d*x + c)^3)/d","A",0
220,1,71,0,0.194765," ","integrate(cos(d*x+c)*sin(d*x+c)*(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{5 \, a^{4} \sin\left(d x + c\right)^{6} + 24 \, a^{4} \sin\left(d x + c\right)^{5} + 45 \, a^{4} \sin\left(d x + c\right)^{4} + 40 \, a^{4} \sin\left(d x + c\right)^{3} + 15 \, a^{4} \sin\left(d x + c\right)^{2}}{30 \, d}"," ",0,"1/30*(5*a^4*sin(d*x + c)^6 + 24*a^4*sin(d*x + c)^5 + 45*a^4*sin(d*x + c)^4 + 40*a^4*sin(d*x + c)^3 + 15*a^4*sin(d*x + c)^2)/d","A",0
221,1,69,0,0.198814," ","integrate(cos(d*x+c)*csc(d*x+c)*(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{3 \, a^{4} \sin\left(d x + c\right)^{4} + 16 \, a^{4} \sin\left(d x + c\right)^{3} + 36 \, a^{4} \sin\left(d x + c\right)^{2} + 12 \, a^{4} \log\left({\left| \sin\left(d x + c\right) \right|}\right) + 48 \, a^{4} \sin\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(3*a^4*sin(d*x + c)^4 + 16*a^4*sin(d*x + c)^3 + 36*a^4*sin(d*x + c)^2 + 12*a^4*log(abs(sin(d*x + c))) + 48*a^4*sin(d*x + c))/d","A",0
222,1,68,0,0.202245," ","integrate(cos(d*x+c)*csc(d*x+c)^2*(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{a^{4} \sin\left(d x + c\right)^{3} + 6 \, a^{4} \sin\left(d x + c\right)^{2} + 12 \, a^{4} \log\left({\left| \sin\left(d x + c\right) \right|}\right) + 18 \, a^{4} \sin\left(d x + c\right) - \frac{3 \, a^{4}}{\sin\left(d x + c\right)}}{3 \, d}"," ",0,"1/3*(a^4*sin(d*x + c)^3 + 6*a^4*sin(d*x + c)^2 + 12*a^4*log(abs(sin(d*x + c))) + 18*a^4*sin(d*x + c) - 3*a^4/sin(d*x + c))/d","A",0
223,1,67,0,0.202079," ","integrate(cos(d*x+c)*csc(d*x+c)^3*(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{a^{4} \sin\left(d x + c\right)^{2} + 12 \, a^{4} \log\left({\left| \sin\left(d x + c\right) \right|}\right) + 8 \, a^{4} \sin\left(d x + c\right) - \frac{8 \, a^{4} \sin\left(d x + c\right) + a^{4}}{\sin\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"1/2*(a^4*sin(d*x + c)^2 + 12*a^4*log(abs(sin(d*x + c))) + 8*a^4*sin(d*x + c) - (8*a^4*sin(d*x + c) + a^4)/sin(d*x + c)^2)/d","A",0
224,1,76,0,0.142580," ","integrate(cos(d*x+c)*sin(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{12 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} + \frac{3 \, a^{3} \sin\left(d x + c\right)^{4} - 4 \, a^{3} \sin\left(d x + c\right)^{3} + 6 \, a^{3} \sin\left(d x + c\right)^{2} - 12 \, a^{3} \sin\left(d x + c\right)}{a^{4}}}{12 \, d}"," ",0,"1/12*(12*log(abs(sin(d*x + c) + 1))/a + (3*a^3*sin(d*x + c)^4 - 4*a^3*sin(d*x + c)^3 + 6*a^3*sin(d*x + c)^2 - 12*a^3*sin(d*x + c))/a^4)/d","A",0
225,1,64,0,0.159305," ","integrate(cos(d*x+c)*sin(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{6 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} - \frac{2 \, a^{2} \sin\left(d x + c\right)^{3} - 3 \, a^{2} \sin\left(d x + c\right)^{2} + 6 \, a^{2} \sin\left(d x + c\right)}{a^{3}}}{6 \, d}"," ",0,"-1/6*(6*log(abs(sin(d*x + c) + 1))/a - (2*a^2*sin(d*x + c)^3 - 3*a^2*sin(d*x + c)^2 + 6*a^2*sin(d*x + c))/a^3)/d","A",0
226,1,45,0,0.160027," ","integrate(cos(d*x+c)*sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{2 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} + \frac{a \sin\left(d x + c\right)^{2} - 2 \, a \sin\left(d x + c\right)}{a^{2}}}{2 \, d}"," ",0,"1/2*(2*log(abs(sin(d*x + c) + 1))/a + (a*sin(d*x + c)^2 - 2*a*sin(d*x + c))/a^2)/d","A",0
227,1,31,0,0.139937," ","integrate(cos(d*x+c)*sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{\log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} - \frac{\sin\left(d x + c\right)}{a}}{d}"," ",0,"-(log(abs(sin(d*x + c) + 1))/a - sin(d*x + c)/a)/d","A",0
228,1,33,0,0.150620," ","integrate(cos(d*x+c)*csc(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{\log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} - \frac{\log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a}}{d}"," ",0,"-(log(abs(sin(d*x + c) + 1))/a - log(abs(sin(d*x + c)))/a)/d","A",0
229,1,45,0,0.195857," ","integrate(cos(d*x+c)*csc(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{\log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} - \frac{\log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a} - \frac{1}{a \sin\left(d x + c\right)}}{d}"," ",0,"(log(abs(sin(d*x + c) + 1))/a - log(abs(sin(d*x + c)))/a - 1/(a*sin(d*x + c)))/d","A",0
230,1,57,0,0.157849," ","integrate(cos(d*x+c)*csc(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{2 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} - \frac{2 \, \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a} - \frac{2 \, \sin\left(d x + c\right) - 1}{a \sin\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(2*log(abs(sin(d*x + c) + 1))/a - 2*log(abs(sin(d*x + c)))/a - (2*sin(d*x + c) - 1)/(a*sin(d*x + c)^2))/d","A",0
231,1,67,0,0.158730," ","integrate(cos(d*x+c)*csc(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{6 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} - \frac{6 \, \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a} - \frac{6 \, \sin\left(d x + c\right)^{2} - 3 \, \sin\left(d x + c\right) + 2}{a \sin\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(6*log(abs(sin(d*x + c) + 1))/a - 6*log(abs(sin(d*x + c)))/a - (6*sin(d*x + c)^2 - 3*sin(d*x + c) + 2)/(a*sin(d*x + c)^3))/d","A",0
232,1,107,0,0.177907," ","integrate(cos(d*x+c)*sin(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{{\left(a \sin\left(d x + c\right) + a\right)}^{3} {\left(\frac{6 \, a}{a \sin\left(d x + c\right) + a} - \frac{18 \, a^{2}}{{\left(a \sin\left(d x + c\right) + a\right)}^{2}} - 1\right)}}{a^{5}} - \frac{12 \, \log\left(\frac{{\left| a \sin\left(d x + c\right) + a \right|}}{{\left(a \sin\left(d x + c\right) + a\right)}^{2} {\left| a \right|}}\right)}{a^{2}} + \frac{3}{{\left(a \sin\left(d x + c\right) + a\right)} a}}{3 \, d}"," ",0,"-1/3*((a*sin(d*x + c) + a)^3*(6*a/(a*sin(d*x + c) + a) - 18*a^2/(a*sin(d*x + c) + a)^2 - 1)/a^5 - 12*log(abs(a*sin(d*x + c) + a)/((a*sin(d*x + c) + a)^2*abs(a)))/a^2 + 3/((a*sin(d*x + c) + a)*a))/d","A",0
233,1,90,0,0.172586," ","integrate(cos(d*x+c)*sin(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{{\left(a \sin\left(d x + c\right) + a\right)}^{2} {\left(\frac{6 \, a}{a \sin\left(d x + c\right) + a} - 1\right)}}{a^{4}} + \frac{6 \, \log\left(\frac{{\left| a \sin\left(d x + c\right) + a \right|}}{{\left(a \sin\left(d x + c\right) + a\right)}^{2} {\left| a \right|}}\right)}{a^{2}} - \frac{2}{{\left(a \sin\left(d x + c\right) + a\right)} a}}{2 \, d}"," ",0,"-1/2*((a*sin(d*x + c) + a)^2*(6*a/(a*sin(d*x + c) + a) - 1)/a^4 + 6*log(abs(a*sin(d*x + c) + a)/((a*sin(d*x + c) + a)^2*abs(a)))/a^2 - 2/((a*sin(d*x + c) + a)*a))/d","A",0
234,1,70,0,0.168954," ","integrate(cos(d*x+c)*sin(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2 \, \log\left(\frac{{\left| a \sin\left(d x + c\right) + a \right|}}{{\left(a \sin\left(d x + c\right) + a\right)}^{2} {\left| a \right|}}\right)}{a^{2}} + \frac{a \sin\left(d x + c\right) + a}{a^{3}} - \frac{1}{{\left(a \sin\left(d x + c\right) + a\right)} a}}{d}"," ",0,"(2*log(abs(a*sin(d*x + c) + a)/((a*sin(d*x + c) + a)^2*abs(a)))/a^2 + (a*sin(d*x + c) + a)/a^3 - 1/((a*sin(d*x + c) + a)*a))/d","A",0
235,1,56,0,0.158320," ","integrate(cos(d*x+c)*sin(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{\log\left(\frac{{\left| a \sin\left(d x + c\right) + a \right|}}{{\left(a \sin\left(d x + c\right) + a\right)}^{2} {\left| a \right|}}\right)}{a} - \frac{1}{a \sin\left(d x + c\right) + a}}{a d}"," ",0,"-(log(abs(a*sin(d*x + c) + a)/((a*sin(d*x + c) + a)^2*abs(a)))/a - 1/(a*sin(d*x + c) + a))/(a*d)","A",0
236,1,45,0,0.153129," ","integrate(cos(d*x+c)*csc(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{a {\left(\frac{\log\left({\left| -\frac{a}{a \sin\left(d x + c\right) + a} + 1 \right|}\right)}{a^{3}} + \frac{1}{{\left(a \sin\left(d x + c\right) + a\right)} a^{2}}\right)}}{d}"," ",0,"a*(log(abs(-a/(a*sin(d*x + c) + a) + 1))/a^3 + 1/((a*sin(d*x + c) + a)*a^2))/d","A",0
237,1,69,0,0.159292," ","integrate(cos(d*x+c)*csc(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{2 \, \log\left({\left| -\frac{a}{a \sin\left(d x + c\right) + a} + 1 \right|}\right)}{a^{2}} + \frac{1}{{\left(a \sin\left(d x + c\right) + a\right)} a} - \frac{1}{a^{2} {\left(\frac{a}{a \sin\left(d x + c\right) + a} - 1\right)}}}{d}"," ",0,"-(2*log(abs(-a/(a*sin(d*x + c) + a) + 1))/a^2 + 1/((a*sin(d*x + c) + a)*a) - 1/(a^2*(a/(a*sin(d*x + c) + a) - 1)))/d","A",0
238,1,87,0,0.189539," ","integrate(cos(d*x+c)*csc(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{6 \, \log\left({\left| -\frac{a}{a \sin\left(d x + c\right) + a} + 1 \right|}\right)}{a^{2}} + \frac{2}{{\left(a \sin\left(d x + c\right) + a\right)} a} - \frac{\frac{6 \, a}{a \sin\left(d x + c\right) + a} - 5}{a^{2} {\left(\frac{a}{a \sin\left(d x + c\right) + a} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(6*log(abs(-a/(a*sin(d*x + c) + a) + 1))/a^2 + 2/((a*sin(d*x + c) + a)*a) - (6*a/(a*sin(d*x + c) + a) - 5)/(a^2*(a/(a*sin(d*x + c) + a) - 1)^2))/d","A",0
239,1,103,0,0.180337," ","integrate(cos(d*x+c)*csc(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{12 \, \log\left({\left| -\frac{a}{a \sin\left(d x + c\right) + a} + 1 \right|}\right)}{a^{2}} + \frac{3}{{\left(a \sin\left(d x + c\right) + a\right)} a} + \frac{\frac{30 \, a}{a \sin\left(d x + c\right) + a} - \frac{18 \, a^{2}}{{\left(a \sin\left(d x + c\right) + a\right)}^{2}} - 13}{a^{2} {\left(\frac{a}{a \sin\left(d x + c\right) + a} - 1\right)}^{3}}}{3 \, d}"," ",0,"-1/3*(12*log(abs(-a/(a*sin(d*x + c) + a) + 1))/a^2 + 3/((a*sin(d*x + c) + a)*a) + (30*a/(a*sin(d*x + c) + a) - 18*a^2/(a*sin(d*x + c) + a)^2 - 13)/(a^2*(a/(a*sin(d*x + c) + a) - 1)^3))/d","A",0
240,1,89,0,0.223399," ","integrate(cos(d*x+c)*sin(d*x+c)^5/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{60 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{3}} + \frac{3 \, {\left(10 \, \sin\left(d x + c\right) + 9\right)}}{a^{3} {\left(\sin\left(d x + c\right) + 1\right)}^{2}} - \frac{2 \, a^{6} \sin\left(d x + c\right)^{3} - 9 \, a^{6} \sin\left(d x + c\right)^{2} + 36 \, a^{6} \sin\left(d x + c\right)}{a^{9}}}{6 \, d}"," ",0,"-1/6*(60*log(abs(sin(d*x + c) + 1))/a^3 + 3*(10*sin(d*x + c) + 9)/(a^3*(sin(d*x + c) + 1)^2) - (2*a^6*sin(d*x + c)^3 - 9*a^6*sin(d*x + c)^2 + 36*a^6*sin(d*x + c))/a^9)/d","A",0
241,1,73,0,0.205001," ","integrate(cos(d*x+c)*sin(d*x+c)^4/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{12 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{3}} + \frac{8 \, \sin\left(d x + c\right) + 7}{a^{3} {\left(\sin\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{3} \sin\left(d x + c\right)^{2} - 6 \, a^{3} \sin\left(d x + c\right)}{a^{6}}}{2 \, d}"," ",0,"1/2*(12*log(abs(sin(d*x + c) + 1))/a^3 + (8*sin(d*x + c) + 7)/(a^3*(sin(d*x + c) + 1)^2) + (a^3*sin(d*x + c)^2 - 6*a^3*sin(d*x + c))/a^6)/d","A",0
242,1,56,0,0.212718," ","integrate(cos(d*x+c)*sin(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{6 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{3}} - \frac{2 \, \sin\left(d x + c\right)}{a^{3}} + \frac{6 \, \sin\left(d x + c\right) + 5}{a^{3} {\left(\sin\left(d x + c\right) + 1\right)}^{2}}}{2 \, d}"," ",0,"-1/2*(6*log(abs(sin(d*x + c) + 1))/a^3 - 2*sin(d*x + c)/a^3 + (6*sin(d*x + c) + 5)/(a^3*(sin(d*x + c) + 1)^2))/d","A",0
243,1,45,0,0.184185," ","integrate(cos(d*x+c)*sin(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{2 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{3}} + \frac{4 \, \sin\left(d x + c\right) + 3}{a^{3} {\left(\sin\left(d x + c\right) + 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*log(abs(sin(d*x + c) + 1))/a^3 + (4*sin(d*x + c) + 3)/(a^3*(sin(d*x + c) + 1)^2))/d","A",0
244,1,28,0,0.159114," ","integrate(cos(d*x+c)*sin(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{2 \, \sin\left(d x + c\right) + 1}{2 \, a^{3} d {\left(\sin\left(d x + c\right) + 1\right)}^{2}}"," ",0,"-1/2*(2*sin(d*x + c) + 1)/(a^3*d*(sin(d*x + c) + 1)^2)","A",0
245,1,59,0,0.178163," ","integrate(cos(d*x+c)*csc(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{2 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{3}} - \frac{2 \, \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a^{3}} - \frac{2 \, \sin\left(d x + c\right) + 3}{a^{3} {\left(\sin\left(d x + c\right) + 1\right)}^{2}}}{2 \, d}"," ",0,"-1/2*(2*log(abs(sin(d*x + c) + 1))/a^3 - 2*log(abs(sin(d*x + c)))/a^3 - (2*sin(d*x + c) + 3)/(a^3*(sin(d*x + c) + 1)^2))/d","A",0
246,1,77,0,0.192632," ","integrate(cos(d*x+c)*csc(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{6 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{3}} - \frac{6 \, \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a^{3}} - \frac{6 \, \sin\left(d x + c\right)^{2} + 9 \, \sin\left(d x + c\right) + 2}{a^{3} {\left(\sin\left(d x + c\right) + 1\right)}^{2} \sin\left(d x + c\right)}}{2 \, d}"," ",0,"1/2*(6*log(abs(sin(d*x + c) + 1))/a^3 - 6*log(abs(sin(d*x + c)))/a^3 - (6*sin(d*x + c)^2 + 9*sin(d*x + c) + 2)/(a^3*(sin(d*x + c) + 1)^2*sin(d*x + c)))/d","A",0
247,1,86,0,0.191083," ","integrate(cos(d*x+c)*csc(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{12 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{3}} - \frac{12 \, \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a^{3}} - \frac{12 \, \sin\left(d x + c\right)^{3} + 18 \, \sin\left(d x + c\right)^{2} + 4 \, \sin\left(d x + c\right) - 1}{{\left(\sin\left(d x + c\right)^{2} + \sin\left(d x + c\right)\right)}^{2} a^{3}}}{2 \, d}"," ",0,"-1/2*(12*log(abs(sin(d*x + c) + 1))/a^3 - 12*log(abs(sin(d*x + c)))/a^3 - (12*sin(d*x + c)^3 + 18*sin(d*x + c)^2 + 4*sin(d*x + c) - 1)/((sin(d*x + c)^2 + sin(d*x + c))^2*a^3))/d","A",0
248,1,97,0,0.211566," ","integrate(cos(d*x+c)*csc(d*x+c)^4/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{60 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{3}} - \frac{60 \, \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a^{3}} - \frac{60 \, \sin\left(d x + c\right)^{4} + 90 \, \sin\left(d x + c\right)^{3} + 20 \, \sin\left(d x + c\right)^{2} - 5 \, \sin\left(d x + c\right) + 2}{a^{3} {\left(\sin\left(d x + c\right) + 1\right)}^{2} \sin\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(60*log(abs(sin(d*x + c) + 1))/a^3 - 60*log(abs(sin(d*x + c)))/a^3 - (60*sin(d*x + c)^4 + 90*sin(d*x + c)^3 + 20*sin(d*x + c)^2 - 5*sin(d*x + c) + 2)/(a^3*(sin(d*x + c) + 1)^2*sin(d*x + c)^3))/d","A",0
249,1,84,0,0.217290," ","integrate(cos(d*x+c)*sin(d*x+c)^5/(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{60 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{4}} + \frac{60 \, \sin\left(d x + c\right)^{2} + 105 \, \sin\left(d x + c\right) + 47}{a^{4} {\left(\sin\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, {\left(a^{4} \sin\left(d x + c\right)^{2} - 8 \, a^{4} \sin\left(d x + c\right)\right)}}{a^{8}}}{6 \, d}"," ",0,"1/6*(60*log(abs(sin(d*x + c) + 1))/a^4 + (60*sin(d*x + c)^2 + 105*sin(d*x + c) + 47)/(a^4*(sin(d*x + c) + 1)^3) + 3*(a^4*sin(d*x + c)^2 - 8*a^4*sin(d*x + c))/a^8)/d","A",0
250,1,66,0,0.206303," ","integrate(cos(d*x+c)*sin(d*x+c)^4/(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{12 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{4}} - \frac{3 \, \sin\left(d x + c\right)}{a^{4}} + \frac{18 \, \sin\left(d x + c\right)^{2} + 30 \, \sin\left(d x + c\right) + 13}{a^{4} {\left(\sin\left(d x + c\right) + 1\right)}^{3}}}{3 \, d}"," ",0,"-1/3*(12*log(abs(sin(d*x + c) + 1))/a^4 - 3*sin(d*x + c)/a^4 + (18*sin(d*x + c)^2 + 30*sin(d*x + c) + 13)/(a^4*(sin(d*x + c) + 1)^3))/d","A",0
251,1,55,0,0.206832," ","integrate(cos(d*x+c)*sin(d*x+c)^3/(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{6 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{4}} + \frac{18 \, \sin\left(d x + c\right)^{2} + 27 \, \sin\left(d x + c\right) + 11}{a^{4} {\left(\sin\left(d x + c\right) + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(6*log(abs(sin(d*x + c) + 1))/a^4 + (18*sin(d*x + c)^2 + 27*sin(d*x + c) + 11)/(a^4*(sin(d*x + c) + 1)^3))/d","A",0
252,1,38,0,0.220510," ","integrate(cos(d*x+c)*sin(d*x+c)^2/(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","-\frac{3 \, \sin\left(d x + c\right)^{2} + 3 \, \sin\left(d x + c\right) + 1}{3 \, a^{4} d {\left(\sin\left(d x + c\right) + 1\right)}^{3}}"," ",0,"-1/3*(3*sin(d*x + c)^2 + 3*sin(d*x + c) + 1)/(a^4*d*(sin(d*x + c) + 1)^3)","A",0
253,1,28,0,0.171735," ","integrate(cos(d*x+c)*sin(d*x+c)/(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","-\frac{3 \, \sin\left(d x + c\right) + 1}{6 \, a^{4} d {\left(\sin\left(d x + c\right) + 1\right)}^{3}}"," ",0,"-1/6*(3*sin(d*x + c) + 1)/(a^4*d*(sin(d*x + c) + 1)^3)","A",0
254,1,69,0,0.185620," ","integrate(cos(d*x+c)*csc(d*x+c)/(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{6 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{4}} - \frac{6 \, \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a^{4}} - \frac{6 \, \sin\left(d x + c\right)^{2} + 15 \, \sin\left(d x + c\right) + 11}{a^{4} {\left(\sin\left(d x + c\right) + 1\right)}^{3}}}{6 \, d}"," ",0,"-1/6*(6*log(abs(sin(d*x + c) + 1))/a^4 - 6*log(abs(sin(d*x + c)))/a^4 - (6*sin(d*x + c)^2 + 15*sin(d*x + c) + 11)/(a^4*(sin(d*x + c) + 1)^3))/d","A",0
255,1,87,0,0.200563," ","integrate(cos(d*x+c)*csc(d*x+c)^2/(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{12 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{4}} - \frac{12 \, \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a^{4}} - \frac{12 \, \sin\left(d x + c\right)^{3} + 30 \, \sin\left(d x + c\right)^{2} + 22 \, \sin\left(d x + c\right) + 3}{a^{4} {\left(\sin\left(d x + c\right) + 1\right)}^{3} \sin\left(d x + c\right)}}{3 \, d}"," ",0,"1/3*(12*log(abs(sin(d*x + c) + 1))/a^4 - 12*log(abs(sin(d*x + c)))/a^4 - (12*sin(d*x + c)^3 + 30*sin(d*x + c)^2 + 22*sin(d*x + c) + 3)/(a^4*(sin(d*x + c) + 1)^3*sin(d*x + c)))/d","A",0
256,1,97,0,0.231741," ","integrate(cos(d*x+c)*csc(d*x+c)^3/(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{60 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{4}} - \frac{60 \, \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a^{4}} - \frac{60 \, \sin\left(d x + c\right)^{4} + 150 \, \sin\left(d x + c\right)^{3} + 110 \, \sin\left(d x + c\right)^{2} + 15 \, \sin\left(d x + c\right) - 3}{a^{4} {\left(\sin\left(d x + c\right) + 1\right)}^{3} \sin\left(d x + c\right)^{2}}}{6 \, d}"," ",0,"-1/6*(60*log(abs(sin(d*x + c) + 1))/a^4 - 60*log(abs(sin(d*x + c)))/a^4 - (60*sin(d*x + c)^4 + 150*sin(d*x + c)^3 + 110*sin(d*x + c)^2 + 15*sin(d*x + c) - 3)/(a^4*(sin(d*x + c) + 1)^3*sin(d*x + c)^2))/d","A",0
257,1,2182,0,2.255473," ","integrate(cos(d*x+c)*csc(d*x+c)*(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{2} \sqrt{a} {\left(\frac{{\left(\sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{6} - 6 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{5} + 3 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{6} - 15 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{4} + 18 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{5} - 3 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{6} + 20 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{3} - 45 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{4} + 18 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{5} - \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{6} + 15 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{2} - 60 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{3} + 45 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{4} - 6 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{5} - 6 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right) + 45 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{2} - 60 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{3} + 15 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{4} - \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} + 18 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right) - 45 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{2} + 20 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{3} - 3 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 18 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right) - 15 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{2} + 3 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) - 6 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right) + \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \log\left(\frac{{\left| 2 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{3} - 6 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right) + 6 \, \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, {\left(\tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)}^{\frac{3}{2}} - 2 \right|}}{{\left| 2 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{3} - 6 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right) + 6 \, \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, {\left(\tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)}^{\frac{3}{2}} - 2 \right|}}\right)}{{\left(\tan\left(\frac{1}{4} \, c\right)^{6} + 3 \, \tan\left(\frac{1}{4} \, c\right)^{4} + 3 \, \tan\left(\frac{1}{4} \, c\right)^{2} + 1\right)} {\left(\tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)}^{\frac{3}{2}}} - \frac{{\left(\sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{6} + 6 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{5} - 3 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{6} - 15 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{4} + 18 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{5} - 3 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{6} - 20 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{3} + 45 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{4} - 18 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{5} + \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{6} + 15 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{2} - 60 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{3} + 45 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{4} - 6 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{5} + 6 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right) - 45 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{2} + 60 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{3} - 15 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{4} - \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} + 18 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right) - 45 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{2} + 20 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{3} + 3 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 18 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right) + 15 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{2} + 3 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) - 6 \, \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right) - \sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \log\left(\frac{{\left| 6 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, c\right)^{3} - 2 \, {\left(\tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)}^{\frac{3}{2}} - 2 \, \tan\left(\frac{1}{4} \, d x + c\right) + 6 \, \tan\left(\frac{1}{2} \, c\right) \right|}}{{\left| 6 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, c\right)^{3} + 2 \, {\left(\tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)}^{\frac{3}{2}} - 2 \, \tan\left(\frac{1}{4} \, d x + c\right) + 6 \, \tan\left(\frac{1}{2} \, c\right) \right|}}\right)}{{\left(\tan\left(\frac{1}{4} \, c\right)^{6} + 3 \, \tan\left(\frac{1}{4} \, c\right)^{4} + 3 \, \tan\left(\frac{1}{4} \, c\right)^{2} + 1\right)} {\left(\tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)}^{\frac{3}{2}}} + \frac{8 \, {\left(\mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{4} \, c\right)^{6} - 6 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{4} \, c\right)^{5} + \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{6} - 15 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{4} \, c\right)^{4} + 6 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{5} + 20 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{4} \, c\right)^{3} - 15 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{4} + 15 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{4} \, c\right)^{2} - 20 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{3} - 6 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{4} \, c\right) + 15 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{2} - \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) + 6 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right) - \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)}}{{\left(\sqrt{2} \tan\left(\frac{1}{4} \, c\right)^{6} + 3 \, \sqrt{2} \tan\left(\frac{1}{4} \, c\right)^{4} + 3 \, \sqrt{2} \tan\left(\frac{1}{4} \, c\right)^{2} + \sqrt{2}\right)} {\left(\tan\left(\frac{1}{4} \, d x + c\right)^{2} + 1\right)}}\right)}}{2 \, d}"," ",0,"-1/2*sqrt(2)*sqrt(a)*((sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^6 - 6*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^5 + 3*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^6 - 15*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^4 + 18*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^5 - 3*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^6 + 20*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^3 - 45*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^4 + 18*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^5 - sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^6 + 15*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^2 - 60*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^3 + 45*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^4 - 6*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^5 - 6*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c) + 45*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^2 - 60*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^3 + 15*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^4 - sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3 + 18*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c) - 45*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^2 + 20*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^3 - 3*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2 + 18*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c) - 15*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^2 + 3*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c) - 6*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c) + sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c)))*log(abs(2*tan(1/4*d*x + c)*tan(1/2*c)^3 - 6*tan(1/4*d*x + c)*tan(1/2*c) + 6*tan(1/2*c)^2 - 2*(tan(1/2*c)^2 + 1)^(3/2) - 2)/abs(2*tan(1/4*d*x + c)*tan(1/2*c)^3 - 6*tan(1/4*d*x + c)*tan(1/2*c) + 6*tan(1/2*c)^2 + 2*(tan(1/2*c)^2 + 1)^(3/2) - 2))/((tan(1/4*c)^6 + 3*tan(1/4*c)^4 + 3*tan(1/4*c)^2 + 1)*(tan(1/2*c)^2 + 1)^(3/2)) - (sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^6 + 6*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^5 - 3*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^6 - 15*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^4 + 18*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^5 - 3*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^6 - 20*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^3 + 45*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^4 - 18*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^5 + sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^6 + 15*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^2 - 60*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^3 + 45*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^4 - 6*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^5 + 6*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c) - 45*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^2 + 60*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^3 - 15*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^4 - sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3 + 18*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c) - 45*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^2 + 20*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^3 + 3*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2 - 18*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c) + 15*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^2 + 3*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c) - 6*sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c) - sqrt(2)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c)))*log(abs(6*tan(1/4*d*x + c)*tan(1/2*c)^2 - 2*tan(1/2*c)^3 - 2*(tan(1/2*c)^2 + 1)^(3/2) - 2*tan(1/4*d*x + c) + 6*tan(1/2*c))/abs(6*tan(1/4*d*x + c)*tan(1/2*c)^2 - 2*tan(1/2*c)^3 + 2*(tan(1/2*c)^2 + 1)^(3/2) - 2*tan(1/4*d*x + c) + 6*tan(1/2*c)))/((tan(1/4*c)^6 + 3*tan(1/4*c)^4 + 3*tan(1/4*c)^2 + 1)*(tan(1/2*c)^2 + 1)^(3/2)) + 8*(sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/4*c)^6 - 6*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/4*c)^5 + sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^6 - 15*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/4*c)^4 + 6*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^5 + 20*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/4*c)^3 - 15*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^4 + 15*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/4*c)^2 - 20*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^3 - 6*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/4*c) + 15*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^2 - sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c) + 6*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c) - sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c)))/((sqrt(2)*tan(1/4*c)^6 + 3*sqrt(2)*tan(1/4*c)^4 + 3*sqrt(2)*tan(1/4*c)^2 + sqrt(2))*(tan(1/4*d*x + c)^2 + 1)))/d","B",0
258,1,593,0,0.348516," ","integrate(cos(d*x+c)*sin(d*x+c)^n*(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{a^{4} n^{4} \sin\left(d x + c\right)^{n} \sin\left(d x + c\right)^{5} + 4 \, a^{4} n^{4} \sin\left(d x + c\right)^{n} \sin\left(d x + c\right)^{4} + 10 \, a^{4} n^{3} \sin\left(d x + c\right)^{n} \sin\left(d x + c\right)^{5} + 6 \, a^{4} n^{4} \sin\left(d x + c\right)^{n} \sin\left(d x + c\right)^{3} + 44 \, a^{4} n^{3} \sin\left(d x + c\right)^{n} \sin\left(d x + c\right)^{4} + 35 \, a^{4} n^{2} \sin\left(d x + c\right)^{n} \sin\left(d x + c\right)^{5} + 4 \, a^{4} n^{4} \sin\left(d x + c\right)^{n} \sin\left(d x + c\right)^{2} + 72 \, a^{4} n^{3} \sin\left(d x + c\right)^{n} \sin\left(d x + c\right)^{3} + 164 \, a^{4} n^{2} \sin\left(d x + c\right)^{n} \sin\left(d x + c\right)^{4} + 50 \, a^{4} n \sin\left(d x + c\right)^{n} \sin\left(d x + c\right)^{5} + a^{4} n^{4} \sin\left(d x + c\right)^{n} \sin\left(d x + c\right) + 52 \, a^{4} n^{3} \sin\left(d x + c\right)^{n} \sin\left(d x + c\right)^{2} + 294 \, a^{4} n^{2} \sin\left(d x + c\right)^{n} \sin\left(d x + c\right)^{3} + 244 \, a^{4} n \sin\left(d x + c\right)^{n} \sin\left(d x + c\right)^{4} + 24 \, a^{4} \sin\left(d x + c\right)^{n} \sin\left(d x + c\right)^{5} + 14 \, a^{4} n^{3} \sin\left(d x + c\right)^{n} \sin\left(d x + c\right) + 236 \, a^{4} n^{2} \sin\left(d x + c\right)^{n} \sin\left(d x + c\right)^{2} + 468 \, a^{4} n \sin\left(d x + c\right)^{n} \sin\left(d x + c\right)^{3} + 120 \, a^{4} \sin\left(d x + c\right)^{n} \sin\left(d x + c\right)^{4} + 71 \, a^{4} n^{2} \sin\left(d x + c\right)^{n} \sin\left(d x + c\right) + 428 \, a^{4} n \sin\left(d x + c\right)^{n} \sin\left(d x + c\right)^{2} + 240 \, a^{4} \sin\left(d x + c\right)^{n} \sin\left(d x + c\right)^{3} + 154 \, a^{4} n \sin\left(d x + c\right)^{n} \sin\left(d x + c\right) + 240 \, a^{4} \sin\left(d x + c\right)^{n} \sin\left(d x + c\right)^{2} + 120 \, a^{4} \sin\left(d x + c\right)^{n} \sin\left(d x + c\right)}{{\left(n^{5} + 15 \, n^{4} + 85 \, n^{3} + 225 \, n^{2} + 274 \, n + 120\right)} d}"," ",0,"(a^4*n^4*sin(d*x + c)^n*sin(d*x + c)^5 + 4*a^4*n^4*sin(d*x + c)^n*sin(d*x + c)^4 + 10*a^4*n^3*sin(d*x + c)^n*sin(d*x + c)^5 + 6*a^4*n^4*sin(d*x + c)^n*sin(d*x + c)^3 + 44*a^4*n^3*sin(d*x + c)^n*sin(d*x + c)^4 + 35*a^4*n^2*sin(d*x + c)^n*sin(d*x + c)^5 + 4*a^4*n^4*sin(d*x + c)^n*sin(d*x + c)^2 + 72*a^4*n^3*sin(d*x + c)^n*sin(d*x + c)^3 + 164*a^4*n^2*sin(d*x + c)^n*sin(d*x + c)^4 + 50*a^4*n*sin(d*x + c)^n*sin(d*x + c)^5 + a^4*n^4*sin(d*x + c)^n*sin(d*x + c) + 52*a^4*n^3*sin(d*x + c)^n*sin(d*x + c)^2 + 294*a^4*n^2*sin(d*x + c)^n*sin(d*x + c)^3 + 244*a^4*n*sin(d*x + c)^n*sin(d*x + c)^4 + 24*a^4*sin(d*x + c)^n*sin(d*x + c)^5 + 14*a^4*n^3*sin(d*x + c)^n*sin(d*x + c) + 236*a^4*n^2*sin(d*x + c)^n*sin(d*x + c)^2 + 468*a^4*n*sin(d*x + c)^n*sin(d*x + c)^3 + 120*a^4*sin(d*x + c)^n*sin(d*x + c)^4 + 71*a^4*n^2*sin(d*x + c)^n*sin(d*x + c) + 428*a^4*n*sin(d*x + c)^n*sin(d*x + c)^2 + 240*a^4*sin(d*x + c)^n*sin(d*x + c)^3 + 154*a^4*n*sin(d*x + c)^n*sin(d*x + c) + 240*a^4*sin(d*x + c)^n*sin(d*x + c)^2 + 120*a^4*sin(d*x + c)^n*sin(d*x + c))/((n^5 + 15*n^4 + 85*n^3 + 225*n^2 + 274*n + 120)*d)","B",0
259,1,379,0,0.316236," ","integrate(cos(d*x+c)*sin(d*x+c)^n*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{a^{3} n^{3} \sin\left(d x + c\right)^{n} \sin\left(d x + c\right)^{4} + 3 \, a^{3} n^{3} \sin\left(d x + c\right)^{n} \sin\left(d x + c\right)^{3} + 6 \, a^{3} n^{2} \sin\left(d x + c\right)^{n} \sin\left(d x + c\right)^{4} + 3 \, a^{3} n^{3} \sin\left(d x + c\right)^{n} \sin\left(d x + c\right)^{2} + 21 \, a^{3} n^{2} \sin\left(d x + c\right)^{n} \sin\left(d x + c\right)^{3} + 11 \, a^{3} n \sin\left(d x + c\right)^{n} \sin\left(d x + c\right)^{4} + a^{3} n^{3} \sin\left(d x + c\right)^{n} \sin\left(d x + c\right) + 24 \, a^{3} n^{2} \sin\left(d x + c\right)^{n} \sin\left(d x + c\right)^{2} + 42 \, a^{3} n \sin\left(d x + c\right)^{n} \sin\left(d x + c\right)^{3} + 6 \, a^{3} \sin\left(d x + c\right)^{n} \sin\left(d x + c\right)^{4} + 9 \, a^{3} n^{2} \sin\left(d x + c\right)^{n} \sin\left(d x + c\right) + 57 \, a^{3} n \sin\left(d x + c\right)^{n} \sin\left(d x + c\right)^{2} + 24 \, a^{3} \sin\left(d x + c\right)^{n} \sin\left(d x + c\right)^{3} + 26 \, a^{3} n \sin\left(d x + c\right)^{n} \sin\left(d x + c\right) + 36 \, a^{3} \sin\left(d x + c\right)^{n} \sin\left(d x + c\right)^{2} + 24 \, a^{3} \sin\left(d x + c\right)^{n} \sin\left(d x + c\right)}{{\left(n^{4} + 10 \, n^{3} + 35 \, n^{2} + 50 \, n + 24\right)} d}"," ",0,"(a^3*n^3*sin(d*x + c)^n*sin(d*x + c)^4 + 3*a^3*n^3*sin(d*x + c)^n*sin(d*x + c)^3 + 6*a^3*n^2*sin(d*x + c)^n*sin(d*x + c)^4 + 3*a^3*n^3*sin(d*x + c)^n*sin(d*x + c)^2 + 21*a^3*n^2*sin(d*x + c)^n*sin(d*x + c)^3 + 11*a^3*n*sin(d*x + c)^n*sin(d*x + c)^4 + a^3*n^3*sin(d*x + c)^n*sin(d*x + c) + 24*a^3*n^2*sin(d*x + c)^n*sin(d*x + c)^2 + 42*a^3*n*sin(d*x + c)^n*sin(d*x + c)^3 + 6*a^3*sin(d*x + c)^n*sin(d*x + c)^4 + 9*a^3*n^2*sin(d*x + c)^n*sin(d*x + c) + 57*a^3*n*sin(d*x + c)^n*sin(d*x + c)^2 + 24*a^3*sin(d*x + c)^n*sin(d*x + c)^3 + 26*a^3*n*sin(d*x + c)^n*sin(d*x + c) + 36*a^3*sin(d*x + c)^n*sin(d*x + c)^2 + 24*a^3*sin(d*x + c)^n*sin(d*x + c))/((n^4 + 10*n^3 + 35*n^2 + 50*n + 24)*d)","B",0
260,1,213,0,0.243106," ","integrate(cos(d*x+c)*sin(d*x+c)^n*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{a^{2} n^{2} \sin\left(d x + c\right)^{n} \sin\left(d x + c\right)^{3} + 2 \, a^{2} n^{2} \sin\left(d x + c\right)^{n} \sin\left(d x + c\right)^{2} + 3 \, a^{2} n \sin\left(d x + c\right)^{n} \sin\left(d x + c\right)^{3} + a^{2} n^{2} \sin\left(d x + c\right)^{n} \sin\left(d x + c\right) + 8 \, a^{2} n \sin\left(d x + c\right)^{n} \sin\left(d x + c\right)^{2} + 2 \, a^{2} \sin\left(d x + c\right)^{n} \sin\left(d x + c\right)^{3} + 5 \, a^{2} n \sin\left(d x + c\right)^{n} \sin\left(d x + c\right) + 6 \, a^{2} \sin\left(d x + c\right)^{n} \sin\left(d x + c\right)^{2} + 6 \, a^{2} \sin\left(d x + c\right)^{n} \sin\left(d x + c\right)}{{\left(n^{3} + 6 \, n^{2} + 11 \, n + 6\right)} d}"," ",0,"(a^2*n^2*sin(d*x + c)^n*sin(d*x + c)^3 + 2*a^2*n^2*sin(d*x + c)^n*sin(d*x + c)^2 + 3*a^2*n*sin(d*x + c)^n*sin(d*x + c)^3 + a^2*n^2*sin(d*x + c)^n*sin(d*x + c) + 8*a^2*n*sin(d*x + c)^n*sin(d*x + c)^2 + 2*a^2*sin(d*x + c)^n*sin(d*x + c)^3 + 5*a^2*n*sin(d*x + c)^n*sin(d*x + c) + 6*a^2*sin(d*x + c)^n*sin(d*x + c)^2 + 6*a^2*sin(d*x + c)^n*sin(d*x + c))/((n^3 + 6*n^2 + 11*n + 6)*d)","B",0
261,1,86,0,0.222014," ","integrate(cos(d*x+c)*sin(d*x+c)^n*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{a n \sin\left(d x + c\right)^{n} \sin\left(d x + c\right)^{2} + a n \sin\left(d x + c\right)^{n} \sin\left(d x + c\right) + a \sin\left(d x + c\right)^{n} \sin\left(d x + c\right)^{2} + 2 \, a \sin\left(d x + c\right)^{n} \sin\left(d x + c\right)}{{\left(n^{2} + 3 \, n + 2\right)} d}"," ",0,"(a*n*sin(d*x + c)^n*sin(d*x + c)^2 + a*n*sin(d*x + c)^n*sin(d*x + c) + a*sin(d*x + c)^n*sin(d*x + c)^2 + 2*a*sin(d*x + c)^n*sin(d*x + c))/((n^2 + 3*n + 2)*d)","B",0
262,0,0,0,0.000000," ","integrate(cos(d*x+c)*sin(d*x+c)^n/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\int \frac{\sin\left(d x + c\right)^{n} \cos\left(d x + c\right)}{a \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sin(d*x + c)^n*cos(d*x + c)/(a*sin(d*x + c) + a), x)","F",0
263,0,0,0,0.000000," ","integrate(cos(d*x+c)*sin(d*x+c)^n/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\sin\left(d x + c\right)^{n} \cos\left(d x + c\right)}{{\left(a \sin\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sin(d*x + c)^n*cos(d*x + c)/(a*sin(d*x + c) + a)^2, x)","F",0
264,0,0,0,0.000000," ","integrate(cos(d*x+c)*sin(d*x+c)^n/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\int \frac{\sin\left(d x + c\right)^{n} \cos\left(d x + c\right)}{{\left(a \sin\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(sin(d*x + c)^n*cos(d*x + c)/(a*sin(d*x + c) + a)^3, x)","F",0
265,0,0,0,0.000000," ","integrate(cos(d*x+c)*sin(d*x+c)^n/(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","\int \frac{\sin\left(d x + c\right)^{n} \cos\left(d x + c\right)}{{\left(a \sin\left(d x + c\right) + a\right)}^{4}}\,{d x}"," ",0,"integrate(sin(d*x + c)^n*cos(d*x + c)/(a*sin(d*x + c) + a)^4, x)","F",0
266,1,92,0,0.165861," ","integrate(cos(d*x+c)^2*sin(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{1}{16} \, a x + \frac{a \cos\left(5 \, d x + 5 \, c\right)}{80 \, d} - \frac{a \cos\left(3 \, d x + 3 \, c\right)}{48 \, d} - \frac{a \cos\left(d x + c\right)}{8 \, d} + \frac{a \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} - \frac{a \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} - \frac{a \sin\left(2 \, d x + 2 \, c\right)}{64 \, d}"," ",0,"1/16*a*x + 1/80*a*cos(5*d*x + 5*c)/d - 1/48*a*cos(3*d*x + 3*c)/d - 1/8*a*cos(d*x + c)/d + 1/192*a*sin(6*d*x + 6*c)/d - 1/64*a*sin(4*d*x + 4*c)/d - 1/64*a*sin(2*d*x + 2*c)/d","A",0
267,1,62,0,0.183413," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{1}{8} \, a x + \frac{a \cos\left(5 \, d x + 5 \, c\right)}{80 \, d} - \frac{a \cos\left(3 \, d x + 3 \, c\right)}{48 \, d} - \frac{a \cos\left(d x + c\right)}{8 \, d} - \frac{a \sin\left(4 \, d x + 4 \, c\right)}{32 \, d}"," ",0,"1/8*a*x + 1/80*a*cos(5*d*x + 5*c)/d - 1/48*a*cos(3*d*x + 3*c)/d - 1/8*a*cos(d*x + c)/d - 1/32*a*sin(4*d*x + 4*c)/d","A",0
268,1,47,0,0.157497," ","integrate(cos(d*x+c)^2*sin(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{1}{8} \, a x - \frac{a \cos\left(3 \, d x + 3 \, c\right)}{12 \, d} - \frac{a \cos\left(d x + c\right)}{4 \, d} - \frac{a \sin\left(4 \, d x + 4 \, c\right)}{32 \, d}"," ",0,"1/8*a*x - 1/12*a*cos(3*d*x + 3*c)/d - 1/4*a*cos(d*x + c)/d - 1/32*a*sin(4*d*x + 4*c)/d","A",0
269,1,87,0,0.146313," ","integrate(cos(d*x+c)^2*csc(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{{\left(d x + c\right)} a + 2 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{2 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, a\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*((d*x + c)*a + 2*a*log(abs(tan(1/2*d*x + 1/2*c))) - 2*(a*tan(1/2*d*x + 1/2*c)^3 - 2*a*tan(1/2*d*x + 1/2*c)^2 - a*tan(1/2*d*x + 1/2*c) - 2*a)/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","A",0
270,1,108,0,0.155676," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{6 \, {\left(d x + c\right)} a - 6 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 10 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}}{6 \, d}"," ",0,"-1/6*(6*(d*x + c)*a - 6*a*log(abs(tan(1/2*d*x + 1/2*c))) - 3*a*tan(1/2*d*x + 1/2*c) + (2*a*tan(1/2*d*x + 1/2*c)^3 + 3*a*tan(1/2*d*x + 1/2*c)^2 - 10*a*tan(1/2*d*x + 1/2*c) + 3*a)/(tan(1/2*d*x + 1/2*c)^3 + tan(1/2*d*x + 1/2*c)))/d","B",0
271,1,95,0,0.163320," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, {\left(d x + c\right)} a - 4 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 4 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{6 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}}{8 \, d}"," ",0,"1/8*(a*tan(1/2*d*x + 1/2*c)^2 - 8*(d*x + c)*a - 4*a*log(abs(tan(1/2*d*x + 1/2*c))) + 4*a*tan(1/2*d*x + 1/2*c) + (6*a*tan(1/2*d*x + 1/2*c)^2 - 4*a*tan(1/2*d*x + 1/2*c) - a)/tan(1/2*d*x + 1/2*c)^2)/d","A",0
272,1,115,0,0.166755," ","integrate(cos(d*x+c)^2*csc(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{22 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{24 \, d}"," ",0,"1/24*(a*tan(1/2*d*x + 1/2*c)^3 + 3*a*tan(1/2*d*x + 1/2*c)^2 - 12*a*log(abs(tan(1/2*d*x + 1/2*c))) - 3*a*tan(1/2*d*x + 1/2*c) + (22*a*tan(1/2*d*x + 1/2*c)^3 + 3*a*tan(1/2*d*x + 1/2*c)^2 - 3*a*tan(1/2*d*x + 1/2*c) - a)/tan(1/2*d*x + 1/2*c)^3)/d","B",0
273,1,116,0,0.202919," ","integrate(cos(d*x+c)^2*csc(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 8 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 24 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{50 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 24 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 8 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}}}{192 \, d}"," ",0,"1/192*(3*a*tan(1/2*d*x + 1/2*c)^4 + 8*a*tan(1/2*d*x + 1/2*c)^3 - 24*a*log(abs(tan(1/2*d*x + 1/2*c))) - 24*a*tan(1/2*d*x + 1/2*c) + (50*a*tan(1/2*d*x + 1/2*c)^4 + 24*a*tan(1/2*d*x + 1/2*c)^3 - 8*a*tan(1/2*d*x + 1/2*c) - 3*a)/tan(1/2*d*x + 1/2*c)^4)/d","A",0
274,1,144,0,0.177467," ","integrate(cos(d*x+c)^2*csc(d*x+c)^6*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{6 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 10 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 60 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{274 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 60 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 10 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{960 \, d}"," ",0,"1/960*(6*a*tan(1/2*d*x + 1/2*c)^5 + 15*a*tan(1/2*d*x + 1/2*c)^4 + 10*a*tan(1/2*d*x + 1/2*c)^3 - 120*a*log(abs(tan(1/2*d*x + 1/2*c))) - 60*a*tan(1/2*d*x + 1/2*c) + (274*a*tan(1/2*d*x + 1/2*c)^5 + 60*a*tan(1/2*d*x + 1/2*c)^4 - 10*a*tan(1/2*d*x + 1/2*c)^2 - 15*a*tan(1/2*d*x + 1/2*c) - 6*a)/tan(1/2*d*x + 1/2*c)^5)/d","A",0
275,1,123,0,0.222781," ","integrate(cos(d*x+c)^2*sin(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{1}{8} \, a^{2} x - \frac{a^{2} \cos\left(7 \, d x + 7 \, c\right)}{448 \, d} + \frac{7 \, a^{2} \cos\left(5 \, d x + 5 \, c\right)}{320 \, d} - \frac{5 \, a^{2} \cos\left(3 \, d x + 3 \, c\right)}{192 \, d} - \frac{13 \, a^{2} \cos\left(d x + c\right)}{64 \, d} + \frac{a^{2} \sin\left(6 \, d x + 6 \, c\right)}{96 \, d} - \frac{a^{2} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} - \frac{a^{2} \sin\left(2 \, d x + 2 \, c\right)}{32 \, d}"," ",0,"1/8*a^2*x - 1/448*a^2*cos(7*d*x + 7*c)/d + 7/320*a^2*cos(5*d*x + 5*c)/d - 5/192*a^2*cos(3*d*x + 3*c)/d - 13/64*a^2*cos(d*x + c)/d + 1/96*a^2*sin(6*d*x + 6*c)/d - 1/32*a^2*sin(4*d*x + 4*c)/d - 1/32*a^2*sin(2*d*x + 2*c)/d","A",0
276,1,106,0,0.191703," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{3}{16} \, a^{2} x + \frac{a^{2} \cos\left(5 \, d x + 5 \, c\right)}{40 \, d} - \frac{a^{2} \cos\left(3 \, d x + 3 \, c\right)}{24 \, d} - \frac{a^{2} \cos\left(d x + c\right)}{4 \, d} + \frac{a^{2} \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} - \frac{3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} - \frac{a^{2} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d}"," ",0,"3/16*a^2*x + 1/40*a^2*cos(5*d*x + 5*c)/d - 1/24*a^2*cos(3*d*x + 3*c)/d - 1/4*a^2*cos(d*x + c)/d + 1/192*a^2*sin(6*d*x + 6*c)/d - 3/64*a^2*sin(4*d*x + 4*c)/d - 1/64*a^2*sin(2*d*x + 2*c)/d","A",0
277,1,72,0,0.171384," ","integrate(cos(d*x+c)^2*sin(d*x+c)*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{1}{4} \, a^{2} x + \frac{a^{2} \cos\left(5 \, d x + 5 \, c\right)}{80 \, d} - \frac{5 \, a^{2} \cos\left(3 \, d x + 3 \, c\right)}{48 \, d} - \frac{3 \, a^{2} \cos\left(d x + c\right)}{8 \, d} - \frac{a^{2} \sin\left(4 \, d x + 4 \, c\right)}{16 \, d}"," ",0,"1/4*a^2*x + 1/80*a^2*cos(5*d*x + 5*c)/d - 5/48*a^2*cos(3*d*x + 3*c)/d - 3/8*a^2*cos(d*x + c)/d - 1/16*a^2*sin(4*d*x + 4*c)/d","A",0
278,1,101,0,0.173402," ","integrate(cos(d*x+c)^2*csc(d*x+c)*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{3 \, {\left(d x + c\right)} a^{2} + 3 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{2 \, {\left(3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, a^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*(d*x + c)*a^2 + 3*a^2*log(abs(tan(1/2*d*x + 1/2*c))) - 2*(3*a^2*tan(1/2*d*x + 1/2*c)^5 - 6*a^2*tan(1/2*d*x + 1/2*c)^2 - 3*a^2*tan(1/2*d*x + 1/2*c) - 2*a^2)/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
279,1,143,0,0.180455," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{{\left(d x + c\right)} a^{2} - 4 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{4 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)} + \frac{2 \, {\left(a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, a^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"-1/2*((d*x + c)*a^2 - 4*a^2*log(abs(tan(1/2*d*x + 1/2*c))) - a^2*tan(1/2*d*x + 1/2*c) + (4*a^2*tan(1/2*d*x + 1/2*c) + a^2)/tan(1/2*d*x + 1/2*c) + 2*(a^2*tan(1/2*d*x + 1/2*c)^3 - 4*a^2*tan(1/2*d*x + 1/2*c)^2 - a^2*tan(1/2*d*x + 1/2*c) - 4*a^2)/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","B",0
280,1,128,0,0.192472," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 16 \, {\left(d x + c\right)} a^{2} + 4 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 8 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{16 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} - \frac{6 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 8 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}}{8 \, d}"," ",0,"1/8*(a^2*tan(1/2*d*x + 1/2*c)^2 - 16*(d*x + c)*a^2 + 4*a^2*log(abs(tan(1/2*d*x + 1/2*c))) + 8*a^2*tan(1/2*d*x + 1/2*c) + 16*a^2/(tan(1/2*d*x + 1/2*c)^2 + 1) - (6*a^2*tan(1/2*d*x + 1/2*c)^2 + 8*a^2*tan(1/2*d*x + 1/2*c) + a^2)/tan(1/2*d*x + 1/2*c)^2)/d","A",0
281,1,141,0,0.196274," ","integrate(cos(d*x+c)^2*csc(d*x+c)^4*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 24 \, {\left(d x + c\right)} a^{2} - 24 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 9 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{44 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 6 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{24 \, d}"," ",0,"1/24*(a^2*tan(1/2*d*x + 1/2*c)^3 + 6*a^2*tan(1/2*d*x + 1/2*c)^2 - 24*(d*x + c)*a^2 - 24*a^2*log(abs(tan(1/2*d*x + 1/2*c))) + 9*a^2*tan(1/2*d*x + 1/2*c) + (44*a^2*tan(1/2*d*x + 1/2*c)^3 - 9*a^2*tan(1/2*d*x + 1/2*c)^2 - 6*a^2*tan(1/2*d*x + 1/2*c) - a^2)/tan(1/2*d*x + 1/2*c)^3)/d","A",0
282,1,164,0,0.240178," ","integrate(cos(d*x+c)^2*csc(d*x+c)^5*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 16 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 24 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 120 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 48 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{250 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 48 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 16 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}}}{192 \, d}"," ",0,"1/192*(3*a^2*tan(1/2*d*x + 1/2*c)^4 + 16*a^2*tan(1/2*d*x + 1/2*c)^3 + 24*a^2*tan(1/2*d*x + 1/2*c)^2 - 120*a^2*log(abs(tan(1/2*d*x + 1/2*c))) - 48*a^2*tan(1/2*d*x + 1/2*c) + (250*a^2*tan(1/2*d*x + 1/2*c)^4 + 48*a^2*tan(1/2*d*x + 1/2*c)^3 - 24*a^2*tan(1/2*d*x + 1/2*c)^2 - 16*a^2*tan(1/2*d*x + 1/2*c) - 3*a^2)/tan(1/2*d*x + 1/2*c)^4)/d","B",0
283,1,164,0,0.223210," ","integrate(cos(d*x+c)^2*csc(d*x+c)^6*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 25 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 90 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{274 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 90 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 25 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{480 \, d}"," ",0,"1/480*(3*a^2*tan(1/2*d*x + 1/2*c)^5 + 15*a^2*tan(1/2*d*x + 1/2*c)^4 + 25*a^2*tan(1/2*d*x + 1/2*c)^3 - 120*a^2*log(abs(tan(1/2*d*x + 1/2*c))) - 90*a^2*tan(1/2*d*x + 1/2*c) + (274*a^2*tan(1/2*d*x + 1/2*c)^5 + 90*a^2*tan(1/2*d*x + 1/2*c)^4 - 25*a^2*tan(1/2*d*x + 1/2*c)^2 - 15*a^2*tan(1/2*d*x + 1/2*c) - 3*a^2)/tan(1/2*d*x + 1/2*c)^5)/d","A",0
284,1,228,0,0.227794," ","integrate(cos(d*x+c)^2*csc(d*x+c)^7*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{5 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 24 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 45 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 40 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 360 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 240 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{882 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 240 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 40 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 45 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 24 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6}}}{1920 \, d}"," ",0,"1/1920*(5*a^2*tan(1/2*d*x + 1/2*c)^6 + 24*a^2*tan(1/2*d*x + 1/2*c)^5 + 45*a^2*tan(1/2*d*x + 1/2*c)^4 + 40*a^2*tan(1/2*d*x + 1/2*c)^3 - 15*a^2*tan(1/2*d*x + 1/2*c)^2 - 360*a^2*log(abs(tan(1/2*d*x + 1/2*c))) - 240*a^2*tan(1/2*d*x + 1/2*c) + (882*a^2*tan(1/2*d*x + 1/2*c)^6 + 240*a^2*tan(1/2*d*x + 1/2*c)^5 + 15*a^2*tan(1/2*d*x + 1/2*c)^4 - 40*a^2*tan(1/2*d*x + 1/2*c)^3 - 45*a^2*tan(1/2*d*x + 1/2*c)^2 - 24*a^2*tan(1/2*d*x + 1/2*c) - 5*a^2)/tan(1/2*d*x + 1/2*c)^6)/d","B",0
285,1,123,0,0.227396," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{5}{16} \, a^{3} x - \frac{a^{3} \cos\left(7 \, d x + 7 \, c\right)}{448 \, d} + \frac{3 \, a^{3} \cos\left(5 \, d x + 5 \, c\right)}{64 \, d} - \frac{13 \, a^{3} \cos\left(3 \, d x + 3 \, c\right)}{192 \, d} - \frac{29 \, a^{3} \cos\left(d x + c\right)}{64 \, d} + \frac{a^{3} \sin\left(6 \, d x + 6 \, c\right)}{64 \, d} - \frac{5 \, a^{3} \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} - \frac{3 \, a^{3} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d}"," ",0,"5/16*a^3*x - 1/448*a^3*cos(7*d*x + 7*c)/d + 3/64*a^3*cos(5*d*x + 5*c)/d - 13/192*a^3*cos(3*d*x + 3*c)/d - 29/64*a^3*cos(d*x + c)/d + 1/64*a^3*sin(6*d*x + 6*c)/d - 5/64*a^3*sin(4*d*x + 4*c)/d - 3/64*a^3*sin(2*d*x + 2*c)/d","A",0
286,1,106,0,0.202200," ","integrate(cos(d*x+c)^2*sin(d*x+c)*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{7}{16} \, a^{3} x + \frac{3 \, a^{3} \cos\left(5 \, d x + 5 \, c\right)}{80 \, d} - \frac{7 \, a^{3} \cos\left(3 \, d x + 3 \, c\right)}{48 \, d} - \frac{5 \, a^{3} \cos\left(d x + c\right)}{8 \, d} + \frac{a^{3} \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} - \frac{7 \, a^{3} \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} - \frac{a^{3} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d}"," ",0,"7/16*a^3*x + 3/80*a^3*cos(5*d*x + 5*c)/d - 7/48*a^3*cos(3*d*x + 3*c)/d - 5/8*a^3*cos(d*x + c)/d + 1/192*a^3*sin(6*d*x + 6*c)/d - 7/64*a^3*sin(4*d*x + 4*c)/d - 1/64*a^3*sin(2*d*x + 2*c)/d","A",0
287,1,144,0,0.205511," ","integrate(cos(d*x+c)^2*csc(d*x+c)*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{13 \, {\left(d x + c\right)} a^{3} + 8 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{2 \, {\left(11 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 16 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 19 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 19 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 16 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 11 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{8 \, d}"," ",0,"1/8*(13*(d*x + c)*a^3 + 8*a^3*log(abs(tan(1/2*d*x + 1/2*c))) - 2*(11*a^3*tan(1/2*d*x + 1/2*c)^7 + 16*a^3*tan(1/2*d*x + 1/2*c)^6 + 19*a^3*tan(1/2*d*x + 1/2*c)^5 - 19*a^3*tan(1/2*d*x + 1/2*c)^3 - 16*a^3*tan(1/2*d*x + 1/2*c)^2 - 11*a^3*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","A",0
288,1,162,0,0.216277," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{3 \, {\left(d x + c\right)} a^{3} + 18 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{3 \, {\left(6 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)} - \frac{2 \, {\left(9 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 36 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 16 \, a^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(d*x + c)*a^3 + 18*a^3*log(abs(tan(1/2*d*x + 1/2*c))) + 3*a^3*tan(1/2*d*x + 1/2*c) - 3*(6*a^3*tan(1/2*d*x + 1/2*c) + a^3)/tan(1/2*d*x + 1/2*c) - 2*(9*a^3*tan(1/2*d*x + 1/2*c)^5 - 12*a^3*tan(1/2*d*x + 1/2*c)^4 - 36*a^3*tan(1/2*d*x + 1/2*c)^2 - 9*a^3*tan(1/2*d*x + 1/2*c) - 16*a^3)/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
289,1,184,0,0.243412," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 20 \, {\left(d x + c\right)} a^{3} + 20 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 12 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{10 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 20 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 16 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}^{2}}}{8 \, d}"," ",0,"1/8*(a^3*tan(1/2*d*x + 1/2*c)^2 - 20*(d*x + c)*a^3 + 20*a^3*log(abs(tan(1/2*d*x + 1/2*c))) + 12*a^3*tan(1/2*d*x + 1/2*c) - (10*a^3*tan(1/2*d*x + 1/2*c)^6 + 20*a^3*tan(1/2*d*x + 1/2*c)^5 - 27*a^3*tan(1/2*d*x + 1/2*c)^4 + 16*a^3*tan(1/2*d*x + 1/2*c)^3 - 36*a^3*tan(1/2*d*x + 1/2*c)^2 + 12*a^3*tan(1/2*d*x + 1/2*c) + a^3)/(tan(1/2*d*x + 1/2*c)^3 + tan(1/2*d*x + 1/2*c))^2)/d","B",0
290,1,161,0,0.242301," ","integrate(cos(d*x+c)^2*csc(d*x+c)^4*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 72 \, {\left(d x + c\right)} a^{3} - 12 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 33 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{48 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + \frac{22 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 33 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{24 \, d}"," ",0,"1/24*(a^3*tan(1/2*d*x + 1/2*c)^3 + 9*a^3*tan(1/2*d*x + 1/2*c)^2 - 72*(d*x + c)*a^3 - 12*a^3*log(abs(tan(1/2*d*x + 1/2*c))) + 33*a^3*tan(1/2*d*x + 1/2*c) + 48*a^3/(tan(1/2*d*x + 1/2*c)^2 + 1) + (22*a^3*tan(1/2*d*x + 1/2*c)^3 - 33*a^3*tan(1/2*d*x + 1/2*c)^2 - 9*a^3*tan(1/2*d*x + 1/2*c) - a^3)/tan(1/2*d*x + 1/2*c)^3)/d","A",0
291,1,174,0,0.242421," ","integrate(cos(d*x+c)^2*csc(d*x+c)^5*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 24 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 72 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 192 \, {\left(d x + c\right)} a^{3} - 312 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 24 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{650 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 24 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 24 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}}}{192 \, d}"," ",0,"1/192*(3*a^3*tan(1/2*d*x + 1/2*c)^4 + 24*a^3*tan(1/2*d*x + 1/2*c)^3 + 72*a^3*tan(1/2*d*x + 1/2*c)^2 - 192*(d*x + c)*a^3 - 312*a^3*log(abs(tan(1/2*d*x + 1/2*c))) + 24*a^3*tan(1/2*d*x + 1/2*c) + (650*a^3*tan(1/2*d*x + 1/2*c)^4 - 24*a^3*tan(1/2*d*x + 1/2*c)^3 - 72*a^3*tan(1/2*d*x + 1/2*c)^2 - 24*a^3*tan(1/2*d*x + 1/2*c) - 3*a^3)/tan(1/2*d*x + 1/2*c)^4)/d","A",0
292,1,196,0,0.265047," ","integrate(cos(d*x+c)^2*csc(d*x+c)^6*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{6 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 45 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 130 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 840 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 420 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{1918 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 420 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 120 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 130 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 45 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{960 \, d}"," ",0,"1/960*(6*a^3*tan(1/2*d*x + 1/2*c)^5 + 45*a^3*tan(1/2*d*x + 1/2*c)^4 + 130*a^3*tan(1/2*d*x + 1/2*c)^3 + 120*a^3*tan(1/2*d*x + 1/2*c)^2 - 840*a^3*log(abs(tan(1/2*d*x + 1/2*c))) - 420*a^3*tan(1/2*d*x + 1/2*c) + (1918*a^3*tan(1/2*d*x + 1/2*c)^5 + 420*a^3*tan(1/2*d*x + 1/2*c)^4 - 120*a^3*tan(1/2*d*x + 1/2*c)^3 - 130*a^3*tan(1/2*d*x + 1/2*c)^2 - 45*a^3*tan(1/2*d*x + 1/2*c) - 6*a^3)/tan(1/2*d*x + 1/2*c)^5)/d","B",0
293,1,228,0,0.281343," ","integrate(cos(d*x+c)^2*csc(d*x+c)^7*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{5 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 36 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 105 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 140 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 840 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 600 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{2058 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 600 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 140 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 105 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 36 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6}}}{1920 \, d}"," ",0,"1/1920*(5*a^3*tan(1/2*d*x + 1/2*c)^6 + 36*a^3*tan(1/2*d*x + 1/2*c)^5 + 105*a^3*tan(1/2*d*x + 1/2*c)^4 + 140*a^3*tan(1/2*d*x + 1/2*c)^3 - 15*a^3*tan(1/2*d*x + 1/2*c)^2 - 840*a^3*log(abs(tan(1/2*d*x + 1/2*c))) - 600*a^3*tan(1/2*d*x + 1/2*c) + (2058*a^3*tan(1/2*d*x + 1/2*c)^6 + 600*a^3*tan(1/2*d*x + 1/2*c)^5 + 15*a^3*tan(1/2*d*x + 1/2*c)^4 - 140*a^3*tan(1/2*d*x + 1/2*c)^3 - 105*a^3*tan(1/2*d*x + 1/2*c)^2 - 36*a^3*tan(1/2*d*x + 1/2*c) - 5*a^3)/tan(1/2*d*x + 1/2*c)^6)/d","B",0
294,1,106,0,0.212906," ","integrate(cos(d*x+c)^2*(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{21}{16} \, a^{4} x + \frac{a^{4} \cos\left(5 \, d x + 5 \, c\right)}{20 \, d} - \frac{5 \, a^{4} \cos\left(3 \, d x + 3 \, c\right)}{12 \, d} - \frac{3 \, a^{4} \cos\left(d x + c\right)}{2 \, d} + \frac{a^{4} \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} - \frac{13 \, a^{4} \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{15 \, a^{4} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d}"," ",0,"21/16*a^4*x + 1/20*a^4*cos(5*d*x + 5*c)/d - 5/12*a^4*cos(3*d*x + 3*c)/d - 3/2*a^4*cos(d*x + c)/d + 1/192*a^4*sin(6*d*x + 6*c)/d - 13/64*a^4*sin(4*d*x + 4*c)/d + 15/64*a^4*sin(2*d*x + 2*c)/d","A",0
295,1,181,0,0.237557," ","integrate(cos(d*x+c)^2*csc(d*x+c)*(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{75 \, {\left(d x + c\right)} a^{4} + 30 \, a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{2 \, {\left(45 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 150 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 210 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 300 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 40 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 210 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 20 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 45 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 34 \, a^{4}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5}}}{30 \, d}"," ",0,"1/30*(75*(d*x + c)*a^4 + 30*a^4*log(abs(tan(1/2*d*x + 1/2*c))) - 2*(45*a^4*tan(1/2*d*x + 1/2*c)^9 + 150*a^4*tan(1/2*d*x + 1/2*c)^8 + 210*a^4*tan(1/2*d*x + 1/2*c)^7 + 300*a^4*tan(1/2*d*x + 1/2*c)^6 + 40*a^4*tan(1/2*d*x + 1/2*c)^4 - 210*a^4*tan(1/2*d*x + 1/2*c)^3 + 20*a^4*tan(1/2*d*x + 1/2*c)^2 - 45*a^4*tan(1/2*d*x + 1/2*c) + 34*a^4)/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","A",0
296,1,194,0,0.248845," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2*(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{51 \, {\left(d x + c\right)} a^{4} + 96 \, a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 12 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{12 \, {\left(8 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{4}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)} - \frac{2 \, {\left(69 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 93 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 192 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 93 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 256 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 69 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 64 \, a^{4}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(51*(d*x + c)*a^4 + 96*a^4*log(abs(tan(1/2*d*x + 1/2*c))) + 12*a^4*tan(1/2*d*x + 1/2*c) - 12*(8*a^4*tan(1/2*d*x + 1/2*c) + a^4)/tan(1/2*d*x + 1/2*c) - 2*(69*a^4*tan(1/2*d*x + 1/2*c)^7 + 93*a^4*tan(1/2*d*x + 1/2*c)^5 - 192*a^4*tan(1/2*d*x + 1/2*c)^4 - 93*a^4*tan(1/2*d*x + 1/2*c)^3 - 256*a^4*tan(1/2*d*x + 1/2*c)^2 - 69*a^4*tan(1/2*d*x + 1/2*c) - 64*a^4)/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","A",0
297,1,114,0,0.170236," ","integrate(cos(d*x+c)^2*sin(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{45 \, {\left(d x + c\right)}}{a} + \frac{2 \, {\left(45 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 210 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 640 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 210 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 320 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 45 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 64\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5} a}}{120 \, d}"," ",0,"1/120*(45*(d*x + c)/a + 2*(45*tan(1/2*d*x + 1/2*c)^9 + 210*tan(1/2*d*x + 1/2*c)^7 + 640*tan(1/2*d*x + 1/2*c)^4 - 210*tan(1/2*d*x + 1/2*c)^3 + 320*tan(1/2*d*x + 1/2*c)^2 - 45*tan(1/2*d*x + 1/2*c) + 64)/((tan(1/2*d*x + 1/2*c)^2 + 1)^5*a))/d","A",0
298,1,114,0,0.146799," ","integrate(cos(d*x+c)^2*sin(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{9 \, {\left(d x + c\right)}}{a} + \frac{2 \, {\left(9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 33 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 48 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 33 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 64 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 16\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4} a}}{24 \, d}"," ",0,"-1/24*(9*(d*x + c)/a + 2*(9*tan(1/2*d*x + 1/2*c)^7 + 33*tan(1/2*d*x + 1/2*c)^5 + 48*tan(1/2*d*x + 1/2*c)^4 - 33*tan(1/2*d*x + 1/2*c)^3 + 64*tan(1/2*d*x + 1/2*c)^2 - 9*tan(1/2*d*x + 1/2*c) + 16)/((tan(1/2*d*x + 1/2*c)^2 + 1)^4*a))/d","A",0
299,1,75,0,0.142031," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{3 \, {\left(d x + c\right)}}{a} + \frac{2 \, {\left(3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} a}}{6 \, d}"," ",0,"1/6*(3*(d*x + c)/a + 2*(3*tan(1/2*d*x + 1/2*c)^5 + 12*tan(1/2*d*x + 1/2*c)^2 - 3*tan(1/2*d*x + 1/2*c) + 4)/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*a))/d","A",0
300,1,72,0,0.137270," ","integrate(cos(d*x+c)^2*sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{d x + c}{a} + \frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a}}{2 \, d}"," ",0,"-1/2*((d*x + c)/a + 2*(tan(1/2*d*x + 1/2*c)^3 + 2*tan(1/2*d*x + 1/2*c)^2 - tan(1/2*d*x + 1/2*c) + 2)/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a))/d","A",0
301,1,31,0,0.149699," ","integrate(cos(d*x+c)^2*csc(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{d x + c}{a} - \frac{\log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a}}{d}"," ",0,"-((d*x + c)/a - log(abs(tan(1/2*d*x + 1/2*c)))/a)/d","A",0
302,1,65,0,0.158276," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{2 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a} - \frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a} - \frac{2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}}{2 \, d}"," ",0,"-1/2*(2*log(abs(tan(1/2*d*x + 1/2*c)))/a - tan(1/2*d*x + 1/2*c)/a - (2*tan(1/2*d*x + 1/2*c) - 1)/(a*tan(1/2*d*x + 1/2*c)))/d","B",0
303,1,94,0,0.198720," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{4 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a} + \frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{2}} - \frac{6 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}}{8 \, d}"," ",0,"1/8*(4*log(abs(tan(1/2*d*x + 1/2*c)))/a + (a*tan(1/2*d*x + 1/2*c)^2 - 4*a*tan(1/2*d*x + 1/2*c))/a^2 - (6*tan(1/2*d*x + 1/2*c)^2 - 4*tan(1/2*d*x + 1/2*c) + 1)/(a*tan(1/2*d*x + 1/2*c)^2))/d","A",0
304,1,128,0,0.171291," ","integrate(cos(d*x+c)^2*csc(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{12 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a} - \frac{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 9 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3}} - \frac{22 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{24 \, d}"," ",0,"-1/24*(12*log(abs(tan(1/2*d*x + 1/2*c)))/a - (a^2*tan(1/2*d*x + 1/2*c)^3 - 3*a^2*tan(1/2*d*x + 1/2*c)^2 + 9*a^2*tan(1/2*d*x + 1/2*c))/a^3 - (22*tan(1/2*d*x + 1/2*c)^3 - 9*tan(1/2*d*x + 1/2*c)^2 + 3*tan(1/2*d*x + 1/2*c) - 1)/(a*tan(1/2*d*x + 1/2*c)^3))/d","A",0
305,1,157,0,0.190804," ","integrate(cos(d*x+c)^2*csc(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{72 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a} + \frac{3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 8 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 24 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 72 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{4}} - \frac{150 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 72 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 24 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}}}{192 \, d}"," ",0,"1/192*(72*log(abs(tan(1/2*d*x + 1/2*c)))/a + (3*a^3*tan(1/2*d*x + 1/2*c)^4 - 8*a^3*tan(1/2*d*x + 1/2*c)^3 + 24*a^3*tan(1/2*d*x + 1/2*c)^2 - 72*a^3*tan(1/2*d*x + 1/2*c))/a^4 - (150*tan(1/2*d*x + 1/2*c)^4 - 72*tan(1/2*d*x + 1/2*c)^3 + 24*tan(1/2*d*x + 1/2*c)^2 - 8*tan(1/2*d*x + 1/2*c) + 3)/(a*tan(1/2*d*x + 1/2*c)^4))/d","A",0
306,1,187,0,0.190253," ","integrate(cos(d*x+c)^2*csc(d*x+c)^6/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{360 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a} - \frac{6 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 50 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 300 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{5}} - \frac{822 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 300 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 120 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 50 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{960 \, d}"," ",0,"-1/960*(360*log(abs(tan(1/2*d*x + 1/2*c)))/a - (6*a^4*tan(1/2*d*x + 1/2*c)^5 - 15*a^4*tan(1/2*d*x + 1/2*c)^4 + 50*a^4*tan(1/2*d*x + 1/2*c)^3 - 120*a^4*tan(1/2*d*x + 1/2*c)^2 + 300*a^4*tan(1/2*d*x + 1/2*c))/a^5 - (822*tan(1/2*d*x + 1/2*c)^5 - 300*tan(1/2*d*x + 1/2*c)^4 + 120*tan(1/2*d*x + 1/2*c)^3 - 50*tan(1/2*d*x + 1/2*c)^2 + 15*tan(1/2*d*x + 1/2*c) - 6)/(a*tan(1/2*d*x + 1/2*c)^5))/d","A",0
307,1,145,0,0.198303," ","integrate(cos(d*x+c)^2*sin(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{81 \, {\left(d x + c\right)}}{a^{2}} + \frac{96}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}} + \frac{2 \, {\left(33 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 48 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 57 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 240 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 57 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 272 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 33 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 80\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4} a^{2}}}{24 \, d}"," ",0,"-1/24*(81*(d*x + c)/a^2 + 96/(a^2*(tan(1/2*d*x + 1/2*c) + 1)) + 2*(33*tan(1/2*d*x + 1/2*c)^7 + 48*tan(1/2*d*x + 1/2*c)^6 + 57*tan(1/2*d*x + 1/2*c)^5 + 240*tan(1/2*d*x + 1/2*c)^4 - 57*tan(1/2*d*x + 1/2*c)^3 + 272*tan(1/2*d*x + 1/2*c)^2 - 33*tan(1/2*d*x + 1/2*c) + 80)/((tan(1/2*d*x + 1/2*c)^2 + 1)^4*a^2))/d","A",0
308,1,106,0,0.195249," ","integrate(cos(d*x+c)^2*sin(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{9 \, {\left(d x + c\right)}}{a^{2}} + \frac{12}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}} + \frac{2 \, {\left(3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 18 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} a^{2}}}{3 \, d}"," ",0,"1/3*(9*(d*x + c)/a^2 + 12/(a^2*(tan(1/2*d*x + 1/2*c) + 1)) + 2*(3*tan(1/2*d*x + 1/2*c)^5 + 6*tan(1/2*d*x + 1/2*c)^4 + 18*tan(1/2*d*x + 1/2*c)^2 - 3*tan(1/2*d*x + 1/2*c) + 8)/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*a^2))/d","A",0
309,1,91,0,0.183756," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{5 \, {\left(d x + c\right)}}{a^{2}} + \frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{2}} + \frac{8}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}}{2 \, d}"," ",0,"-1/2*(5*(d*x + c)/a^2 + 2*(tan(1/2*d*x + 1/2*c)^3 + 4*tan(1/2*d*x + 1/2*c)^2 - tan(1/2*d*x + 1/2*c) + 4)/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^2) + 8/(a^2*(tan(1/2*d*x + 1/2*c) + 1)))/d","A",0
310,1,78,0,0.157670," ","integrate(cos(d*x+c)^2*sin(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{d x + c}{a^{2}} + \frac{2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} a^{2}}\right)}}{d}"," ",0,"2*((d*x + c)/a^2 + (2*tan(1/2*d*x + 1/2*c)^2 + tan(1/2*d*x + 1/2*c) + 3)/((tan(1/2*d*x + 1/2*c)^3 + tan(1/2*d*x + 1/2*c)^2 + tan(1/2*d*x + 1/2*c) + 1)*a^2))/d","A",0
311,1,38,0,0.164338," ","integrate(cos(d*x+c)^2*csc(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{\log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} + \frac{4}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}}{d}"," ",0,"(log(abs(tan(1/2*d*x + 1/2*c)))/a^2 + 4/(a^2*(tan(1/2*d*x + 1/2*c) + 1)))/d","A",0
312,1,90,0,0.193142," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{4 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} - \frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{2}} - \frac{2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 7 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} a^{2}}}{2 \, d}"," ",0,"-1/2*(4*log(abs(tan(1/2*d*x + 1/2*c)))/a^2 - tan(1/2*d*x + 1/2*c)/a^2 - (2*tan(1/2*d*x + 1/2*c)^2 - 7*tan(1/2*d*x + 1/2*c) - 1)/((tan(1/2*d*x + 1/2*c)^2 + tan(1/2*d*x + 1/2*c))*a^2))/d","A",0
313,1,116,0,0.193126," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{20 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} + \frac{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{4}} + \frac{32}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}} - \frac{30 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1}{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}}{8 \, d}"," ",0,"1/8*(20*log(abs(tan(1/2*d*x + 1/2*c)))/a^2 + (a^2*tan(1/2*d*x + 1/2*c)^2 - 8*a^2*tan(1/2*d*x + 1/2*c))/a^4 + 32/(a^2*(tan(1/2*d*x + 1/2*c) + 1)) - (30*tan(1/2*d*x + 1/2*c)^2 - 8*tan(1/2*d*x + 1/2*c) + 1)/(a^2*tan(1/2*d*x + 1/2*c)^2))/d","A",0
314,1,146,0,0.198724," ","integrate(cos(d*x+c)^2*csc(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{72 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} + \frac{96}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}} - \frac{132 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 33 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 6 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1}{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}} - \frac{a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 33 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{24 \, d}"," ",0,"-1/24*(72*log(abs(tan(1/2*d*x + 1/2*c)))/a^2 + 96/(a^2*(tan(1/2*d*x + 1/2*c) + 1)) - (132*tan(1/2*d*x + 1/2*c)^3 - 33*tan(1/2*d*x + 1/2*c)^2 + 6*tan(1/2*d*x + 1/2*c) - 1)/(a^2*tan(1/2*d*x + 1/2*c)^3) - (a^4*tan(1/2*d*x + 1/2*c)^3 - 6*a^4*tan(1/2*d*x + 1/2*c)^2 + 33*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
315,1,117,0,0.215644," ","integrate(cos(d*x+c)^2*sin(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{33 \, {\left(d x + c\right)}}{a^{3}} + \frac{6 \, {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{3}} + \frac{4 \, {\left(15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 36 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 17\right)}}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{3}}}{6 \, d}"," ",0,"-1/6*(33*(d*x + c)/a^3 + 6*(tan(1/2*d*x + 1/2*c)^3 + 6*tan(1/2*d*x + 1/2*c)^2 - tan(1/2*d*x + 1/2*c) + 6)/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^3) + 4*(15*tan(1/2*d*x + 1/2*c)^2 + 36*tan(1/2*d*x + 1/2*c) + 17)/(a^3*(tan(1/2*d*x + 1/2*c) + 1)^3))/d","A",0
316,1,80,0,0.178183," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{9 \, {\left(d x + c\right)}}{a^{3}} + \frac{6}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a^{3}} + \frac{2 \, {\left(9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 11\right)}}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{3}}}{3 \, d}"," ",0,"1/3*(9*(d*x + c)/a^3 + 6/((tan(1/2*d*x + 1/2*c)^2 + 1)*a^3) + 2*(9*tan(1/2*d*x + 1/2*c)^2 + 24*tan(1/2*d*x + 1/2*c) + 11)/(a^3*(tan(1/2*d*x + 1/2*c) + 1)^3))/d","A",0
317,1,60,0,0.218966," ","integrate(cos(d*x+c)^2*sin(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(d x + c\right)}}{a^{3}} + \frac{2 \, {\left(3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5\right)}}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{3}}}{3 \, d}"," ",0,"-1/3*(3*(d*x + c)/a^3 + 2*(3*tan(1/2*d*x + 1/2*c)^2 + 12*tan(1/2*d*x + 1/2*c) + 5)/(a^3*(tan(1/2*d*x + 1/2*c) + 1)^3))/d","A",0
318,1,66,0,0.182988," ","integrate(cos(d*x+c)^2*csc(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{3 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} + \frac{2 \, {\left(9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 7\right)}}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*log(abs(tan(1/2*d*x + 1/2*c)))/a^3 + 2*(9*tan(1/2*d*x + 1/2*c)^2 + 12*tan(1/2*d*x + 1/2*c) + 7)/(a^3*(tan(1/2*d*x + 1/2*c) + 1)^3))/d","A",0
319,1,109,0,0.212433," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{18 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} - \frac{3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3}} - \frac{3 \, {\left(6 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}}{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)} + \frac{4 \, {\left(15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 13\right)}}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{3}}}{6 \, d}"," ",0,"-1/6*(18*log(abs(tan(1/2*d*x + 1/2*c)))/a^3 - 3*tan(1/2*d*x + 1/2*c)/a^3 - 3*(6*tan(1/2*d*x + 1/2*c) - 1)/(a^3*tan(1/2*d*x + 1/2*c)) + 4*(15*tan(1/2*d*x + 1/2*c)^2 + 24*tan(1/2*d*x + 1/2*c) + 13)/(a^3*(tan(1/2*d*x + 1/2*c) + 1)^3))/d","A",0
320,1,143,0,0.222608," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{132 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} - \frac{3 \, {\left(66 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}} + \frac{3 \, {\left(a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a^{6}} + \frac{16 \, {\left(21 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 36 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 19\right)}}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{3}}}{24 \, d}"," ",0,"1/24*(132*log(abs(tan(1/2*d*x + 1/2*c)))/a^3 - 3*(66*tan(1/2*d*x + 1/2*c)^2 - 12*tan(1/2*d*x + 1/2*c) + 1)/(a^3*tan(1/2*d*x + 1/2*c)^2) + 3*(a^3*tan(1/2*d*x + 1/2*c)^2 - 12*a^3*tan(1/2*d*x + 1/2*c))/a^6 + 16*(21*tan(1/2*d*x + 1/2*c)^2 + 36*tan(1/2*d*x + 1/2*c) + 19)/(a^3*(tan(1/2*d*x + 1/2*c) + 1)^3))/d","A",0
321,1,120,0,0.249171," ","integrate(cos(f*x+e)^2*sin(f*x+e)/(a+a*sin(f*x+e))^6,x, algorithm=""giac"")","-\frac{2 \, {\left(315 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + 315 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 945 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 441 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 609 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 81 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 99 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 11\right)}}{315 \, a^{6} f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}^{9}}"," ",0,"-2/315*(315*tan(1/2*f*x + 1/2*e)^7 + 315*tan(1/2*f*x + 1/2*e)^6 + 945*tan(1/2*f*x + 1/2*e)^5 + 441*tan(1/2*f*x + 1/2*e)^4 + 609*tan(1/2*f*x + 1/2*e)^3 + 81*tan(1/2*f*x + 1/2*e)^2 + 99*tan(1/2*f*x + 1/2*e) + 11)/(a^6*f*(tan(1/2*f*x + 1/2*e) + 1)^9)","A",0
322,1,189,0,0.263349," ","integrate(cos(d*x+c)^2*sin(d*x+c)^3*(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{1}{55440} \, \sqrt{2} \sqrt{a} {\left(\frac{385 \, \cos\left(\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{693 \, \cos\left(\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{6930 \, \cos\left(\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{315 \, \cos\left(-\frac{1}{4} \, \pi + \frac{11}{2} \, d x + \frac{11}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{495 \, \cos\left(-\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{2310 \, \cos\left(-\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d}\right)}"," ",0,"1/55440*sqrt(2)*sqrt(a)*(385*cos(1/4*pi + 9/2*d*x + 9/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 693*cos(1/4*pi + 5/2*d*x + 5/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 6930*cos(1/4*pi + 1/2*d*x + 1/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 315*cos(-1/4*pi + 11/2*d*x + 11/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 495*cos(-1/4*pi + 7/2*d*x + 7/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 2310*cos(-1/4*pi + 3/2*d*x + 3/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d)","A",0
323,1,99,0,0.271570," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2*(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{1}{504} \, \sqrt{2} \sqrt{a} {\left(\frac{9 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} + \frac{7 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} - \frac{126 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)}"," ",0,"-1/504*sqrt(2)*sqrt(a)*(9*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 7/2*d*x + 7/2*c)/d + 7*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 9/2*d*x + 9/2*c)/d - 126*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 1/2*d*x + 1/2*c)/d)","A",0
324,1,129,0,0.218094," ","integrate(cos(d*x+c)^2*sin(d*x+c)*(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{1}{420} \, \sqrt{2} \sqrt{a} {\left(\frac{21 \, \cos\left(\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{105 \, \cos\left(\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{15 \, \cos\left(-\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{35 \, \cos\left(-\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d}\right)}"," ",0,"-1/420*sqrt(2)*sqrt(a)*(21*cos(1/4*pi + 5/2*d*x + 5/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 105*cos(1/4*pi + 1/2*d*x + 1/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 15*cos(-1/4*pi + 7/2*d*x + 7/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 35*cos(-1/4*pi + 3/2*d*x + 3/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d)","A",0
325,-1,0,0,0.000000," ","integrate(cos(d*x+c)^2*csc(d*x+c)*(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
326,-1,0,0,0.000000," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2*(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
327,-1,0,0,0.000000," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3*(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
328,-1,0,0,0.000000," ","integrate(cos(d*x+c)^2*csc(d*x+c)^4*(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
329,1,412,0,0.641252," ","integrate(cos(d*x+c)^2*sin(d*x+c)^3*(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{1}{1441440} \, \sqrt{2} {\left(\frac{10010 \, a \cos\left(\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{18018 \, a \cos\left(\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{180180 \, a \cos\left(\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{8190 \, a \cos\left(-\frac{1}{4} \, \pi + \frac{11}{2} \, d x + \frac{11}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{12870 \, a \cos\left(-\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{60060 \, a \cos\left(-\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{4095 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{11}{2} \, d x + \frac{11}{2} \, c\right)}{d} - \frac{12870 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} - \frac{15015 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{3465 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{13}{2} \, d x + \frac{13}{2} \, c\right)}{d} - \frac{10010 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} - \frac{9009 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{180180 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/1441440*sqrt(2)*(10010*a*cos(1/4*pi + 9/2*d*x + 9/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 18018*a*cos(1/4*pi + 5/2*d*x + 5/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 180180*a*cos(1/4*pi + 1/2*d*x + 1/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 8190*a*cos(-1/4*pi + 11/2*d*x + 11/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 12870*a*cos(-1/4*pi + 7/2*d*x + 7/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 60060*a*cos(-1/4*pi + 3/2*d*x + 3/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 4095*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 11/2*d*x + 11/2*c)/d - 12870*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 7/2*d*x + 7/2*c)/d - 15015*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 3/2*d*x + 3/2*c)/d + 3465*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 13/2*d*x + 13/2*c)/d - 10010*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 9/2*d*x + 9/2*c)/d - 9009*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 5/2*d*x + 5/2*c)/d + 180180*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 1/2*d*x + 1/2*c)/d)*sqrt(a)","B",0
330,1,288,0,0.497081," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2*(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{1}{55440} \, \sqrt{2} {\left(\frac{385 \, a \cos\left(\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{693 \, a \cos\left(\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{6930 \, a \cos\left(\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{315 \, a \cos\left(-\frac{1}{4} \, \pi + \frac{11}{2} \, d x + \frac{11}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{495 \, a \cos\left(-\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{2310 \, a \cos\left(-\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{990 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} - \frac{770 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} + \frac{13860 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/55440*sqrt(2)*(385*a*cos(1/4*pi + 9/2*d*x + 9/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 693*a*cos(1/4*pi + 5/2*d*x + 5/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 6930*a*cos(1/4*pi + 1/2*d*x + 1/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 315*a*cos(-1/4*pi + 11/2*d*x + 11/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 495*a*cos(-1/4*pi + 7/2*d*x + 7/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 2310*a*cos(-1/4*pi + 3/2*d*x + 3/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 990*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 7/2*d*x + 7/2*c)/d - 770*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 9/2*d*x + 9/2*c)/d + 13860*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 1/2*d*x + 1/2*c)/d)*sqrt(a)","B",0
331,1,226,0,0.382178," ","integrate(cos(d*x+c)^2*sin(d*x+c)*(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{1}{2520} \, \sqrt{2} {\left(\frac{126 \, a \cos\left(\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{630 \, a \cos\left(\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{90 \, a \cos\left(-\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{210 \, a \cos\left(-\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{45 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} + \frac{35 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} - \frac{630 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"-1/2520*sqrt(2)*(126*a*cos(1/4*pi + 5/2*d*x + 5/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 630*a*cos(1/4*pi + 1/2*d*x + 1/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 90*a*cos(-1/4*pi + 7/2*d*x + 7/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 210*a*cos(-1/4*pi + 3/2*d*x + 3/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 45*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 7/2*d*x + 7/2*c)/d + 35*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 9/2*d*x + 9/2*c)/d - 630*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 1/2*d*x + 1/2*c)/d)*sqrt(a)","B",0
332,-1,0,0,0.000000," ","integrate(cos(d*x+c)^2*csc(d*x+c)*(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
333,-1,0,0,0.000000," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2*(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
334,-1,0,0,0.000000," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3*(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
335,-1,0,0,0.000000," ","integrate(cos(d*x+c)^2*csc(d*x+c)^4*(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
336,1,224,0,0.600314," ","integrate(cos(d*x+c)^2*sin(d*x+c)^3/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{4 \, {\left(\frac{13 \, \sqrt{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{\sqrt{a}} + \frac{4 \, {\left(\frac{2 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{9 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{63 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{63 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{2 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{9 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{9}{2}}}\right)}}{315 \, d}"," ",0,"-4/315*(13*sqrt(2)*sgn(tan(1/2*d*x + 1/2*c) + 1)/sqrt(a) + 4*(2*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) + (9*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) - (63*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) - (63*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) - (2*a^4*tan(1/2*d*x + 1/2*c)^2/sgn(tan(1/2*d*x + 1/2*c) + 1) + 9*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(9/2))/d","A",0
337,1,220,0,0.562625," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{4 \, {\left(\frac{11 \, \sqrt{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{\sqrt{a}} - \frac{2 \, {\left({\left(\frac{7 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{35 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{35 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{2 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{7 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{2 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{7}{2}}}\right)}}{105 \, d}"," ",0,"4/105*(11*sqrt(2)*sgn(tan(1/2*d*x + 1/2*c) + 1)/sqrt(a) - 2*((7*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1) - (35*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1) - (35*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1) - (2*a^3*tan(1/2*d*x + 1/2*c)^2/sgn(tan(1/2*d*x + 1/2*c) + 1) + 7*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c)^2 + 2*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1))/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(7/2))/d","B",0
338,1,155,0,0.520177," ","integrate(cos(d*x+c)^2*sin(d*x+c)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{4 \, {\left(\frac{\sqrt{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{\sqrt{a}} - \frac{{\left({\left(\frac{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{5 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{5 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{5}{2}}}\right)}}{15 \, d}"," ",0,"-4/15*(sqrt(2)*sgn(tan(1/2*d*x + 1/2*c) + 1)/sqrt(a) - (((a^2*tan(1/2*d*x + 1/2*c)^2/sgn(tan(1/2*d*x + 1/2*c) + 1) - 5*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 5*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c)^2 - a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(5/2))/d","B",0
339,1,258,0,0.636077," ","integrate(cos(d*x+c)^2*csc(d*x+c)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{1}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)}}{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}} + \frac{{\left(2 \, a \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - \sqrt{-a} \sqrt{a} \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) + 2 \, \sqrt{2} \sqrt{-a} \sqrt{a}\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{\sqrt{-a} a} - \frac{2 \, \arctan\left(-\frac{\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{\log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{d}"," ",0,"-(2*(tan(1/2*d*x + 1/2*c)/sgn(tan(1/2*d*x + 1/2*c) + 1) - 1/sgn(tan(1/2*d*x + 1/2*c) + 1))/sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + (2*a*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - sqrt(-a)*sqrt(a)*log(sqrt(2)*sqrt(a) + sqrt(a)) + 2*sqrt(2)*sqrt(-a)*sqrt(a))*sgn(tan(1/2*d*x + 1/2*c) + 1)/(sqrt(-a)*a) - 2*arctan(-(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))/sqrt(-a))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c) + 1)) + log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(a)*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
340,1,360,0,0.629855," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\frac{{\left(2 \, \sqrt{2} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - \sqrt{2} \sqrt{-a} \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) + 2 \, \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - \sqrt{-a} \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) - \sqrt{2} \sqrt{-a} - 3 \, \sqrt{-a}\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{\sqrt{2} \sqrt{-a} \sqrt{a} + \sqrt{-a} \sqrt{a}} - \frac{2 \, \arctan\left(-\frac{\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{\log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{2 \, \sqrt{a}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{2 \, d}"," ",0,"1/2*((2*sqrt(2)*sqrt(a)*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - sqrt(2)*sqrt(-a)*log(sqrt(2)*sqrt(a) + sqrt(a)) + 2*sqrt(a)*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - sqrt(-a)*log(sqrt(2)*sqrt(a) + sqrt(a)) - sqrt(2)*sqrt(-a) - 3*sqrt(-a))*sgn(tan(1/2*d*x + 1/2*c) + 1)/(sqrt(2)*sqrt(-a)*sqrt(a) + sqrt(-a)*sqrt(a)) - 2*arctan(-(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))/sqrt(-a))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c) + 1)) + log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(a)*sgn(tan(1/2*d*x + 1/2*c) + 1)) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)/(a*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 2*sqrt(a)/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a)*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
341,1,505,0,0.690506," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left(\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{2}{a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} + \frac{{\left(4 \, \sqrt{2} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - 2 \, \sqrt{2} \sqrt{-a} \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) + 6 \, \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - 3 \, \sqrt{-a} \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) + 14 \, \sqrt{2} \sqrt{-a} + 18 \, \sqrt{-a}\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{2 \, \sqrt{2} \sqrt{-a} \sqrt{a} + 3 \, \sqrt{-a} \sqrt{a}} - \frac{2 \, \arctan\left(-\frac{\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{\log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{2 \, {\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{3} - 2 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} \sqrt{a} + {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a + 2 \, a^{\frac{3}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a\right)}^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{8 \, d}"," ",0,"1/8*(sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)*(tan(1/2*d*x + 1/2*c)/(a*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 2/(a*sgn(tan(1/2*d*x + 1/2*c) + 1))) + (4*sqrt(2)*sqrt(a)*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - 2*sqrt(2)*sqrt(-a)*log(sqrt(2)*sqrt(a) + sqrt(a)) + 6*sqrt(a)*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - 3*sqrt(-a)*log(sqrt(2)*sqrt(a) + sqrt(a)) + 14*sqrt(2)*sqrt(-a) + 18*sqrt(-a))*sgn(tan(1/2*d*x + 1/2*c) + 1)/(2*sqrt(2)*sqrt(-a)*sqrt(a) + 3*sqrt(-a)*sqrt(a)) - 2*arctan(-(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))/sqrt(-a))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c) + 1)) + log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(a)*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 2*((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^3 - 2*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*sqrt(a) + (sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a + 2*a^(3/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a)^2*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
342,1,546,0,0.762152," ","integrate(cos(d*x+c)^2*csc(d*x+c)^4/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left({\left(\frac{2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{3}{a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{2}{a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} + \frac{{\left(30 \, \sqrt{2} a^{\frac{3}{2}} \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - 15 \, \sqrt{2} \sqrt{-a} a \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) + 42 \, a^{\frac{3}{2}} \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - 21 \, \sqrt{-a} a \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) - 88 \, \sqrt{2} \sqrt{-a} a - 126 \, \sqrt{-a} a\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{5 \, \sqrt{2} \sqrt{-a} a^{\frac{3}{2}} + 7 \, \sqrt{-a} a^{\frac{3}{2}}} - \frac{6 \, \arctan\left(-\frac{\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{3 \, \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{2 \, {\left(3 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{5} - 6 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} \sqrt{a} - 3 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a^{2} - 2 \, a^{\frac{5}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a\right)}^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{48 \, d}"," ",0,"1/48*(sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)*((2*tan(1/2*d*x + 1/2*c)/(a*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 3/(a*sgn(tan(1/2*d*x + 1/2*c) + 1)))*tan(1/2*d*x + 1/2*c) + 2/(a*sgn(tan(1/2*d*x + 1/2*c) + 1))) + (30*sqrt(2)*a^(3/2)*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - 15*sqrt(2)*sqrt(-a)*a*log(sqrt(2)*sqrt(a) + sqrt(a)) + 42*a^(3/2)*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - 21*sqrt(-a)*a*log(sqrt(2)*sqrt(a) + sqrt(a)) - 88*sqrt(2)*sqrt(-a)*a - 126*sqrt(-a)*a)*sgn(tan(1/2*d*x + 1/2*c) + 1)/(5*sqrt(2)*sqrt(-a)*a^(3/2) + 7*sqrt(-a)*a^(3/2)) - 6*arctan(-(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))/sqrt(-a))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 3*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(a)*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 2*(3*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^5 - 6*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4*sqrt(a) - 3*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a^2 - 2*a^(5/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a)^3*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
343,1,375,0,0.700185," ","integrate(cos(d*x+c)^2*sin(d*x+c)^3/(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{\sqrt{2} {\left(210 \, a \arctan\left(\frac{\sqrt{a}}{\sqrt{-a}}\right) + 211 \, \sqrt{-a} \sqrt{a}\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{\sqrt{-a} a^{2}} - \frac{210 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{2 \, {\left({\left({\left({\left({\left({\left({\left(\frac{67 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{105 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{287 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{385 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{385 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{287 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{105 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{67 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{7}{2}}}\right)}}{105 \, d}"," ",0,"2/105*(sqrt(2)*(210*a*arctan(sqrt(a)/sqrt(-a)) + 211*sqrt(-a)*sqrt(a))*sgn(tan(1/2*d*x + 1/2*c) + 1)/(sqrt(-a)*a^2) - 210*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/sqrt(-a))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 2*(((((((67*a^2*tan(1/2*d*x + 1/2*c)/sgn(tan(1/2*d*x + 1/2*c) + 1) - 105*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 287*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) - 385*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 385*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) - 287*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 105*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) - 67*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(7/2))/d","B",0
344,1,303,0,0.674934," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2/(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{\sqrt{2} {\left(10 \, a \arctan\left(\frac{\sqrt{a}}{\sqrt{-a}}\right) + 9 \, \sqrt{-a} \sqrt{a}\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{\sqrt{-a} a^{2}} - \frac{10 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{2 \, {\left({\left({\left({\left({\left(\frac{3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{5 \, a}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{10 \, a}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{10 \, a}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{5 \, a}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{3 \, a}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{5}{2}}}\right)}}{5 \, d}"," ",0,"-2/5*(sqrt(2)*(10*a*arctan(sqrt(a)/sqrt(-a)) + 9*sqrt(-a)*sqrt(a))*sgn(tan(1/2*d*x + 1/2*c) + 1)/(sqrt(-a)*a^2) - 10*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/sqrt(-a))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 2*(((((3*a*tan(1/2*d*x + 1/2*c)/sgn(tan(1/2*d*x + 1/2*c) + 1) - 5*a/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 10*a/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) - 10*a/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 5*a/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) - 3*a/sgn(tan(1/2*d*x + 1/2*c) + 1))/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(5/2))/d","B",0
345,1,246,0,0.625760," ","integrate(cos(d*x+c)^2*sin(d*x+c)/(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{2 \, {\left({\left({\left(\frac{2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{3}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{3}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{2}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{3}{2}}} + \frac{{\left(6 \, \sqrt{2} a \arctan\left(\frac{\sqrt{a}}{\sqrt{-a}}\right) + 5 \, \sqrt{2} \sqrt{-a} \sqrt{a}\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{\sqrt{-a} a^{2}} - \frac{6 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)}}{3 \, d}"," ",0,"2/3*(2*(((2*tan(1/2*d*x + 1/2*c)/sgn(tan(1/2*d*x + 1/2*c) + 1) - 3/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 3/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) - 2/sgn(tan(1/2*d*x + 1/2*c) + 1))/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(3/2) + (6*sqrt(2)*a*arctan(sqrt(a)/sqrt(-a)) + 5*sqrt(2)*sqrt(-a)*sqrt(a))*sgn(tan(1/2*d*x + 1/2*c) + 1)/(sqrt(-a)*a^2) - 6*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/sqrt(-a))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
346,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*csc(d*x+c)/(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos((d*t_nostep+c)/2-pi/4))]Discontinuities at zeroes of cos((d*t_nostep+c)/2-pi/4) were not checkedWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep+1)]Evaluation time: 0.47Error: Bad Argument Type","F(-2)",0
347,1,471,0,0.797817," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2/(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\frac{{\left(6 \, \sqrt{2} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - 8 \, \sqrt{2} \sqrt{a} \arctan\left(\frac{\sqrt{a}}{\sqrt{-a}}\right) - 3 \, \sqrt{2} \sqrt{-a} \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) + 6 \, \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - 16 \, \sqrt{a} \arctan\left(\frac{\sqrt{a}}{\sqrt{-a}}\right) - 3 \, \sqrt{-a} \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) - \sqrt{2} \sqrt{-a} - 3 \, \sqrt{-a}\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{\sqrt{2} \sqrt{-a} a^{\frac{3}{2}} + \sqrt{-a} a^{\frac{3}{2}}} + \frac{8 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{6 \, \arctan\left(-\frac{\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{3 \, \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{3}{2}} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{2}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a\right)} \sqrt{a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{2 \, d}"," ",0,"1/2*((6*sqrt(2)*sqrt(a)*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - 8*sqrt(2)*sqrt(a)*arctan(sqrt(a)/sqrt(-a)) - 3*sqrt(2)*sqrt(-a)*log(sqrt(2)*sqrt(a) + sqrt(a)) + 6*sqrt(a)*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - 16*sqrt(a)*arctan(sqrt(a)/sqrt(-a)) - 3*sqrt(-a)*log(sqrt(2)*sqrt(a) + sqrt(a)) - sqrt(2)*sqrt(-a) - 3*sqrt(-a))*sgn(tan(1/2*d*x + 1/2*c) + 1)/(sqrt(2)*sqrt(-a)*a^(3/2) + sqrt(-a)*a^(3/2)) + 8*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/sqrt(-a))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 6*arctan(-(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))/sqrt(-a))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 3*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/(a^(3/2)*sgn(tan(1/2*d*x + 1/2*c) + 1)) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)/(a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 2/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a)*sqrt(a)*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
348,1,620,0,0.890127," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3/(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left(\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{6}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} - \frac{{\left(44 \, \sqrt{2} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - 96 \, \sqrt{2} \sqrt{a} \arctan\left(\frac{\sqrt{a}}{\sqrt{-a}}\right) - 22 \, \sqrt{2} \sqrt{-a} \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) + 66 \, \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - 128 \, \sqrt{a} \arctan\left(\frac{\sqrt{a}}{\sqrt{-a}}\right) - 33 \, \sqrt{-a} \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) - 30 \, \sqrt{2} \sqrt{-a} - 38 \, \sqrt{-a}\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{2 \, \sqrt{2} \sqrt{-a} a^{\frac{3}{2}} + 3 \, \sqrt{-a} a^{\frac{3}{2}}} - \frac{32 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{22 \, \arctan\left(-\frac{\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{11 \, \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{3}{2}} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{2 \, {\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{3} - 6 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} \sqrt{a} + {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a + 6 \, a^{\frac{3}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a\right)}^{2} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{8 \, d}"," ",0,"1/8*(sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)*(tan(1/2*d*x + 1/2*c)/(a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 6/(a^2*sgn(tan(1/2*d*x + 1/2*c) + 1))) - (44*sqrt(2)*sqrt(a)*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - 96*sqrt(2)*sqrt(a)*arctan(sqrt(a)/sqrt(-a)) - 22*sqrt(2)*sqrt(-a)*log(sqrt(2)*sqrt(a) + sqrt(a)) + 66*sqrt(a)*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - 128*sqrt(a)*arctan(sqrt(a)/sqrt(-a)) - 33*sqrt(-a)*log(sqrt(2)*sqrt(a) + sqrt(a)) - 30*sqrt(2)*sqrt(-a) - 38*sqrt(-a))*sgn(tan(1/2*d*x + 1/2*c) + 1)/(2*sqrt(2)*sqrt(-a)*a^(3/2) + 3*sqrt(-a)*a^(3/2)) - 32*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/sqrt(-a))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 22*arctan(-(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))/sqrt(-a))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 11*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/(a^(3/2)*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 2*((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^3 - 6*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*sqrt(a) + (sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a + 6*a^(3/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a)^2*a*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
349,1,695,0,0.939616," ","integrate(cos(d*x+c)^2*csc(d*x+c)^4/(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left({\left(\frac{2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{9}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{38}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} + \frac{{\left(690 \, \sqrt{2} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - 1344 \, \sqrt{2} \sqrt{a} \arctan\left(\frac{\sqrt{a}}{\sqrt{-a}}\right) - 345 \, \sqrt{2} \sqrt{-a} \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) + 966 \, \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - 1920 \, \sqrt{a} \arctan\left(\frac{\sqrt{a}}{\sqrt{-a}}\right) - 483 \, \sqrt{-a} \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) - 496 \, \sqrt{2} \sqrt{-a} - 714 \, \sqrt{-a}\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{5 \, \sqrt{2} \sqrt{-a} a^{\frac{3}{2}} + 7 \, \sqrt{-a} a^{\frac{3}{2}}} + \frac{192 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{138 \, \arctan\left(-\frac{\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{69 \, \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{3}{2}} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{2 \, {\left(9 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{5} - 42 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} \sqrt{a} + 72 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a^{\frac{3}{2}} - 9 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a^{2} - 38 \, a^{\frac{5}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a\right)}^{3} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{48 \, d}"," ",0,"1/48*(sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)*((2*tan(1/2*d*x + 1/2*c)/(a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 9/(a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)))*tan(1/2*d*x + 1/2*c) + 38/(a^2*sgn(tan(1/2*d*x + 1/2*c) + 1))) + (690*sqrt(2)*sqrt(a)*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - 1344*sqrt(2)*sqrt(a)*arctan(sqrt(a)/sqrt(-a)) - 345*sqrt(2)*sqrt(-a)*log(sqrt(2)*sqrt(a) + sqrt(a)) + 966*sqrt(a)*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - 1920*sqrt(a)*arctan(sqrt(a)/sqrt(-a)) - 483*sqrt(-a)*log(sqrt(2)*sqrt(a) + sqrt(a)) - 496*sqrt(2)*sqrt(-a) - 714*sqrt(-a))*sgn(tan(1/2*d*x + 1/2*c) + 1)/(5*sqrt(2)*sqrt(-a)*a^(3/2) + 7*sqrt(-a)*a^(3/2)) + 192*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/sqrt(-a))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 138*arctan(-(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))/sqrt(-a))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 69*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/(a^(3/2)*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 2*(9*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^5 - 42*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4*sqrt(a) + 72*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a^(3/2) - 9*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a^2 - 38*a^(5/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a)^3*a*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
350,1,50,0,0.207096," ","integrate(cos(d*x+c)^3*sin(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{60 \, a \sin\left(d x + c\right)^{7} + 70 \, a \sin\left(d x + c\right)^{6} - 84 \, a \sin\left(d x + c\right)^{5} - 105 \, a \sin\left(d x + c\right)^{4}}{420 \, d}"," ",0,"-1/420*(60*a*sin(d*x + c)^7 + 70*a*sin(d*x + c)^6 - 84*a*sin(d*x + c)^5 - 105*a*sin(d*x + c)^4)/d","A",0
351,1,50,0,0.210126," ","integrate(cos(d*x+c)^3*sin(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{10 \, a \sin\left(d x + c\right)^{6} + 12 \, a \sin\left(d x + c\right)^{5} - 15 \, a \sin\left(d x + c\right)^{4} - 20 \, a \sin\left(d x + c\right)^{3}}{60 \, d}"," ",0,"-1/60*(10*a*sin(d*x + c)^6 + 12*a*sin(d*x + c)^5 - 15*a*sin(d*x + c)^4 - 20*a*sin(d*x + c)^3)/d","A",0
352,1,50,0,0.170545," ","integrate(cos(d*x+c)^3*sin(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{12 \, a \sin\left(d x + c\right)^{5} + 15 \, a \sin\left(d x + c\right)^{4} - 20 \, a \sin\left(d x + c\right)^{3} - 30 \, a \sin\left(d x + c\right)^{2}}{60 \, d}"," ",0,"-1/60*(12*a*sin(d*x + c)^5 + 15*a*sin(d*x + c)^4 - 20*a*sin(d*x + c)^3 - 30*a*sin(d*x + c)^2)/d","A",0
353,1,48,0,0.145574," ","integrate(cos(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{3 \, a \sin\left(d x + c\right)^{4} + 4 \, a \sin\left(d x + c\right)^{3} - 6 \, a \sin\left(d x + c\right)^{2} - 12 \, a \sin\left(d x + c\right)}{12 \, d}"," ",0,"-1/12*(3*a*sin(d*x + c)^4 + 4*a*sin(d*x + c)^3 - 6*a*sin(d*x + c)^2 - 12*a*sin(d*x + c))/d","A",0
354,1,48,0,0.180698," ","integrate(cos(d*x+c)^3*csc(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{2 \, a \sin\left(d x + c\right)^{3} + 3 \, a \sin\left(d x + c\right)^{2} - 6 \, a \log\left({\left| \sin\left(d x + c\right) \right|}\right) - 6 \, a \sin\left(d x + c\right)}{6 \, d}"," ",0,"-1/6*(2*a*sin(d*x + c)^3 + 3*a*sin(d*x + c)^2 - 6*a*log(abs(sin(d*x + c))) - 6*a*sin(d*x + c))/d","A",0
355,1,47,0,0.182547," ","integrate(cos(d*x+c)^3*csc(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{a \sin\left(d x + c\right)^{2} - 2 \, a \log\left({\left| \sin\left(d x + c\right) \right|}\right) + 2 \, a \sin\left(d x + c\right) + \frac{2 \, a}{\sin\left(d x + c\right)}}{2 \, d}"," ",0,"-1/2*(a*sin(d*x + c)^2 - 2*a*log(abs(sin(d*x + c))) + 2*a*sin(d*x + c) + 2*a/sin(d*x + c))/d","A",0
356,1,46,0,0.164357," ","integrate(cos(d*x+c)^3*csc(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{2 \, a \log\left({\left| \sin\left(d x + c\right) \right|}\right) + 2 \, a \sin\left(d x + c\right) + \frac{2 \, a \sin\left(d x + c\right) + a}{\sin\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(2*a*log(abs(sin(d*x + c))) + 2*a*sin(d*x + c) + (2*a*sin(d*x + c) + a)/sin(d*x + c)^2)/d","A",0
357,1,29,0,0.148064," ","integrate(cos(d*x+c)^3*sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{3 \, \sin\left(d x + c\right)^{4} - 4 \, \sin\left(d x + c\right)^{3}}{12 \, a d}"," ",0,"-1/12*(3*sin(d*x + c)^4 - 4*sin(d*x + c)^3)/(a*d)","A",0
358,1,29,0,0.139593," ","integrate(cos(d*x+c)^3*sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{2 \, \sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)^{2}}{6 \, a d}"," ",0,"-1/6*(2*sin(d*x + c)^3 - 3*sin(d*x + c)^2)/(a*d)","A",0
359,1,25,0,0.153386," ","integrate(cos(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right)}{2 \, a d}"," ",0,"-1/2*(sin(d*x + c)^2 - 2*sin(d*x + c))/(a*d)","A",0
360,1,28,0,0.171676," ","integrate(cos(d*x+c)^3*csc(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{\log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a} - \frac{\sin\left(d x + c\right)}{a}}{d}"," ",0,"(log(abs(sin(d*x + c)))/a - sin(d*x + c)/a)/d","A",0
361,1,30,0,0.155658," ","integrate(cos(d*x+c)^3*csc(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{\log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a} + \frac{1}{a \sin\left(d x + c\right)}}{d}"," ",0,"-(log(abs(sin(d*x + c)))/a + 1/(a*sin(d*x + c)))/d","A",0
362,1,26,0,0.155285," ","integrate(cos(d*x+c)^3*csc(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{2 \, \sin\left(d x + c\right) - 1}{2 \, a d \sin\left(d x + c\right)^{2}}"," ",0,"1/2*(2*sin(d*x + c) - 1)/(a*d*sin(d*x + c)^2)","A",0
363,1,26,0,0.172405," ","integrate(cos(d*x+c)^3*csc(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{3 \, \sin\left(d x + c\right) - 2}{6 \, a d \sin\left(d x + c\right)^{3}}"," ",0,"1/6*(3*sin(d*x + c) - 2)/(a*d*sin(d*x + c)^3)","A",0
364,1,26,0,0.185235," ","integrate(cos(d*x+c)^3*csc(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{4 \, \sin\left(d x + c\right) - 3}{12 \, a d \sin\left(d x + c\right)^{4}}"," ",0,"1/12*(4*sin(d*x + c) - 3)/(a*d*sin(d*x + c)^4)","A",0
365,1,107,0,0.241723," ","integrate(cos(d*x+c)^4*sin(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{3}{128} \, a x - \frac{a \cos\left(9 \, d x + 9 \, c\right)}{2304 \, d} + \frac{a \cos\left(7 \, d x + 7 \, c\right)}{1792 \, d} + \frac{a \cos\left(5 \, d x + 5 \, c\right)}{320 \, d} - \frac{a \cos\left(3 \, d x + 3 \, c\right)}{192 \, d} - \frac{3 \, a \cos\left(d x + c\right)}{128 \, d} + \frac{a \sin\left(8 \, d x + 8 \, c\right)}{1024 \, d} - \frac{a \sin\left(4 \, d x + 4 \, c\right)}{128 \, d}"," ",0,"3/128*a*x - 1/2304*a*cos(9*d*x + 9*c)/d + 1/1792*a*cos(7*d*x + 7*c)/d + 1/320*a*cos(5*d*x + 5*c)/d - 1/192*a*cos(3*d*x + 3*c)/d - 3/128*a*cos(d*x + c)/d + 1/1024*a*sin(8*d*x + 8*c)/d - 1/128*a*sin(4*d*x + 4*c)/d","A",0
366,1,92,0,0.221070," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{3}{128} \, a x + \frac{a \cos\left(7 \, d x + 7 \, c\right)}{448 \, d} + \frac{a \cos\left(5 \, d x + 5 \, c\right)}{320 \, d} - \frac{a \cos\left(3 \, d x + 3 \, c\right)}{64 \, d} - \frac{3 \, a \cos\left(d x + c\right)}{64 \, d} + \frac{a \sin\left(8 \, d x + 8 \, c\right)}{1024 \, d} - \frac{a \sin\left(4 \, d x + 4 \, c\right)}{128 \, d}"," ",0,"3/128*a*x + 1/448*a*cos(7*d*x + 7*c)/d + 1/320*a*cos(5*d*x + 5*c)/d - 1/64*a*cos(3*d*x + 3*c)/d - 3/64*a*cos(d*x + c)/d + 1/1024*a*sin(8*d*x + 8*c)/d - 1/128*a*sin(4*d*x + 4*c)/d","A",0
367,1,107,0,0.190450," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{1}{16} \, a x + \frac{a \cos\left(7 \, d x + 7 \, c\right)}{448 \, d} + \frac{a \cos\left(5 \, d x + 5 \, c\right)}{320 \, d} - \frac{a \cos\left(3 \, d x + 3 \, c\right)}{64 \, d} - \frac{3 \, a \cos\left(d x + c\right)}{64 \, d} - \frac{a \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} - \frac{a \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{a \sin\left(2 \, d x + 2 \, c\right)}{64 \, d}"," ",0,"1/16*a*x + 1/448*a*cos(7*d*x + 7*c)/d + 1/320*a*cos(5*d*x + 5*c)/d - 1/64*a*cos(3*d*x + 3*c)/d - 3/64*a*cos(d*x + c)/d - 1/192*a*sin(6*d*x + 6*c)/d - 1/64*a*sin(4*d*x + 4*c)/d + 1/64*a*sin(2*d*x + 2*c)/d","A",0
368,1,92,0,0.167376," ","integrate(cos(d*x+c)^4*sin(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{1}{16} \, a x - \frac{a \cos\left(5 \, d x + 5 \, c\right)}{80 \, d} - \frac{a \cos\left(3 \, d x + 3 \, c\right)}{16 \, d} - \frac{a \cos\left(d x + c\right)}{8 \, d} - \frac{a \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} - \frac{a \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{a \sin\left(2 \, d x + 2 \, c\right)}{64 \, d}"," ",0,"1/16*a*x - 1/80*a*cos(5*d*x + 5*c)/d - 1/16*a*cos(3*d*x + 3*c)/d - 1/8*a*cos(d*x + c)/d - 1/192*a*sin(6*d*x + 6*c)/d - 1/64*a*sin(4*d*x + 4*c)/d + 1/64*a*sin(2*d*x + 2*c)/d","A",0
369,1,145,0,0.191156," ","integrate(cos(d*x+c)^4*csc(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{9 \, {\left(d x + c\right)} a + 24 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{2 \, {\left(15 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 48 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 9 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 96 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 9 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 80 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 32 \, a\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(9*(d*x + c)*a + 24*a*log(abs(tan(1/2*d*x + 1/2*c))) - 2*(15*a*tan(1/2*d*x + 1/2*c)^7 - 48*a*tan(1/2*d*x + 1/2*c)^6 - 9*a*tan(1/2*d*x + 1/2*c)^5 - 96*a*tan(1/2*d*x + 1/2*c)^4 + 9*a*tan(1/2*d*x + 1/2*c)^3 - 80*a*tan(1/2*d*x + 1/2*c)^2 - 15*a*tan(1/2*d*x + 1/2*c) - 32*a)/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","A",0
370,1,142,0,0.200074," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{9 \, {\left(d x + c\right)} a - 6 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{3 \, {\left(2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)} - \frac{2 \, {\left(3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 12 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8 \, a\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"-1/6*(9*(d*x + c)*a - 6*a*log(abs(tan(1/2*d*x + 1/2*c))) - 3*a*tan(1/2*d*x + 1/2*c) + 3*(2*a*tan(1/2*d*x + 1/2*c) + a)/tan(1/2*d*x + 1/2*c) - 2*(3*a*tan(1/2*d*x + 1/2*c)^5 + 12*a*tan(1/2*d*x + 1/2*c)^4 + 12*a*tan(1/2*d*x + 1/2*c)^2 - 3*a*tan(1/2*d*x + 1/2*c) + 8*a)/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
371,1,163,0,0.215826," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, {\left(d x + c\right)} a - 12 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 4 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{6 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 4 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 5 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 16 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}^{2}}}{8 \, d}"," ",0,"1/8*(a*tan(1/2*d*x + 1/2*c)^2 - 12*(d*x + c)*a - 12*a*log(abs(tan(1/2*d*x + 1/2*c))) + 4*a*tan(1/2*d*x + 1/2*c) + (6*a*tan(1/2*d*x + 1/2*c)^6 + 4*a*tan(1/2*d*x + 1/2*c)^5 - 5*a*tan(1/2*d*x + 1/2*c)^4 - 16*a*tan(1/2*d*x + 1/2*c)^3 - 12*a*tan(1/2*d*x + 1/2*c)^2 - 4*a*tan(1/2*d*x + 1/2*c) - a)/(tan(1/2*d*x + 1/2*c)^3 + tan(1/2*d*x + 1/2*c))^2)/d","A",0
372,1,141,0,0.193275," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 \, {\left(d x + c\right)} a - 36 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 15 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{48 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + \frac{66 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{24 \, d}"," ",0,"1/24*(a*tan(1/2*d*x + 1/2*c)^3 + 3*a*tan(1/2*d*x + 1/2*c)^2 + 24*(d*x + c)*a - 36*a*log(abs(tan(1/2*d*x + 1/2*c))) - 15*a*tan(1/2*d*x + 1/2*c) - 48*a/(tan(1/2*d*x + 1/2*c)^2 + 1) + (66*a*tan(1/2*d*x + 1/2*c)^3 + 15*a*tan(1/2*d*x + 1/2*c)^2 - 3*a*tan(1/2*d*x + 1/2*c) - a)/tan(1/2*d*x + 1/2*c)^3)/d","A",0
373,1,153,0,0.224445," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 8 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 192 \, {\left(d x + c\right)} a + 72 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 120 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{150 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 120 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 8 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}}}{192 \, d}"," ",0,"1/192*(3*a*tan(1/2*d*x + 1/2*c)^4 + 8*a*tan(1/2*d*x + 1/2*c)^3 - 24*a*tan(1/2*d*x + 1/2*c)^2 + 192*(d*x + c)*a + 72*a*log(abs(tan(1/2*d*x + 1/2*c))) - 120*a*tan(1/2*d*x + 1/2*c) - (150*a*tan(1/2*d*x + 1/2*c)^4 - 120*a*tan(1/2*d*x + 1/2*c)^3 - 24*a*tan(1/2*d*x + 1/2*c)^2 + 8*a*tan(1/2*d*x + 1/2*c) + 3*a)/tan(1/2*d*x + 1/2*c)^4)/d","A",0
374,1,173,0,0.267133," ","integrate(cos(d*x+c)^4*csc(d*x+c)^6*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 5 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 10 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 120 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 20 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{274 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 20 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 40 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 10 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 5 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{320 \, d}"," ",0,"1/320*(2*a*tan(1/2*d*x + 1/2*c)^5 + 5*a*tan(1/2*d*x + 1/2*c)^4 - 10*a*tan(1/2*d*x + 1/2*c)^3 - 40*a*tan(1/2*d*x + 1/2*c)^2 + 120*a*log(abs(tan(1/2*d*x + 1/2*c))) + 20*a*tan(1/2*d*x + 1/2*c) - (274*a*tan(1/2*d*x + 1/2*c)^5 + 20*a*tan(1/2*d*x + 1/2*c)^4 - 40*a*tan(1/2*d*x + 1/2*c)^3 - 10*a*tan(1/2*d*x + 1/2*c)^2 + 5*a*tan(1/2*d*x + 1/2*c) + 2*a)/tan(1/2*d*x + 1/2*c)^5)/d","B",0
375,1,201,0,0.218154," ","integrate(cos(d*x+c)^4*csc(d*x+c)^7*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{5 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 12 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 60 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 120 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 120 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{294 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 120 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 60 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6}}}{1920 \, d}"," ",0,"1/1920*(5*a*tan(1/2*d*x + 1/2*c)^6 + 12*a*tan(1/2*d*x + 1/2*c)^5 - 15*a*tan(1/2*d*x + 1/2*c)^4 - 60*a*tan(1/2*d*x + 1/2*c)^3 - 15*a*tan(1/2*d*x + 1/2*c)^2 + 120*a*log(abs(tan(1/2*d*x + 1/2*c))) + 120*a*tan(1/2*d*x + 1/2*c) - (294*a*tan(1/2*d*x + 1/2*c)^6 + 120*a*tan(1/2*d*x + 1/2*c)^5 - 15*a*tan(1/2*d*x + 1/2*c)^4 - 60*a*tan(1/2*d*x + 1/2*c)^3 - 15*a*tan(1/2*d*x + 1/2*c)^2 + 12*a*tan(1/2*d*x + 1/2*c) + 5*a)/tan(1/2*d*x + 1/2*c)^6)/d","B",0
376,1,229,0,0.218439," ","integrate(cos(d*x+c)^4*csc(d*x+c)^8*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{15 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 35 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 21 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 105 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 105 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 105 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 840 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 315 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{2178 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 315 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 105 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 105 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 105 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 21 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 35 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7}}}{13440 \, d}"," ",0,"1/13440*(15*a*tan(1/2*d*x + 1/2*c)^7 + 35*a*tan(1/2*d*x + 1/2*c)^6 - 21*a*tan(1/2*d*x + 1/2*c)^5 - 105*a*tan(1/2*d*x + 1/2*c)^4 - 105*a*tan(1/2*d*x + 1/2*c)^3 - 105*a*tan(1/2*d*x + 1/2*c)^2 + 840*a*log(abs(tan(1/2*d*x + 1/2*c))) + 315*a*tan(1/2*d*x + 1/2*c) - (2178*a*tan(1/2*d*x + 1/2*c)^7 + 315*a*tan(1/2*d*x + 1/2*c)^6 - 105*a*tan(1/2*d*x + 1/2*c)^5 - 105*a*tan(1/2*d*x + 1/2*c)^4 - 105*a*tan(1/2*d*x + 1/2*c)^3 - 21*a*tan(1/2*d*x + 1/2*c)^2 + 35*a*tan(1/2*d*x + 1/2*c) + 15*a)/tan(1/2*d*x + 1/2*c)^7)/d","B",0
377,1,201,0,0.239736," ","integrate(cos(d*x+c)^4*csc(d*x+c)^9*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{35 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 80 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 112 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 280 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 560 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1680 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 1680 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{4566 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 1680 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 560 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 280 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 112 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 80 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 35 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8}}}{71680 \, d}"," ",0,"1/71680*(35*a*tan(1/2*d*x + 1/2*c)^8 + 80*a*tan(1/2*d*x + 1/2*c)^7 - 112*a*tan(1/2*d*x + 1/2*c)^5 - 280*a*tan(1/2*d*x + 1/2*c)^4 - 560*a*tan(1/2*d*x + 1/2*c)^3 + 1680*a*log(abs(tan(1/2*d*x + 1/2*c))) + 1680*a*tan(1/2*d*x + 1/2*c) - (4566*a*tan(1/2*d*x + 1/2*c)^8 + 1680*a*tan(1/2*d*x + 1/2*c)^7 - 560*a*tan(1/2*d*x + 1/2*c)^5 - 280*a*tan(1/2*d*x + 1/2*c)^4 - 112*a*tan(1/2*d*x + 1/2*c)^3 + 80*a*tan(1/2*d*x + 1/2*c) + 35*a)/tan(1/2*d*x + 1/2*c)^8)/d","A",0
378,1,174,0,0.321568," ","integrate(cos(d*x+c)^4*sin(d*x+c)^4*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{9}{256} \, a^{2} x - \frac{a^{2} \cos\left(9 \, d x + 9 \, c\right)}{1152 \, d} + \frac{a^{2} \cos\left(7 \, d x + 7 \, c\right)}{896 \, d} + \frac{a^{2} \cos\left(5 \, d x + 5 \, c\right)}{160 \, d} - \frac{a^{2} \cos\left(3 \, d x + 3 \, c\right)}{96 \, d} - \frac{3 \, a^{2} \cos\left(d x + c\right)}{64 \, d} - \frac{a^{2} \sin\left(10 \, d x + 10 \, c\right)}{5120 \, d} + \frac{3 \, a^{2} \sin\left(8 \, d x + 8 \, c\right)}{2048 \, d} + \frac{a^{2} \sin\left(6 \, d x + 6 \, c\right)}{1024 \, d} - \frac{3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)}{256 \, d} - \frac{a^{2} \sin\left(2 \, d x + 2 \, c\right)}{512 \, d}"," ",0,"9/256*a^2*x - 1/1152*a^2*cos(9*d*x + 9*c)/d + 1/896*a^2*cos(7*d*x + 7*c)/d + 1/160*a^2*cos(5*d*x + 5*c)/d - 1/96*a^2*cos(3*d*x + 3*c)/d - 3/64*a^2*cos(d*x + c)/d - 1/5120*a^2*sin(10*d*x + 10*c)/d + 3/2048*a^2*sin(8*d*x + 8*c)/d + 1/1024*a^2*sin(6*d*x + 6*c)/d - 3/256*a^2*sin(4*d*x + 4*c)/d - 1/512*a^2*sin(2*d*x + 2*c)/d","A",0
379,1,123,0,0.311078," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{3}{64} \, a^{2} x - \frac{a^{2} \cos\left(9 \, d x + 9 \, c\right)}{2304 \, d} + \frac{5 \, a^{2} \cos\left(7 \, d x + 7 \, c\right)}{1792 \, d} + \frac{a^{2} \cos\left(5 \, d x + 5 \, c\right)}{160 \, d} - \frac{a^{2} \cos\left(3 \, d x + 3 \, c\right)}{48 \, d} - \frac{9 \, a^{2} \cos\left(d x + c\right)}{128 \, d} + \frac{a^{2} \sin\left(8 \, d x + 8 \, c\right)}{512 \, d} - \frac{a^{2} \sin\left(4 \, d x + 4 \, c\right)}{64 \, d}"," ",0,"3/64*a^2*x - 1/2304*a^2*cos(9*d*x + 9*c)/d + 5/1792*a^2*cos(7*d*x + 7*c)/d + 1/160*a^2*cos(5*d*x + 5*c)/d - 1/48*a^2*cos(3*d*x + 3*c)/d - 9/128*a^2*cos(d*x + c)/d + 1/512*a^2*sin(8*d*x + 8*c)/d - 1/64*a^2*sin(4*d*x + 4*c)/d","A",0
380,1,140,0,0.265088," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{11}{128} \, a^{2} x + \frac{a^{2} \cos\left(7 \, d x + 7 \, c\right)}{224 \, d} + \frac{a^{2} \cos\left(5 \, d x + 5 \, c\right)}{160 \, d} - \frac{a^{2} \cos\left(3 \, d x + 3 \, c\right)}{32 \, d} - \frac{3 \, a^{2} \cos\left(d x + c\right)}{32 \, d} + \frac{a^{2} \sin\left(8 \, d x + 8 \, c\right)}{1024 \, d} - \frac{a^{2} \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} - \frac{3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)}{128 \, d} + \frac{a^{2} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d}"," ",0,"11/128*a^2*x + 1/224*a^2*cos(7*d*x + 7*c)/d + 1/160*a^2*cos(5*d*x + 5*c)/d - 1/32*a^2*cos(3*d*x + 3*c)/d - 3/32*a^2*cos(d*x + c)/d + 1/1024*a^2*sin(8*d*x + 8*c)/d - 1/192*a^2*sin(6*d*x + 6*c)/d - 3/128*a^2*sin(4*d*x + 4*c)/d + 1/64*a^2*sin(2*d*x + 2*c)/d","A",0
381,1,123,0,0.260045," ","integrate(cos(d*x+c)^4*sin(d*x+c)*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{1}{8} \, a^{2} x + \frac{a^{2} \cos\left(7 \, d x + 7 \, c\right)}{448 \, d} - \frac{3 \, a^{2} \cos\left(5 \, d x + 5 \, c\right)}{320 \, d} - \frac{5 \, a^{2} \cos\left(3 \, d x + 3 \, c\right)}{64 \, d} - \frac{11 \, a^{2} \cos\left(d x + c\right)}{64 \, d} - \frac{a^{2} \sin\left(6 \, d x + 6 \, c\right)}{96 \, d} - \frac{a^{2} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{a^{2} \sin\left(2 \, d x + 2 \, c\right)}{32 \, d}"," ",0,"1/8*a^2*x + 1/448*a^2*cos(7*d*x + 7*c)/d - 3/320*a^2*cos(5*d*x + 5*c)/d - 5/64*a^2*cos(3*d*x + 3*c)/d - 11/64*a^2*cos(d*x + c)/d - 1/96*a^2*sin(6*d*x + 6*c)/d - 1/32*a^2*sin(4*d*x + 4*c)/d + 1/32*a^2*sin(2*d*x + 2*c)/d","A",0
382,1,181,0,0.223906," ","integrate(cos(d*x+c)^4*csc(d*x+c)*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{45 \, {\left(d x + c\right)} a^{2} + 60 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{2 \, {\left(75 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 60 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 30 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 360 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 320 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 30 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 280 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 75 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 68 \, a^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5}}}{60 \, d}"," ",0,"1/60*(45*(d*x + c)*a^2 + 60*a^2*log(abs(tan(1/2*d*x + 1/2*c))) - 2*(75*a^2*tan(1/2*d*x + 1/2*c)^9 - 60*a^2*tan(1/2*d*x + 1/2*c)^8 + 30*a^2*tan(1/2*d*x + 1/2*c)^7 - 360*a^2*tan(1/2*d*x + 1/2*c)^6 - 320*a^2*tan(1/2*d*x + 1/2*c)^4 - 30*a^2*tan(1/2*d*x + 1/2*c)^3 - 280*a^2*tan(1/2*d*x + 1/2*c)^2 - 75*a^2*tan(1/2*d*x + 1/2*c) - 68*a^2)/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","A",0
383,1,210,0,0.226117," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{27 \, {\left(d x + c\right)} a^{2} - 48 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 12 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{12 \, {\left(4 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)} + \frac{2 \, {\left(3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 96 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 21 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 192 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 21 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 160 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 64 \, a^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"-1/24*(27*(d*x + c)*a^2 - 48*a^2*log(abs(tan(1/2*d*x + 1/2*c))) - 12*a^2*tan(1/2*d*x + 1/2*c) + 12*(4*a^2*tan(1/2*d*x + 1/2*c) + a^2)/tan(1/2*d*x + 1/2*c) + 2*(3*a^2*tan(1/2*d*x + 1/2*c)^7 - 96*a^2*tan(1/2*d*x + 1/2*c)^6 - 21*a^2*tan(1/2*d*x + 1/2*c)^5 - 192*a^2*tan(1/2*d*x + 1/2*c)^4 + 21*a^2*tan(1/2*d*x + 1/2*c)^3 - 160*a^2*tan(1/2*d*x + 1/2*c)^2 - 3*a^2*tan(1/2*d*x + 1/2*c) - 64*a^2)/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","A",0
384,1,178,0,0.235800," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 72 \, {\left(d x + c\right)} a^{2} - 12 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 24 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{3 \, {\left(6 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{2}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}} + \frac{16 \, {\left(3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{24 \, d}"," ",0,"1/24*(3*a^2*tan(1/2*d*x + 1/2*c)^2 - 72*(d*x + c)*a^2 - 12*a^2*log(abs(tan(1/2*d*x + 1/2*c))) + 24*a^2*tan(1/2*d*x + 1/2*c) + 3*(6*a^2*tan(1/2*d*x + 1/2*c)^2 - 8*a^2*tan(1/2*d*x + 1/2*c) - a^2)/tan(1/2*d*x + 1/2*c)^2 + 16*(3*a^2*tan(1/2*d*x + 1/2*c)^5 + 3*a^2*tan(1/2*d*x + 1/2*c)^4 - 3*a^2*tan(1/2*d*x + 1/2*c) + a^2)/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
385,1,209,0,0.252098," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, {\left(d x + c\right)} a^{2} - 72 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{24 \, {\left(a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, a^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}} + \frac{132 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 6 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{24 \, d}"," ",0,"1/24*(a^2*tan(1/2*d*x + 1/2*c)^3 + 6*a^2*tan(1/2*d*x + 1/2*c)^2 - 12*(d*x + c)*a^2 - 72*a^2*log(abs(tan(1/2*d*x + 1/2*c))) - 3*a^2*tan(1/2*d*x + 1/2*c) + 24*(a^2*tan(1/2*d*x + 1/2*c)^3 - 4*a^2*tan(1/2*d*x + 1/2*c)^2 - a^2*tan(1/2*d*x + 1/2*c) - 4*a^2)/(tan(1/2*d*x + 1/2*c)^2 + 1)^2 + (132*a^2*tan(1/2*d*x + 1/2*c)^3 + 3*a^2*tan(1/2*d*x + 1/2*c)^2 - 6*a^2*tan(1/2*d*x + 1/2*c) - a^2)/tan(1/2*d*x + 1/2*c)^3)/d","B",0
386,1,162,0,0.279200," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 16 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 384 \, {\left(d x + c\right)} a^{2} - 216 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 240 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{384 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + \frac{450 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 240 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 16 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}}}{192 \, d}"," ",0,"1/192*(3*a^2*tan(1/2*d*x + 1/2*c)^4 + 16*a^2*tan(1/2*d*x + 1/2*c)^3 + 384*(d*x + c)*a^2 - 216*a^2*log(abs(tan(1/2*d*x + 1/2*c))) - 240*a^2*tan(1/2*d*x + 1/2*c) - 384*a^2/(tan(1/2*d*x + 1/2*c)^2 + 1) + (450*a^2*tan(1/2*d*x + 1/2*c)^4 + 240*a^2*tan(1/2*d*x + 1/2*c)^3 - 16*a^2*tan(1/2*d*x + 1/2*c) - 3*a^2)/tan(1/2*d*x + 1/2*c)^4)/d","A",0
387,1,207,0,0.254230," ","integrate(cos(d*x+c)^4*csc(d*x+c)^6*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 5 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 480 \, {\left(d x + c\right)} a^{2} + 360 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 270 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{822 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 270 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 120 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{480 \, d}"," ",0,"1/480*(3*a^2*tan(1/2*d*x + 1/2*c)^5 + 15*a^2*tan(1/2*d*x + 1/2*c)^4 + 5*a^2*tan(1/2*d*x + 1/2*c)^3 - 120*a^2*tan(1/2*d*x + 1/2*c)^2 + 480*(d*x + c)*a^2 + 360*a^2*log(abs(tan(1/2*d*x + 1/2*c))) - 270*a^2*tan(1/2*d*x + 1/2*c) - (822*a^2*tan(1/2*d*x + 1/2*c)^5 - 270*a^2*tan(1/2*d*x + 1/2*c)^4 - 120*a^2*tan(1/2*d*x + 1/2*c)^3 + 5*a^2*tan(1/2*d*x + 1/2*c)^2 + 15*a^2*tan(1/2*d*x + 1/2*c) + 3*a^2)/tan(1/2*d*x + 1/2*c)^5)/d","A",0
388,1,229,0,0.288038," ","integrate(cos(d*x+c)^4*csc(d*x+c)^7*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{5 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 24 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 120 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 255 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 840 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 240 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{2058 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 240 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 255 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 120 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6}}}{1920 \, d}"," ",0,"1/1920*(5*a^2*tan(1/2*d*x + 1/2*c)^6 + 24*a^2*tan(1/2*d*x + 1/2*c)^5 + 15*a^2*tan(1/2*d*x + 1/2*c)^4 - 120*a^2*tan(1/2*d*x + 1/2*c)^3 - 255*a^2*tan(1/2*d*x + 1/2*c)^2 + 840*a^2*log(abs(tan(1/2*d*x + 1/2*c))) + 240*a^2*tan(1/2*d*x + 1/2*c) - (2058*a^2*tan(1/2*d*x + 1/2*c)^6 + 240*a^2*tan(1/2*d*x + 1/2*c)^5 - 255*a^2*tan(1/2*d*x + 1/2*c)^4 - 120*a^2*tan(1/2*d*x + 1/2*c)^3 + 15*a^2*tan(1/2*d*x + 1/2*c)^2 + 24*a^2*tan(1/2*d*x + 1/2*c) + 5*a^2)/tan(1/2*d*x + 1/2*c)^6)/d","A",0
389,1,293,0,0.304105," ","integrate(cos(d*x+c)^4*csc(d*x+c)^9*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{105 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 480 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 560 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 672 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 2520 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 3360 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1680 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 18480 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 10080 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{50226 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 10080 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1680 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 3360 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 2520 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 672 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 560 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 480 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 105 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8}}}{215040 \, d}"," ",0,"1/215040*(105*a^2*tan(1/2*d*x + 1/2*c)^8 + 480*a^2*tan(1/2*d*x + 1/2*c)^7 + 560*a^2*tan(1/2*d*x + 1/2*c)^6 - 672*a^2*tan(1/2*d*x + 1/2*c)^5 - 2520*a^2*tan(1/2*d*x + 1/2*c)^4 - 3360*a^2*tan(1/2*d*x + 1/2*c)^3 - 1680*a^2*tan(1/2*d*x + 1/2*c)^2 + 18480*a^2*log(abs(tan(1/2*d*x + 1/2*c))) + 10080*a^2*tan(1/2*d*x + 1/2*c) - (50226*a^2*tan(1/2*d*x + 1/2*c)^8 + 10080*a^2*tan(1/2*d*x + 1/2*c)^7 - 1680*a^2*tan(1/2*d*x + 1/2*c)^6 - 3360*a^2*tan(1/2*d*x + 1/2*c)^5 - 2520*a^2*tan(1/2*d*x + 1/2*c)^4 - 672*a^2*tan(1/2*d*x + 1/2*c)^3 + 560*a^2*tan(1/2*d*x + 1/2*c)^2 + 480*a^2*tan(1/2*d*x + 1/2*c) + 105*a^2)/tan(1/2*d*x + 1/2*c)^8)/d","A",0
390,1,261,0,0.299286," ","integrate(cos(d*x+c)^4*csc(d*x+c)^10*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{70 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 315 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 450 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1008 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 2520 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 3360 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15120 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 11340 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{42774 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 11340 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 3360 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 2520 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1008 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 450 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 315 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 70 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9}}}{322560 \, d}"," ",0,"1/322560*(70*a^2*tan(1/2*d*x + 1/2*c)^9 + 315*a^2*tan(1/2*d*x + 1/2*c)^8 + 450*a^2*tan(1/2*d*x + 1/2*c)^7 - 1008*a^2*tan(1/2*d*x + 1/2*c)^5 - 2520*a^2*tan(1/2*d*x + 1/2*c)^4 - 3360*a^2*tan(1/2*d*x + 1/2*c)^3 + 15120*a^2*log(abs(tan(1/2*d*x + 1/2*c))) + 11340*a^2*tan(1/2*d*x + 1/2*c) - (42774*a^2*tan(1/2*d*x + 1/2*c)^9 + 11340*a^2*tan(1/2*d*x + 1/2*c)^8 - 3360*a^2*tan(1/2*d*x + 1/2*c)^6 - 2520*a^2*tan(1/2*d*x + 1/2*c)^5 - 1008*a^2*tan(1/2*d*x + 1/2*c)^4 + 450*a^2*tan(1/2*d*x + 1/2*c)^2 + 315*a^2*tan(1/2*d*x + 1/2*c) + 70*a^2)/tan(1/2*d*x + 1/2*c)^9)/d","A",0
391,1,357,0,0.321568," ","integrate(cos(d*x+c)^4*csc(d*x+c)^11*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{126 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 560 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 945 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 720 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 630 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 4032 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 7560 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 6720 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1260 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 45360 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 30240 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{132858 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 30240 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1260 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 6720 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 7560 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 4032 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 630 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 720 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 945 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 560 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 126 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10}}}{1290240 \, d}"," ",0,"1/1290240*(126*a^2*tan(1/2*d*x + 1/2*c)^10 + 560*a^2*tan(1/2*d*x + 1/2*c)^9 + 945*a^2*tan(1/2*d*x + 1/2*c)^8 + 720*a^2*tan(1/2*d*x + 1/2*c)^7 - 630*a^2*tan(1/2*d*x + 1/2*c)^6 - 4032*a^2*tan(1/2*d*x + 1/2*c)^5 - 7560*a^2*tan(1/2*d*x + 1/2*c)^4 - 6720*a^2*tan(1/2*d*x + 1/2*c)^3 + 1260*a^2*tan(1/2*d*x + 1/2*c)^2 + 45360*a^2*log(abs(tan(1/2*d*x + 1/2*c))) + 30240*a^2*tan(1/2*d*x + 1/2*c) - (132858*a^2*tan(1/2*d*x + 1/2*c)^10 + 30240*a^2*tan(1/2*d*x + 1/2*c)^9 + 1260*a^2*tan(1/2*d*x + 1/2*c)^8 - 6720*a^2*tan(1/2*d*x + 1/2*c)^7 - 7560*a^2*tan(1/2*d*x + 1/2*c)^6 - 4032*a^2*tan(1/2*d*x + 1/2*c)^5 - 630*a^2*tan(1/2*d*x + 1/2*c)^4 + 720*a^2*tan(1/2*d*x + 1/2*c)^3 + 945*a^2*tan(1/2*d*x + 1/2*c)^2 + 560*a^2*tan(1/2*d*x + 1/2*c) + 126*a^2)/tan(1/2*d*x + 1/2*c)^10)/d","A",0
392,1,191,0,0.424656," ","integrate(cos(d*x+c)^4*sin(d*x+c)^4*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{15}{256} \, a^{3} x + \frac{a^{3} \cos\left(11 \, d x + 11 \, c\right)}{11264 \, d} - \frac{5 \, a^{3} \cos\left(9 \, d x + 9 \, c\right)}{3072 \, d} + \frac{11 \, a^{3} \cos\left(7 \, d x + 7 \, c\right)}{7168 \, d} + \frac{59 \, a^{3} \cos\left(5 \, d x + 5 \, c\right)}{5120 \, d} - \frac{9 \, a^{3} \cos\left(3 \, d x + 3 \, c\right)}{512 \, d} - \frac{43 \, a^{3} \cos\left(d x + c\right)}{512 \, d} - \frac{3 \, a^{3} \sin\left(10 \, d x + 10 \, c\right)}{5120 \, d} + \frac{5 \, a^{3} \sin\left(8 \, d x + 8 \, c\right)}{2048 \, d} + \frac{3 \, a^{3} \sin\left(6 \, d x + 6 \, c\right)}{1024 \, d} - \frac{5 \, a^{3} \sin\left(4 \, d x + 4 \, c\right)}{256 \, d} - \frac{3 \, a^{3} \sin\left(2 \, d x + 2 \, c\right)}{512 \, d}"," ",0,"15/256*a^3*x + 1/11264*a^3*cos(11*d*x + 11*c)/d - 5/3072*a^3*cos(9*d*x + 9*c)/d + 11/7168*a^3*cos(7*d*x + 7*c)/d + 59/5120*a^3*cos(5*d*x + 5*c)/d - 9/512*a^3*cos(3*d*x + 3*c)/d - 43/512*a^3*cos(d*x + c)/d - 3/5120*a^3*sin(10*d*x + 10*c)/d + 5/2048*a^3*sin(8*d*x + 8*c)/d + 3/1024*a^3*sin(6*d*x + 6*c)/d - 5/256*a^3*sin(4*d*x + 4*c)/d - 3/512*a^3*sin(2*d*x + 2*c)/d","A",0
393,1,174,0,0.396210," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{21}{256} \, a^{3} x - \frac{a^{3} \cos\left(9 \, d x + 9 \, c\right)}{768 \, d} + \frac{a^{3} \cos\left(7 \, d x + 7 \, c\right)}{256 \, d} + \frac{a^{3} \cos\left(5 \, d x + 5 \, c\right)}{80 \, d} - \frac{a^{3} \cos\left(3 \, d x + 3 \, c\right)}{32 \, d} - \frac{15 \, a^{3} \cos\left(d x + c\right)}{128 \, d} - \frac{a^{3} \sin\left(10 \, d x + 10 \, c\right)}{5120 \, d} + \frac{7 \, a^{3} \sin\left(8 \, d x + 8 \, c\right)}{2048 \, d} + \frac{a^{3} \sin\left(6 \, d x + 6 \, c\right)}{1024 \, d} - \frac{7 \, a^{3} \sin\left(4 \, d x + 4 \, c\right)}{256 \, d} - \frac{a^{3} \sin\left(2 \, d x + 2 \, c\right)}{512 \, d}"," ",0,"21/256*a^3*x - 1/768*a^3*cos(9*d*x + 9*c)/d + 1/256*a^3*cos(7*d*x + 7*c)/d + 1/80*a^3*cos(5*d*x + 5*c)/d - 1/32*a^3*cos(3*d*x + 3*c)/d - 15/128*a^3*cos(d*x + c)/d - 1/5120*a^3*sin(10*d*x + 10*c)/d + 7/2048*a^3*sin(8*d*x + 8*c)/d + 1/1024*a^3*sin(6*d*x + 6*c)/d - 7/256*a^3*sin(4*d*x + 4*c)/d - 1/512*a^3*sin(2*d*x + 2*c)/d","A",0
394,1,157,0,0.329001," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{17}{128} \, a^{3} x - \frac{a^{3} \cos\left(9 \, d x + 9 \, c\right)}{2304 \, d} + \frac{13 \, a^{3} \cos\left(7 \, d x + 7 \, c\right)}{1792 \, d} + \frac{a^{3} \cos\left(5 \, d x + 5 \, c\right)}{80 \, d} - \frac{5 \, a^{3} \cos\left(3 \, d x + 3 \, c\right)}{96 \, d} - \frac{21 \, a^{3} \cos\left(d x + c\right)}{128 \, d} + \frac{3 \, a^{3} \sin\left(8 \, d x + 8 \, c\right)}{1024 \, d} - \frac{a^{3} \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} - \frac{5 \, a^{3} \sin\left(4 \, d x + 4 \, c\right)}{128 \, d} + \frac{a^{3} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d}"," ",0,"17/128*a^3*x - 1/2304*a^3*cos(9*d*x + 9*c)/d + 13/1792*a^3*cos(7*d*x + 7*c)/d + 1/80*a^3*cos(5*d*x + 5*c)/d - 5/96*a^3*cos(3*d*x + 3*c)/d - 21/128*a^3*cos(d*x + c)/d + 3/1024*a^3*sin(8*d*x + 8*c)/d - 1/192*a^3*sin(6*d*x + 6*c)/d - 5/128*a^3*sin(4*d*x + 4*c)/d + 1/64*a^3*sin(2*d*x + 2*c)/d","A",0
395,1,140,0,0.285260," ","integrate(cos(d*x+c)^4*sin(d*x+c)*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{27}{128} \, a^{3} x + \frac{3 \, a^{3} \cos\left(7 \, d x + 7 \, c\right)}{448 \, d} - \frac{a^{3} \cos\left(5 \, d x + 5 \, c\right)}{320 \, d} - \frac{7 \, a^{3} \cos\left(3 \, d x + 3 \, c\right)}{64 \, d} - \frac{17 \, a^{3} \cos\left(d x + c\right)}{64 \, d} + \frac{a^{3} \sin\left(8 \, d x + 8 \, c\right)}{1024 \, d} - \frac{a^{3} \sin\left(6 \, d x + 6 \, c\right)}{64 \, d} - \frac{7 \, a^{3} \sin\left(4 \, d x + 4 \, c\right)}{128 \, d} + \frac{3 \, a^{3} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d}"," ",0,"27/128*a^3*x + 3/448*a^3*cos(7*d*x + 7*c)/d - 1/320*a^3*cos(5*d*x + 5*c)/d - 7/64*a^3*cos(3*d*x + 3*c)/d - 17/64*a^3*cos(d*x + c)/d + 1/1024*a^3*sin(8*d*x + 8*c)/d - 1/64*a^3*sin(6*d*x + 6*c)/d - 7/128*a^3*sin(4*d*x + 4*c)/d + 3/64*a^3*sin(2*d*x + 2*c)/d","A",0
396,1,229,0,0.326419," ","integrate(cos(d*x+c)^4*csc(d*x+c)*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{285 \, {\left(d x + c\right)} a^{3} + 240 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{2 \, {\left(435 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 240 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 865 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1200 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 210 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1760 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 210 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1440 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 865 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1296 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 435 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 176 \, a^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(285*(d*x + c)*a^3 + 240*a^3*log(abs(tan(1/2*d*x + 1/2*c))) - 2*(435*a^3*tan(1/2*d*x + 1/2*c)^11 + 240*a^3*tan(1/2*d*x + 1/2*c)^10 + 865*a^3*tan(1/2*d*x + 1/2*c)^9 - 1200*a^3*tan(1/2*d*x + 1/2*c)^8 - 210*a^3*tan(1/2*d*x + 1/2*c)^7 - 1760*a^3*tan(1/2*d*x + 1/2*c)^6 + 210*a^3*tan(1/2*d*x + 1/2*c)^5 - 1440*a^3*tan(1/2*d*x + 1/2*c)^4 - 865*a^3*tan(1/2*d*x + 1/2*c)^3 - 1296*a^3*tan(1/2*d*x + 1/2*c)^2 - 435*a^3*tan(1/2*d*x + 1/2*c) - 176*a^3)/(tan(1/2*d*x + 1/2*c)^2 + 1)^6)/d","A",0
397,1,226,0,0.271909," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{15 \, {\left(d x + c\right)} a^{3} - 120 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 20 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{20 \, {\left(6 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)} + \frac{2 \, {\left(55 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 200 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 10 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 720 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 800 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 10 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 560 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 55 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 152 \, a^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5}}}{40 \, d}"," ",0,"-1/40*(15*(d*x + c)*a^3 - 120*a^3*log(abs(tan(1/2*d*x + 1/2*c))) - 20*a^3*tan(1/2*d*x + 1/2*c) + 20*(6*a^3*tan(1/2*d*x + 1/2*c) + a^3)/tan(1/2*d*x + 1/2*c) + 2*(55*a^3*tan(1/2*d*x + 1/2*c)^9 - 200*a^3*tan(1/2*d*x + 1/2*c)^8 - 10*a^3*tan(1/2*d*x + 1/2*c)^7 - 720*a^3*tan(1/2*d*x + 1/2*c)^6 - 800*a^3*tan(1/2*d*x + 1/2*c)^4 + 10*a^3*tan(1/2*d*x + 1/2*c)^3 - 560*a^3*tan(1/2*d*x + 1/2*c)^2 - 55*a^3*tan(1/2*d*x + 1/2*c) - 152*a^3)/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","A",0
398,1,241,0,0.321558," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 33 \, {\left(d x + c\right)} a^{3} + 12 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 12 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{18 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}} + \frac{2 \, {\left(7 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 40 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 15 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 15 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 56 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 7 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, a^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{8 \, d}"," ",0,"1/8*(a^3*tan(1/2*d*x + 1/2*c)^2 - 33*(d*x + c)*a^3 + 12*a^3*log(abs(tan(1/2*d*x + 1/2*c))) + 12*a^3*tan(1/2*d*x + 1/2*c) - (18*a^3*tan(1/2*d*x + 1/2*c)^2 + 12*a^3*tan(1/2*d*x + 1/2*c) + a^3)/tan(1/2*d*x + 1/2*c)^2 + 2*(7*a^3*tan(1/2*d*x + 1/2*c)^7 + 40*a^3*tan(1/2*d*x + 1/2*c)^6 + 15*a^3*tan(1/2*d*x + 1/2*c)^5 + 72*a^3*tan(1/2*d*x + 1/2*c)^4 - 15*a^3*tan(1/2*d*x + 1/2*c)^3 + 56*a^3*tan(1/2*d*x + 1/2*c)^2 - 7*a^3*tan(1/2*d*x + 1/2*c) + 24*a^3)/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","A",0
399,1,250,0,0.287771," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 27 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 252 \, {\left(d x + c\right)} a^{3} - 252 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 63 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{154 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 153 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 291 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 192 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 195 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 414 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 167 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 27 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a^{3}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}^{3}}}{72 \, d}"," ",0,"1/72*(3*a^3*tan(1/2*d*x + 1/2*c)^3 + 27*a^3*tan(1/2*d*x + 1/2*c)^2 - 252*(d*x + c)*a^3 - 252*a^3*log(abs(tan(1/2*d*x + 1/2*c))) + 63*a^3*tan(1/2*d*x + 1/2*c) + (154*a^3*tan(1/2*d*x + 1/2*c)^9 + 153*a^3*tan(1/2*d*x + 1/2*c)^8 + 291*a^3*tan(1/2*d*x + 1/2*c)^7 - 192*a^3*tan(1/2*d*x + 1/2*c)^6 - 195*a^3*tan(1/2*d*x + 1/2*c)^5 - 414*a^3*tan(1/2*d*x + 1/2*c)^4 - 167*a^3*tan(1/2*d*x + 1/2*c)^3 - 72*a^3*tan(1/2*d*x + 1/2*c)^2 - 27*a^3*tan(1/2*d*x + 1/2*c) - 3*a^3)/(tan(1/2*d*x + 1/2*c)^3 + tan(1/2*d*x + 1/2*c))^3)/d","B",0
400,1,241,0,0.313977," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 8 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 16 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 96 \, {\left(d x + c\right)} a^{3} - 264 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 88 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{64 \, {\left(a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, a^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}} + \frac{550 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 88 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 16 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}}}{64 \, d}"," ",0,"1/64*(a^3*tan(1/2*d*x + 1/2*c)^4 + 8*a^3*tan(1/2*d*x + 1/2*c)^3 + 16*a^3*tan(1/2*d*x + 1/2*c)^2 + 96*(d*x + c)*a^3 - 264*a^3*log(abs(tan(1/2*d*x + 1/2*c))) - 88*a^3*tan(1/2*d*x + 1/2*c) + 64*(a^3*tan(1/2*d*x + 1/2*c)^3 - 6*a^3*tan(1/2*d*x + 1/2*c)^2 - a^3*tan(1/2*d*x + 1/2*c) - 6*a^3)/(tan(1/2*d*x + 1/2*c)^2 + 1)^2 + (550*a^3*tan(1/2*d*x + 1/2*c)^4 + 88*a^3*tan(1/2*d*x + 1/2*c)^3 - 16*a^3*tan(1/2*d*x + 1/2*c)^2 - 8*a^3*tan(1/2*d*x + 1/2*c) - a^3)/tan(1/2*d*x + 1/2*c)^4)/d","A",0
401,1,226,0,0.323051," ","integrate(cos(d*x+c)^4*csc(d*x+c)^6*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{2 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 30 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 80 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 960 \, {\left(d x + c\right)} a^{3} - 120 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 580 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{640 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + \frac{274 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 580 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 80 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 30 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{320 \, d}"," ",0,"1/320*(2*a^3*tan(1/2*d*x + 1/2*c)^5 + 15*a^3*tan(1/2*d*x + 1/2*c)^4 + 30*a^3*tan(1/2*d*x + 1/2*c)^3 - 80*a^3*tan(1/2*d*x + 1/2*c)^2 + 960*(d*x + c)*a^3 - 120*a^3*log(abs(tan(1/2*d*x + 1/2*c))) - 580*a^3*tan(1/2*d*x + 1/2*c) - 640*a^3/(tan(1/2*d*x + 1/2*c)^2 + 1) + (274*a^3*tan(1/2*d*x + 1/2*c)^5 + 580*a^3*tan(1/2*d*x + 1/2*c)^4 + 80*a^3*tan(1/2*d*x + 1/2*c)^3 - 30*a^3*tan(1/2*d*x + 1/2*c)^2 - 15*a^3*tan(1/2*d*x + 1/2*c) - 2*a^3)/tan(1/2*d*x + 1/2*c)^5)/d","A",0
402,1,239,0,0.338609," ","integrate(cos(d*x+c)^4*csc(d*x+c)^7*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{5 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 36 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 75 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 100 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 735 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1920 \, {\left(d x + c\right)} a^{3} + 2280 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 840 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{5586 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 840 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 735 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 100 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 75 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 36 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6}}}{1920 \, d}"," ",0,"1/1920*(5*a^3*tan(1/2*d*x + 1/2*c)^6 + 36*a^3*tan(1/2*d*x + 1/2*c)^5 + 75*a^3*tan(1/2*d*x + 1/2*c)^4 - 100*a^3*tan(1/2*d*x + 1/2*c)^3 - 735*a^3*tan(1/2*d*x + 1/2*c)^2 + 1920*(d*x + c)*a^3 + 2280*a^3*log(abs(tan(1/2*d*x + 1/2*c))) - 840*a^3*tan(1/2*d*x + 1/2*c) - (5586*a^3*tan(1/2*d*x + 1/2*c)^6 - 840*a^3*tan(1/2*d*x + 1/2*c)^5 - 735*a^3*tan(1/2*d*x + 1/2*c)^4 - 100*a^3*tan(1/2*d*x + 1/2*c)^3 + 75*a^3*tan(1/2*d*x + 1/2*c)^2 + 36*a^3*tan(1/2*d*x + 1/2*c) + 5*a^3)/tan(1/2*d*x + 1/2*c)^6)/d","A",0
403,1,261,0,0.338185," ","integrate(cos(d*x+c)^4*csc(d*x+c)^8*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{5 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 35 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 77 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 35 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 455 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 665 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2520 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 945 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{6534 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 945 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 665 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 455 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 35 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 77 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 35 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7}}}{4480 \, d}"," ",0,"1/4480*(5*a^3*tan(1/2*d*x + 1/2*c)^7 + 35*a^3*tan(1/2*d*x + 1/2*c)^6 + 77*a^3*tan(1/2*d*x + 1/2*c)^5 - 35*a^3*tan(1/2*d*x + 1/2*c)^4 - 455*a^3*tan(1/2*d*x + 1/2*c)^3 - 665*a^3*tan(1/2*d*x + 1/2*c)^2 + 2520*a^3*log(abs(tan(1/2*d*x + 1/2*c))) + 945*a^3*tan(1/2*d*x + 1/2*c) - (6534*a^3*tan(1/2*d*x + 1/2*c)^7 + 945*a^3*tan(1/2*d*x + 1/2*c)^6 - 665*a^3*tan(1/2*d*x + 1/2*c)^5 - 455*a^3*tan(1/2*d*x + 1/2*c)^4 - 35*a^3*tan(1/2*d*x + 1/2*c)^3 + 77*a^3*tan(1/2*d*x + 1/2*c)^2 + 35*a^3*tan(1/2*d*x + 1/2*c) + 5*a^3)/tan(1/2*d*x + 1/2*c)^7)/d","A",0
404,1,293,0,0.379710," ","integrate(cos(d*x+c)^4*csc(d*x+c)^9*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{35 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 240 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 560 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 112 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1960 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 3920 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1680 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 15120 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 9520 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{41094 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 9520 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1680 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 3920 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1960 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 112 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 560 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 240 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 35 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8}}}{71680 \, d}"," ",0,"1/71680*(35*a^3*tan(1/2*d*x + 1/2*c)^8 + 240*a^3*tan(1/2*d*x + 1/2*c)^7 + 560*a^3*tan(1/2*d*x + 1/2*c)^6 + 112*a^3*tan(1/2*d*x + 1/2*c)^5 - 1960*a^3*tan(1/2*d*x + 1/2*c)^4 - 3920*a^3*tan(1/2*d*x + 1/2*c)^3 - 1680*a^3*tan(1/2*d*x + 1/2*c)^2 + 15120*a^3*log(abs(tan(1/2*d*x + 1/2*c))) + 9520*a^3*tan(1/2*d*x + 1/2*c) - (41094*a^3*tan(1/2*d*x + 1/2*c)^8 + 9520*a^3*tan(1/2*d*x + 1/2*c)^7 - 1680*a^3*tan(1/2*d*x + 1/2*c)^6 - 3920*a^3*tan(1/2*d*x + 1/2*c)^5 - 1960*a^3*tan(1/2*d*x + 1/2*c)^4 + 112*a^3*tan(1/2*d*x + 1/2*c)^3 + 560*a^3*tan(1/2*d*x + 1/2*c)^2 + 240*a^3*tan(1/2*d*x + 1/2*c) + 35*a^3)/tan(1/2*d*x + 1/2*c)^8)/d","A",0
405,1,325,0,0.370884," ","integrate(cos(d*x+c)^4*csc(d*x+c)^10*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{140 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 945 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 2340 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1680 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 4032 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12600 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 16800 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5040 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 85680 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 52920 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{242386 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 52920 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 5040 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 16800 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 12600 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4032 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 1680 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2340 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 945 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 140 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9}}}{645120 \, d}"," ",0,"1/645120*(140*a^3*tan(1/2*d*x + 1/2*c)^9 + 945*a^3*tan(1/2*d*x + 1/2*c)^8 + 2340*a^3*tan(1/2*d*x + 1/2*c)^7 + 1680*a^3*tan(1/2*d*x + 1/2*c)^6 - 4032*a^3*tan(1/2*d*x + 1/2*c)^5 - 12600*a^3*tan(1/2*d*x + 1/2*c)^4 - 16800*a^3*tan(1/2*d*x + 1/2*c)^3 - 5040*a^3*tan(1/2*d*x + 1/2*c)^2 + 85680*a^3*log(abs(tan(1/2*d*x + 1/2*c))) + 52920*a^3*tan(1/2*d*x + 1/2*c) - (242386*a^3*tan(1/2*d*x + 1/2*c)^9 + 52920*a^3*tan(1/2*d*x + 1/2*c)^8 - 5040*a^3*tan(1/2*d*x + 1/2*c)^7 - 16800*a^3*tan(1/2*d*x + 1/2*c)^6 - 12600*a^3*tan(1/2*d*x + 1/2*c)^5 - 4032*a^3*tan(1/2*d*x + 1/2*c)^4 + 1680*a^3*tan(1/2*d*x + 1/2*c)^3 + 2340*a^3*tan(1/2*d*x + 1/2*c)^2 + 945*a^3*tan(1/2*d*x + 1/2*c) + 140*a^3)/tan(1/2*d*x + 1/2*c)^9)/d","A",0
406,1,357,0,0.405887," ","integrate(cos(d*x+c)^4*csc(d*x+c)^11*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{6 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 40 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 105 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 120 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 30 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 384 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 840 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 960 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 60 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 5040 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 3600 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{14762 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 3600 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 60 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 960 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 840 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 384 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 30 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 120 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 105 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 40 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10}}}{61440 \, d}"," ",0,"1/61440*(6*a^3*tan(1/2*d*x + 1/2*c)^10 + 40*a^3*tan(1/2*d*x + 1/2*c)^9 + 105*a^3*tan(1/2*d*x + 1/2*c)^8 + 120*a^3*tan(1/2*d*x + 1/2*c)^7 - 30*a^3*tan(1/2*d*x + 1/2*c)^6 - 384*a^3*tan(1/2*d*x + 1/2*c)^5 - 840*a^3*tan(1/2*d*x + 1/2*c)^4 - 960*a^3*tan(1/2*d*x + 1/2*c)^3 + 60*a^3*tan(1/2*d*x + 1/2*c)^2 + 5040*a^3*log(abs(tan(1/2*d*x + 1/2*c))) + 3600*a^3*tan(1/2*d*x + 1/2*c) - (14762*a^3*tan(1/2*d*x + 1/2*c)^10 + 3600*a^3*tan(1/2*d*x + 1/2*c)^9 + 60*a^3*tan(1/2*d*x + 1/2*c)^8 - 960*a^3*tan(1/2*d*x + 1/2*c)^7 - 840*a^3*tan(1/2*d*x + 1/2*c)^6 - 384*a^3*tan(1/2*d*x + 1/2*c)^5 - 30*a^3*tan(1/2*d*x + 1/2*c)^4 + 120*a^3*tan(1/2*d*x + 1/2*c)^3 + 105*a^3*tan(1/2*d*x + 1/2*c)^2 + 40*a^3*tan(1/2*d*x + 1/2*c) + 6*a^3)/tan(1/2*d*x + 1/2*c)^10)/d","A",0
407,1,174,0,0.417255," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2*(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{55}{256} \, a^{4} x - \frac{a^{4} \cos\left(9 \, d x + 9 \, c\right)}{576 \, d} + \frac{5 \, a^{4} \cos\left(7 \, d x + 7 \, c\right)}{448 \, d} + \frac{a^{4} \cos\left(5 \, d x + 5 \, c\right)}{40 \, d} - \frac{a^{4} \cos\left(3 \, d x + 3 \, c\right)}{12 \, d} - \frac{9 \, a^{4} \cos\left(d x + c\right)}{32 \, d} - \frac{a^{4} \sin\left(10 \, d x + 10 \, c\right)}{5120 \, d} + \frac{13 \, a^{4} \sin\left(8 \, d x + 8 \, c\right)}{2048 \, d} - \frac{13 \, a^{4} \sin\left(6 \, d x + 6 \, c\right)}{3072 \, d} - \frac{17 \, a^{4} \sin\left(4 \, d x + 4 \, c\right)}{256 \, d} + \frac{7 \, a^{4} \sin\left(2 \, d x + 2 \, c\right)}{512 \, d}"," ",0,"55/256*a^4*x - 1/576*a^4*cos(9*d*x + 9*c)/d + 5/448*a^4*cos(7*d*x + 7*c)/d + 1/40*a^4*cos(5*d*x + 5*c)/d - 1/12*a^4*cos(3*d*x + 3*c)/d - 9/32*a^4*cos(d*x + c)/d - 1/5120*a^4*sin(10*d*x + 10*c)/d + 13/2048*a^4*sin(8*d*x + 8*c)/d - 13/3072*a^4*sin(6*d*x + 6*c)/d - 17/256*a^4*sin(4*d*x + 4*c)/d + 7/512*a^4*sin(2*d*x + 2*c)/d","A",0
408,1,274,0,0.369808," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4*(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 183 \, {\left(d x + c\right)} a^{4} - 48 \, a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 57 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{88 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 57 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{4}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}} + \frac{2 \, {\left(57 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 96 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 81 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 96 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 81 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 32 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 57 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 32 \, a^{4}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(a^4*tan(1/2*d*x + 1/2*c)^3 + 12*a^4*tan(1/2*d*x + 1/2*c)^2 - 183*(d*x + c)*a^4 - 48*a^4*log(abs(tan(1/2*d*x + 1/2*c))) + 57*a^4*tan(1/2*d*x + 1/2*c) + (88*a^4*tan(1/2*d*x + 1/2*c)^3 - 57*a^4*tan(1/2*d*x + 1/2*c)^2 - 12*a^4*tan(1/2*d*x + 1/2*c) - a^4)/tan(1/2*d*x + 1/2*c)^3 + 2*(57*a^4*tan(1/2*d*x + 1/2*c)^7 + 96*a^4*tan(1/2*d*x + 1/2*c)^6 + 81*a^4*tan(1/2*d*x + 1/2*c)^5 + 96*a^4*tan(1/2*d*x + 1/2*c)^4 - 81*a^4*tan(1/2*d*x + 1/2*c)^3 + 32*a^4*tan(1/2*d*x + 1/2*c)^2 - 57*a^4*tan(1/2*d*x + 1/2*c) + 32*a^4)/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","B",0
409,1,166,0,0.199897," ","integrate(cos(d*x+c)^4*sin(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{105 \, {\left(d x + c\right)}}{a} + \frac{2 \, {\left(105 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 700 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 3395 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 8960 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 4480 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 3395 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2688 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 700 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 896 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 105 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 128\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{7} a}}{1680 \, d}"," ",0,"1/1680*(105*(d*x + c)/a + 2*(105*tan(1/2*d*x + 1/2*c)^13 + 700*tan(1/2*d*x + 1/2*c)^11 - 3395*tan(1/2*d*x + 1/2*c)^9 + 8960*tan(1/2*d*x + 1/2*c)^8 - 4480*tan(1/2*d*x + 1/2*c)^6 + 3395*tan(1/2*d*x + 1/2*c)^5 + 2688*tan(1/2*d*x + 1/2*c)^4 - 700*tan(1/2*d*x + 1/2*c)^3 + 896*tan(1/2*d*x + 1/2*c)^2 - 105*tan(1/2*d*x + 1/2*c) + 128)/((tan(1/2*d*x + 1/2*c)^2 + 1)^7*a))/d","A",0
410,1,153,0,0.195973," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{15 \, {\left(d x + c\right)}}{a} + \frac{2 \, {\left(15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 85 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 480 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 570 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 320 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 570 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 85 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 192 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 32\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6} a}}{240 \, d}"," ",0,"-1/240*(15*(d*x + c)/a + 2*(15*tan(1/2*d*x + 1/2*c)^11 + 85*tan(1/2*d*x + 1/2*c)^9 + 480*tan(1/2*d*x + 1/2*c)^8 - 570*tan(1/2*d*x + 1/2*c)^7 + 320*tan(1/2*d*x + 1/2*c)^6 + 570*tan(1/2*d*x + 1/2*c)^5 - 85*tan(1/2*d*x + 1/2*c)^3 + 192*tan(1/2*d*x + 1/2*c)^2 - 15*tan(1/2*d*x + 1/2*c) + 32)/((tan(1/2*d*x + 1/2*c)^2 + 1)^6*a))/d","A",0
411,1,127,0,0.158402," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{15 \, {\left(d x + c\right)}}{a} + \frac{2 \, {\left(15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 90 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 240 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 80 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 90 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 80 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 16\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5} a}}{120 \, d}"," ",0,"1/120*(15*(d*x + c)/a + 2*(15*tan(1/2*d*x + 1/2*c)^9 - 90*tan(1/2*d*x + 1/2*c)^7 + 240*tan(1/2*d*x + 1/2*c)^6 - 80*tan(1/2*d*x + 1/2*c)^4 + 90*tan(1/2*d*x + 1/2*c)^3 + 80*tan(1/2*d*x + 1/2*c)^2 - 15*tan(1/2*d*x + 1/2*c) + 16)/((tan(1/2*d*x + 1/2*c)^2 + 1)^5*a))/d","A",0
412,1,127,0,0.169985," ","integrate(cos(d*x+c)^4*sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(d x + c\right)}}{a} + \frac{2 \, {\left(3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 21 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 24 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 21 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4} a}}{24 \, d}"," ",0,"-1/24*(3*(d*x + c)/a + 2*(3*tan(1/2*d*x + 1/2*c)^7 + 24*tan(1/2*d*x + 1/2*c)^6 - 21*tan(1/2*d*x + 1/2*c)^5 + 24*tan(1/2*d*x + 1/2*c)^4 + 21*tan(1/2*d*x + 1/2*c)^3 + 8*tan(1/2*d*x + 1/2*c)^2 - 3*tan(1/2*d*x + 1/2*c) + 8)/((tan(1/2*d*x + 1/2*c)^2 + 1)^4*a))/d","A",0
413,1,88,0,0.157831," ","integrate(cos(d*x+c)^4*csc(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{d x + c}{a} - \frac{2 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a} - \frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a}}{2 \, d}"," ",0,"-1/2*((d*x + c)/a - 2*log(abs(tan(1/2*d*x + 1/2*c)))/a - 2*(tan(1/2*d*x + 1/2*c)^3 + 2*tan(1/2*d*x + 1/2*c)^2 - tan(1/2*d*x + 1/2*c) + 2)/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a))/d","A",0
414,1,113,0,0.170118," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{6 \, {\left(d x + c\right)}}{a} + \frac{6 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a} - \frac{3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a} - \frac{2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 10 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} a}}{6 \, d}"," ",0,"-1/6*(6*(d*x + c)/a + 6*log(abs(tan(1/2*d*x + 1/2*c)))/a - 3*tan(1/2*d*x + 1/2*c)/a - (2*tan(1/2*d*x + 1/2*c)^3 - 3*tan(1/2*d*x + 1/2*c)^2 - 10*tan(1/2*d*x + 1/2*c) - 3)/((tan(1/2*d*x + 1/2*c)^3 + tan(1/2*d*x + 1/2*c))*a))/d","B",0
415,1,103,0,0.223670," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{8 \, {\left(d x + c\right)}}{a} - \frac{4 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a} + \frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{2}} + \frac{6 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 4 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}}{8 \, d}"," ",0,"1/8*(8*(d*x + c)/a - 4*log(abs(tan(1/2*d*x + 1/2*c)))/a + (a*tan(1/2*d*x + 1/2*c)^2 - 4*a*tan(1/2*d*x + 1/2*c))/a^2 + (6*tan(1/2*d*x + 1/2*c)^2 + 4*tan(1/2*d*x + 1/2*c) - 1)/(a*tan(1/2*d*x + 1/2*c)^2))/d","A",0
416,1,127,0,0.190218," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{12 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a} + \frac{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3}} - \frac{22 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{24 \, d}"," ",0,"1/24*(12*log(abs(tan(1/2*d*x + 1/2*c)))/a + (a^2*tan(1/2*d*x + 1/2*c)^3 - 3*a^2*tan(1/2*d*x + 1/2*c)^2 - 3*a^2*tan(1/2*d*x + 1/2*c))/a^3 - (22*tan(1/2*d*x + 1/2*c)^3 - 3*tan(1/2*d*x + 1/2*c)^2 - 3*tan(1/2*d*x + 1/2*c) + 1)/(a*tan(1/2*d*x + 1/2*c)^3))/d","B",0
417,1,129,0,0.230102," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{24 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a} - \frac{3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 8 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 24 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{4}} - \frac{50 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 24 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}}}{192 \, d}"," ",0,"-1/192*(24*log(abs(tan(1/2*d*x + 1/2*c)))/a - (3*a^3*tan(1/2*d*x + 1/2*c)^4 - 8*a^3*tan(1/2*d*x + 1/2*c)^3 + 24*a^3*tan(1/2*d*x + 1/2*c))/a^4 - (50*tan(1/2*d*x + 1/2*c)^4 - 24*tan(1/2*d*x + 1/2*c)^3 + 8*tan(1/2*d*x + 1/2*c) - 3)/(a*tan(1/2*d*x + 1/2*c)^4))/d","A",0
418,1,157,0,0.195934," ","integrate(cos(d*x+c)^4*csc(d*x+c)^6/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{120 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a} + \frac{6 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 10 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 60 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{5}} - \frac{274 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 60 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 10 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{960 \, d}"," ",0,"1/960*(120*log(abs(tan(1/2*d*x + 1/2*c)))/a + (6*a^4*tan(1/2*d*x + 1/2*c)^5 - 15*a^4*tan(1/2*d*x + 1/2*c)^4 + 10*a^4*tan(1/2*d*x + 1/2*c)^3 - 60*a^4*tan(1/2*d*x + 1/2*c))/a^5 - (274*tan(1/2*d*x + 1/2*c)^5 - 60*tan(1/2*d*x + 1/2*c)^4 + 10*tan(1/2*d*x + 1/2*c)^2 - 15*tan(1/2*d*x + 1/2*c) + 6)/(a*tan(1/2*d*x + 1/2*c)^5))/d","A",0
419,1,216,0,0.221699," ","integrate(cos(d*x+c)^4*csc(d*x+c)^7/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{120 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a} - \frac{5 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 12 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 20 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 120 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}} - \frac{294 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 120 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 20 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6}}}{1920 \, d}"," ",0,"-1/1920*(120*log(abs(tan(1/2*d*x + 1/2*c)))/a - (5*a^5*tan(1/2*d*x + 1/2*c)^6 - 12*a^5*tan(1/2*d*x + 1/2*c)^5 + 15*a^5*tan(1/2*d*x + 1/2*c)^4 - 20*a^5*tan(1/2*d*x + 1/2*c)^3 - 15*a^5*tan(1/2*d*x + 1/2*c)^2 + 120*a^5*tan(1/2*d*x + 1/2*c))/a^6 - (294*tan(1/2*d*x + 1/2*c)^6 - 120*tan(1/2*d*x + 1/2*c)^5 + 15*tan(1/2*d*x + 1/2*c)^4 + 20*tan(1/2*d*x + 1/2*c)^3 - 15*tan(1/2*d*x + 1/2*c)^2 + 12*tan(1/2*d*x + 1/2*c) - 5)/(a*tan(1/2*d*x + 1/2*c)^6))/d","A",0
420,1,166,0,0.228456," ","integrate(cos(d*x+c)^4*sin(d*x+c)^5/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{525 \, {\left(d x + c\right)}}{a^{2}} + \frac{2 \, {\left(525 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 3500 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 9905 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 4480 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 24640 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 9905 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 17472 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 3500 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5824 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 525 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 832\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{7} a^{2}}}{840 \, d}"," ",0,"-1/840*(525*(d*x + c)/a^2 + 2*(525*tan(1/2*d*x + 1/2*c)^13 + 3500*tan(1/2*d*x + 1/2*c)^11 + 9905*tan(1/2*d*x + 1/2*c)^9 + 4480*tan(1/2*d*x + 1/2*c)^8 + 24640*tan(1/2*d*x + 1/2*c)^6 - 9905*tan(1/2*d*x + 1/2*c)^5 + 17472*tan(1/2*d*x + 1/2*c)^4 - 3500*tan(1/2*d*x + 1/2*c)^3 + 5824*tan(1/2*d*x + 1/2*c)^2 - 525*tan(1/2*d*x + 1/2*c) + 832)/((tan(1/2*d*x + 1/2*c)^2 + 1)^7*a^2))/d","A",0
421,1,153,0,0.196688," ","integrate(cos(d*x+c)^4*sin(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{165 \, {\left(d x + c\right)}}{a^{2}} + \frac{2 \, {\left(165 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 935 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1410 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 2560 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 1410 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3840 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 935 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1536 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 165 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 256\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6} a^{2}}}{240 \, d}"," ",0,"1/240*(165*(d*x + c)/a^2 + 2*(165*tan(1/2*d*x + 1/2*c)^11 + 935*tan(1/2*d*x + 1/2*c)^9 + 1410*tan(1/2*d*x + 1/2*c)^7 + 2560*tan(1/2*d*x + 1/2*c)^6 - 1410*tan(1/2*d*x + 1/2*c)^5 + 3840*tan(1/2*d*x + 1/2*c)^4 - 935*tan(1/2*d*x + 1/2*c)^3 + 1536*tan(1/2*d*x + 1/2*c)^2 - 165*tan(1/2*d*x + 1/2*c) + 256)/((tan(1/2*d*x + 1/2*c)^2 + 1)^6*a^2))/d","A",0
422,1,127,0,0.219476," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{15 \, {\left(d x + c\right)}}{a^{2}} + \frac{2 \, {\left(15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 70 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 40 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 200 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 70 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5} a^{2}}}{20 \, d}"," ",0,"-1/20*(15*(d*x + c)/a^2 + 2*(15*tan(1/2*d*x + 1/2*c)^9 + 70*tan(1/2*d*x + 1/2*c)^7 + 40*tan(1/2*d*x + 1/2*c)^6 + 200*tan(1/2*d*x + 1/2*c)^4 - 70*tan(1/2*d*x + 1/2*c)^3 + 120*tan(1/2*d*x + 1/2*c)^2 - 15*tan(1/2*d*x + 1/2*c) + 24)/((tan(1/2*d*x + 1/2*c)^2 + 1)^5*a^2))/d","A",0
423,1,114,0,0.171635," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{21 \, {\left(d x + c\right)}}{a^{2}} + \frac{2 \, {\left(21 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 45 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 96 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 45 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 128 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 21 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 32\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4} a^{2}}}{24 \, d}"," ",0,"1/24*(21*(d*x + c)/a^2 + 2*(21*tan(1/2*d*x + 1/2*c)^7 + 45*tan(1/2*d*x + 1/2*c)^5 + 96*tan(1/2*d*x + 1/2*c)^4 - 45*tan(1/2*d*x + 1/2*c)^3 + 128*tan(1/2*d*x + 1/2*c)^2 - 21*tan(1/2*d*x + 1/2*c) + 32)/((tan(1/2*d*x + 1/2*c)^2 + 1)^4*a^2))/d","A",0
424,1,88,0,0.163037," ","integrate(cos(d*x+c)^4*sin(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(d x + c\right)}}{a^{2}} + \frac{2 \, {\left(3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 12 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} a^{2}}}{3 \, d}"," ",0,"-1/3*(3*(d*x + c)/a^2 + 2*(3*tan(1/2*d*x + 1/2*c)^5 + 3*tan(1/2*d*x + 1/2*c)^4 + 12*tan(1/2*d*x + 1/2*c)^2 - 3*tan(1/2*d*x + 1/2*c) + 5)/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*a^2))/d","A",0
425,1,52,0,0.188064," ","integrate(cos(d*x+c)^4*csc(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(d x + c\right)}}{a^{2}} - \frac{\log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} + \frac{2}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a^{2}}}{d}"," ",0,"-(2*(d*x + c)/a^2 - log(abs(tan(1/2*d*x + 1/2*c)))/a^2 + 2/((tan(1/2*d*x + 1/2*c)^2 + 1)*a^2))/d","A",0
426,1,73,0,0.191617," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(d x + c\right)}}{a^{2}} - \frac{4 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} + \frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{2}} + \frac{4 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1}{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}}{2 \, d}"," ",0,"1/2*(2*(d*x + c)/a^2 - 4*log(abs(tan(1/2*d*x + 1/2*c)))/a^2 + tan(1/2*d*x + 1/2*c)/a^2 + (4*tan(1/2*d*x + 1/2*c) - 1)/(a^2*tan(1/2*d*x + 1/2*c)))/d","B",0
427,1,98,0,0.215111," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{12 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} + \frac{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{4}} - \frac{18 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1}{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}}{8 \, d}"," ",0,"1/8*(12*log(abs(tan(1/2*d*x + 1/2*c)))/a^2 + (a^2*tan(1/2*d*x + 1/2*c)^2 - 8*a^2*tan(1/2*d*x + 1/2*c))/a^4 - (18*tan(1/2*d*x + 1/2*c)^2 - 8*tan(1/2*d*x + 1/2*c) + 1)/(a^2*tan(1/2*d*x + 1/2*c)^2))/d","A",0
428,1,128,0,0.218665," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{24 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} - \frac{44 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 21 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 6 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1}{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}} - \frac{a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 21 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{24 \, d}"," ",0,"-1/24*(24*log(abs(tan(1/2*d*x + 1/2*c)))/a^2 - (44*tan(1/2*d*x + 1/2*c)^3 - 21*tan(1/2*d*x + 1/2*c)^2 + 6*tan(1/2*d*x + 1/2*c) - 1)/(a^2*tan(1/2*d*x + 1/2*c)^3) - (a^4*tan(1/2*d*x + 1/2*c)^3 - 6*a^4*tan(1/2*d*x + 1/2*c)^2 + 21*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
429,1,157,0,0.237336," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{168 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} - \frac{350 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 144 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 48 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 16 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3}{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}} + \frac{3 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 16 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 48 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 144 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{8}}}{192 \, d}"," ",0,"1/192*(168*log(abs(tan(1/2*d*x + 1/2*c)))/a^2 - (350*tan(1/2*d*x + 1/2*c)^4 - 144*tan(1/2*d*x + 1/2*c)^3 + 48*tan(1/2*d*x + 1/2*c)^2 - 16*tan(1/2*d*x + 1/2*c) + 3)/(a^2*tan(1/2*d*x + 1/2*c)^4) + (3*a^6*tan(1/2*d*x + 1/2*c)^4 - 16*a^6*tan(1/2*d*x + 1/2*c)^3 + 48*a^6*tan(1/2*d*x + 1/2*c)^2 - 144*a^6*tan(1/2*d*x + 1/2*c))/a^8)/d","A",0
430,1,186,0,0.230201," ","integrate(cos(d*x+c)^4*csc(d*x+c)^6/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{120 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} - \frac{274 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 110 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 40 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 5 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1}{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}} - \frac{a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 5 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 15 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 110 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{10}}}{160 \, d}"," ",0,"-1/160*(120*log(abs(tan(1/2*d*x + 1/2*c)))/a^2 - (274*tan(1/2*d*x + 1/2*c)^5 - 110*tan(1/2*d*x + 1/2*c)^4 + 40*tan(1/2*d*x + 1/2*c)^3 - 15*tan(1/2*d*x + 1/2*c)^2 + 5*tan(1/2*d*x + 1/2*c) - 1)/(a^2*tan(1/2*d*x + 1/2*c)^5) - (a^8*tan(1/2*d*x + 1/2*c)^5 - 5*a^8*tan(1/2*d*x + 1/2*c)^4 + 15*a^8*tan(1/2*d*x + 1/2*c)^3 - 40*a^8*tan(1/2*d*x + 1/2*c)^2 + 110*a^8*tan(1/2*d*x + 1/2*c))/a^10)/d","A",0
431,1,215,0,0.267417," ","integrate(cos(d*x+c)^4*csc(d*x+c)^7/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{1320 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} - \frac{3234 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 1200 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 465 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 200 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 75 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 24 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5}{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6}} + \frac{5 \, a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 24 \, a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 75 \, a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 200 \, a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 465 \, a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1200 \, a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{12}}}{1920 \, d}"," ",0,"1/1920*(1320*log(abs(tan(1/2*d*x + 1/2*c)))/a^2 - (3234*tan(1/2*d*x + 1/2*c)^6 - 1200*tan(1/2*d*x + 1/2*c)^5 + 465*tan(1/2*d*x + 1/2*c)^4 - 200*tan(1/2*d*x + 1/2*c)^3 + 75*tan(1/2*d*x + 1/2*c)^2 - 24*tan(1/2*d*x + 1/2*c) + 5)/(a^2*tan(1/2*d*x + 1/2*c)^6) + (5*a^10*tan(1/2*d*x + 1/2*c)^6 - 24*a^10*tan(1/2*d*x + 1/2*c)^5 + 75*a^10*tan(1/2*d*x + 1/2*c)^4 - 200*a^10*tan(1/2*d*x + 1/2*c)^3 + 465*a^10*tan(1/2*d*x + 1/2*c)^2 - 1200*a^10*tan(1/2*d*x + 1/2*c))/a^12)/d","A",0
432,1,145,0,0.239796," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{51 \, {\left(d x + c\right)}}{a^{3}} + \frac{64}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}} + \frac{2 \, {\left(19 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 32 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 27 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 144 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 27 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 160 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 19 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 48\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4} a^{3}}}{8 \, d}"," ",0,"1/8*(51*(d*x + c)/a^3 + 64/(a^3*(tan(1/2*d*x + 1/2*c) + 1)) + 2*(19*tan(1/2*d*x + 1/2*c)^7 + 32*tan(1/2*d*x + 1/2*c)^6 + 27*tan(1/2*d*x + 1/2*c)^5 + 144*tan(1/2*d*x + 1/2*c)^4 - 27*tan(1/2*d*x + 1/2*c)^3 + 160*tan(1/2*d*x + 1/2*c)^2 - 19*tan(1/2*d*x + 1/2*c) + 48)/((tan(1/2*d*x + 1/2*c)^2 + 1)^4*a^3))/d","A",0
433,1,106,0,0.227445," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{33 \, {\left(d x + c\right)}}{a^{3}} + \frac{48}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}} + \frac{2 \, {\left(9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 24 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 60 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 28\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} a^{3}}}{6 \, d}"," ",0,"-1/6*(33*(d*x + c)/a^3 + 48/(a^3*(tan(1/2*d*x + 1/2*c) + 1)) + 2*(9*tan(1/2*d*x + 1/2*c)^5 + 24*tan(1/2*d*x + 1/2*c)^4 + 60*tan(1/2*d*x + 1/2*c)^2 - 9*tan(1/2*d*x + 1/2*c) + 28)/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*a^3))/d","A",0
434,1,91,0,0.204782," ","integrate(cos(d*x+c)^4*sin(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{9 \, {\left(d x + c\right)}}{a^{3}} + \frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{3}} + \frac{16}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}}{2 \, d}"," ",0,"1/2*(9*(d*x + c)/a^3 + 2*(tan(1/2*d*x + 1/2*c)^3 + 6*tan(1/2*d*x + 1/2*c)^2 - tan(1/2*d*x + 1/2*c) + 6)/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^3) + 16/(a^3*(tan(1/2*d*x + 1/2*c) + 1)))/d","A",0
435,1,47,0,0.207137," ","integrate(cos(d*x+c)^4*csc(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{d x + c}{a^{3}} + \frac{\log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} + \frac{8}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}}{d}"," ",0,"((d*x + c)/a^3 + log(abs(tan(1/2*d*x + 1/2*c)))/a^3 + 8/(a^3*(tan(1/2*d*x + 1/2*c) + 1)))/d","A",0
436,1,90,0,0.223727," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{6 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} - \frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3}} - \frac{3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 14 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} a^{3}}}{2 \, d}"," ",0,"-1/2*(6*log(abs(tan(1/2*d*x + 1/2*c)))/a^3 - tan(1/2*d*x + 1/2*c)/a^3 - (3*tan(1/2*d*x + 1/2*c)^2 - 14*tan(1/2*d*x + 1/2*c) - 1)/((tan(1/2*d*x + 1/2*c)^2 + tan(1/2*d*x + 1/2*c))*a^3))/d","A",0
437,1,116,0,0.248549," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{36 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} + \frac{64}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}} - \frac{54 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1}{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}} + \frac{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{8 \, d}"," ",0,"1/8*(36*log(abs(tan(1/2*d*x + 1/2*c)))/a^3 + 64/(a^3*(tan(1/2*d*x + 1/2*c) + 1)) - (54*tan(1/2*d*x + 1/2*c)^2 - 12*tan(1/2*d*x + 1/2*c) + 1)/(a^3*tan(1/2*d*x + 1/2*c)^2) + (a^3*tan(1/2*d*x + 1/2*c)^2 - 12*a^3*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
438,1,146,0,0.237643," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{132 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} + \frac{192}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}} - \frac{242 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 57 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1}{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}} - \frac{a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 57 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{9}}}{24 \, d}"," ",0,"-1/24*(132*log(abs(tan(1/2*d*x + 1/2*c)))/a^3 + 192/(a^3*(tan(1/2*d*x + 1/2*c) + 1)) - (242*tan(1/2*d*x + 1/2*c)^3 - 57*tan(1/2*d*x + 1/2*c)^2 + 9*tan(1/2*d*x + 1/2*c) - 1)/(a^3*tan(1/2*d*x + 1/2*c)^3) - (a^6*tan(1/2*d*x + 1/2*c)^3 - 9*a^6*tan(1/2*d*x + 1/2*c)^2 + 57*a^6*tan(1/2*d*x + 1/2*c))/a^9)/d","A",0
439,1,174,0,0.277860," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{408 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} + \frac{512}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}} - \frac{850 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 200 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1}{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}} + \frac{a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 8 \, a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 200 \, a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{12}}}{64 \, d}"," ",0,"1/64*(408*log(abs(tan(1/2*d*x + 1/2*c)))/a^3 + 512/(a^3*(tan(1/2*d*x + 1/2*c) + 1)) - (850*tan(1/2*d*x + 1/2*c)^4 - 200*tan(1/2*d*x + 1/2*c)^3 + 40*tan(1/2*d*x + 1/2*c)^2 - 8*tan(1/2*d*x + 1/2*c) + 1)/(a^3*tan(1/2*d*x + 1/2*c)^4) + (a^9*tan(1/2*d*x + 1/2*c)^4 - 8*a^9*tan(1/2*d*x + 1/2*c)^3 + 40*a^9*tan(1/2*d*x + 1/2*c)^2 - 200*a^9*tan(1/2*d*x + 1/2*c))/a^12)/d","A",0
440,1,92,0,0.292329," ","integrate(cos(f*x+e)^4*sin(f*x+e)/(a+a*sin(f*x+e))^6,x, algorithm=""giac"")","-\frac{2 \, {\left(35 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 35 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 70 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 14 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 7 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}}{35 \, a^{6} f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}^{7}}"," ",0,"-2/35*(35*tan(1/2*f*x + 1/2*e)^5 - 35*tan(1/2*f*x + 1/2*e)^4 + 70*tan(1/2*f*x + 1/2*e)^3 - 14*tan(1/2*f*x + 1/2*e)^2 + 7*tan(1/2*f*x + 1/2*e) + 1)/(a^6*f*(tan(1/2*f*x + 1/2*e) + 1)^7)","A",0
441,1,106,0,0.380402," ","integrate(cos(f*x+e)^4*sin(f*x+e)^2/(a+a*sin(f*x+e))^7,x, algorithm=""giac"")","-\frac{4 \, {\left(210 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 315 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 441 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 126 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 36 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 9 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}}{315 \, a^{7} f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}^{9}}"," ",0,"-4/315*(210*tan(1/2*f*x + 1/2*e)^6 - 315*tan(1/2*f*x + 1/2*e)^5 + 441*tan(1/2*f*x + 1/2*e)^4 - 126*tan(1/2*f*x + 1/2*e)^3 + 36*tan(1/2*f*x + 1/2*e)^2 + 9*tan(1/2*f*x + 1/2*e) + 1)/(a^7*f*(tan(1/2*f*x + 1/2*e) + 1)^9)","A",0
442,1,120,0,0.475582," ","integrate(cos(f*x+e)^4*sin(f*x+e)^3/(a+a*sin(f*x+e))^8,x, algorithm=""giac"")","-\frac{4 \, {\left(1155 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} - 2079 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 2541 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 825 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 165 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 55 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 11 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}}{1155 \, a^{8} f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}^{11}}"," ",0,"-4/1155*(1155*tan(1/2*f*x + 1/2*e)^7 - 2079*tan(1/2*f*x + 1/2*e)^6 + 2541*tan(1/2*f*x + 1/2*e)^5 - 825*tan(1/2*f*x + 1/2*e)^4 + 165*tan(1/2*f*x + 1/2*e)^3 + 55*tan(1/2*f*x + 1/2*e)^2 + 11*tan(1/2*f*x + 1/2*e) + 1)/(a^8*f*(tan(1/2*f*x + 1/2*e) + 1)^11)","A",0
443,1,219,0,0.285027," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2*(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{1}{1441440} \, \sqrt{2} \sqrt{a} {\left(\frac{4095 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{11}{2} \, d x + \frac{11}{2} \, c\right)}{d} + \frac{12870 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} - \frac{15015 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{3465 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{13}{2} \, d x + \frac{13}{2} \, c\right)}{d} + \frac{10010 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} - \frac{9009 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} - \frac{180180 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)}"," ",0,"-1/1441440*sqrt(2)*sqrt(a)*(4095*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 11/2*d*x + 11/2*c)/d + 12870*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 7/2*d*x + 7/2*c)/d - 15015*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 3/2*d*x + 3/2*c)/d + 3465*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 13/2*d*x + 13/2*c)/d + 10010*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 9/2*d*x + 9/2*c)/d - 9009*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 5/2*d*x + 5/2*c)/d - 180180*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 1/2*d*x + 1/2*c)/d)","A",0
444,1,189,0,0.254110," ","integrate(cos(d*x+c)^4*sin(d*x+c)*(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{1}{55440} \, \sqrt{2} \sqrt{a} {\left(\frac{385 \, \cos\left(\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{2079 \, \cos\left(\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{6930 \, \cos\left(\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{315 \, \cos\left(-\frac{1}{4} \, \pi + \frac{11}{2} \, d x + \frac{11}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{1485 \, \cos\left(-\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{2310 \, \cos\left(-\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d}\right)}"," ",0,"-1/55440*sqrt(2)*sqrt(a)*(385*cos(1/4*pi + 9/2*d*x + 9/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 2079*cos(1/4*pi + 5/2*d*x + 5/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 6930*cos(1/4*pi + 1/2*d*x + 1/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 315*cos(-1/4*pi + 11/2*d*x + 11/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 1485*cos(-1/4*pi + 7/2*d*x + 7/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 2310*cos(-1/4*pi + 3/2*d*x + 3/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d)","A",0
445,-1,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)*(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
446,-1,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2*(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
447,-1,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3*(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
448,-1,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4*(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
449,-1,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5*(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
450,-1,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^6*(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
451,-1,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^7*(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
452,-1,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^8*(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
453,1,474,0,1.429041," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2*(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{1}{2882880} \, \sqrt{2} {\left(\frac{3465 \, a \cos\left(\frac{1}{4} \, \pi + \frac{13}{2} \, d x + \frac{13}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{5005 \, a \cos\left(\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{27027 \, a \cos\left(\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{135135 \, a \cos\left(\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{3003 \, a \cos\left(-\frac{1}{4} \, \pi + \frac{15}{2} \, d x + \frac{15}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{4095 \, a \cos\left(-\frac{1}{4} \, \pi + \frac{11}{2} \, d x + \frac{11}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{19305 \, a \cos\left(-\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{45045 \, a \cos\left(-\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{8190 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{11}{2} \, d x + \frac{11}{2} \, c\right)}{d} - \frac{25740 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} + \frac{30030 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} - \frac{6930 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{13}{2} \, d x + \frac{13}{2} \, c\right)}{d} - \frac{20020 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} + \frac{18018 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{360360 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/2882880*sqrt(2)*(3465*a*cos(1/4*pi + 13/2*d*x + 13/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 5005*a*cos(1/4*pi + 9/2*d*x + 9/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 27027*a*cos(1/4*pi + 5/2*d*x + 5/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 135135*a*cos(1/4*pi + 1/2*d*x + 1/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 3003*a*cos(-1/4*pi + 15/2*d*x + 15/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 4095*a*cos(-1/4*pi + 11/2*d*x + 11/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 19305*a*cos(-1/4*pi + 7/2*d*x + 7/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 45045*a*cos(-1/4*pi + 3/2*d*x + 3/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 8190*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 11/2*d*x + 11/2*c)/d - 25740*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 7/2*d*x + 7/2*c)/d + 30030*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 3/2*d*x + 3/2*c)/d - 6930*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 13/2*d*x + 13/2*c)/d - 20020*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 9/2*d*x + 9/2*c)/d + 18018*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 5/2*d*x + 5/2*c)/d + 360360*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 1/2*d*x + 1/2*c)/d)*sqrt(a)","B",0
454,1,412,0,0.809402," ","integrate(cos(d*x+c)^4*sin(d*x+c)*(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{1}{1441440} \, \sqrt{2} {\left(\frac{10010 \, a \cos\left(\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{54054 \, a \cos\left(\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{180180 \, a \cos\left(\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{8190 \, a \cos\left(-\frac{1}{4} \, \pi + \frac{11}{2} \, d x + \frac{11}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{38610 \, a \cos\left(-\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{60060 \, a \cos\left(-\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{4095 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{11}{2} \, d x + \frac{11}{2} \, c\right)}{d} + \frac{12870 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} - \frac{15015 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{3465 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{13}{2} \, d x + \frac{13}{2} \, c\right)}{d} + \frac{10010 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} - \frac{9009 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} - \frac{180180 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"-1/1441440*sqrt(2)*(10010*a*cos(1/4*pi + 9/2*d*x + 9/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 54054*a*cos(1/4*pi + 5/2*d*x + 5/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 180180*a*cos(1/4*pi + 1/2*d*x + 1/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 8190*a*cos(-1/4*pi + 11/2*d*x + 11/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 38610*a*cos(-1/4*pi + 7/2*d*x + 7/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 60060*a*cos(-1/4*pi + 3/2*d*x + 3/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 4095*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 11/2*d*x + 11/2*c)/d + 12870*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 7/2*d*x + 7/2*c)/d - 15015*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 3/2*d*x + 3/2*c)/d + 3465*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 13/2*d*x + 13/2*c)/d + 10010*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 9/2*d*x + 9/2*c)/d - 9009*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 5/2*d*x + 5/2*c)/d - 180180*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 1/2*d*x + 1/2*c)/d)*sqrt(a)","B",0
455,-1,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)*(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
456,-1,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2*(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
457,-1,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3*(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
458,-1,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4*(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
459,-1,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5*(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
460,-1,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^6*(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
461,-1,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^7*(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
462,-1,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^8*(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
463,-1,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^9*(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
464,1,342,0,0.809988," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{8 \, {\left(\frac{76 \, \sqrt{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{\sqrt{a}} - \frac{\frac{34 \, a^{5}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{187 \, a^{5}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{1155 \, a^{5}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{1287 \, a^{5}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{231 \, a^{5}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{231 \, a^{5}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{1287 \, a^{5}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{1155 \, a^{5}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - 17 \, {\left(\frac{2 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{11 \, a^{5}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{11}{2}}}\right)}}{3465 \, d}"," ",0,"8/3465*(76*sqrt(2)*sgn(tan(1/2*d*x + 1/2*c) + 1)/sqrt(a) - (34*a^5/sgn(tan(1/2*d*x + 1/2*c) + 1) + (187*a^5/sgn(tan(1/2*d*x + 1/2*c) + 1) - (1155*a^5/sgn(tan(1/2*d*x + 1/2*c) + 1) - (1287*a^5/sgn(tan(1/2*d*x + 1/2*c) + 1) + (231*a^5/sgn(tan(1/2*d*x + 1/2*c) + 1) - (231*a^5/sgn(tan(1/2*d*x + 1/2*c) + 1) + (1287*a^5/sgn(tan(1/2*d*x + 1/2*c) + 1) - (1155*a^5/sgn(tan(1/2*d*x + 1/2*c) + 1) - 17*(2*a^5*tan(1/2*d*x + 1/2*c)^2/sgn(tan(1/2*d*x + 1/2*c) + 1) + 11*a^5/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c)^2)/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(11/2))/d","B",0
465,1,279,0,0.601904," ","integrate(cos(d*x+c)^4*sin(d*x+c)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{4 \, {\left(\frac{8 \, \sqrt{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{\sqrt{a}} + \frac{\frac{13 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{99 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{105 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{63 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{63 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{105 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{13 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{99 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{9}{2}}}\right)}}{315 \, d}"," ",0,"-4/315*(8*sqrt(2)*sgn(tan(1/2*d*x + 1/2*c) + 1)/sqrt(a) + (13*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) - (99*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) - (105*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) + (63*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) - (63*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) + (105*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) + (13*a^4*tan(1/2*d*x + 1/2*c)^2/sgn(tan(1/2*d*x + 1/2*c) + 1) - 99*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c)^2)/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(9/2))/d","B",0
466,1,386,0,0.697302," ","integrate(cos(d*x+c)^4*csc(d*x+c)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\frac{{\left(30 \, a \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - 15 \, \sqrt{-a} \sqrt{a} \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) + 26 \, \sqrt{2} \sqrt{-a} \sqrt{a}\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{\sqrt{-a} a} - \frac{30 \, \arctan\left(-\frac{\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{15 \, \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{2 \, {\left({\left({\left({\left({\left(\frac{17 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{15 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{20 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{20 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{15 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{17 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{5}{2}}}}{15 \, d}"," ",0,"-1/15*((30*a*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - 15*sqrt(-a)*sqrt(a)*log(sqrt(2)*sqrt(a) + sqrt(a)) + 26*sqrt(2)*sqrt(-a)*sqrt(a))*sgn(tan(1/2*d*x + 1/2*c) + 1)/(sqrt(-a)*a) - 30*arctan(-(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))/sqrt(-a))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 15*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(a)*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 2*(((((17*a^2*tan(1/2*d*x + 1/2*c)/sgn(tan(1/2*d*x + 1/2*c) + 1) - 15*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 20*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) - 20*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 15*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) - 17*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(5/2))/d","B",0
467,1,476,0,0.798706," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\frac{{\left(6 \, \sqrt{2} a \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - 3 \, \sqrt{2} \sqrt{-a} \sqrt{a} \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) + 6 \, a \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - 3 \, \sqrt{-a} \sqrt{a} \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) - 11 \, \sqrt{2} \sqrt{-a} \sqrt{a} - 25 \, \sqrt{-a} \sqrt{a}\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{\sqrt{2} \sqrt{-a} a + \sqrt{-a} a} + \frac{{\left({\left({\left(\frac{3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{4 \, a}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{18 \, a}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{12 \, a}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{7 \, a}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{3}{2}}} - \frac{6 \, \arctan\left(-\frac{\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{3 \, \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{6 \, \sqrt{a}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{6 \, d}"," ",0,"1/6*((6*sqrt(2)*a*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - 3*sqrt(2)*sqrt(-a)*sqrt(a)*log(sqrt(2)*sqrt(a) + sqrt(a)) + 6*a*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - 3*sqrt(-a)*sqrt(a)*log(sqrt(2)*sqrt(a) + sqrt(a)) - 11*sqrt(2)*sqrt(-a)*sqrt(a) - 25*sqrt(-a)*sqrt(a))*sgn(tan(1/2*d*x + 1/2*c) + 1)/(sqrt(2)*sqrt(-a)*a + sqrt(-a)*a) + ((((3*a*tan(1/2*d*x + 1/2*c)/sgn(tan(1/2*d*x + 1/2*c) + 1) - 4*a/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 18*a/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) - 12*a/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 7*a/sgn(tan(1/2*d*x + 1/2*c) + 1))/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(3/2) - 6*arctan(-(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))/sqrt(-a))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 3*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(a)*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 6*sqrt(a)/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a)*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
468,1,554,0,0.794949," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\frac{{\left(36 \, \sqrt{2} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - 18 \, \sqrt{2} \sqrt{-a} \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) + 54 \, \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - 27 \, \sqrt{-a} \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) + 62 \, \sqrt{2} \sqrt{-a} + 82 \, \sqrt{-a}\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{2 \, \sqrt{2} \sqrt{-a} \sqrt{a} + 3 \, \sqrt{-a} \sqrt{a}} + \frac{{\left({\left(\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{2}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{17}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{18}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}} - \frac{18 \, \arctan\left(-\frac{\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{9 \, \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{2 \, {\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{3} - 2 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} \sqrt{a} + {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a + 2 \, a^{\frac{3}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a\right)}^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{8 \, d}"," ",0,"1/8*((36*sqrt(2)*sqrt(a)*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - 18*sqrt(2)*sqrt(-a)*log(sqrt(2)*sqrt(a) + sqrt(a)) + 54*sqrt(a)*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - 27*sqrt(-a)*log(sqrt(2)*sqrt(a) + sqrt(a)) + 62*sqrt(2)*sqrt(-a) + 82*sqrt(-a))*sgn(tan(1/2*d*x + 1/2*c) + 1)/(2*sqrt(2)*sqrt(-a)*sqrt(a) + 3*sqrt(-a)*sqrt(a)) + (((tan(1/2*d*x + 1/2*c)/sgn(tan(1/2*d*x + 1/2*c) + 1) - 2/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 17/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) - 18/sgn(tan(1/2*d*x + 1/2*c) + 1))/sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) - 18*arctan(-(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))/sqrt(-a))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 9*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(a)*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 2*((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^3 - 2*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*sqrt(a) + (sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a + 2*a^(3/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a)^2*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
469,1,583,0,0.803892," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left({\left(\frac{2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{3}{a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{22}{a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} - \frac{{\left(210 \, \sqrt{2} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - 105 \, \sqrt{2} \sqrt{-a} \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) + 294 \, \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - 147 \, \sqrt{-a} \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) - 128 \, \sqrt{2} \sqrt{-a} - 186 \, \sqrt{-a}\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{5 \, \sqrt{2} \sqrt{-a} \sqrt{a} + 7 \, \sqrt{-a} \sqrt{a}} + \frac{42 \, \arctan\left(-\frac{\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{21 \, \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{2 \, {\left(3 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{5} + 18 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} \sqrt{a} - 48 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a^{\frac{3}{2}} - 3 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a^{2} + 22 \, a^{\frac{5}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a\right)}^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{48 \, d}"," ",0,"1/48*(sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)*((2*tan(1/2*d*x + 1/2*c)/(a*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 3/(a*sgn(tan(1/2*d*x + 1/2*c) + 1)))*tan(1/2*d*x + 1/2*c) - 22/(a*sgn(tan(1/2*d*x + 1/2*c) + 1))) - (210*sqrt(2)*sqrt(a)*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - 105*sqrt(2)*sqrt(-a)*log(sqrt(2)*sqrt(a) + sqrt(a)) + 294*sqrt(a)*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - 147*sqrt(-a)*log(sqrt(2)*sqrt(a) + sqrt(a)) - 128*sqrt(2)*sqrt(-a) - 186*sqrt(-a))*sgn(tan(1/2*d*x + 1/2*c) + 1)/(5*sqrt(2)*sqrt(-a)*sqrt(a) + 7*sqrt(-a)*sqrt(a)) + 42*arctan(-(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))/sqrt(-a))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 21*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(a)*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 2*(3*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^5 + 18*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4*sqrt(a) - 48*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a^(3/2) - 3*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a^2 + 22*a^(5/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a)^3*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
470,1,736,0,0.923237," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left({\left(2 \, {\left(\frac{3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{4}{a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{33}{a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{64}{a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} - \frac{{\left(792 \, \sqrt{2} a^{\frac{3}{2}} \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - 396 \, \sqrt{2} \sqrt{-a} a \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) + 1122 \, a^{\frac{3}{2}} \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - 561 \, \sqrt{-a} a \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) + 2054 \, \sqrt{2} \sqrt{-a} a + 2896 \, \sqrt{-a} a\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{12 \, \sqrt{2} \sqrt{-a} a^{\frac{3}{2}} + 17 \, \sqrt{-a} a^{\frac{3}{2}}} + \frac{66 \, \arctan\left(-\frac{\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{33 \, \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{2 \, {\left(33 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{7} - 48 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} \sqrt{a} - 57 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{5} a + 192 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} a^{\frac{3}{2}} - 57 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{3} a^{2} - 208 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a^{\frac{5}{2}} + 33 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a^{3} + 64 \, a^{\frac{7}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a\right)}^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{384 \, d}"," ",0,"1/384*(sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)*((2*(3*tan(1/2*d*x + 1/2*c)/(a*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 4/(a*sgn(tan(1/2*d*x + 1/2*c) + 1)))*tan(1/2*d*x + 1/2*c) - 33/(a*sgn(tan(1/2*d*x + 1/2*c) + 1)))*tan(1/2*d*x + 1/2*c) + 64/(a*sgn(tan(1/2*d*x + 1/2*c) + 1))) - (792*sqrt(2)*a^(3/2)*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - 396*sqrt(2)*sqrt(-a)*a*log(sqrt(2)*sqrt(a) + sqrt(a)) + 1122*a^(3/2)*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - 561*sqrt(-a)*a*log(sqrt(2)*sqrt(a) + sqrt(a)) + 2054*sqrt(2)*sqrt(-a)*a + 2896*sqrt(-a)*a)*sgn(tan(1/2*d*x + 1/2*c) + 1)/(12*sqrt(2)*sqrt(-a)*a^(3/2) + 17*sqrt(-a)*a^(3/2)) + 66*arctan(-(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))/sqrt(-a))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 33*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(a)*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 2*(33*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^7 - 48*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^6*sqrt(a) - 57*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^5*a + 192*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4*a^(3/2) - 57*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^3*a^2 - 208*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a^(5/2) + 33*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a^3 + 64*a^(7/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a)^4*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
471,1,802,0,0.951943," ","integrate(cos(d*x+c)^4*csc(d*x+c)^6/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left({\left(2 \, {\left({\left(\frac{4 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{5}{a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{12}{a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{35}{a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{32}{a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} - \frac{{\left(2610 \, \sqrt{2} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - 1305 \, \sqrt{2} \sqrt{-a} \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) + 3690 \, \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - 1845 \, \sqrt{-a} \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) - 5058 \, \sqrt{2} \sqrt{-a} - 7156 \, \sqrt{-a}\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{29 \, \sqrt{2} \sqrt{-a} \sqrt{a} + 41 \, \sqrt{-a} \sqrt{a}} + \frac{90 \, \arctan\left(-\frac{\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{45 \, \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{2 \, {\left(35 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{9} - 80 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} \sqrt{a} - 110 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{7} a + 240 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} a^{\frac{3}{2}} - 80 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} a^{\frac{5}{2}} + 110 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{3} a^{3} + 80 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a^{\frac{7}{2}} - 35 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a^{4} - 32 \, a^{\frac{9}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a\right)}^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{1280 \, d}"," ",0,"1/1280*(sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)*((2*((4*tan(1/2*d*x + 1/2*c)/(a*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 5/(a*sgn(tan(1/2*d*x + 1/2*c) + 1)))*tan(1/2*d*x + 1/2*c) - 12/(a*sgn(tan(1/2*d*x + 1/2*c) + 1)))*tan(1/2*d*x + 1/2*c) + 35/(a*sgn(tan(1/2*d*x + 1/2*c) + 1)))*tan(1/2*d*x + 1/2*c) - 32/(a*sgn(tan(1/2*d*x + 1/2*c) + 1))) - (2610*sqrt(2)*sqrt(a)*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - 1305*sqrt(2)*sqrt(-a)*log(sqrt(2)*sqrt(a) + sqrt(a)) + 3690*sqrt(a)*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - 1845*sqrt(-a)*log(sqrt(2)*sqrt(a) + sqrt(a)) - 5058*sqrt(2)*sqrt(-a) - 7156*sqrt(-a))*sgn(tan(1/2*d*x + 1/2*c) + 1)/(29*sqrt(2)*sqrt(-a)*sqrt(a) + 41*sqrt(-a)*sqrt(a)) + 90*arctan(-(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))/sqrt(-a))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 45*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(a)*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 2*(35*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^9 - 80*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^8*sqrt(a) - 110*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^7*a + 240*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^6*a^(3/2) - 80*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4*a^(5/2) + 110*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^3*a^3 + 80*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a^(7/2) - 35*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a^4 - 32*a^(9/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a)^5*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
472,1,286,0,0.727353," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3/(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{8 \, {\left(\frac{59 \, \sqrt{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a^{\frac{3}{2}}} + \frac{2 \, {\left(\frac{2 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{11 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{264 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{693 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{693 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{264 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{2 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{11 \, a^{4}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{11}{2}}}\right)}}{1155 \, d}"," ",0,"-8/1155*(59*sqrt(2)*sgn(tan(1/2*d*x + 1/2*c) + 1)/a^(3/2) + 2*(2*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) + (11*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) - (264*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) - (693*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) - (693*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) - (264*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) - (2*a^4*tan(1/2*d*x + 1/2*c)^2/sgn(tan(1/2*d*x + 1/2*c) + 1) + 11*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c)^2)*tan(1/2*d*x + 1/2*c)^2)/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(11/2))/d","A",0
473,1,282,0,0.719076," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2/(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{8 \, {\left(\frac{23 \, \sqrt{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a^{\frac{3}{2}}} - \frac{{\left(\frac{9 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{105 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{252 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{252 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{105 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{2 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{9 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{2 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{9}{2}}}\right)}}{315 \, d}"," ",0,"8/315*(23*sqrt(2)*sgn(tan(1/2*d*x + 1/2*c) + 1)/a^(3/2) - ((9*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1) - (105*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1) - (252*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1) - (252*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1) - (105*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1) - (2*a^3*tan(1/2*d*x + 1/2*c)^2/sgn(tan(1/2*d*x + 1/2*c) + 1) + 9*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c)^2 + 2*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1))/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(9/2))/d","B",0
474,1,216,0,0.672979," ","integrate(cos(d*x+c)^4*sin(d*x+c)/(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{4 \, {\left(\frac{6 \, \sqrt{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a^{\frac{3}{2}}} - \frac{{\left({\left({\left({\left(\frac{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{14 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{35 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{35 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{14 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{7}{2}}}\right)}}{35 \, d}"," ",0,"-4/35*(6*sqrt(2)*sgn(tan(1/2*d*x + 1/2*c) + 1)/a^(3/2) - (((((a^2*tan(1/2*d*x + 1/2*c)^2/sgn(tan(1/2*d*x + 1/2*c) + 1) - 14*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 35*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) - 35*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 14*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c)^2 - a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(7/2))/d","B",0
475,1,313,0,0.835488," ","integrate(cos(d*x+c)^4*csc(d*x+c)/(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{\frac{{\left(6 \, \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - 3 \, \sqrt{-a} \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) + 10 \, \sqrt{2} \sqrt{-a}\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{\sqrt{-a} a^{\frac{3}{2}}} + \frac{4 \, {\left({\left({\left(\frac{2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{3}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{3}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{2}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{3}{2}}} - \frac{6 \, \arctan\left(-\frac{\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{3 \, \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{3}{2}} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{3 \, d}"," ",0,"-1/3*((6*sqrt(a)*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - 3*sqrt(-a)*log(sqrt(2)*sqrt(a) + sqrt(a)) + 10*sqrt(2)*sqrt(-a))*sgn(tan(1/2*d*x + 1/2*c) + 1)/(sqrt(-a)*a^(3/2)) + 4*(((2*tan(1/2*d*x + 1/2*c)/sgn(tan(1/2*d*x + 1/2*c) + 1) - 3/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 3/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) - 2/sgn(tan(1/2*d*x + 1/2*c) + 1))/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(3/2) - 6*arctan(-(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))/sqrt(-a))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 3*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/(a^(3/2)*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
476,1,424,0,0.851685," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2/(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\frac{{\left(6 \, \sqrt{2} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - 3 \, \sqrt{2} \sqrt{-a} \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) + 6 \, \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - 3 \, \sqrt{-a} \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) + 3 \, \sqrt{2} \sqrt{-a} + 5 \, \sqrt{-a}\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{\sqrt{2} \sqrt{-a} a^{\frac{3}{2}} + \sqrt{-a} a^{\frac{3}{2}}} + \frac{{\left(\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{4}{a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{3}{a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}} - \frac{6 \, \arctan\left(-\frac{\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{3 \, \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{3}{2}} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{2}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a\right)} \sqrt{a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{2 \, d}"," ",0,"1/2*((6*sqrt(2)*sqrt(a)*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - 3*sqrt(2)*sqrt(-a)*log(sqrt(2)*sqrt(a) + sqrt(a)) + 6*sqrt(a)*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - 3*sqrt(-a)*log(sqrt(2)*sqrt(a) + sqrt(a)) + 3*sqrt(2)*sqrt(-a) + 5*sqrt(-a))*sgn(tan(1/2*d*x + 1/2*c) + 1)/(sqrt(2)*sqrt(-a)*a^(3/2) + sqrt(-a)*a^(3/2)) + ((tan(1/2*d*x + 1/2*c)/(a*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 4/(a*sgn(tan(1/2*d*x + 1/2*c) + 1)))*tan(1/2*d*x + 1/2*c) - 3/(a*sgn(tan(1/2*d*x + 1/2*c) + 1)))/sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) - 6*arctan(-(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))/sqrt(-a))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 3*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/(a^(3/2)*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 2/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a)*sqrt(a)*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
477,1,513,0,0.886614," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3/(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left(\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{6}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} - \frac{{\left(12 \, \sqrt{2} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - 6 \, \sqrt{2} \sqrt{-a} \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) + 18 \, \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - 9 \, \sqrt{-a} \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) - 30 \, \sqrt{2} \sqrt{-a} - 38 \, \sqrt{-a}\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{2 \, \sqrt{2} \sqrt{-a} a^{\frac{3}{2}} + 3 \, \sqrt{-a} a^{\frac{3}{2}}} + \frac{6 \, \arctan\left(-\frac{\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{3 \, \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{3}{2}} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{2 \, {\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{3} - 6 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} \sqrt{a} + {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a + 6 \, a^{\frac{3}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a\right)}^{2} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{8 \, d}"," ",0,"1/8*(sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)*(tan(1/2*d*x + 1/2*c)/(a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 6/(a^2*sgn(tan(1/2*d*x + 1/2*c) + 1))) - (12*sqrt(2)*sqrt(a)*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - 6*sqrt(2)*sqrt(-a)*log(sqrt(2)*sqrt(a) + sqrt(a)) + 18*sqrt(a)*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - 9*sqrt(-a)*log(sqrt(2)*sqrt(a) + sqrt(a)) - 30*sqrt(2)*sqrt(-a) - 38*sqrt(-a))*sgn(tan(1/2*d*x + 1/2*c) + 1)/(2*sqrt(2)*sqrt(-a)*a^(3/2) + 3*sqrt(-a)*a^(3/2)) + 6*arctan(-(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))/sqrt(-a))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 3*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/(a^(3/2)*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 2*((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^3 - 6*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*sqrt(a) + (sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a + 6*a^(3/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a)^2*a*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
478,1,589,0,0.952148," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4/(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left({\left(\frac{2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{9}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{14}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} - \frac{{\left(30 \, \sqrt{2} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - 15 \, \sqrt{2} \sqrt{-a} \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) + 42 \, \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - 21 \, \sqrt{-a} \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) + 280 \, \sqrt{2} \sqrt{-a} + 402 \, \sqrt{-a}\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{5 \, \sqrt{2} \sqrt{-a} a^{\frac{3}{2}} + 7 \, \sqrt{-a} a^{\frac{3}{2}}} + \frac{6 \, \arctan\left(-\frac{\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{3 \, \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{3}{2}} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{2 \, {\left(9 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{5} - 18 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} \sqrt{a} + 24 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a^{\frac{3}{2}} - 9 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a^{2} - 14 \, a^{\frac{5}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a\right)}^{3} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{48 \, d}"," ",0,"1/48*(sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)*((2*tan(1/2*d*x + 1/2*c)/(a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 9/(a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)))*tan(1/2*d*x + 1/2*c) + 14/(a^2*sgn(tan(1/2*d*x + 1/2*c) + 1))) - (30*sqrt(2)*sqrt(a)*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - 15*sqrt(2)*sqrt(-a)*log(sqrt(2)*sqrt(a) + sqrt(a)) + 42*sqrt(a)*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - 21*sqrt(-a)*log(sqrt(2)*sqrt(a) + sqrt(a)) + 280*sqrt(2)*sqrt(-a) + 402*sqrt(-a))*sgn(tan(1/2*d*x + 1/2*c) + 1)/(5*sqrt(2)*sqrt(-a)*a^(3/2) + 7*sqrt(-a)*a^(3/2)) + 6*arctan(-(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))/sqrt(-a))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 3*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/(a^(3/2)*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 2*(9*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^5 - 18*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4*sqrt(a) + 24*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a^(3/2) - 9*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a^2 - 14*a^(5/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a)^3*a*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
479,1,737,0,1.106560," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5/(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left({\left(2 \, {\left(\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{4}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{13}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{16}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} - \frac{{\left(72 \, \sqrt{2} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - 36 \, \sqrt{2} \sqrt{-a} \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) + 102 \, \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - 51 \, \sqrt{-a} \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) - 1134 \, \sqrt{2} \sqrt{-a} - 1600 \, \sqrt{-a}\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{12 \, \sqrt{2} \sqrt{-a} a^{\frac{3}{2}} + 17 \, \sqrt{-a} a^{\frac{3}{2}}} + \frac{6 \, \arctan\left(-\frac{\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{3 \, \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{3}{2}} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{2 \, {\left(13 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{7} - 32 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} \sqrt{a} - 5 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{5} a + 48 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} a^{\frac{3}{2}} - 5 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{3} a^{2} - 32 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a^{\frac{5}{2}} + 13 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a^{3} + 16 \, a^{\frac{7}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a\right)}^{4} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{128 \, d}"," ",0,"1/128*(sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)*((2*(tan(1/2*d*x + 1/2*c)/(a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 4/(a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)))*tan(1/2*d*x + 1/2*c) + 13/(a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)))*tan(1/2*d*x + 1/2*c) - 16/(a^2*sgn(tan(1/2*d*x + 1/2*c) + 1))) - (72*sqrt(2)*sqrt(a)*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - 36*sqrt(2)*sqrt(-a)*log(sqrt(2)*sqrt(a) + sqrt(a)) + 102*sqrt(a)*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - 51*sqrt(-a)*log(sqrt(2)*sqrt(a) + sqrt(a)) - 1134*sqrt(2)*sqrt(-a) - 1600*sqrt(-a))*sgn(tan(1/2*d*x + 1/2*c) + 1)/(12*sqrt(2)*sqrt(-a)*a^(3/2) + 17*sqrt(-a)*a^(3/2)) + 6*arctan(-(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))/sqrt(-a))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 3*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/(a^(3/2)*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 2*(13*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^7 - 32*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^6*sqrt(a) - 5*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^5*a + 48*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4*a^(3/2) - 5*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^3*a^2 - 32*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a^(5/2) + 13*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a^3 + 16*a^(7/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a)^4*a*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
480,1,808,0,1.155685," ","integrate(cos(d*x+c)^4*csc(d*x+c)^6/(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left({\left(2 \, {\left({\left(\frac{4 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{15}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{28}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{95}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{128}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} - \frac{{\left(870 \, \sqrt{2} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - 435 \, \sqrt{2} \sqrt{-a} \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) + 1230 \, \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - 615 \, \sqrt{-a} \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) + 22282 \, \sqrt{2} \sqrt{-a} + 31524 \, \sqrt{-a}\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{29 \, \sqrt{2} \sqrt{-a} a^{\frac{3}{2}} + 41 \, \sqrt{-a} a^{\frac{3}{2}}} + \frac{30 \, \arctan\left(-\frac{\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{15 \, \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{3}{2}} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{2 \, {\left(95 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{9} - 240 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{8} \sqrt{a} - 70 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{7} a + 560 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} a^{\frac{3}{2}} - 720 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} a^{\frac{5}{2}} + 70 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{3} a^{3} + 400 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a^{\frac{7}{2}} - 95 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a^{4} - 128 \, a^{\frac{9}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a\right)}^{5} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{1280 \, d}"," ",0,"1/1280*(sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)*((2*((4*tan(1/2*d*x + 1/2*c)/(a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 15/(a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)))*tan(1/2*d*x + 1/2*c) + 28/(a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)))*tan(1/2*d*x + 1/2*c) - 95/(a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)))*tan(1/2*d*x + 1/2*c) + 128/(a^2*sgn(tan(1/2*d*x + 1/2*c) + 1))) - (870*sqrt(2)*sqrt(a)*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - 435*sqrt(2)*sqrt(-a)*log(sqrt(2)*sqrt(a) + sqrt(a)) + 1230*sqrt(a)*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - 615*sqrt(-a)*log(sqrt(2)*sqrt(a) + sqrt(a)) + 22282*sqrt(2)*sqrt(-a) + 31524*sqrt(-a))*sgn(tan(1/2*d*x + 1/2*c) + 1)/(29*sqrt(2)*sqrt(-a)*a^(3/2) + 41*sqrt(-a)*a^(3/2)) + 30*arctan(-(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))/sqrt(-a))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 15*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/(a^(3/2)*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 2*(95*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^9 - 240*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^8*sqrt(a) - 70*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^7*a + 560*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^6*a^(3/2) - 720*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4*a^(5/2) + 70*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^3*a^3 + 400*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a^(7/2) - 95*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a^4 - 128*a^(9/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a)^5*a*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
481,1,504,0,0.956174," ","integrate(cos(d*x+c)^4*sin(d*x+c)^4/(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{8 \, {\left(\frac{\sqrt{2} {\left(693 \, a \arctan\left(\frac{\sqrt{a}}{\sqrt{-a}}\right) + 746 \, \sqrt{-a} \sqrt{a}\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{\sqrt{-a} a^{3}} - \frac{693 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{\frac{431 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{693 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{2717 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{3927 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{7326 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{8778 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{8778 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{7326 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{3927 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - {\left(\frac{2717 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + {\left(\frac{431 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{693 \, a^{3}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{11}{2}}}\right)}}{693 \, d}"," ",0,"-8/693*(sqrt(2)*(693*a*arctan(sqrt(a)/sqrt(-a)) + 746*sqrt(-a)*sqrt(a))*sgn(tan(1/2*d*x + 1/2*c) + 1)/(sqrt(-a)*a^3) - 693*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/sqrt(-a))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)) - (431*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1) - (693*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1) - (2717*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1) - (3927*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1) - (7326*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1) - (8778*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1) - (8778*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1) - (7326*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1) - (3927*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1) - (2717*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1) + (431*a^3*tan(1/2*d*x + 1/2*c)/sgn(tan(1/2*d*x + 1/2*c) + 1) - 693*a^3/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(11/2))/d","B",0
482,1,434,0,0.906046," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3/(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{8 \, {\left(\frac{\sqrt{2} {\left(315 \, a \arctan\left(\frac{\sqrt{a}}{\sqrt{-a}}\right) + 323 \, \sqrt{-a} \sqrt{a}\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{\sqrt{-a} a^{3}} - \frac{315 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{{\left({\left({\left({\left({\left({\left({\left({\left(\frac{197 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{315 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{1044 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{1470 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{2142 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{2142 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{1470 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{1044 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{315 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{197 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{9}{2}}}\right)}}{315 \, d}"," ",0,"8/315*(sqrt(2)*(315*a*arctan(sqrt(a)/sqrt(-a)) + 323*sqrt(-a)*sqrt(a))*sgn(tan(1/2*d*x + 1/2*c) + 1)/(sqrt(-a)*a^3) - 315*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/sqrt(-a))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)) + (((((((((197*a^2*tan(1/2*d*x + 1/2*c)/sgn(tan(1/2*d*x + 1/2*c) + 1) - 315*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 1044*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) - 1470*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 2142*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) - 2142*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 1470*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) - 1044*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 315*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) - 197*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(9/2))/d","B",0
483,1,358,0,0.894135," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2/(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{8 \, {\left(\frac{\sqrt{2} {\left(21 \, a \arctan\left(\frac{\sqrt{a}}{\sqrt{-a}}\right) + 20 \, \sqrt{-a} \sqrt{a}\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{\sqrt{-a} a^{3}} - \frac{21 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{{\left({\left({\left({\left({\left({\left(\frac{13 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{21 \, a}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{56 \, a}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{70 \, a}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{70 \, a}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{56 \, a}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{21 \, a}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{13 \, a}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{7}{2}}}\right)}}{21 \, d}"," ",0,"-8/21*(sqrt(2)*(21*a*arctan(sqrt(a)/sqrt(-a)) + 20*sqrt(-a)*sqrt(a))*sgn(tan(1/2*d*x + 1/2*c) + 1)/(sqrt(-a)*a^3) - 21*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/sqrt(-a))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)) + (((((((13*a*tan(1/2*d*x + 1/2*c)/sgn(tan(1/2*d*x + 1/2*c) + 1) - 21*a/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 56*a/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) - 70*a/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 70*a/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) - 56*a/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 21*a/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) - 13*a/sgn(tan(1/2*d*x + 1/2*c) + 1))/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(7/2))/d","B",0
484,1,297,0,0.822981," ","integrate(cos(d*x+c)^4*sin(d*x+c)/(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{4 \, {\left(\frac{2 \, \sqrt{2} {\left(15 \, a \arctan\left(\frac{\sqrt{a}}{\sqrt{-a}}\right) + 13 \, \sqrt{-a} \sqrt{a}\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{\sqrt{-a} a^{3}} + \frac{{\left({\left({\left({\left(\frac{19 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{30}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{55}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{55}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{30}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{19}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{5}{2}}} - \frac{30 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)}}{15 \, d}"," ",0,"4/15*(2*sqrt(2)*(15*a*arctan(sqrt(a)/sqrt(-a)) + 13*sqrt(-a)*sqrt(a))*sgn(tan(1/2*d*x + 1/2*c) + 1)/(sqrt(-a)*a^3) + (((((19*tan(1/2*d*x + 1/2*c)/sgn(tan(1/2*d*x + 1/2*c) + 1) - 30/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 55/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) - 55/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 30/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) - 19/sgn(tan(1/2*d*x + 1/2*c) + 1))/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(5/2) - 30*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/sqrt(-a))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
485,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)/(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos((d*t_nostep+c)/2-pi/4))]Discontinuities at zeroes of cos((d*t_nostep+c)/2-pi/4) were not checkedWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep+1)]Evaluation time: 0.62Error: Bad Argument Type","F(-2)",0
486,1,472,0,0.984134," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2/(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{\frac{{\left(10 \, \sqrt{2} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - 32 \, \sqrt{2} \sqrt{a} \arctan\left(\frac{\sqrt{a}}{\sqrt{-a}}\right) - 5 \, \sqrt{2} \sqrt{-a} \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) + 20 \, \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - 32 \, \sqrt{a} \arctan\left(\frac{\sqrt{a}}{\sqrt{-a}}\right) - 10 \, \sqrt{-a} \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) - 3 \, \sqrt{2} \sqrt{-a} - 2 \, \sqrt{-a}\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{\sqrt{2} \sqrt{-a} a^{\frac{5}{2}} + 2 \, \sqrt{-a} a^{\frac{5}{2}}} + \frac{16 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{10 \, \arctan\left(-\frac{\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{5 \, \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{5}{2}} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{a^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{2}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a\right)} a^{\frac{3}{2}} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{2 \, d}"," ",0,"1/2*((10*sqrt(2)*sqrt(a)*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - 32*sqrt(2)*sqrt(a)*arctan(sqrt(a)/sqrt(-a)) - 5*sqrt(2)*sqrt(-a)*log(sqrt(2)*sqrt(a) + sqrt(a)) + 20*sqrt(a)*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - 32*sqrt(a)*arctan(sqrt(a)/sqrt(-a)) - 10*sqrt(-a)*log(sqrt(2)*sqrt(a) + sqrt(a)) - 3*sqrt(2)*sqrt(-a) - 2*sqrt(-a))*sgn(tan(1/2*d*x + 1/2*c) + 1)/(sqrt(2)*sqrt(-a)*a^(5/2) + 2*sqrt(-a)*a^(5/2)) + 16*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/sqrt(-a))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 10*arctan(-(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))/sqrt(-a))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 5*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/(a^(5/2)*sgn(tan(1/2*d*x + 1/2*c) + 1)) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)/(a^3*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 2/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a)*a^(3/2)*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
487,1,620,0,1.495331," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3/(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left(\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{10}{a^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} - \frac{{\left(138 \, \sqrt{2} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - 256 \, \sqrt{2} \sqrt{a} \arctan\left(\frac{\sqrt{a}}{\sqrt{-a}}\right) - 69 \, \sqrt{2} \sqrt{-a} \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) + 184 \, \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - 384 \, \sqrt{a} \arctan\left(\frac{\sqrt{a}}{\sqrt{-a}}\right) - 92 \, \sqrt{-a} \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) - 58 \, \sqrt{2} \sqrt{-a} - 92 \, \sqrt{-a}\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{3 \, \sqrt{2} \sqrt{-a} a^{\frac{5}{2}} + 4 \, \sqrt{-a} a^{\frac{5}{2}}} - \frac{64 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{46 \, \arctan\left(-\frac{\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{23 \, \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{5}{2}} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{2 \, {\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{3} - 10 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} \sqrt{a} + {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a + 10 \, a^{\frac{3}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a\right)}^{2} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{8 \, d}"," ",0,"1/8*(sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)*(tan(1/2*d*x + 1/2*c)/(a^3*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 10/(a^3*sgn(tan(1/2*d*x + 1/2*c) + 1))) - (138*sqrt(2)*sqrt(a)*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - 256*sqrt(2)*sqrt(a)*arctan(sqrt(a)/sqrt(-a)) - 69*sqrt(2)*sqrt(-a)*log(sqrt(2)*sqrt(a) + sqrt(a)) + 184*sqrt(a)*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - 384*sqrt(a)*arctan(sqrt(a)/sqrt(-a)) - 92*sqrt(-a)*log(sqrt(2)*sqrt(a) + sqrt(a)) - 58*sqrt(2)*sqrt(-a) - 92*sqrt(-a))*sgn(tan(1/2*d*x + 1/2*c) + 1)/(3*sqrt(2)*sqrt(-a)*a^(5/2) + 4*sqrt(-a)*a^(5/2)) - 64*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/sqrt(-a))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 46*arctan(-(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))/sqrt(-a))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 23*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/(a^(5/2)*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 2*((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^3 - 10*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*sqrt(a) + (sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a + 10*a^(3/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a)^2*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
488,1,695,0,1.158899," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4/(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left({\left(\frac{2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{15}{a^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{74}{a^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} + \frac{{\left(1890 \, \sqrt{2} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - 3840 \, \sqrt{2} \sqrt{a} \arctan\left(\frac{\sqrt{a}}{\sqrt{-a}}\right) - 945 \, \sqrt{2} \sqrt{-a} \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) + 2700 \, \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - 5376 \, \sqrt{a} \arctan\left(\frac{\sqrt{a}}{\sqrt{-a}}\right) - 1350 \, \sqrt{-a} \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) - 1302 \, \sqrt{2} \sqrt{-a} - 1808 \, \sqrt{-a}\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{7 \, \sqrt{2} \sqrt{-a} a^{\frac{5}{2}} + 10 \, \sqrt{-a} a^{\frac{5}{2}}} + \frac{384 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{270 \, \arctan\left(-\frac{\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{135 \, \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{5}{2}} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{2 \, {\left(15 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{5} - 78 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} \sqrt{a} + 144 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a^{\frac{3}{2}} - 15 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a^{2} - 74 \, a^{\frac{5}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a\right)}^{3} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{48 \, d}"," ",0,"1/48*(sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)*((2*tan(1/2*d*x + 1/2*c)/(a^3*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 15/(a^3*sgn(tan(1/2*d*x + 1/2*c) + 1)))*tan(1/2*d*x + 1/2*c) + 74/(a^3*sgn(tan(1/2*d*x + 1/2*c) + 1))) + (1890*sqrt(2)*sqrt(a)*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - 3840*sqrt(2)*sqrt(a)*arctan(sqrt(a)/sqrt(-a)) - 945*sqrt(2)*sqrt(-a)*log(sqrt(2)*sqrt(a) + sqrt(a)) + 2700*sqrt(a)*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - 5376*sqrt(a)*arctan(sqrt(a)/sqrt(-a)) - 1350*sqrt(-a)*log(sqrt(2)*sqrt(a) + sqrt(a)) - 1302*sqrt(2)*sqrt(-a) - 1808*sqrt(-a))*sgn(tan(1/2*d*x + 1/2*c) + 1)/(7*sqrt(2)*sqrt(-a)*a^(5/2) + 10*sqrt(-a)*a^(5/2)) + 384*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/sqrt(-a))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 270*arctan(-(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))/sqrt(-a))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 135*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/(a^(5/2)*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 2*(15*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^5 - 78*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4*sqrt(a) + 144*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a^(3/2) - 15*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a^2 - 74*a^(5/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a)^3*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
489,1,845,0,1.294096," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5/(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left({\left(2 \, {\left(\frac{3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{20}{a^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{159}{a^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{640}{a^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} - \frac{{\left(37026 \, \sqrt{2} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - 73728 \, \sqrt{2} \sqrt{a} \arctan\left(\frac{\sqrt{a}}{\sqrt{-a}}\right) - 18513 \, \sqrt{2} \sqrt{-a} \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) + 52272 \, \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - 104448 \, \sqrt{a} \arctan\left(\frac{\sqrt{a}}{\sqrt{-a}}\right) - 26136 \, \sqrt{-a} \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) - 29680 \, \sqrt{2} \sqrt{-a} - 42100 \, \sqrt{-a}\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{17 \, \sqrt{2} \sqrt{-a} a^{\frac{5}{2}} + 24 \, \sqrt{-a} a^{\frac{5}{2}}} - \frac{3072 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{2178 \, \arctan\left(-\frac{\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{1089 \, \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{5}{2}} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{2 \, {\left(159 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{7} - 720 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} \sqrt{a} - 135 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{5} a + 1920 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} a^{\frac{3}{2}} - 135 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{3} a^{2} - 1840 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a^{\frac{5}{2}} + 159 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a^{3} + 640 \, a^{\frac{7}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a\right)}^{4} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{384 \, d}"," ",0,"1/384*(sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)*((2*(3*tan(1/2*d*x + 1/2*c)/(a^3*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 20/(a^3*sgn(tan(1/2*d*x + 1/2*c) + 1)))*tan(1/2*d*x + 1/2*c) + 159/(a^3*sgn(tan(1/2*d*x + 1/2*c) + 1)))*tan(1/2*d*x + 1/2*c) - 640/(a^3*sgn(tan(1/2*d*x + 1/2*c) + 1))) - (37026*sqrt(2)*sqrt(a)*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - 73728*sqrt(2)*sqrt(a)*arctan(sqrt(a)/sqrt(-a)) - 18513*sqrt(2)*sqrt(-a)*log(sqrt(2)*sqrt(a) + sqrt(a)) + 52272*sqrt(a)*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - 104448*sqrt(a)*arctan(sqrt(a)/sqrt(-a)) - 26136*sqrt(-a)*log(sqrt(2)*sqrt(a) + sqrt(a)) - 29680*sqrt(2)*sqrt(-a) - 42100*sqrt(-a))*sgn(tan(1/2*d*x + 1/2*c) + 1)/(17*sqrt(2)*sqrt(-a)*a^(5/2) + 24*sqrt(-a)*a^(5/2)) - 3072*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/sqrt(-a))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 2178*arctan(-(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))/sqrt(-a))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 1089*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/(a^(5/2)*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 2*(159*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^7 - 720*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^6*sqrt(a) - 135*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^5*a + 1920*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4*a^(3/2) - 135*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^3*a^2 - 1840*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a^(5/2) + 159*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a^3 + 640*a^(7/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a)^4*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
490,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^n*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{2} \sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^2*sin(d*x + c)^n*cos(d*x + c)^4, x)","F",0
491,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^n*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\int {\left(a \sin\left(d x + c\right) + a\right)} \sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)*sin(d*x + c)^n*cos(d*x + c)^4, x)","F",0
492,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^n/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\int \frac{\sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{4}}{a \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sin(d*x + c)^n*cos(d*x + c)^4/(a*sin(d*x + c) + a), x)","F",0
493,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^n/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{4}}{{\left(a \sin\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sin(d*x + c)^n*cos(d*x + c)^4/(a*sin(d*x + c) + a)^2, x)","F",0
494,1,133,0,0.313528," ","integrate(cos(d*x+c)^5*sin(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{a \cos\left(10 \, d x + 10 \, c\right)}{5120 \, d} + \frac{5 \, a \cos\left(6 \, d x + 6 \, c\right)}{3072 \, d} - \frac{5 \, a \cos\left(2 \, d x + 2 \, c\right)}{512 \, d} - \frac{a \sin\left(11 \, d x + 11 \, c\right)}{11264 \, d} + \frac{a \sin\left(9 \, d x + 9 \, c\right)}{9216 \, d} + \frac{5 \, a \sin\left(7 \, d x + 7 \, c\right)}{7168 \, d} - \frac{a \sin\left(5 \, d x + 5 \, c\right)}{1024 \, d} - \frac{5 \, a \sin\left(3 \, d x + 3 \, c\right)}{1536 \, d} + \frac{5 \, a \sin\left(d x + c\right)}{512 \, d}"," ",0,"-1/5120*a*cos(10*d*x + 10*c)/d + 5/3072*a*cos(6*d*x + 6*c)/d - 5/512*a*cos(2*d*x + 2*c)/d - 1/11264*a*sin(11*d*x + 11*c)/d + 1/9216*a*sin(9*d*x + 9*c)/d + 5/7168*a*sin(7*d*x + 7*c)/d - 1/1024*a*sin(5*d*x + 5*c)/d - 5/1536*a*sin(3*d*x + 3*c)/d + 5/512*a*sin(d*x + c)/d","A",0
495,1,118,0,0.257503," ","integrate(cos(d*x+c)^5*sin(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{a \cos\left(10 \, d x + 10 \, c\right)}{5120 \, d} + \frac{5 \, a \cos\left(6 \, d x + 6 \, c\right)}{3072 \, d} - \frac{5 \, a \cos\left(2 \, d x + 2 \, c\right)}{512 \, d} + \frac{a \sin\left(9 \, d x + 9 \, c\right)}{2304 \, d} + \frac{a \sin\left(7 \, d x + 7 \, c\right)}{1792 \, d} - \frac{a \sin\left(5 \, d x + 5 \, c\right)}{320 \, d} - \frac{a \sin\left(3 \, d x + 3 \, c\right)}{192 \, d} + \frac{3 \, a \sin\left(d x + c\right)}{128 \, d}"," ",0,"-1/5120*a*cos(10*d*x + 10*c)/d + 5/3072*a*cos(6*d*x + 6*c)/d - 5/512*a*cos(2*d*x + 2*c)/d + 1/2304*a*sin(9*d*x + 9*c)/d + 1/1792*a*sin(7*d*x + 7*c)/d - 1/320*a*sin(5*d*x + 5*c)/d - 1/192*a*sin(3*d*x + 3*c)/d + 3/128*a*sin(d*x + c)/d","A",0
496,1,133,0,0.233571," ","integrate(cos(d*x+c)^5*sin(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{a \cos\left(8 \, d x + 8 \, c\right)}{1024 \, d} + \frac{a \cos\left(6 \, d x + 6 \, c\right)}{384 \, d} - \frac{a \cos\left(4 \, d x + 4 \, c\right)}{256 \, d} - \frac{3 \, a \cos\left(2 \, d x + 2 \, c\right)}{128 \, d} + \frac{a \sin\left(9 \, d x + 9 \, c\right)}{2304 \, d} + \frac{a \sin\left(7 \, d x + 7 \, c\right)}{1792 \, d} - \frac{a \sin\left(5 \, d x + 5 \, c\right)}{320 \, d} - \frac{a \sin\left(3 \, d x + 3 \, c\right)}{192 \, d} + \frac{3 \, a \sin\left(d x + c\right)}{128 \, d}"," ",0,"1/1024*a*cos(8*d*x + 8*c)/d + 1/384*a*cos(6*d*x + 6*c)/d - 1/256*a*cos(4*d*x + 4*c)/d - 3/128*a*cos(2*d*x + 2*c)/d + 1/2304*a*sin(9*d*x + 9*c)/d + 1/1792*a*sin(7*d*x + 7*c)/d - 1/320*a*sin(5*d*x + 5*c)/d - 1/192*a*sin(3*d*x + 3*c)/d + 3/128*a*sin(d*x + c)/d","A",0
497,1,118,0,0.213334," ","integrate(cos(d*x+c)^5*sin(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{a \cos\left(8 \, d x + 8 \, c\right)}{1024 \, d} + \frac{a \cos\left(6 \, d x + 6 \, c\right)}{384 \, d} - \frac{a \cos\left(4 \, d x + 4 \, c\right)}{256 \, d} - \frac{3 \, a \cos\left(2 \, d x + 2 \, c\right)}{128 \, d} - \frac{a \sin\left(7 \, d x + 7 \, c\right)}{448 \, d} - \frac{3 \, a \sin\left(5 \, d x + 5 \, c\right)}{320 \, d} - \frac{a \sin\left(3 \, d x + 3 \, c\right)}{192 \, d} + \frac{5 \, a \sin\left(d x + c\right)}{64 \, d}"," ",0,"1/1024*a*cos(8*d*x + 8*c)/d + 1/384*a*cos(6*d*x + 6*c)/d - 1/256*a*cos(4*d*x + 4*c)/d - 3/128*a*cos(2*d*x + 2*c)/d - 1/448*a*sin(7*d*x + 7*c)/d - 3/320*a*sin(5*d*x + 5*c)/d - 1/192*a*sin(3*d*x + 3*c)/d + 5/64*a*sin(d*x + c)/d","A",0
498,1,103,0,0.203362," ","integrate(cos(d*x+c)^5*sin(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{a \cos\left(6 \, d x + 6 \, c\right)}{192 \, d} - \frac{a \cos\left(4 \, d x + 4 \, c\right)}{32 \, d} - \frac{5 \, a \cos\left(2 \, d x + 2 \, c\right)}{64 \, d} - \frac{a \sin\left(7 \, d x + 7 \, c\right)}{448 \, d} - \frac{3 \, a \sin\left(5 \, d x + 5 \, c\right)}{320 \, d} - \frac{a \sin\left(3 \, d x + 3 \, c\right)}{192 \, d} + \frac{5 \, a \sin\left(d x + c\right)}{64 \, d}"," ",0,"-1/192*a*cos(6*d*x + 6*c)/d - 1/32*a*cos(4*d*x + 4*c)/d - 5/64*a*cos(2*d*x + 2*c)/d - 1/448*a*sin(7*d*x + 7*c)/d - 3/320*a*sin(5*d*x + 5*c)/d - 1/192*a*sin(3*d*x + 3*c)/d + 5/64*a*sin(d*x + c)/d","A",0
499,1,70,0,0.172906," ","integrate(cos(d*x+c)^5*csc(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{12 \, a \sin\left(d x + c\right)^{5} + 15 \, a \sin\left(d x + c\right)^{4} - 40 \, a \sin\left(d x + c\right)^{3} - 60 \, a \sin\left(d x + c\right)^{2} + 60 \, a \log\left({\left| \sin\left(d x + c\right) \right|}\right) + 60 \, a \sin\left(d x + c\right)}{60 \, d}"," ",0,"1/60*(12*a*sin(d*x + c)^5 + 15*a*sin(d*x + c)^4 - 40*a*sin(d*x + c)^3 - 60*a*sin(d*x + c)^2 + 60*a*log(abs(sin(d*x + c))) + 60*a*sin(d*x + c))/d","A",0
500,1,79,0,0.194087," ","integrate(cos(d*x+c)^5*csc(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{3 \, a \sin\left(d x + c\right)^{4} + 4 \, a \sin\left(d x + c\right)^{3} - 12 \, a \sin\left(d x + c\right)^{2} + 12 \, a \log\left({\left| \sin\left(d x + c\right) \right|}\right) - 24 \, a \sin\left(d x + c\right) - \frac{12 \, {\left(a \sin\left(d x + c\right) + a\right)}}{\sin\left(d x + c\right)}}{12 \, d}"," ",0,"1/12*(3*a*sin(d*x + c)^4 + 4*a*sin(d*x + c)^3 - 12*a*sin(d*x + c)^2 + 12*a*log(abs(sin(d*x + c))) - 24*a*sin(d*x + c) - 12*(a*sin(d*x + c) + a)/sin(d*x + c))/d","A",0
501,1,82,0,0.197778," ","integrate(cos(d*x+c)^5*csc(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{2 \, a \sin\left(d x + c\right)^{3} + 3 \, a \sin\left(d x + c\right)^{2} - 12 \, a \log\left({\left| \sin\left(d x + c\right) \right|}\right) - 12 \, a \sin\left(d x + c\right) + \frac{3 \, {\left(6 \, a \sin\left(d x + c\right)^{2} - 2 \, a \sin\left(d x + c\right) - a\right)}}{\sin\left(d x + c\right)^{2}}}{6 \, d}"," ",0,"1/6*(2*a*sin(d*x + c)^3 + 3*a*sin(d*x + c)^2 - 12*a*log(abs(sin(d*x + c))) - 12*a*sin(d*x + c) + 3*(6*a*sin(d*x + c)^2 - 2*a*sin(d*x + c) - a)/sin(d*x + c)^2)/d","A",0
502,1,81,0,0.198116," ","integrate(cos(d*x+c)^5*csc(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{3 \, a \sin\left(d x + c\right)^{2} - 12 \, a \log\left({\left| \sin\left(d x + c\right) \right|}\right) + 6 \, a \sin\left(d x + c\right) + \frac{22 \, a \sin\left(d x + c\right)^{3} + 12 \, a \sin\left(d x + c\right)^{2} - 3 \, a \sin\left(d x + c\right) - 2 \, a}{\sin\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(3*a*sin(d*x + c)^2 - 12*a*log(abs(sin(d*x + c))) + 6*a*sin(d*x + c) + (22*a*sin(d*x + c)^3 + 12*a*sin(d*x + c)^2 - 3*a*sin(d*x + c) - 2*a)/sin(d*x + c)^3)/d","A",0
503,1,82,0,0.213461," ","integrate(cos(d*x+c)^5*csc(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{12 \, a \log\left({\left| \sin\left(d x + c\right) \right|}\right) + 12 \, a \sin\left(d x + c\right) - \frac{25 \, a \sin\left(d x + c\right)^{4} - 24 \, a \sin\left(d x + c\right)^{3} - 12 \, a \sin\left(d x + c\right)^{2} + 4 \, a \sin\left(d x + c\right) + 3 \, a}{\sin\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"1/12*(12*a*log(abs(sin(d*x + c))) + 12*a*sin(d*x + c) - (25*a*sin(d*x + c)^4 - 24*a*sin(d*x + c)^3 - 12*a*sin(d*x + c)^2 + 4*a*sin(d*x + c) + 3*a)/sin(d*x + c)^4)/d","A",0
504,1,84,0,0.251740," ","integrate(cos(d*x+c)^5*csc(d*x+c)^6*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{60 \, a \log\left({\left| \sin\left(d x + c\right) \right|}\right) - \frac{137 \, a \sin\left(d x + c\right)^{5} + 60 \, a \sin\left(d x + c\right)^{4} - 60 \, a \sin\left(d x + c\right)^{3} - 40 \, a \sin\left(d x + c\right)^{2} + 15 \, a \sin\left(d x + c\right) + 12 \, a}{\sin\left(d x + c\right)^{5}}}{60 \, d}"," ",0,"1/60*(60*a*log(abs(sin(d*x + c))) - (137*a*sin(d*x + c)^5 + 60*a*sin(d*x + c)^4 - 60*a*sin(d*x + c)^3 - 40*a*sin(d*x + c)^2 + 15*a*sin(d*x + c) + 12*a)/sin(d*x + c)^5)/d","A",0
505,1,70,0,0.245201," ","integrate(cos(d*x+c)^5*csc(d*x+c)^7*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{30 \, a \sin\left(d x + c\right)^{5} + 15 \, a \sin\left(d x + c\right)^{4} - 20 \, a \sin\left(d x + c\right)^{3} - 15 \, a \sin\left(d x + c\right)^{2} + 6 \, a \sin\left(d x + c\right) + 5 \, a}{30 \, d \sin\left(d x + c\right)^{6}}"," ",0,"-1/30*(30*a*sin(d*x + c)^5 + 15*a*sin(d*x + c)^4 - 20*a*sin(d*x + c)^3 - 15*a*sin(d*x + c)^2 + 6*a*sin(d*x + c) + 5*a)/(d*sin(d*x + c)^6)","A",0
506,1,70,0,0.246888," ","integrate(cos(d*x+c)^5*csc(d*x+c)^8*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{105 \, a \sin\left(d x + c\right)^{5} + 70 \, a \sin\left(d x + c\right)^{4} - 105 \, a \sin\left(d x + c\right)^{3} - 84 \, a \sin\left(d x + c\right)^{2} + 35 \, a \sin\left(d x + c\right) + 30 \, a}{210 \, d \sin\left(d x + c\right)^{7}}"," ",0,"-1/210*(105*a*sin(d*x + c)^5 + 70*a*sin(d*x + c)^4 - 105*a*sin(d*x + c)^3 - 84*a*sin(d*x + c)^2 + 35*a*sin(d*x + c) + 30*a)/(d*sin(d*x + c)^7)","A",0
507,1,70,0,0.240627," ","integrate(cos(d*x+c)^5*csc(d*x+c)^9*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{280 \, a \sin\left(d x + c\right)^{5} + 210 \, a \sin\left(d x + c\right)^{4} - 336 \, a \sin\left(d x + c\right)^{3} - 280 \, a \sin\left(d x + c\right)^{2} + 120 \, a \sin\left(d x + c\right) + 105 \, a}{840 \, d \sin\left(d x + c\right)^{8}}"," ",0,"-1/840*(280*a*sin(d*x + c)^5 + 210*a*sin(d*x + c)^4 - 336*a*sin(d*x + c)^3 - 280*a*sin(d*x + c)^2 + 120*a*sin(d*x + c) + 105*a)/(d*sin(d*x + c)^8)","A",0
508,1,70,0,0.236552," ","integrate(cos(d*x+c)^5*csc(d*x+c)^10*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{630 \, a \sin\left(d x + c\right)^{5} + 504 \, a \sin\left(d x + c\right)^{4} - 840 \, a \sin\left(d x + c\right)^{3} - 720 \, a \sin\left(d x + c\right)^{2} + 315 \, a \sin\left(d x + c\right) + 280 \, a}{2520 \, d \sin\left(d x + c\right)^{9}}"," ",0,"-1/2520*(630*a*sin(d*x + c)^5 + 504*a*sin(d*x + c)^4 - 840*a*sin(d*x + c)^3 - 720*a*sin(d*x + c)^2 + 315*a*sin(d*x + c) + 280*a)/(d*sin(d*x + c)^9)","A",0
509,1,70,0,0.262419," ","integrate(cos(d*x+c)^5*csc(d*x+c)^11*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{252 \, a \sin\left(d x + c\right)^{5} + 210 \, a \sin\left(d x + c\right)^{4} - 360 \, a \sin\left(d x + c\right)^{3} - 315 \, a \sin\left(d x + c\right)^{2} + 140 \, a \sin\left(d x + c\right) + 126 \, a}{1260 \, d \sin\left(d x + c\right)^{10}}"," ",0,"-1/1260*(252*a*sin(d*x + c)^5 + 210*a*sin(d*x + c)^4 - 360*a*sin(d*x + c)^3 - 315*a*sin(d*x + c)^2 + 140*a*sin(d*x + c) + 126*a)/(d*sin(d*x + c)^10)","A",0
510,1,70,0,0.248313," ","integrate(cos(d*x+c)^5*csc(d*x+c)^12*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{2310 \, a \sin\left(d x + c\right)^{5} + 1980 \, a \sin\left(d x + c\right)^{4} - 3465 \, a \sin\left(d x + c\right)^{3} - 3080 \, a \sin\left(d x + c\right)^{2} + 1386 \, a \sin\left(d x + c\right) + 1260 \, a}{13860 \, d \sin\left(d x + c\right)^{11}}"," ",0,"-1/13860*(2310*a*sin(d*x + c)^5 + 1980*a*sin(d*x + c)^4 - 3465*a*sin(d*x + c)^3 - 3080*a*sin(d*x + c)^2 + 1386*a*sin(d*x + c) + 1260*a)/(d*sin(d*x + c)^11)","A",0
511,1,168,0,0.327248," ","integrate(cos(d*x+c)^5*sin(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{a^{2} \cos\left(10 \, d x + 10 \, c\right)}{5120 \, d} + \frac{a^{2} \cos\left(8 \, d x + 8 \, c\right)}{1024 \, d} + \frac{13 \, a^{2} \cos\left(6 \, d x + 6 \, c\right)}{3072 \, d} - \frac{a^{2} \cos\left(4 \, d x + 4 \, c\right)}{256 \, d} - \frac{17 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)}{512 \, d} + \frac{a^{2} \sin\left(9 \, d x + 9 \, c\right)}{1152 \, d} + \frac{a^{2} \sin\left(7 \, d x + 7 \, c\right)}{896 \, d} - \frac{a^{2} \sin\left(5 \, d x + 5 \, c\right)}{160 \, d} - \frac{a^{2} \sin\left(3 \, d x + 3 \, c\right)}{96 \, d} + \frac{3 \, a^{2} \sin\left(d x + c\right)}{64 \, d}"," ",0,"-1/5120*a^2*cos(10*d*x + 10*c)/d + 1/1024*a^2*cos(8*d*x + 8*c)/d + 13/3072*a^2*cos(6*d*x + 6*c)/d - 1/256*a^2*cos(4*d*x + 4*c)/d - 17/512*a^2*cos(2*d*x + 2*c)/d + 1/1152*a^2*sin(9*d*x + 9*c)/d + 1/896*a^2*sin(7*d*x + 7*c)/d - 1/160*a^2*sin(5*d*x + 5*c)/d - 1/96*a^2*sin(3*d*x + 3*c)/d + 3/64*a^2*sin(d*x + c)/d","A",0
512,1,151,0,0.284465," ","integrate(cos(d*x+c)^5*sin(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{a^{2} \cos\left(8 \, d x + 8 \, c\right)}{512 \, d} + \frac{a^{2} \cos\left(6 \, d x + 6 \, c\right)}{192 \, d} - \frac{a^{2} \cos\left(4 \, d x + 4 \, c\right)}{128 \, d} - \frac{3 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)}{64 \, d} + \frac{a^{2} \sin\left(9 \, d x + 9 \, c\right)}{2304 \, d} - \frac{3 \, a^{2} \sin\left(7 \, d x + 7 \, c\right)}{1792 \, d} - \frac{a^{2} \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} - \frac{a^{2} \sin\left(3 \, d x + 3 \, c\right)}{96 \, d} + \frac{13 \, a^{2} \sin\left(d x + c\right)}{128 \, d}"," ",0,"1/512*a^2*cos(8*d*x + 8*c)/d + 1/192*a^2*cos(6*d*x + 6*c)/d - 1/128*a^2*cos(4*d*x + 4*c)/d - 3/64*a^2*cos(2*d*x + 2*c)/d + 1/2304*a^2*sin(9*d*x + 9*c)/d - 3/1792*a^2*sin(7*d*x + 7*c)/d - 1/80*a^2*sin(5*d*x + 5*c)/d - 1/96*a^2*sin(3*d*x + 3*c)/d + 13/128*a^2*sin(d*x + c)/d","A",0
513,1,134,0,0.247218," ","integrate(cos(d*x+c)^5*sin(d*x+c)*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{a^{2} \cos\left(8 \, d x + 8 \, c\right)}{1024 \, d} - \frac{a^{2} \cos\left(6 \, d x + 6 \, c\right)}{384 \, d} - \frac{9 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)}{256 \, d} - \frac{13 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)}{128 \, d} - \frac{a^{2} \sin\left(7 \, d x + 7 \, c\right)}{224 \, d} - \frac{3 \, a^{2} \sin\left(5 \, d x + 5 \, c\right)}{160 \, d} - \frac{a^{2} \sin\left(3 \, d x + 3 \, c\right)}{96 \, d} + \frac{5 \, a^{2} \sin\left(d x + c\right)}{32 \, d}"," ",0,"1/1024*a^2*cos(8*d*x + 8*c)/d - 1/384*a^2*cos(6*d*x + 6*c)/d - 9/256*a^2*cos(4*d*x + 4*c)/d - 13/128*a^2*cos(2*d*x + 2*c)/d - 1/224*a^2*sin(7*d*x + 7*c)/d - 3/160*a^2*sin(5*d*x + 5*c)/d - 1/96*a^2*sin(3*d*x + 3*c)/d + 5/32*a^2*sin(d*x + c)/d","A",0
514,1,95,0,0.235737," ","integrate(cos(d*x+c)^5*csc(d*x+c)*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{10 \, a^{2} \sin\left(d x + c\right)^{6} + 24 \, a^{2} \sin\left(d x + c\right)^{5} - 15 \, a^{2} \sin\left(d x + c\right)^{4} - 80 \, a^{2} \sin\left(d x + c\right)^{3} - 30 \, a^{2} \sin\left(d x + c\right)^{2} + 60 \, a^{2} \log\left({\left| \sin\left(d x + c\right) \right|}\right) + 120 \, a^{2} \sin\left(d x + c\right)}{60 \, d}"," ",0,"1/60*(10*a^2*sin(d*x + c)^6 + 24*a^2*sin(d*x + c)^5 - 15*a^2*sin(d*x + c)^4 - 80*a^2*sin(d*x + c)^3 - 30*a^2*sin(d*x + c)^2 + 60*a^2*log(abs(sin(d*x + c))) + 120*a^2*sin(d*x + c))/d","A",0
515,1,107,0,0.233736," ","integrate(cos(d*x+c)^5*csc(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{6 \, a^{2} \sin\left(d x + c\right)^{5} + 15 \, a^{2} \sin\left(d x + c\right)^{4} - 10 \, a^{2} \sin\left(d x + c\right)^{3} - 60 \, a^{2} \sin\left(d x + c\right)^{2} + 60 \, a^{2} \log\left({\left| \sin\left(d x + c\right) \right|}\right) - 30 \, a^{2} \sin\left(d x + c\right) - \frac{30 \, {\left(2 \, a^{2} \sin\left(d x + c\right) + a^{2}\right)}}{\sin\left(d x + c\right)}}{30 \, d}"," ",0,"1/30*(6*a^2*sin(d*x + c)^5 + 15*a^2*sin(d*x + c)^4 - 10*a^2*sin(d*x + c)^3 - 60*a^2*sin(d*x + c)^2 + 60*a^2*log(abs(sin(d*x + c))) - 30*a^2*sin(d*x + c) - 30*(2*a^2*sin(d*x + c) + a^2)/sin(d*x + c))/d","A",0
516,1,109,0,0.259246," ","integrate(cos(d*x+c)^5*csc(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{3 \, a^{2} \sin\left(d x + c\right)^{4} + 8 \, a^{2} \sin\left(d x + c\right)^{3} - 6 \, a^{2} \sin\left(d x + c\right)^{2} - 12 \, a^{2} \log\left({\left| \sin\left(d x + c\right) \right|}\right) - 48 \, a^{2} \sin\left(d x + c\right) + \frac{6 \, {\left(3 \, a^{2} \sin\left(d x + c\right)^{2} - 4 \, a^{2} \sin\left(d x + c\right) - a^{2}\right)}}{\sin\left(d x + c\right)^{2}}}{12 \, d}"," ",0,"1/12*(3*a^2*sin(d*x + c)^4 + 8*a^2*sin(d*x + c)^3 - 6*a^2*sin(d*x + c)^2 - 12*a^2*log(abs(sin(d*x + c))) - 48*a^2*sin(d*x + c) + 6*(3*a^2*sin(d*x + c)^2 - 4*a^2*sin(d*x + c) - a^2)/sin(d*x + c)^2)/d","A",0
517,1,107,0,0.273456," ","integrate(cos(d*x+c)^5*csc(d*x+c)^4*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{a^{2} \sin\left(d x + c\right)^{3} + 3 \, a^{2} \sin\left(d x + c\right)^{2} - 12 \, a^{2} \log\left({\left| \sin\left(d x + c\right) \right|}\right) - 3 \, a^{2} \sin\left(d x + c\right) + \frac{22 \, a^{2} \sin\left(d x + c\right)^{3} + 3 \, a^{2} \sin\left(d x + c\right)^{2} - 3 \, a^{2} \sin\left(d x + c\right) - a^{2}}{\sin\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"1/3*(a^2*sin(d*x + c)^3 + 3*a^2*sin(d*x + c)^2 - 12*a^2*log(abs(sin(d*x + c))) - 3*a^2*sin(d*x + c) + (22*a^2*sin(d*x + c)^3 + 3*a^2*sin(d*x + c)^2 - 3*a^2*sin(d*x + c) - a^2)/sin(d*x + c)^3)/d","A",0
518,1,108,0,0.284852," ","integrate(cos(d*x+c)^5*csc(d*x+c)^5*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{6 \, a^{2} \sin\left(d x + c\right)^{2} - 12 \, a^{2} \log\left({\left| \sin\left(d x + c\right) \right|}\right) + 24 \, a^{2} \sin\left(d x + c\right) + \frac{25 \, a^{2} \sin\left(d x + c\right)^{4} + 48 \, a^{2} \sin\left(d x + c\right)^{3} + 6 \, a^{2} \sin\left(d x + c\right)^{2} - 8 \, a^{2} \sin\left(d x + c\right) - 3 \, a^{2}}{\sin\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"1/12*(6*a^2*sin(d*x + c)^2 - 12*a^2*log(abs(sin(d*x + c))) + 24*a^2*sin(d*x + c) + (25*a^2*sin(d*x + c)^4 + 48*a^2*sin(d*x + c)^3 + 6*a^2*sin(d*x + c)^2 - 8*a^2*sin(d*x + c) - 3*a^2)/sin(d*x + c)^4)/d","A",0
519,1,109,0,0.266878," ","integrate(cos(d*x+c)^5*csc(d*x+c)^6*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{60 \, a^{2} \log\left({\left| \sin\left(d x + c\right) \right|}\right) + 30 \, a^{2} \sin\left(d x + c\right) - \frac{137 \, a^{2} \sin\left(d x + c\right)^{5} - 30 \, a^{2} \sin\left(d x + c\right)^{4} - 60 \, a^{2} \sin\left(d x + c\right)^{3} - 10 \, a^{2} \sin\left(d x + c\right)^{2} + 15 \, a^{2} \sin\left(d x + c\right) + 6 \, a^{2}}{\sin\left(d x + c\right)^{5}}}{30 \, d}"," ",0,"1/30*(60*a^2*log(abs(sin(d*x + c))) + 30*a^2*sin(d*x + c) - (137*a^2*sin(d*x + c)^5 - 30*a^2*sin(d*x + c)^4 - 60*a^2*sin(d*x + c)^3 - 10*a^2*sin(d*x + c)^2 + 15*a^2*sin(d*x + c) + 6*a^2)/sin(d*x + c)^5)/d","A",0
520,1,111,0,0.289476," ","integrate(cos(d*x+c)^5*csc(d*x+c)^7*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{60 \, a^{2} \log\left({\left| \sin\left(d x + c\right) \right|}\right) - \frac{147 \, a^{2} \sin\left(d x + c\right)^{6} + 120 \, a^{2} \sin\left(d x + c\right)^{5} - 30 \, a^{2} \sin\left(d x + c\right)^{4} - 80 \, a^{2} \sin\left(d x + c\right)^{3} - 15 \, a^{2} \sin\left(d x + c\right)^{2} + 24 \, a^{2} \sin\left(d x + c\right) + 10 \, a^{2}}{\sin\left(d x + c\right)^{6}}}{60 \, d}"," ",0,"1/60*(60*a^2*log(abs(sin(d*x + c))) - (147*a^2*sin(d*x + c)^6 + 120*a^2*sin(d*x + c)^5 - 30*a^2*sin(d*x + c)^4 - 80*a^2*sin(d*x + c)^3 - 15*a^2*sin(d*x + c)^2 + 24*a^2*sin(d*x + c) + 10*a^2)/sin(d*x + c)^6)/d","A",0
521,1,168,0,0.390339," ","integrate(cos(d*x+c)^5*sin(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{a^{3} \cos\left(10 \, d x + 10 \, c\right)}{5120 \, d} + \frac{3 \, a^{3} \cos\left(8 \, d x + 8 \, c\right)}{1024 \, d} + \frac{29 \, a^{3} \cos\left(6 \, d x + 6 \, c\right)}{3072 \, d} - \frac{3 \, a^{3} \cos\left(4 \, d x + 4 \, c\right)}{256 \, d} - \frac{41 \, a^{3} \cos\left(2 \, d x + 2 \, c\right)}{512 \, d} + \frac{a^{3} \sin\left(9 \, d x + 9 \, c\right)}{768 \, d} - \frac{a^{3} \sin\left(7 \, d x + 7 \, c\right)}{1792 \, d} - \frac{3 \, a^{3} \sin\left(5 \, d x + 5 \, c\right)}{160 \, d} - \frac{a^{3} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{19 \, a^{3} \sin\left(d x + c\right)}{128 \, d}"," ",0,"-1/5120*a^3*cos(10*d*x + 10*c)/d + 3/1024*a^3*cos(8*d*x + 8*c)/d + 29/3072*a^3*cos(6*d*x + 6*c)/d - 3/256*a^3*cos(4*d*x + 4*c)/d - 41/512*a^3*cos(2*d*x + 2*c)/d + 1/768*a^3*sin(9*d*x + 9*c)/d - 1/1792*a^3*sin(7*d*x + 7*c)/d - 3/160*a^3*sin(5*d*x + 5*c)/d - 1/48*a^3*sin(3*d*x + 3*c)/d + 19/128*a^3*sin(d*x + c)/d","A",0
522,1,151,0,0.315727," ","integrate(cos(d*x+c)^5*sin(d*x+c)*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{3 \, a^{3} \cos\left(8 \, d x + 8 \, c\right)}{1024 \, d} + \frac{a^{3} \cos\left(6 \, d x + 6 \, c\right)}{384 \, d} - \frac{11 \, a^{3} \cos\left(4 \, d x + 4 \, c\right)}{256 \, d} - \frac{19 \, a^{3} \cos\left(2 \, d x + 2 \, c\right)}{128 \, d} + \frac{a^{3} \sin\left(9 \, d x + 9 \, c\right)}{2304 \, d} - \frac{11 \, a^{3} \sin\left(7 \, d x + 7 \, c\right)}{1792 \, d} - \frac{a^{3} \sin\left(5 \, d x + 5 \, c\right)}{32 \, d} - \frac{a^{3} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{33 \, a^{3} \sin\left(d x + c\right)}{128 \, d}"," ",0,"3/1024*a^3*cos(8*d*x + 8*c)/d + 1/384*a^3*cos(6*d*x + 6*c)/d - 11/256*a^3*cos(4*d*x + 4*c)/d - 19/128*a^3*cos(2*d*x + 2*c)/d + 1/2304*a^3*sin(9*d*x + 9*c)/d - 11/1792*a^3*sin(7*d*x + 7*c)/d - 1/32*a^3*sin(5*d*x + 5*c)/d - 1/48*a^3*sin(3*d*x + 3*c)/d + 33/128*a^3*sin(d*x + c)/d","A",0
523,1,108,0,0.276404," ","integrate(cos(d*x+c)^5*csc(d*x+c)*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{60 \, a^{3} \sin\left(d x + c\right)^{7} + 210 \, a^{3} \sin\left(d x + c\right)^{6} + 84 \, a^{3} \sin\left(d x + c\right)^{5} - 525 \, a^{3} \sin\left(d x + c\right)^{4} - 700 \, a^{3} \sin\left(d x + c\right)^{3} + 210 \, a^{3} \sin\left(d x + c\right)^{2} + 420 \, a^{3} \log\left({\left| \sin\left(d x + c\right) \right|}\right) + 1260 \, a^{3} \sin\left(d x + c\right)}{420 \, d}"," ",0,"1/420*(60*a^3*sin(d*x + c)^7 + 210*a^3*sin(d*x + c)^6 + 84*a^3*sin(d*x + c)^5 - 525*a^3*sin(d*x + c)^4 - 700*a^3*sin(d*x + c)^3 + 210*a^3*sin(d*x + c)^2 + 420*a^3*log(abs(sin(d*x + c))) + 1260*a^3*sin(d*x + c))/d","A",0
524,1,120,0,0.312652," ","integrate(cos(d*x+c)^5*csc(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{10 \, a^{3} \sin\left(d x + c\right)^{6} + 36 \, a^{3} \sin\left(d x + c\right)^{5} + 15 \, a^{3} \sin\left(d x + c\right)^{4} - 100 \, a^{3} \sin\left(d x + c\right)^{3} - 150 \, a^{3} \sin\left(d x + c\right)^{2} + 180 \, a^{3} \log\left({\left| \sin\left(d x + c\right) \right|}\right) + 60 \, a^{3} \sin\left(d x + c\right) - \frac{60 \, {\left(3 \, a^{3} \sin\left(d x + c\right) + a^{3}\right)}}{\sin\left(d x + c\right)}}{60 \, d}"," ",0,"1/60*(10*a^3*sin(d*x + c)^6 + 36*a^3*sin(d*x + c)^5 + 15*a^3*sin(d*x + c)^4 - 100*a^3*sin(d*x + c)^3 - 150*a^3*sin(d*x + c)^2 + 180*a^3*log(abs(sin(d*x + c))) + 60*a^3*sin(d*x + c) - 60*(3*a^3*sin(d*x + c) + a^3)/sin(d*x + c))/d","A",0
525,1,120,0,0.321183," ","integrate(cos(d*x+c)^5*csc(d*x+c)^3*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{12 \, a^{3} \sin\left(d x + c\right)^{5} + 45 \, a^{3} \sin\left(d x + c\right)^{4} + 20 \, a^{3} \sin\left(d x + c\right)^{3} - 150 \, a^{3} \sin\left(d x + c\right)^{2} + 60 \, a^{3} \log\left({\left| \sin\left(d x + c\right) \right|}\right) - 300 \, a^{3} \sin\left(d x + c\right) - \frac{30 \, {\left(3 \, a^{3} \sin\left(d x + c\right)^{2} + 6 \, a^{3} \sin\left(d x + c\right) + a^{3}\right)}}{\sin\left(d x + c\right)^{2}}}{60 \, d}"," ",0,"1/60*(12*a^3*sin(d*x + c)^5 + 45*a^3*sin(d*x + c)^4 + 20*a^3*sin(d*x + c)^3 - 150*a^3*sin(d*x + c)^2 + 60*a^3*log(abs(sin(d*x + c))) - 300*a^3*sin(d*x + c) - 30*(3*a^3*sin(d*x + c)^2 + 6*a^3*sin(d*x + c) + a^3)/sin(d*x + c)^2)/d","A",0
526,1,122,0,0.319987," ","integrate(cos(d*x+c)^5*csc(d*x+c)^4*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{3 \, a^{3} \sin\left(d x + c\right)^{4} + 12 \, a^{3} \sin\left(d x + c\right)^{3} + 6 \, a^{3} \sin\left(d x + c\right)^{2} - 60 \, a^{3} \log\left({\left| \sin\left(d x + c\right) \right|}\right) - 60 \, a^{3} \sin\left(d x + c\right) + \frac{2 \, {\left(55 \, a^{3} \sin\left(d x + c\right)^{3} - 6 \, a^{3} \sin\left(d x + c\right)^{2} - 9 \, a^{3} \sin\left(d x + c\right) - 2 \, a^{3}\right)}}{\sin\left(d x + c\right)^{3}}}{12 \, d}"," ",0,"1/12*(3*a^3*sin(d*x + c)^4 + 12*a^3*sin(d*x + c)^3 + 6*a^3*sin(d*x + c)^2 - 60*a^3*log(abs(sin(d*x + c))) - 60*a^3*sin(d*x + c) + 2*(55*a^3*sin(d*x + c)^3 - 6*a^3*sin(d*x + c)^2 - 9*a^3*sin(d*x + c) - 2*a^3)/sin(d*x + c)^3)/d","A",0
527,1,121,0,0.358317," ","integrate(cos(d*x+c)^5*csc(d*x+c)^5*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{4 \, a^{3} \sin\left(d x + c\right)^{3} + 18 \, a^{3} \sin\left(d x + c\right)^{2} - 60 \, a^{3} \log\left({\left| \sin\left(d x + c\right) \right|}\right) + 12 \, a^{3} \sin\left(d x + c\right) + \frac{125 \, a^{3} \sin\left(d x + c\right)^{4} + 60 \, a^{3} \sin\left(d x + c\right)^{3} - 6 \, a^{3} \sin\left(d x + c\right)^{2} - 12 \, a^{3} \sin\left(d x + c\right) - 3 \, a^{3}}{\sin\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"1/12*(4*a^3*sin(d*x + c)^3 + 18*a^3*sin(d*x + c)^2 - 60*a^3*log(abs(sin(d*x + c))) + 12*a^3*sin(d*x + c) + (125*a^3*sin(d*x + c)^4 + 60*a^3*sin(d*x + c)^3 - 6*a^3*sin(d*x + c)^2 - 12*a^3*sin(d*x + c) - 3*a^3)/sin(d*x + c)^4)/d","A",0
528,1,122,0,0.353220," ","integrate(cos(d*x+c)^5*csc(d*x+c)^6*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{30 \, a^{3} \sin\left(d x + c\right)^{2} + 60 \, a^{3} \log\left({\left| \sin\left(d x + c\right) \right|}\right) + 180 \, a^{3} \sin\left(d x + c\right) - \frac{137 \, a^{3} \sin\left(d x + c\right)^{5} - 300 \, a^{3} \sin\left(d x + c\right)^{4} - 150 \, a^{3} \sin\left(d x + c\right)^{3} + 20 \, a^{3} \sin\left(d x + c\right)^{2} + 45 \, a^{3} \sin\left(d x + c\right) + 12 \, a^{3}}{\sin\left(d x + c\right)^{5}}}{60 \, d}"," ",0,"1/60*(30*a^3*sin(d*x + c)^2 + 60*a^3*log(abs(sin(d*x + c))) + 180*a^3*sin(d*x + c) - (137*a^3*sin(d*x + c)^5 - 300*a^3*sin(d*x + c)^4 - 150*a^3*sin(d*x + c)^3 + 20*a^3*sin(d*x + c)^2 + 45*a^3*sin(d*x + c) + 12*a^3)/sin(d*x + c)^5)/d","A",0
529,1,122,0,0.407105," ","integrate(cos(d*x+c)^5*csc(d*x+c)^7*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{180 \, a^{3} \log\left({\left| \sin\left(d x + c\right) \right|}\right) + 60 \, a^{3} \sin\left(d x + c\right) - \frac{441 \, a^{3} \sin\left(d x + c\right)^{6} + 60 \, a^{3} \sin\left(d x + c\right)^{5} - 150 \, a^{3} \sin\left(d x + c\right)^{4} - 100 \, a^{3} \sin\left(d x + c\right)^{3} + 15 \, a^{3} \sin\left(d x + c\right)^{2} + 36 \, a^{3} \sin\left(d x + c\right) + 10 \, a^{3}}{\sin\left(d x + c\right)^{6}}}{60 \, d}"," ",0,"1/60*(180*a^3*log(abs(sin(d*x + c))) + 60*a^3*sin(d*x + c) - (441*a^3*sin(d*x + c)^6 + 60*a^3*sin(d*x + c)^5 - 150*a^3*sin(d*x + c)^4 - 100*a^3*sin(d*x + c)^3 + 15*a^3*sin(d*x + c)^2 + 36*a^3*sin(d*x + c) + 10*a^3)/sin(d*x + c)^6)/d","A",0
530,1,135,0,0.414051," ","integrate(cos(d*x+c)^5*csc(d*x+c)^4*(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{3 \, a^{4} \sin\left(d x + c\right)^{5} + 15 \, a^{4} \sin\left(d x + c\right)^{4} + 20 \, a^{4} \sin\left(d x + c\right)^{3} - 30 \, a^{4} \sin\left(d x + c\right)^{2} - 60 \, a^{4} \log\left({\left| \sin\left(d x + c\right) \right|}\right) - 150 \, a^{4} \sin\left(d x + c\right) + \frac{5 \, {\left(22 \, a^{4} \sin\left(d x + c\right)^{3} - 12 \, a^{4} \sin\left(d x + c\right)^{2} - 6 \, a^{4} \sin\left(d x + c\right) - a^{4}\right)}}{\sin\left(d x + c\right)^{3}}}{15 \, d}"," ",0,"1/15*(3*a^4*sin(d*x + c)^5 + 15*a^4*sin(d*x + c)^4 + 20*a^4*sin(d*x + c)^3 - 30*a^4*sin(d*x + c)^2 - 60*a^4*log(abs(sin(d*x + c))) - 150*a^4*sin(d*x + c) + 5*(22*a^4*sin(d*x + c)^3 - 12*a^4*sin(d*x + c)^2 - 6*a^4*sin(d*x + c) - a^4)/sin(d*x + c)^3)/d","A",0
531,1,134,0,0.455911," ","integrate(cos(d*x+c)^5*csc(d*x+c)^5*(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{3 \, a^{4} \sin\left(d x + c\right)^{4} + 16 \, a^{4} \sin\left(d x + c\right)^{3} + 24 \, a^{4} \sin\left(d x + c\right)^{2} - 120 \, a^{4} \log\left({\left| \sin\left(d x + c\right) \right|}\right) - 48 \, a^{4} \sin\left(d x + c\right) + \frac{250 \, a^{4} \sin\left(d x + c\right)^{4} + 48 \, a^{4} \sin\left(d x + c\right)^{3} - 24 \, a^{4} \sin\left(d x + c\right)^{2} - 16 \, a^{4} \sin\left(d x + c\right) - 3 \, a^{4}}{\sin\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"1/12*(3*a^4*sin(d*x + c)^4 + 16*a^4*sin(d*x + c)^3 + 24*a^4*sin(d*x + c)^2 - 120*a^4*log(abs(sin(d*x + c))) - 48*a^4*sin(d*x + c) + (250*a^4*sin(d*x + c)^4 + 48*a^4*sin(d*x + c)^3 - 24*a^4*sin(d*x + c)^2 - 16*a^4*sin(d*x + c) - 3*a^4)/sin(d*x + c)^4)/d","A",0
532,1,134,0,0.453130," ","integrate(cos(d*x+c)^5*csc(d*x+c)^6*(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{5 \, a^{4} \sin\left(d x + c\right)^{3} + 30 \, a^{4} \sin\left(d x + c\right)^{2} - 60 \, a^{4} \log\left({\left| \sin\left(d x + c\right) \right|}\right) + 60 \, a^{4} \sin\left(d x + c\right) + \frac{137 \, a^{4} \sin\left(d x + c\right)^{5} + 150 \, a^{4} \sin\left(d x + c\right)^{4} + 30 \, a^{4} \sin\left(d x + c\right)^{3} - 20 \, a^{4} \sin\left(d x + c\right)^{2} - 15 \, a^{4} \sin\left(d x + c\right) - 3 \, a^{4}}{\sin\left(d x + c\right)^{5}}}{15 \, d}"," ",0,"1/15*(5*a^4*sin(d*x + c)^3 + 30*a^4*sin(d*x + c)^2 - 60*a^4*log(abs(sin(d*x + c))) + 60*a^4*sin(d*x + c) + (137*a^4*sin(d*x + c)^5 + 150*a^4*sin(d*x + c)^4 + 30*a^4*sin(d*x + c)^3 - 20*a^4*sin(d*x + c)^2 - 15*a^4*sin(d*x + c) - 3*a^4)/sin(d*x + c)^5)/d","A",0
533,1,49,0,0.168832," ","integrate(cos(d*x+c)^5*sin(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{60 \, \sin\left(d x + c\right)^{7} - 70 \, \sin\left(d x + c\right)^{6} - 84 \, \sin\left(d x + c\right)^{5} + 105 \, \sin\left(d x + c\right)^{4}}{420 \, a d}"," ",0,"1/420*(60*sin(d*x + c)^7 - 70*sin(d*x + c)^6 - 84*sin(d*x + c)^5 + 105*sin(d*x + c)^4)/(a*d)","A",0
534,1,49,0,0.182477," ","integrate(cos(d*x+c)^5*sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{10 \, \sin\left(d x + c\right)^{6} - 12 \, \sin\left(d x + c\right)^{5} - 15 \, \sin\left(d x + c\right)^{4} + 20 \, \sin\left(d x + c\right)^{3}}{60 \, a d}"," ",0,"1/60*(10*sin(d*x + c)^6 - 12*sin(d*x + c)^5 - 15*sin(d*x + c)^4 + 20*sin(d*x + c)^3)/(a*d)","A",0
535,1,49,0,0.180602," ","integrate(cos(d*x+c)^5*sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{12 \, \sin\left(d x + c\right)^{5} - 15 \, \sin\left(d x + c\right)^{4} - 20 \, \sin\left(d x + c\right)^{3} + 30 \, \sin\left(d x + c\right)^{2}}{60 \, a d}"," ",0,"1/60*(12*sin(d*x + c)^5 - 15*sin(d*x + c)^4 - 20*sin(d*x + c)^3 + 30*sin(d*x + c)^2)/(a*d)","A",0
536,1,61,0,0.172405," ","integrate(cos(d*x+c)^5*csc(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{6 \, \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a} + \frac{2 \, a^{2} \sin\left(d x + c\right)^{3} - 3 \, a^{2} \sin\left(d x + c\right)^{2} - 6 \, a^{2} \sin\left(d x + c\right)}{a^{3}}}{6 \, d}"," ",0,"1/6*(6*log(abs(sin(d*x + c)))/a + (2*a^2*sin(d*x + c)^3 - 3*a^2*sin(d*x + c)^2 - 6*a^2*sin(d*x + c))/a^3)/d","A",0
537,1,65,0,0.193125," ","integrate(cos(d*x+c)^5*csc(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{2 \, \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a} - \frac{a \sin\left(d x + c\right)^{2} - 2 \, a \sin\left(d x + c\right)}{a^{2}} - \frac{2 \, {\left(\sin\left(d x + c\right) - 1\right)}}{a \sin\left(d x + c\right)}}{2 \, d}"," ",0,"-1/2*(2*log(abs(sin(d*x + c)))/a - (a*sin(d*x + c)^2 - 2*a*sin(d*x + c))/a^2 - 2*(sin(d*x + c) - 1)/(a*sin(d*x + c)))/d","A",0
538,1,63,0,0.187124," ","integrate(cos(d*x+c)^5*csc(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{2 \, \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a} - \frac{2 \, \sin\left(d x + c\right)}{a} - \frac{3 \, \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) - 1}{a \sin\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(2*log(abs(sin(d*x + c)))/a - 2*sin(d*x + c)/a - (3*sin(d*x + c)^2 + 2*sin(d*x + c) - 1)/(a*sin(d*x + c)^2))/d","A",0
539,1,62,0,0.197094," ","integrate(cos(d*x+c)^5*csc(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{6 \, \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a} - \frac{11 \, \sin\left(d x + c\right)^{3} - 6 \, \sin\left(d x + c\right)^{2} - 3 \, \sin\left(d x + c\right) + 2}{a \sin\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(6*log(abs(sin(d*x + c)))/a - (11*sin(d*x + c)^3 - 6*sin(d*x + c)^2 - 3*sin(d*x + c) + 2)/(a*sin(d*x + c)^3))/d","A",0
540,1,46,0,0.195786," ","integrate(cos(d*x+c)^5*csc(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{12 \, \sin\left(d x + c\right)^{3} - 6 \, \sin\left(d x + c\right)^{2} - 4 \, \sin\left(d x + c\right) + 3}{12 \, a d \sin\left(d x + c\right)^{4}}"," ",0,"-1/12*(12*sin(d*x + c)^3 - 6*sin(d*x + c)^2 - 4*sin(d*x + c) + 3)/(a*d*sin(d*x + c)^4)","A",0
541,1,46,0,0.228799," ","integrate(cos(d*x+c)^5*csc(d*x+c)^6/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{30 \, \sin\left(d x + c\right)^{3} - 20 \, \sin\left(d x + c\right)^{2} - 15 \, \sin\left(d x + c\right) + 12}{60 \, a d \sin\left(d x + c\right)^{5}}"," ",0,"-1/60*(30*sin(d*x + c)^3 - 20*sin(d*x + c)^2 - 15*sin(d*x + c) + 12)/(a*d*sin(d*x + c)^5)","A",0
542,1,46,0,0.215174," ","integrate(cos(d*x+c)^5*csc(d*x+c)^7/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{20 \, \sin\left(d x + c\right)^{3} - 15 \, \sin\left(d x + c\right)^{2} - 12 \, \sin\left(d x + c\right) + 10}{60 \, a d \sin\left(d x + c\right)^{6}}"," ",0,"-1/60*(20*sin(d*x + c)^3 - 15*sin(d*x + c)^2 - 12*sin(d*x + c) + 10)/(a*d*sin(d*x + c)^6)","A",0
543,1,46,0,0.230122," ","integrate(cos(d*x+c)^5*csc(d*x+c)^8/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{105 \, \sin\left(d x + c\right)^{3} - 84 \, \sin\left(d x + c\right)^{2} - 70 \, \sin\left(d x + c\right) + 60}{420 \, a d \sin\left(d x + c\right)^{7}}"," ",0,"-1/420*(105*sin(d*x + c)^3 - 84*sin(d*x + c)^2 - 70*sin(d*x + c) + 60)/(a*d*sin(d*x + c)^7)","A",0
544,1,39,0,0.226367," ","integrate(cos(d*x+c)^5*sin(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{10 \, \sin\left(d x + c\right)^{6} - 24 \, \sin\left(d x + c\right)^{5} + 15 \, \sin\left(d x + c\right)^{4}}{60 \, a^{2} d}"," ",0,"1/60*(10*sin(d*x + c)^6 - 24*sin(d*x + c)^5 + 15*sin(d*x + c)^4)/(a^2*d)","A",0
545,1,39,0,0.177670," ","integrate(cos(d*x+c)^5*sin(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{6 \, \sin\left(d x + c\right)^{5} - 15 \, \sin\left(d x + c\right)^{4} + 10 \, \sin\left(d x + c\right)^{3}}{30 \, a^{2} d}"," ",0,"1/30*(6*sin(d*x + c)^5 - 15*sin(d*x + c)^4 + 10*sin(d*x + c)^3)/(a^2*d)","A",0
546,1,39,0,0.172538," ","integrate(cos(d*x+c)^5*sin(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{3 \, \sin\left(d x + c\right)^{4} - 8 \, \sin\left(d x + c\right)^{3} + 6 \, \sin\left(d x + c\right)^{2}}{12 \, a^{2} d}"," ",0,"1/12*(3*sin(d*x + c)^4 - 8*sin(d*x + c)^3 + 6*sin(d*x + c)^2)/(a^2*d)","A",0
547,1,47,0,0.175876," ","integrate(cos(d*x+c)^5*csc(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2 \, \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a^{2}} + \frac{a^{2} \sin\left(d x + c\right)^{2} - 4 \, a^{2} \sin\left(d x + c\right)}{a^{4}}}{2 \, d}"," ",0,"1/2*(2*log(abs(sin(d*x + c)))/a^2 + (a^2*sin(d*x + c)^2 - 4*a^2*sin(d*x + c))/a^4)/d","A",0
548,1,53,0,0.199726," ","integrate(cos(d*x+c)^5*csc(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{2 \, \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a^{2}} - \frac{\sin\left(d x + c\right)}{a^{2}} - \frac{2 \, \sin\left(d x + c\right) - 1}{a^{2} \sin\left(d x + c\right)}}{d}"," ",0,"-(2*log(abs(sin(d*x + c)))/a^2 - sin(d*x + c)/a^2 - (2*sin(d*x + c) - 1)/(a^2*sin(d*x + c)))/d","A",0
549,1,52,0,0.222741," ","integrate(cos(d*x+c)^5*csc(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2 \, \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a^{2}} - \frac{3 \, \sin\left(d x + c\right)^{2} - 4 \, \sin\left(d x + c\right) + 1}{a^{2} \sin\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"1/2*(2*log(abs(sin(d*x + c)))/a^2 - (3*sin(d*x + c)^2 - 4*sin(d*x + c) + 1)/(a^2*sin(d*x + c)^2))/d","A",0
550,1,36,0,0.232790," ","integrate(cos(d*x+c)^5*csc(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{3 \, \sin\left(d x + c\right)^{2} - 3 \, \sin\left(d x + c\right) + 1}{3 \, a^{2} d \sin\left(d x + c\right)^{3}}"," ",0,"-1/3*(3*sin(d*x + c)^2 - 3*sin(d*x + c) + 1)/(a^2*d*sin(d*x + c)^3)","A",0
551,1,36,0,0.261192," ","integrate(cos(d*x+c)^5*csc(d*x+c)^5/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{6 \, \sin\left(d x + c\right)^{2} - 8 \, \sin\left(d x + c\right) + 3}{12 \, a^{2} d \sin\left(d x + c\right)^{4}}"," ",0,"-1/12*(6*sin(d*x + c)^2 - 8*sin(d*x + c) + 3)/(a^2*d*sin(d*x + c)^4)","A",0
552,1,36,0,0.228618," ","integrate(cos(d*x+c)^5*csc(d*x+c)^6/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{10 \, \sin\left(d x + c\right)^{2} - 15 \, \sin\left(d x + c\right) + 6}{30 \, a^{2} d \sin\left(d x + c\right)^{5}}"," ",0,"-1/30*(10*sin(d*x + c)^2 - 15*sin(d*x + c) + 6)/(a^2*d*sin(d*x + c)^5)","A",0
553,1,36,0,0.273065," ","integrate(cos(d*x+c)^5*csc(d*x+c)^7/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{15 \, \sin\left(d x + c\right)^{2} - 24 \, \sin\left(d x + c\right) + 10}{60 \, a^{2} d \sin\left(d x + c\right)^{6}}"," ",0,"-1/60*(15*sin(d*x + c)^2 - 24*sin(d*x + c) + 10)/(a^2*d*sin(d*x + c)^6)","A",0
554,1,193,0,0.276473," ","integrate(cos(d*x+c)^5*sin(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{60 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}{a^{3}} - \frac{120 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{137 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 120 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 805 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 640 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1910 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 1136 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1910 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 640 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 805 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 120 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 137}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5} a^{3}}}{15 \, d}"," ",0,"1/15*(60*log(tan(1/2*d*x + 1/2*c)^2 + 1)/a^3 - 120*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - (137*tan(1/2*d*x + 1/2*c)^10 - 120*tan(1/2*d*x + 1/2*c)^9 + 805*tan(1/2*d*x + 1/2*c)^8 - 640*tan(1/2*d*x + 1/2*c)^7 + 1910*tan(1/2*d*x + 1/2*c)^6 - 1136*tan(1/2*d*x + 1/2*c)^5 + 1910*tan(1/2*d*x + 1/2*c)^4 - 640*tan(1/2*d*x + 1/2*c)^3 + 805*tan(1/2*d*x + 1/2*c)^2 - 120*tan(1/2*d*x + 1/2*c) + 137)/((tan(1/2*d*x + 1/2*c)^2 + 1)^5*a^3))/d","B",0
555,1,167,0,0.220599," ","integrate(cos(d*x+c)^5*sin(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{12 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}{a^{3}} - \frac{24 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{25 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 24 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 124 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 96 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 210 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 96 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 124 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 24 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 25}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4} a^{3}}}{3 \, d}"," ",0,"-1/3*(12*log(tan(1/2*d*x + 1/2*c)^2 + 1)/a^3 - 24*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - (25*tan(1/2*d*x + 1/2*c)^8 - 24*tan(1/2*d*x + 1/2*c)^7 + 124*tan(1/2*d*x + 1/2*c)^6 - 96*tan(1/2*d*x + 1/2*c)^5 + 210*tan(1/2*d*x + 1/2*c)^4 - 96*tan(1/2*d*x + 1/2*c)^3 + 124*tan(1/2*d*x + 1/2*c)^2 - 24*tan(1/2*d*x + 1/2*c) + 25)/((tan(1/2*d*x + 1/2*c)^2 + 1)^4*a^3))/d","B",0
556,1,141,0,0.210470," ","integrate(cos(d*x+c)^5*sin(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{6 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}{a^{3}} - \frac{12 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{11 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 12 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 42 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 28 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 42 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 11}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} a^{3}}\right)}}{3 \, d}"," ",0,"2/3*(6*log(tan(1/2*d*x + 1/2*c)^2 + 1)/a^3 - 12*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - (11*tan(1/2*d*x + 1/2*c)^6 - 12*tan(1/2*d*x + 1/2*c)^5 + 42*tan(1/2*d*x + 1/2*c)^4 - 28*tan(1/2*d*x + 1/2*c)^3 + 42*tan(1/2*d*x + 1/2*c)^2 - 12*tan(1/2*d*x + 1/2*c) + 11)/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*a^3))/d","B",0
557,1,103,0,0.210596," ","integrate(cos(d*x+c)^5*csc(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{3 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}{a^{3}} - \frac{8 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} + \frac{\log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} - \frac{3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a^{3}}}{d}"," ",0,"(3*log(tan(1/2*d*x + 1/2*c)^2 + 1)/a^3 - 8*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 + log(abs(tan(1/2*d*x + 1/2*c)))/a^3 - (3*tan(1/2*d*x + 1/2*c)^2 - 2*tan(1/2*d*x + 1/2*c) + 3)/((tan(1/2*d*x + 1/2*c)^2 + 1)*a^3))/d","B",0
558,1,101,0,0.250217," ","integrate(cos(d*x+c)^5*csc(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{2 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}{a^{3}} - \frac{16 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} + \frac{6 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} + \frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3}} - \frac{6 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1}{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}}{2 \, d}"," ",0,"-1/2*(2*log(tan(1/2*d*x + 1/2*c)^2 + 1)/a^3 - 16*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 + 6*log(abs(tan(1/2*d*x + 1/2*c)))/a^3 + tan(1/2*d*x + 1/2*c)/a^3 - (6*tan(1/2*d*x + 1/2*c) - 1)/(a^3*tan(1/2*d*x + 1/2*c)))/d","B",0
559,1,115,0,0.247859," ","integrate(cos(d*x+c)^5*csc(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{64 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{32 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} + \frac{48 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1}{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}} + \frac{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{8 \, d}"," ",0,"-1/8*(64*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - 32*log(abs(tan(1/2*d*x + 1/2*c)))/a^3 + (48*tan(1/2*d*x + 1/2*c)^2 - 12*tan(1/2*d*x + 1/2*c) + 1)/(a^3*tan(1/2*d*x + 1/2*c)^2) + (a^3*tan(1/2*d*x + 1/2*c)^2 - 12*a^3*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
560,1,145,0,0.249195," ","integrate(cos(d*x+c)^5*csc(d*x+c)^4/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{192 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{96 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} + \frac{176 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 51 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1}{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}} - \frac{a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 51 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{9}}}{24 \, d}"," ",0,"1/24*(192*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - 96*log(abs(tan(1/2*d*x + 1/2*c)))/a^3 + (176*tan(1/2*d*x + 1/2*c)^3 - 51*tan(1/2*d*x + 1/2*c)^2 + 9*tan(1/2*d*x + 1/2*c) - 1)/(a^3*tan(1/2*d*x + 1/2*c)^3) - (a^6*tan(1/2*d*x + 1/2*c)^3 - 9*a^6*tan(1/2*d*x + 1/2*c)^2 + 51*a^6*tan(1/2*d*x + 1/2*c))/a^9)/d","A",0
561,1,174,0,0.264889," ","integrate(cos(d*x+c)^5*csc(d*x+c)^5/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{1536 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{768 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} + \frac{1600 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 456 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 108 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 24 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3}{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}} + \frac{3 \, {\left(a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 8 \, a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 152 \, a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a^{12}}}{192 \, d}"," ",0,"-1/192*(1536*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - 768*log(abs(tan(1/2*d*x + 1/2*c)))/a^3 + (1600*tan(1/2*d*x + 1/2*c)^4 - 456*tan(1/2*d*x + 1/2*c)^3 + 108*tan(1/2*d*x + 1/2*c)^2 - 24*tan(1/2*d*x + 1/2*c) + 3)/(a^3*tan(1/2*d*x + 1/2*c)^4) + 3*(a^9*tan(1/2*d*x + 1/2*c)^4 - 8*a^9*tan(1/2*d*x + 1/2*c)^3 + 36*a^9*tan(1/2*d*x + 1/2*c)^2 - 152*a^9*tan(1/2*d*x + 1/2*c))/a^12)/d","A",0
562,1,204,0,0.270096," ","integrate(cos(d*x+c)^5*csc(d*x+c)^6/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{7680 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{3}} - \frac{3840 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} + \frac{8768 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 2460 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 660 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 190 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 45 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6}{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}} - \frac{6 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 45 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 190 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 660 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2460 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{960 \, d}"," ",0,"1/960*(7680*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^3 - 3840*log(abs(tan(1/2*d*x + 1/2*c)))/a^3 + (8768*tan(1/2*d*x + 1/2*c)^5 - 2460*tan(1/2*d*x + 1/2*c)^4 + 660*tan(1/2*d*x + 1/2*c)^3 - 190*tan(1/2*d*x + 1/2*c)^2 + 45*tan(1/2*d*x + 1/2*c) - 6)/(a^3*tan(1/2*d*x + 1/2*c)^5) - (6*a^12*tan(1/2*d*x + 1/2*c)^5 - 45*a^12*tan(1/2*d*x + 1/2*c)^4 + 190*a^12*tan(1/2*d*x + 1/2*c)^3 - 660*a^12*tan(1/2*d*x + 1/2*c)^2 + 2460*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
563,1,218,0,0.301309," ","integrate(cos(d*x+c)^5*csc(d*x+c)^5/(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{6144 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{4}} - \frac{3072 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{4}} - \frac{1536 \, {\left(6 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 11 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6\right)}}{a^{4} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{2}} + \frac{6400 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1248 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 204 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 32 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3}{a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}} + \frac{3 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 32 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 204 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1248 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{16}}}{192 \, d}"," ",0,"-1/192*(6144*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^4 - 3072*log(abs(tan(1/2*d*x + 1/2*c)))/a^4 - 1536*(6*tan(1/2*d*x + 1/2*c)^2 + 11*tan(1/2*d*x + 1/2*c) + 6)/(a^4*(tan(1/2*d*x + 1/2*c) + 1)^2) + (6400*tan(1/2*d*x + 1/2*c)^4 - 1248*tan(1/2*d*x + 1/2*c)^3 + 204*tan(1/2*d*x + 1/2*c)^2 - 32*tan(1/2*d*x + 1/2*c) + 3)/(a^4*tan(1/2*d*x + 1/2*c)^4) + (3*a^12*tan(1/2*d*x + 1/2*c)^4 - 32*a^12*tan(1/2*d*x + 1/2*c)^3 + 204*a^12*tan(1/2*d*x + 1/2*c)^2 - 1248*a^12*tan(1/2*d*x + 1/2*c))/a^16)/d","A",0
564,1,248,0,0.314695," ","integrate(cos(d*x+c)^5*csc(d*x+c)^6/(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{19200 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{a^{4}} - \frac{9600 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{4}} - \frac{1920 \, {\left(15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 28 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15\right)}}{a^{4} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{2}} + \frac{21920 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4350 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 840 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 175 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 30 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3}{a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}} - \frac{3 \, a^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 30 \, a^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 175 \, a^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 840 \, a^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 4350 \, a^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{20}}}{480 \, d}"," ",0,"1/480*(19200*log(abs(tan(1/2*d*x + 1/2*c) + 1))/a^4 - 9600*log(abs(tan(1/2*d*x + 1/2*c)))/a^4 - 1920*(15*tan(1/2*d*x + 1/2*c)^2 + 28*tan(1/2*d*x + 1/2*c) + 15)/(a^4*(tan(1/2*d*x + 1/2*c) + 1)^2) + (21920*tan(1/2*d*x + 1/2*c)^5 - 4350*tan(1/2*d*x + 1/2*c)^4 + 840*tan(1/2*d*x + 1/2*c)^3 - 175*tan(1/2*d*x + 1/2*c)^2 + 30*tan(1/2*d*x + 1/2*c) - 3)/(a^4*tan(1/2*d*x + 1/2*c)^5) - (3*a^16*tan(1/2*d*x + 1/2*c)^5 - 30*a^16*tan(1/2*d*x + 1/2*c)^4 + 175*a^16*tan(1/2*d*x + 1/2*c)^3 - 840*a^16*tan(1/2*d*x + 1/2*c)^2 + 4350*a^16*tan(1/2*d*x + 1/2*c))/a^20)/d","A",0
565,-1,0,0,0.000000," ","integrate(cos(d*x+c)^5*sin(d*x+c)^n*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
566,-1,0,0,0.000000," ","integrate(cos(d*x+c)^5*sin(d*x+c)^n*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
567,-1,0,0,0.000000," ","integrate(cos(d*x+c)^5*sin(d*x+c)^n*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
568,0,0,0,0.000000," ","integrate(cos(d*x+c)^5*sin(d*x+c)^n/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\int \frac{\sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{5}}{a \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sin(d*x + c)^n*cos(d*x + c)^5/(a*sin(d*x + c) + a), x)","F",0
569,0,0,0,0.000000," ","integrate(cos(d*x+c)^5*sin(d*x+c)^n/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{5}}{{\left(a \sin\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sin(d*x + c)^n*cos(d*x + c)^5/(a*sin(d*x + c) + a)^2, x)","F",0
570,0,0,0,0.000000," ","integrate(cos(d*x+c)^5*sin(d*x+c)^n/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\int \frac{\sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{5}}{{\left(a \sin\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(sin(d*x + c)^n*cos(d*x + c)^5/(a*sin(d*x + c) + a)^3, x)","F",0
571,0,0,0,0.000000," ","integrate(cos(d*x+c)^5*sin(d*x+c)^n/(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","\int \frac{\sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{5}}{{\left(a \sin\left(d x + c\right) + a\right)}^{4}}\,{d x}"," ",0,"integrate(sin(d*x + c)^n*cos(d*x + c)^5/(a*sin(d*x + c) + a)^4, x)","F",0
572,1,167,0,0.295343," ","integrate(cos(d*x+c)^6*sin(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{3}{256} \, a x - \frac{a \cos\left(11 \, d x + 11 \, c\right)}{11264 \, d} - \frac{a \cos\left(9 \, d x + 9 \, c\right)}{9216 \, d} + \frac{5 \, a \cos\left(7 \, d x + 7 \, c\right)}{7168 \, d} + \frac{a \cos\left(5 \, d x + 5 \, c\right)}{1024 \, d} - \frac{5 \, a \cos\left(3 \, d x + 3 \, c\right)}{1536 \, d} - \frac{5 \, a \cos\left(d x + c\right)}{512 \, d} + \frac{a \sin\left(10 \, d x + 10 \, c\right)}{5120 \, d} + \frac{a \sin\left(8 \, d x + 8 \, c\right)}{2048 \, d} - \frac{a \sin\left(6 \, d x + 6 \, c\right)}{1024 \, d} - \frac{a \sin\left(4 \, d x + 4 \, c\right)}{256 \, d} + \frac{a \sin\left(2 \, d x + 2 \, c\right)}{512 \, d}"," ",0,"3/256*a*x - 1/11264*a*cos(11*d*x + 11*c)/d - 1/9216*a*cos(9*d*x + 9*c)/d + 5/7168*a*cos(7*d*x + 7*c)/d + 1/1024*a*cos(5*d*x + 5*c)/d - 5/1536*a*cos(3*d*x + 3*c)/d - 5/512*a*cos(d*x + c)/d + 1/5120*a*sin(10*d*x + 10*c)/d + 1/2048*a*sin(8*d*x + 8*c)/d - 1/1024*a*sin(6*d*x + 6*c)/d - 1/256*a*sin(4*d*x + 4*c)/d + 1/512*a*sin(2*d*x + 2*c)/d","A",0
573,1,137,0,0.263397," ","integrate(cos(d*x+c)^6*sin(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{3}{256} \, a x + \frac{a \cos\left(9 \, d x + 9 \, c\right)}{2304 \, d} + \frac{3 \, a \cos\left(7 \, d x + 7 \, c\right)}{1792 \, d} - \frac{a \cos\left(3 \, d x + 3 \, c\right)}{96 \, d} - \frac{3 \, a \cos\left(d x + c\right)}{128 \, d} + \frac{a \sin\left(10 \, d x + 10 \, c\right)}{5120 \, d} + \frac{a \sin\left(8 \, d x + 8 \, c\right)}{2048 \, d} - \frac{a \sin\left(6 \, d x + 6 \, c\right)}{1024 \, d} - \frac{a \sin\left(4 \, d x + 4 \, c\right)}{256 \, d} + \frac{a \sin\left(2 \, d x + 2 \, c\right)}{512 \, d}"," ",0,"3/256*a*x + 1/2304*a*cos(9*d*x + 9*c)/d + 3/1792*a*cos(7*d*x + 7*c)/d - 1/96*a*cos(3*d*x + 3*c)/d - 3/128*a*cos(d*x + c)/d + 1/5120*a*sin(10*d*x + 10*c)/d + 1/2048*a*sin(8*d*x + 8*c)/d - 1/1024*a*sin(6*d*x + 6*c)/d - 1/256*a*sin(4*d*x + 4*c)/d + 1/512*a*sin(2*d*x + 2*c)/d","A",0
574,1,122,0,0.260448," ","integrate(cos(d*x+c)^6*sin(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{5}{128} \, a x + \frac{a \cos\left(9 \, d x + 9 \, c\right)}{2304 \, d} + \frac{3 \, a \cos\left(7 \, d x + 7 \, c\right)}{1792 \, d} - \frac{a \cos\left(3 \, d x + 3 \, c\right)}{96 \, d} - \frac{3 \, a \cos\left(d x + c\right)}{128 \, d} - \frac{a \sin\left(8 \, d x + 8 \, c\right)}{1024 \, d} - \frac{a \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} - \frac{a \sin\left(4 \, d x + 4 \, c\right)}{128 \, d} + \frac{a \sin\left(2 \, d x + 2 \, c\right)}{64 \, d}"," ",0,"5/128*a*x + 1/2304*a*cos(9*d*x + 9*c)/d + 3/1792*a*cos(7*d*x + 7*c)/d - 1/96*a*cos(3*d*x + 3*c)/d - 3/128*a*cos(d*x + c)/d - 1/1024*a*sin(8*d*x + 8*c)/d - 1/192*a*sin(6*d*x + 6*c)/d - 1/128*a*sin(4*d*x + 4*c)/d + 1/64*a*sin(2*d*x + 2*c)/d","A",0
575,1,122,0,0.192158," ","integrate(cos(d*x+c)^6*sin(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{5}{128} \, a x - \frac{a \cos\left(7 \, d x + 7 \, c\right)}{448 \, d} - \frac{a \cos\left(5 \, d x + 5 \, c\right)}{64 \, d} - \frac{3 \, a \cos\left(3 \, d x + 3 \, c\right)}{64 \, d} - \frac{5 \, a \cos\left(d x + c\right)}{64 \, d} - \frac{a \sin\left(8 \, d x + 8 \, c\right)}{1024 \, d} - \frac{a \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} - \frac{a \sin\left(4 \, d x + 4 \, c\right)}{128 \, d} + \frac{a \sin\left(2 \, d x + 2 \, c\right)}{64 \, d}"," ",0,"5/128*a*x - 1/448*a*cos(7*d*x + 7*c)/d - 1/64*a*cos(5*d*x + 5*c)/d - 3/64*a*cos(3*d*x + 3*c)/d - 5/64*a*cos(d*x + c)/d - 1/1024*a*sin(8*d*x + 8*c)/d - 1/192*a*sin(6*d*x + 6*c)/d - 1/128*a*sin(4*d*x + 4*c)/d + 1/64*a*sin(2*d*x + 2*c)/d","A",0
576,1,201,0,0.193207," ","integrate(cos(d*x+c)^6*csc(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{75 \, {\left(d x + c\right)} a + 240 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{2 \, {\left(165 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 720 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 25 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 2160 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 450 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 3680 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 450 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3360 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 25 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1488 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 165 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 368 \, a\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(75*(d*x + c)*a + 240*a*log(abs(tan(1/2*d*x + 1/2*c))) - 2*(165*a*tan(1/2*d*x + 1/2*c)^11 - 720*a*tan(1/2*d*x + 1/2*c)^10 - 25*a*tan(1/2*d*x + 1/2*c)^9 - 2160*a*tan(1/2*d*x + 1/2*c)^8 + 450*a*tan(1/2*d*x + 1/2*c)^7 - 3680*a*tan(1/2*d*x + 1/2*c)^6 - 450*a*tan(1/2*d*x + 1/2*c)^5 - 3360*a*tan(1/2*d*x + 1/2*c)^4 + 25*a*tan(1/2*d*x + 1/2*c)^3 - 1488*a*tan(1/2*d*x + 1/2*c)^2 - 165*a*tan(1/2*d*x + 1/2*c) - 368*a)/(tan(1/2*d*x + 1/2*c)^2 + 1)^6)/d","A",0
577,1,198,0,0.198536," ","integrate(cos(d*x+c)^6*csc(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{225 \, {\left(d x + c\right)} a - 120 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 60 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{60 \, {\left(2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)} - \frac{2 \, {\left(135 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 360 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 150 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 720 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 1120 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 150 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 560 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 135 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 184 \, a\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5}}}{120 \, d}"," ",0,"-1/120*(225*(d*x + c)*a - 120*a*log(abs(tan(1/2*d*x + 1/2*c))) - 60*a*tan(1/2*d*x + 1/2*c) + 60*(2*a*tan(1/2*d*x + 1/2*c) + a)/tan(1/2*d*x + 1/2*c) - 2*(135*a*tan(1/2*d*x + 1/2*c)^9 + 360*a*tan(1/2*d*x + 1/2*c)^8 + 150*a*tan(1/2*d*x + 1/2*c)^7 + 720*a*tan(1/2*d*x + 1/2*c)^6 + 1120*a*tan(1/2*d*x + 1/2*c)^4 - 150*a*tan(1/2*d*x + 1/2*c)^3 + 560*a*tan(1/2*d*x + 1/2*c)^2 - 135*a*tan(1/2*d*x + 1/2*c) + 184*a)/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","A",0
578,1,214,0,0.203363," ","integrate(cos(d*x+c)^6*csc(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 45 \, {\left(d x + c\right)} a - 60 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 12 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{3 \, {\left(30 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}} + \frac{2 \, {\left(27 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 72 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 168 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 152 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 27 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 56 \, a\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*a*tan(1/2*d*x + 1/2*c)^2 - 45*(d*x + c)*a - 60*a*log(abs(tan(1/2*d*x + 1/2*c))) + 12*a*tan(1/2*d*x + 1/2*c) + 3*(30*a*tan(1/2*d*x + 1/2*c)^2 - 4*a*tan(1/2*d*x + 1/2*c) - a)/tan(1/2*d*x + 1/2*c)^2 + 2*(27*a*tan(1/2*d*x + 1/2*c)^7 - 72*a*tan(1/2*d*x + 1/2*c)^6 + 3*a*tan(1/2*d*x + 1/2*c)^5 - 168*a*tan(1/2*d*x + 1/2*c)^4 - 3*a*tan(1/2*d*x + 1/2*c)^3 - 152*a*tan(1/2*d*x + 1/2*c)^2 - 27*a*tan(1/2*d*x + 1/2*c) - 56*a)/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","A",0
579,1,220,0,0.214123," ","integrate(cos(d*x+c)^6*csc(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 180 \, {\left(d x + c\right)} a - 180 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 81 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{110 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 9 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 111 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 240 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 273 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 306 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 253 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 72 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}^{3}}}{72 \, d}"," ",0,"1/72*(3*a*tan(1/2*d*x + 1/2*c)^3 + 9*a*tan(1/2*d*x + 1/2*c)^2 + 180*(d*x + c)*a - 180*a*log(abs(tan(1/2*d*x + 1/2*c))) - 81*a*tan(1/2*d*x + 1/2*c) + (110*a*tan(1/2*d*x + 1/2*c)^9 + 9*a*tan(1/2*d*x + 1/2*c)^8 - 111*a*tan(1/2*d*x + 1/2*c)^7 + 240*a*tan(1/2*d*x + 1/2*c)^6 - 273*a*tan(1/2*d*x + 1/2*c)^5 + 306*a*tan(1/2*d*x + 1/2*c)^4 - 253*a*tan(1/2*d*x + 1/2*c)^3 + 72*a*tan(1/2*d*x + 1/2*c)^2 - 9*a*tan(1/2*d*x + 1/2*c) - 3*a)/(tan(1/2*d*x + 1/2*c)^3 + tan(1/2*d*x + 1/2*c))^3)/d","A",0
580,1,213,0,0.235681," ","integrate(cos(d*x+c)^6*csc(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 8 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 48 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 480 \, {\left(d x + c\right)} a + 360 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 216 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{192 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, a\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}} - \frac{750 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 216 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 48 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 8 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}}}{192 \, d}"," ",0,"1/192*(3*a*tan(1/2*d*x + 1/2*c)^4 + 8*a*tan(1/2*d*x + 1/2*c)^3 - 48*a*tan(1/2*d*x + 1/2*c)^2 + 480*(d*x + c)*a + 360*a*log(abs(tan(1/2*d*x + 1/2*c))) - 216*a*tan(1/2*d*x + 1/2*c) - 192*(a*tan(1/2*d*x + 1/2*c)^3 - 2*a*tan(1/2*d*x + 1/2*c)^2 - a*tan(1/2*d*x + 1/2*c) - 2*a)/(tan(1/2*d*x + 1/2*c)^2 + 1)^2 - (750*a*tan(1/2*d*x + 1/2*c)^4 - 216*a*tan(1/2*d*x + 1/2*c)^3 - 48*a*tan(1/2*d*x + 1/2*c)^2 + 8*a*tan(1/2*d*x + 1/2*c) + 3*a)/tan(1/2*d*x + 1/2*c)^4)/d","A",0
581,1,199,0,0.221900," ","integrate(cos(d*x+c)^6*csc(d*x+c)^6*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{6 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 70 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 240 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 960 \, {\left(d x + c\right)} a + 1800 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 660 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{1920 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} - \frac{4110 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 660 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 240 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 70 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 15 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{960 \, d}"," ",0,"1/960*(6*a*tan(1/2*d*x + 1/2*c)^5 + 15*a*tan(1/2*d*x + 1/2*c)^4 - 70*a*tan(1/2*d*x + 1/2*c)^3 - 240*a*tan(1/2*d*x + 1/2*c)^2 - 960*(d*x + c)*a + 1800*a*log(abs(tan(1/2*d*x + 1/2*c))) + 660*a*tan(1/2*d*x + 1/2*c) + 1920*a/(tan(1/2*d*x + 1/2*c)^2 + 1) - (4110*a*tan(1/2*d*x + 1/2*c)^5 + 660*a*tan(1/2*d*x + 1/2*c)^4 - 240*a*tan(1/2*d*x + 1/2*c)^3 - 70*a*tan(1/2*d*x + 1/2*c)^2 + 15*a*tan(1/2*d*x + 1/2*c) + 6*a)/tan(1/2*d*x + 1/2*c)^5)/d","A",0
582,1,208,0,0.267868," ","integrate(cos(d*x+c)^6*csc(d*x+c)^7*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{5 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 12 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 45 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 140 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 225 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1920 \, {\left(d x + c\right)} a - 600 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 1320 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{1470 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 1320 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 225 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 140 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 45 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6}}}{1920 \, d}"," ",0,"1/1920*(5*a*tan(1/2*d*x + 1/2*c)^6 + 12*a*tan(1/2*d*x + 1/2*c)^5 - 45*a*tan(1/2*d*x + 1/2*c)^4 - 140*a*tan(1/2*d*x + 1/2*c)^3 + 225*a*tan(1/2*d*x + 1/2*c)^2 - 1920*(d*x + c)*a - 600*a*log(abs(tan(1/2*d*x + 1/2*c))) + 1320*a*tan(1/2*d*x + 1/2*c) + (1470*a*tan(1/2*d*x + 1/2*c)^6 - 1320*a*tan(1/2*d*x + 1/2*c)^5 - 225*a*tan(1/2*d*x + 1/2*c)^4 + 140*a*tan(1/2*d*x + 1/2*c)^3 + 45*a*tan(1/2*d*x + 1/2*c)^2 - 12*a*tan(1/2*d*x + 1/2*c) - 5*a)/tan(1/2*d*x + 1/2*c)^6)/d","A",0
583,1,228,0,0.235971," ","integrate(cos(d*x+c)^6*csc(d*x+c)^8*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 7 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 21 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 63 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 63 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 315 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 840 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 105 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{2178 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 105 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 315 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 63 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 63 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 21 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 7 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7}}}{2688 \, d}"," ",0,"1/2688*(3*a*tan(1/2*d*x + 1/2*c)^7 + 7*a*tan(1/2*d*x + 1/2*c)^6 - 21*a*tan(1/2*d*x + 1/2*c)^5 - 63*a*tan(1/2*d*x + 1/2*c)^4 + 63*a*tan(1/2*d*x + 1/2*c)^3 + 315*a*tan(1/2*d*x + 1/2*c)^2 - 840*a*log(abs(tan(1/2*d*x + 1/2*c))) - 105*a*tan(1/2*d*x + 1/2*c) + (2178*a*tan(1/2*d*x + 1/2*c)^7 + 105*a*tan(1/2*d*x + 1/2*c)^6 - 315*a*tan(1/2*d*x + 1/2*c)^5 - 63*a*tan(1/2*d*x + 1/2*c)^4 + 63*a*tan(1/2*d*x + 1/2*c)^3 + 21*a*tan(1/2*d*x + 1/2*c)^2 - 7*a*tan(1/2*d*x + 1/2*c) - 3*a)/tan(1/2*d*x + 1/2*c)^7)/d","B",0
584,1,256,0,0.282237," ","integrate(cos(d*x+c)^6*csc(d*x+c)^9*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{21 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 48 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 112 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 336 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 168 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 1008 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 336 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1680 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 1680 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{4566 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 1680 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 336 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 1008 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 168 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 336 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 112 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 48 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 21 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8}}}{43008 \, d}"," ",0,"1/43008*(21*a*tan(1/2*d*x + 1/2*c)^8 + 48*a*tan(1/2*d*x + 1/2*c)^7 - 112*a*tan(1/2*d*x + 1/2*c)^6 - 336*a*tan(1/2*d*x + 1/2*c)^5 + 168*a*tan(1/2*d*x + 1/2*c)^4 + 1008*a*tan(1/2*d*x + 1/2*c)^3 + 336*a*tan(1/2*d*x + 1/2*c)^2 - 1680*a*log(abs(tan(1/2*d*x + 1/2*c))) - 1680*a*tan(1/2*d*x + 1/2*c) + (4566*a*tan(1/2*d*x + 1/2*c)^8 + 1680*a*tan(1/2*d*x + 1/2*c)^7 - 336*a*tan(1/2*d*x + 1/2*c)^6 - 1008*a*tan(1/2*d*x + 1/2*c)^5 - 168*a*tan(1/2*d*x + 1/2*c)^4 + 336*a*tan(1/2*d*x + 1/2*c)^3 + 112*a*tan(1/2*d*x + 1/2*c)^2 - 48*a*tan(1/2*d*x + 1/2*c) - 21*a)/tan(1/2*d*x + 1/2*c)^8)/d","B",0
585,1,256,0,0.269697," ","integrate(cos(d*x+c)^6*csc(d*x+c)^10*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{28 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 63 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 108 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 336 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 504 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 672 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1008 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 5040 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 1512 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{14258 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1512 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 1008 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 672 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 504 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 336 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 108 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 63 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 28 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9}}}{129024 \, d}"," ",0,"1/129024*(28*a*tan(1/2*d*x + 1/2*c)^9 + 63*a*tan(1/2*d*x + 1/2*c)^8 - 108*a*tan(1/2*d*x + 1/2*c)^7 - 336*a*tan(1/2*d*x + 1/2*c)^6 + 504*a*tan(1/2*d*x + 1/2*c)^4 + 672*a*tan(1/2*d*x + 1/2*c)^3 + 1008*a*tan(1/2*d*x + 1/2*c)^2 - 5040*a*log(abs(tan(1/2*d*x + 1/2*c))) - 1512*a*tan(1/2*d*x + 1/2*c) + (14258*a*tan(1/2*d*x + 1/2*c)^9 + 1512*a*tan(1/2*d*x + 1/2*c)^8 - 1008*a*tan(1/2*d*x + 1/2*c)^7 - 672*a*tan(1/2*d*x + 1/2*c)^6 - 504*a*tan(1/2*d*x + 1/2*c)^5 + 336*a*tan(1/2*d*x + 1/2*c)^3 + 108*a*tan(1/2*d*x + 1/2*c)^2 - 63*a*tan(1/2*d*x + 1/2*c) - 28*a)/tan(1/2*d*x + 1/2*c)^9)/d","B",0
586,1,284,0,0.294179," ","integrate(cos(d*x+c)^6*csc(d*x+c)^11*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{126 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 280 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 315 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 1080 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 630 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 2520 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 6720 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1260 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15120 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 15120 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{44286 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 15120 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1260 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 6720 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2520 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 630 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 1080 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 315 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 280 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 126 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10}}}{1290240 \, d}"," ",0,"1/1290240*(126*a*tan(1/2*d*x + 1/2*c)^10 + 280*a*tan(1/2*d*x + 1/2*c)^9 - 315*a*tan(1/2*d*x + 1/2*c)^8 - 1080*a*tan(1/2*d*x + 1/2*c)^7 - 630*a*tan(1/2*d*x + 1/2*c)^6 + 2520*a*tan(1/2*d*x + 1/2*c)^4 + 6720*a*tan(1/2*d*x + 1/2*c)^3 + 1260*a*tan(1/2*d*x + 1/2*c)^2 - 15120*a*log(abs(tan(1/2*d*x + 1/2*c))) - 15120*a*tan(1/2*d*x + 1/2*c) + (44286*a*tan(1/2*d*x + 1/2*c)^10 + 15120*a*tan(1/2*d*x + 1/2*c)^9 - 1260*a*tan(1/2*d*x + 1/2*c)^8 - 6720*a*tan(1/2*d*x + 1/2*c)^7 - 2520*a*tan(1/2*d*x + 1/2*c)^6 + 630*a*tan(1/2*d*x + 1/2*c)^4 + 1080*a*tan(1/2*d*x + 1/2*c)^3 + 315*a*tan(1/2*d*x + 1/2*c)^2 - 280*a*tan(1/2*d*x + 1/2*c) - 126*a)/tan(1/2*d*x + 1/2*c)^10)/d","A",0
587,1,340,0,0.291298," ","integrate(cos(d*x+c)^6*csc(d*x+c)^12*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{630 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 1386 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 770 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 3465 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 4950 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 6930 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 6930 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 27720 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 23100 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 13860 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 166320 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 69300 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{502266 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 69300 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 13860 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 23100 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 27720 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 6930 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 6930 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4950 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 3465 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 770 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1386 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 630 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11}}}{14192640 \, d}"," ",0,"1/14192640*(630*a*tan(1/2*d*x + 1/2*c)^11 + 1386*a*tan(1/2*d*x + 1/2*c)^10 - 770*a*tan(1/2*d*x + 1/2*c)^9 - 3465*a*tan(1/2*d*x + 1/2*c)^8 - 4950*a*tan(1/2*d*x + 1/2*c)^7 - 6930*a*tan(1/2*d*x + 1/2*c)^6 + 6930*a*tan(1/2*d*x + 1/2*c)^5 + 27720*a*tan(1/2*d*x + 1/2*c)^4 + 23100*a*tan(1/2*d*x + 1/2*c)^3 + 13860*a*tan(1/2*d*x + 1/2*c)^2 - 166320*a*log(abs(tan(1/2*d*x + 1/2*c))) - 69300*a*tan(1/2*d*x + 1/2*c) + (502266*a*tan(1/2*d*x + 1/2*c)^11 + 69300*a*tan(1/2*d*x + 1/2*c)^10 - 13860*a*tan(1/2*d*x + 1/2*c)^9 - 23100*a*tan(1/2*d*x + 1/2*c)^8 - 27720*a*tan(1/2*d*x + 1/2*c)^7 - 6930*a*tan(1/2*d*x + 1/2*c)^6 + 6930*a*tan(1/2*d*x + 1/2*c)^5 + 4950*a*tan(1/2*d*x + 1/2*c)^4 + 3465*a*tan(1/2*d*x + 1/2*c)^3 + 770*a*tan(1/2*d*x + 1/2*c)^2 - 1386*a*tan(1/2*d*x + 1/2*c) - 630*a)/tan(1/2*d*x + 1/2*c)^11)/d","B",0
588,1,208,0,0.428674," ","integrate(cos(d*x+c)^6*sin(d*x+c)^4*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{17}{1024} \, a^{2} x - \frac{a^{2} \cos\left(11 \, d x + 11 \, c\right)}{5632 \, d} - \frac{a^{2} \cos\left(9 \, d x + 9 \, c\right)}{4608 \, d} + \frac{5 \, a^{2} \cos\left(7 \, d x + 7 \, c\right)}{3584 \, d} + \frac{a^{2} \cos\left(5 \, d x + 5 \, c\right)}{512 \, d} - \frac{5 \, a^{2} \cos\left(3 \, d x + 3 \, c\right)}{768 \, d} - \frac{5 \, a^{2} \cos\left(d x + c\right)}{256 \, d} - \frac{a^{2} \sin\left(12 \, d x + 12 \, c\right)}{24576 \, d} + \frac{a^{2} \sin\left(10 \, d x + 10 \, c\right)}{5120 \, d} + \frac{7 \, a^{2} \sin\left(8 \, d x + 8 \, c\right)}{8192 \, d} - \frac{a^{2} \sin\left(6 \, d x + 6 \, c\right)}{1024 \, d} - \frac{47 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)}{8192 \, d} + \frac{a^{2} \sin\left(2 \, d x + 2 \, c\right)}{512 \, d}"," ",0,"17/1024*a^2*x - 1/5632*a^2*cos(11*d*x + 11*c)/d - 1/4608*a^2*cos(9*d*x + 9*c)/d + 5/3584*a^2*cos(7*d*x + 7*c)/d + 1/512*a^2*cos(5*d*x + 5*c)/d - 5/768*a^2*cos(3*d*x + 3*c)/d - 5/256*a^2*cos(d*x + c)/d - 1/24576*a^2*sin(12*d*x + 12*c)/d + 1/5120*a^2*sin(10*d*x + 10*c)/d + 7/8192*a^2*sin(8*d*x + 8*c)/d - 1/1024*a^2*sin(6*d*x + 6*c)/d - 47/8192*a^2*sin(4*d*x + 4*c)/d + 1/512*a^2*sin(2*d*x + 2*c)/d","A",0
589,1,191,0,0.368812," ","integrate(cos(d*x+c)^6*sin(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{3}{128} \, a^{2} x - \frac{a^{2} \cos\left(11 \, d x + 11 \, c\right)}{11264 \, d} + \frac{a^{2} \cos\left(9 \, d x + 9 \, c\right)}{3072 \, d} + \frac{17 \, a^{2} \cos\left(7 \, d x + 7 \, c\right)}{7168 \, d} + \frac{a^{2} \cos\left(5 \, d x + 5 \, c\right)}{1024 \, d} - \frac{7 \, a^{2} \cos\left(3 \, d x + 3 \, c\right)}{512 \, d} - \frac{17 \, a^{2} \cos\left(d x + c\right)}{512 \, d} + \frac{a^{2} \sin\left(10 \, d x + 10 \, c\right)}{2560 \, d} + \frac{a^{2} \sin\left(8 \, d x + 8 \, c\right)}{1024 \, d} - \frac{a^{2} \sin\left(6 \, d x + 6 \, c\right)}{512 \, d} - \frac{a^{2} \sin\left(4 \, d x + 4 \, c\right)}{128 \, d} + \frac{a^{2} \sin\left(2 \, d x + 2 \, c\right)}{256 \, d}"," ",0,"3/128*a^2*x - 1/11264*a^2*cos(11*d*x + 11*c)/d + 1/3072*a^2*cos(9*d*x + 9*c)/d + 17/7168*a^2*cos(7*d*x + 7*c)/d + 1/1024*a^2*cos(5*d*x + 5*c)/d - 7/512*a^2*cos(3*d*x + 3*c)/d - 17/512*a^2*cos(d*x + c)/d + 1/2560*a^2*sin(10*d*x + 10*c)/d + 1/1024*a^2*sin(8*d*x + 8*c)/d - 1/512*a^2*sin(6*d*x + 6*c)/d - 1/128*a^2*sin(4*d*x + 4*c)/d + 1/256*a^2*sin(2*d*x + 2*c)/d","A",0
590,1,157,0,0.312421," ","integrate(cos(d*x+c)^6*sin(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{13}{256} \, a^{2} x + \frac{a^{2} \cos\left(9 \, d x + 9 \, c\right)}{1152 \, d} + \frac{3 \, a^{2} \cos\left(7 \, d x + 7 \, c\right)}{896 \, d} - \frac{a^{2} \cos\left(3 \, d x + 3 \, c\right)}{48 \, d} - \frac{3 \, a^{2} \cos\left(d x + c\right)}{64 \, d} + \frac{a^{2} \sin\left(10 \, d x + 10 \, c\right)}{5120 \, d} - \frac{a^{2} \sin\left(8 \, d x + 8 \, c\right)}{2048 \, d} - \frac{19 \, a^{2} \sin\left(6 \, d x + 6 \, c\right)}{3072 \, d} - \frac{3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)}{256 \, d} + \frac{9 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)}{512 \, d}"," ",0,"13/256*a^2*x + 1/1152*a^2*cos(9*d*x + 9*c)/d + 3/896*a^2*cos(7*d*x + 7*c)/d - 1/48*a^2*cos(3*d*x + 3*c)/d - 3/64*a^2*cos(d*x + c)/d + 1/5120*a^2*sin(10*d*x + 10*c)/d - 1/2048*a^2*sin(8*d*x + 8*c)/d - 19/3072*a^2*sin(6*d*x + 6*c)/d - 3/256*a^2*sin(4*d*x + 4*c)/d + 9/512*a^2*sin(2*d*x + 2*c)/d","A",0
591,1,157,0,0.258667," ","integrate(cos(d*x+c)^6*sin(d*x+c)*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{5}{64} \, a^{2} x + \frac{a^{2} \cos\left(9 \, d x + 9 \, c\right)}{2304 \, d} - \frac{a^{2} \cos\left(7 \, d x + 7 \, c\right)}{1792 \, d} - \frac{a^{2} \cos\left(5 \, d x + 5 \, c\right)}{64 \, d} - \frac{11 \, a^{2} \cos\left(3 \, d x + 3 \, c\right)}{192 \, d} - \frac{13 \, a^{2} \cos\left(d x + c\right)}{128 \, d} - \frac{a^{2} \sin\left(8 \, d x + 8 \, c\right)}{512 \, d} - \frac{a^{2} \sin\left(6 \, d x + 6 \, c\right)}{96 \, d} - \frac{a^{2} \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{a^{2} \sin\left(2 \, d x + 2 \, c\right)}{32 \, d}"," ",0,"5/64*a^2*x + 1/2304*a^2*cos(9*d*x + 9*c)/d - 1/1792*a^2*cos(7*d*x + 7*c)/d - 1/64*a^2*cos(5*d*x + 5*c)/d - 11/192*a^2*cos(3*d*x + 3*c)/d - 13/128*a^2*cos(d*x + c)/d - 1/512*a^2*sin(8*d*x + 8*c)/d - 1/96*a^2*sin(6*d*x + 6*c)/d - 1/64*a^2*sin(4*d*x + 4*c)/d + 1/32*a^2*sin(2*d*x + 2*c)/d","A",0
592,1,245,0,0.247203," ","integrate(cos(d*x+c)^6*csc(d*x+c)*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{525 \, {\left(d x + c\right)} a^{2} + 840 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{2 \, {\left(1155 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 1680 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 980 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 10080 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 2975 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 16240 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 24640 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 2975 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 14448 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 980 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6496 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1155 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1168 \, a^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{7}}}{840 \, d}"," ",0,"1/840*(525*(d*x + c)*a^2 + 840*a^2*log(abs(tan(1/2*d*x + 1/2*c))) - 2*(1155*a^2*tan(1/2*d*x + 1/2*c)^13 - 1680*a^2*tan(1/2*d*x + 1/2*c)^12 + 980*a^2*tan(1/2*d*x + 1/2*c)^11 - 10080*a^2*tan(1/2*d*x + 1/2*c)^10 + 2975*a^2*tan(1/2*d*x + 1/2*c)^9 - 16240*a^2*tan(1/2*d*x + 1/2*c)^8 - 24640*a^2*tan(1/2*d*x + 1/2*c)^6 - 2975*a^2*tan(1/2*d*x + 1/2*c)^5 - 14448*a^2*tan(1/2*d*x + 1/2*c)^4 - 980*a^2*tan(1/2*d*x + 1/2*c)^3 - 6496*a^2*tan(1/2*d*x + 1/2*c)^2 - 1155*a^2*tan(1/2*d*x + 1/2*c) - 1168*a^2)/(tan(1/2*d*x + 1/2*c)^2 + 1)^7)/d","A",0
593,1,274,0,0.265521," ","integrate(cos(d*x+c)^6*csc(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{375 \, {\left(d x + c\right)} a^{2} - 480 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 120 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{120 \, {\left(4 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)} - \frac{2 \, {\left(105 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 1440 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 595 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 4320 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 150 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 7360 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 150 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6720 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 595 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2976 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 105 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 736 \, a^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6}}}{240 \, d}"," ",0,"-1/240*(375*(d*x + c)*a^2 - 480*a^2*log(abs(tan(1/2*d*x + 1/2*c))) - 120*a^2*tan(1/2*d*x + 1/2*c) + 120*(4*a^2*tan(1/2*d*x + 1/2*c) + a^2)/tan(1/2*d*x + 1/2*c) - 2*(105*a^2*tan(1/2*d*x + 1/2*c)^11 + 1440*a^2*tan(1/2*d*x + 1/2*c)^10 + 595*a^2*tan(1/2*d*x + 1/2*c)^9 + 4320*a^2*tan(1/2*d*x + 1/2*c)^8 - 150*a^2*tan(1/2*d*x + 1/2*c)^7 + 7360*a^2*tan(1/2*d*x + 1/2*c)^6 + 150*a^2*tan(1/2*d*x + 1/2*c)^5 + 6720*a^2*tan(1/2*d*x + 1/2*c)^4 - 595*a^2*tan(1/2*d*x + 1/2*c)^3 + 2976*a^2*tan(1/2*d*x + 1/2*c)^2 - 105*a^2*tan(1/2*d*x + 1/2*c) + 736*a^2)/(tan(1/2*d*x + 1/2*c)^2 + 1)^6)/d","A",0
594,1,244,0,0.264436," ","integrate(cos(d*x+c)^6*csc(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{5 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 150 \, {\left(d x + c\right)} a^{2} - 60 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 40 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{5 \, {\left(18 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{2}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}} + \frac{4 \, {\left(45 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 50 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 80 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 80 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 50 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 80 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 45 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 16 \, a^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5}}}{40 \, d}"," ",0,"1/40*(5*a^2*tan(1/2*d*x + 1/2*c)^2 - 150*(d*x + c)*a^2 - 60*a^2*log(abs(tan(1/2*d*x + 1/2*c))) + 40*a^2*tan(1/2*d*x + 1/2*c) + 5*(18*a^2*tan(1/2*d*x + 1/2*c)^2 - 8*a^2*tan(1/2*d*x + 1/2*c) - a^2)/tan(1/2*d*x + 1/2*c)^2 + 4*(45*a^2*tan(1/2*d*x + 1/2*c)^9 + 50*a^2*tan(1/2*d*x + 1/2*c)^7 - 80*a^2*tan(1/2*d*x + 1/2*c)^6 - 80*a^2*tan(1/2*d*x + 1/2*c)^4 - 50*a^2*tan(1/2*d*x + 1/2*c)^3 - 80*a^2*tan(1/2*d*x + 1/2*c)^2 - 45*a^2*tan(1/2*d*x + 1/2*c) - 16*a^2)/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","A",0
595,1,274,0,0.277006," ","integrate(cos(d*x+c)^6*csc(d*x+c)^4*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 15 \, {\left(d x + c\right)} a^{2} - 120 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{220 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 6 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}} + \frac{2 \, {\left(15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 144 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 9 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 336 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 9 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 304 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 112 \, a^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(a^2*tan(1/2*d*x + 1/2*c)^3 + 6*a^2*tan(1/2*d*x + 1/2*c)^2 + 15*(d*x + c)*a^2 - 120*a^2*log(abs(tan(1/2*d*x + 1/2*c))) - 15*a^2*tan(1/2*d*x + 1/2*c) + (220*a^2*tan(1/2*d*x + 1/2*c)^3 + 15*a^2*tan(1/2*d*x + 1/2*c)^2 - 6*a^2*tan(1/2*d*x + 1/2*c) - a^2)/tan(1/2*d*x + 1/2*c)^3 + 2*(15*a^2*tan(1/2*d*x + 1/2*c)^7 - 144*a^2*tan(1/2*d*x + 1/2*c)^6 - 9*a^2*tan(1/2*d*x + 1/2*c)^5 - 336*a^2*tan(1/2*d*x + 1/2*c)^4 + 9*a^2*tan(1/2*d*x + 1/2*c)^3 - 304*a^2*tan(1/2*d*x + 1/2*c)^2 - 15*a^2*tan(1/2*d*x + 1/2*c) - 112*a^2)/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","A",0
596,1,259,0,0.300286," ","integrate(cos(d*x+c)^6*csc(d*x+c)^5*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 16 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 960 \, {\left(d x + c\right)} a^{2} - 120 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 432 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{128 \, {\left(3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 6 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, a^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}} + \frac{250 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 432 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 24 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 16 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}}}{192 \, d}"," ",0,"1/192*(3*a^2*tan(1/2*d*x + 1/2*c)^4 + 16*a^2*tan(1/2*d*x + 1/2*c)^3 - 24*a^2*tan(1/2*d*x + 1/2*c)^2 + 960*(d*x + c)*a^2 - 120*a^2*log(abs(tan(1/2*d*x + 1/2*c))) - 432*a^2*tan(1/2*d*x + 1/2*c) - 128*(3*a^2*tan(1/2*d*x + 1/2*c)^5 + 6*a^2*tan(1/2*d*x + 1/2*c)^4 + 6*a^2*tan(1/2*d*x + 1/2*c)^2 - 3*a^2*tan(1/2*d*x + 1/2*c) + 4*a^2)/(tan(1/2*d*x + 1/2*c)^2 + 1)^3 + (250*a^2*tan(1/2*d*x + 1/2*c)^4 + 432*a^2*tan(1/2*d*x + 1/2*c)^3 + 24*a^2*tan(1/2*d*x + 1/2*c)^2 - 16*a^2*tan(1/2*d*x + 1/2*c) - 3*a^2)/tan(1/2*d*x + 1/2*c)^4)/d","A",0
597,1,272,0,0.294365," ","integrate(cos(d*x+c)^6*csc(d*x+c)^6*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 5 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 5 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 80 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 240 \, {\left(d x + c\right)} a^{2} + 600 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 70 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{160 \, {\left(a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, a^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}} - \frac{1370 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 70 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 80 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 5 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{160 \, d}"," ",0,"1/160*(a^2*tan(1/2*d*x + 1/2*c)^5 + 5*a^2*tan(1/2*d*x + 1/2*c)^4 - 5*a^2*tan(1/2*d*x + 1/2*c)^3 - 80*a^2*tan(1/2*d*x + 1/2*c)^2 + 240*(d*x + c)*a^2 + 600*a^2*log(abs(tan(1/2*d*x + 1/2*c))) - 70*a^2*tan(1/2*d*x + 1/2*c) - 160*(a^2*tan(1/2*d*x + 1/2*c)^3 - 4*a^2*tan(1/2*d*x + 1/2*c)^2 - a^2*tan(1/2*d*x + 1/2*c) - 4*a^2)/(tan(1/2*d*x + 1/2*c)^2 + 1)^2 - (1370*a^2*tan(1/2*d*x + 1/2*c)^5 - 70*a^2*tan(1/2*d*x + 1/2*c)^4 - 80*a^2*tan(1/2*d*x + 1/2*c)^3 - 5*a^2*tan(1/2*d*x + 1/2*c)^2 + 5*a^2*tan(1/2*d*x + 1/2*c) + a^2)/tan(1/2*d*x + 1/2*c)^5)/d","B",0
598,1,259,0,0.313385," ","integrate(cos(d*x+c)^6*csc(d*x+c)^7*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{5 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 24 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 280 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 255 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3840 \, {\left(d x + c\right)} a^{2} + 3000 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 2640 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{3840 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} - \frac{7350 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 2640 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 255 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 280 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6}}}{1920 \, d}"," ",0,"1/1920*(5*a^2*tan(1/2*d*x + 1/2*c)^6 + 24*a^2*tan(1/2*d*x + 1/2*c)^5 - 15*a^2*tan(1/2*d*x + 1/2*c)^4 - 280*a^2*tan(1/2*d*x + 1/2*c)^3 - 255*a^2*tan(1/2*d*x + 1/2*c)^2 - 3840*(d*x + c)*a^2 + 3000*a^2*log(abs(tan(1/2*d*x + 1/2*c))) + 2640*a^2*tan(1/2*d*x + 1/2*c) + 3840*a^2/(tan(1/2*d*x + 1/2*c)^2 + 1) - (7350*a^2*tan(1/2*d*x + 1/2*c)^6 + 2640*a^2*tan(1/2*d*x + 1/2*c)^5 - 255*a^2*tan(1/2*d*x + 1/2*c)^4 - 280*a^2*tan(1/2*d*x + 1/2*c)^3 - 15*a^2*tan(1/2*d*x + 1/2*c)^2 + 24*a^2*tan(1/2*d*x + 1/2*c) + 5*a^2)/tan(1/2*d*x + 1/2*c)^6)/d","A",0
599,1,270,0,0.312611," ","integrate(cos(d*x+c)^6*csc(d*x+c)^8*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 70 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 21 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 630 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 665 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3150 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 13440 \, {\left(d x + c\right)} a^{2} - 8400 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 8715 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{21780 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 8715 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 3150 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 665 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 630 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 21 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 70 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7}}}{13440 \, d}"," ",0,"1/13440*(15*a^2*tan(1/2*d*x + 1/2*c)^7 + 70*a^2*tan(1/2*d*x + 1/2*c)^6 - 21*a^2*tan(1/2*d*x + 1/2*c)^5 - 630*a^2*tan(1/2*d*x + 1/2*c)^4 - 665*a^2*tan(1/2*d*x + 1/2*c)^3 + 3150*a^2*tan(1/2*d*x + 1/2*c)^2 - 13440*(d*x + c)*a^2 - 8400*a^2*log(abs(tan(1/2*d*x + 1/2*c))) + 8715*a^2*tan(1/2*d*x + 1/2*c) + (21780*a^2*tan(1/2*d*x + 1/2*c)^7 - 8715*a^2*tan(1/2*d*x + 1/2*c)^6 - 3150*a^2*tan(1/2*d*x + 1/2*c)^5 + 665*a^2*tan(1/2*d*x + 1/2*c)^4 + 630*a^2*tan(1/2*d*x + 1/2*c)^3 + 21*a^2*tan(1/2*d*x + 1/2*c)^2 - 70*a^2*tan(1/2*d*x + 1/2*c) - 15*a^2)/tan(1/2*d*x + 1/2*c)^7)/d","A",0
600,1,260,0,0.358185," ","integrate(cos(d*x+c)^6*csc(d*x+c)^9*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{7 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 32 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 224 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 280 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 672 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1792 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 5040 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 1120 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{13698 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 1120 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1792 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 672 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 280 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 224 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 32 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 7 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8}}}{14336 \, d}"," ",0,"1/14336*(7*a^2*tan(1/2*d*x + 1/2*c)^8 + 32*a^2*tan(1/2*d*x + 1/2*c)^7 - 224*a^2*tan(1/2*d*x + 1/2*c)^5 - 280*a^2*tan(1/2*d*x + 1/2*c)^4 + 672*a^2*tan(1/2*d*x + 1/2*c)^3 + 1792*a^2*tan(1/2*d*x + 1/2*c)^2 - 5040*a^2*log(abs(tan(1/2*d*x + 1/2*c))) - 1120*a^2*tan(1/2*d*x + 1/2*c) + (13698*a^2*tan(1/2*d*x + 1/2*c)^8 + 1120*a^2*tan(1/2*d*x + 1/2*c)^7 - 1792*a^2*tan(1/2*d*x + 1/2*c)^6 - 672*a^2*tan(1/2*d*x + 1/2*c)^5 + 280*a^2*tan(1/2*d*x + 1/2*c)^4 + 224*a^2*tan(1/2*d*x + 1/2*c)^3 - 32*a^2*tan(1/2*d*x + 1/2*c) - 7*a^2)/tan(1/2*d*x + 1/2*c)^8)/d","A",0
601,1,324,0,0.340452," ","integrate(cos(d*x+c)^6*csc(d*x+c)^10*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{14 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 63 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 18 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 336 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 504 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 504 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 1848 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1008 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 5040 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 3276 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{14258 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 3276 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 1008 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1848 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 504 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 504 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 336 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 18 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 63 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 14 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9}}}{64512 \, d}"," ",0,"1/64512*(14*a^2*tan(1/2*d*x + 1/2*c)^9 + 63*a^2*tan(1/2*d*x + 1/2*c)^8 + 18*a^2*tan(1/2*d*x + 1/2*c)^7 - 336*a^2*tan(1/2*d*x + 1/2*c)^6 - 504*a^2*tan(1/2*d*x + 1/2*c)^5 + 504*a^2*tan(1/2*d*x + 1/2*c)^4 + 1848*a^2*tan(1/2*d*x + 1/2*c)^3 + 1008*a^2*tan(1/2*d*x + 1/2*c)^2 - 5040*a^2*log(abs(tan(1/2*d*x + 1/2*c))) - 3276*a^2*tan(1/2*d*x + 1/2*c) + (14258*a^2*tan(1/2*d*x + 1/2*c)^9 + 3276*a^2*tan(1/2*d*x + 1/2*c)^8 - 1008*a^2*tan(1/2*d*x + 1/2*c)^7 - 1848*a^2*tan(1/2*d*x + 1/2*c)^6 - 504*a^2*tan(1/2*d*x + 1/2*c)^5 + 504*a^2*tan(1/2*d*x + 1/2*c)^4 + 336*a^2*tan(1/2*d*x + 1/2*c)^3 - 18*a^2*tan(1/2*d*x + 1/2*c)^2 - 63*a^2*tan(1/2*d*x + 1/2*c) - 14*a^2)/tan(1/2*d*x + 1/2*c)^9)/d","B",0
602,1,324,0,0.359433," ","integrate(cos(d*x+c)^6*csc(d*x+c)^11*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{126 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 560 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 315 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 2160 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 3990 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 7560 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 13440 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 11340 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 65520 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 30240 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{191906 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 30240 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 11340 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 13440 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 7560 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 3990 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2160 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 315 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 560 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 126 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10}}}{1290240 \, d}"," ",0,"1/1290240*(126*a^2*tan(1/2*d*x + 1/2*c)^10 + 560*a^2*tan(1/2*d*x + 1/2*c)^9 + 315*a^2*tan(1/2*d*x + 1/2*c)^8 - 2160*a^2*tan(1/2*d*x + 1/2*c)^7 - 3990*a^2*tan(1/2*d*x + 1/2*c)^6 + 7560*a^2*tan(1/2*d*x + 1/2*c)^4 + 13440*a^2*tan(1/2*d*x + 1/2*c)^3 + 11340*a^2*tan(1/2*d*x + 1/2*c)^2 - 65520*a^2*log(abs(tan(1/2*d*x + 1/2*c))) - 30240*a^2*tan(1/2*d*x + 1/2*c) + (191906*a^2*tan(1/2*d*x + 1/2*c)^10 + 30240*a^2*tan(1/2*d*x + 1/2*c)^9 - 11340*a^2*tan(1/2*d*x + 1/2*c)^8 - 13440*a^2*tan(1/2*d*x + 1/2*c)^7 - 7560*a^2*tan(1/2*d*x + 1/2*c)^6 + 3990*a^2*tan(1/2*d*x + 1/2*c)^4 + 2160*a^2*tan(1/2*d*x + 1/2*c)^3 - 315*a^2*tan(1/2*d*x + 1/2*c)^2 - 560*a^2*tan(1/2*d*x + 1/2*c) - 126*a^2)/tan(1/2*d*x + 1/2*c)^10)/d","A",0
603,1,388,0,0.368497," ","integrate(cos(d*x+c)^6*csc(d*x+c)^12*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{105 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 462 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 385 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1155 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 2805 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2310 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 1155 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9240 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 16170 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4620 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 55440 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 39270 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{167422 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 39270 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 4620 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 16170 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 9240 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1155 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 2310 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2805 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 1155 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 385 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 462 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 105 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11}}}{2365440 \, d}"," ",0,"1/2365440*(105*a^2*tan(1/2*d*x + 1/2*c)^11 + 462*a^2*tan(1/2*d*x + 1/2*c)^10 + 385*a^2*tan(1/2*d*x + 1/2*c)^9 - 1155*a^2*tan(1/2*d*x + 1/2*c)^8 - 2805*a^2*tan(1/2*d*x + 1/2*c)^7 - 2310*a^2*tan(1/2*d*x + 1/2*c)^6 + 1155*a^2*tan(1/2*d*x + 1/2*c)^5 + 9240*a^2*tan(1/2*d*x + 1/2*c)^4 + 16170*a^2*tan(1/2*d*x + 1/2*c)^3 + 4620*a^2*tan(1/2*d*x + 1/2*c)^2 - 55440*a^2*log(abs(tan(1/2*d*x + 1/2*c))) - 39270*a^2*tan(1/2*d*x + 1/2*c) + (167422*a^2*tan(1/2*d*x + 1/2*c)^11 + 39270*a^2*tan(1/2*d*x + 1/2*c)^10 - 4620*a^2*tan(1/2*d*x + 1/2*c)^9 - 16170*a^2*tan(1/2*d*x + 1/2*c)^8 - 9240*a^2*tan(1/2*d*x + 1/2*c)^7 - 1155*a^2*tan(1/2*d*x + 1/2*c)^6 + 2310*a^2*tan(1/2*d*x + 1/2*c)^5 + 2805*a^2*tan(1/2*d*x + 1/2*c)^4 + 1155*a^2*tan(1/2*d*x + 1/2*c)^3 - 385*a^2*tan(1/2*d*x + 1/2*c)^2 - 462*a^2*tan(1/2*d*x + 1/2*c) - 105*a^2)/tan(1/2*d*x + 1/2*c)^11)/d","B",0
604,1,420,0,0.421267," ","integrate(cos(d*x+c)^6*csc(d*x+c)^13*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{1155 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 5040 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 5544 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 6160 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 24255 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 39600 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 27720 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 55440 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 162855 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 184800 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 55440 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 942480 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 554400 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{2924714 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 554400 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 55440 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 184800 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 162855 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 55440 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 27720 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 39600 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 24255 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 6160 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5544 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 5040 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1155 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12}}}{56770560 \, d}"," ",0,"1/56770560*(1155*a^2*tan(1/2*d*x + 1/2*c)^12 + 5040*a^2*tan(1/2*d*x + 1/2*c)^11 + 5544*a^2*tan(1/2*d*x + 1/2*c)^10 - 6160*a^2*tan(1/2*d*x + 1/2*c)^9 - 24255*a^2*tan(1/2*d*x + 1/2*c)^8 - 39600*a^2*tan(1/2*d*x + 1/2*c)^7 - 27720*a^2*tan(1/2*d*x + 1/2*c)^6 + 55440*a^2*tan(1/2*d*x + 1/2*c)^5 + 162855*a^2*tan(1/2*d*x + 1/2*c)^4 + 184800*a^2*tan(1/2*d*x + 1/2*c)^3 + 55440*a^2*tan(1/2*d*x + 1/2*c)^2 - 942480*a^2*log(abs(tan(1/2*d*x + 1/2*c))) - 554400*a^2*tan(1/2*d*x + 1/2*c) + (2924714*a^2*tan(1/2*d*x + 1/2*c)^12 + 554400*a^2*tan(1/2*d*x + 1/2*c)^11 - 55440*a^2*tan(1/2*d*x + 1/2*c)^10 - 184800*a^2*tan(1/2*d*x + 1/2*c)^9 - 162855*a^2*tan(1/2*d*x + 1/2*c)^8 - 55440*a^2*tan(1/2*d*x + 1/2*c)^7 + 27720*a^2*tan(1/2*d*x + 1/2*c)^6 + 39600*a^2*tan(1/2*d*x + 1/2*c)^5 + 24255*a^2*tan(1/2*d*x + 1/2*c)^4 + 6160*a^2*tan(1/2*d*x + 1/2*c)^3 - 5544*a^2*tan(1/2*d*x + 1/2*c)^2 - 5040*a^2*tan(1/2*d*x + 1/2*c) - 1155*a^2)/tan(1/2*d*x + 1/2*c)^12)/d","A",0
605,1,225,0,0.552360," ","integrate(cos(d*x+c)^6*sin(d*x+c)^4*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{27}{1024} \, a^{3} x + \frac{a^{3} \cos\left(13 \, d x + 13 \, c\right)}{53248 \, d} - \frac{13 \, a^{3} \cos\left(11 \, d x + 11 \, c\right)}{45056 \, d} - \frac{a^{3} \cos\left(9 \, d x + 9 \, c\right)}{2048 \, d} + \frac{33 \, a^{3} \cos\left(7 \, d x + 7 \, c\right)}{14336 \, d} + \frac{15 \, a^{3} \cos\left(5 \, d x + 5 \, c\right)}{4096 \, d} - \frac{45 \, a^{3} \cos\left(3 \, d x + 3 \, c\right)}{4096 \, d} - \frac{35 \, a^{3} \cos\left(d x + c\right)}{1024 \, d} - \frac{a^{3} \sin\left(12 \, d x + 12 \, c\right)}{8192 \, d} + \frac{a^{3} \sin\left(10 \, d x + 10 \, c\right)}{5120 \, d} + \frac{13 \, a^{3} \sin\left(8 \, d x + 8 \, c\right)}{8192 \, d} - \frac{a^{3} \sin\left(6 \, d x + 6 \, c\right)}{1024 \, d} - \frac{77 \, a^{3} \sin\left(4 \, d x + 4 \, c\right)}{8192 \, d} + \frac{a^{3} \sin\left(2 \, d x + 2 \, c\right)}{512 \, d}"," ",0,"27/1024*a^3*x + 1/53248*a^3*cos(13*d*x + 13*c)/d - 13/45056*a^3*cos(11*d*x + 11*c)/d - 1/2048*a^3*cos(9*d*x + 9*c)/d + 33/14336*a^3*cos(7*d*x + 7*c)/d + 15/4096*a^3*cos(5*d*x + 5*c)/d - 45/4096*a^3*cos(3*d*x + 3*c)/d - 35/1024*a^3*cos(d*x + c)/d - 1/8192*a^3*sin(12*d*x + 12*c)/d + 1/5120*a^3*sin(10*d*x + 10*c)/d + 13/8192*a^3*sin(8*d*x + 8*c)/d - 1/1024*a^3*sin(6*d*x + 6*c)/d - 77/8192*a^3*sin(4*d*x + 4*c)/d + 1/512*a^3*sin(2*d*x + 2*c)/d","A",0
606,1,208,0,0.512855," ","integrate(cos(d*x+c)^6*sin(d*x+c)^3*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{41}{1024} \, a^{3} x - \frac{3 \, a^{3} \cos\left(11 \, d x + 11 \, c\right)}{11264 \, d} + \frac{a^{3} \cos\left(9 \, d x + 9 \, c\right)}{9216 \, d} + \frac{27 \, a^{3} \cos\left(7 \, d x + 7 \, c\right)}{7168 \, d} + \frac{3 \, a^{3} \cos\left(5 \, d x + 5 \, c\right)}{1024 \, d} - \frac{31 \, a^{3} \cos\left(3 \, d x + 3 \, c\right)}{1536 \, d} - \frac{27 \, a^{3} \cos\left(d x + c\right)}{512 \, d} - \frac{a^{3} \sin\left(12 \, d x + 12 \, c\right)}{24576 \, d} + \frac{3 \, a^{3} \sin\left(10 \, d x + 10 \, c\right)}{5120 \, d} + \frac{15 \, a^{3} \sin\left(8 \, d x + 8 \, c\right)}{8192 \, d} - \frac{3 \, a^{3} \sin\left(6 \, d x + 6 \, c\right)}{1024 \, d} - \frac{111 \, a^{3} \sin\left(4 \, d x + 4 \, c\right)}{8192 \, d} + \frac{3 \, a^{3} \sin\left(2 \, d x + 2 \, c\right)}{512 \, d}"," ",0,"41/1024*a^3*x - 3/11264*a^3*cos(11*d*x + 11*c)/d + 1/9216*a^3*cos(9*d*x + 9*c)/d + 27/7168*a^3*cos(7*d*x + 7*c)/d + 3/1024*a^3*cos(5*d*x + 5*c)/d - 31/1536*a^3*cos(3*d*x + 3*c)/d - 27/512*a^3*cos(d*x + c)/d - 1/24576*a^3*sin(12*d*x + 12*c)/d + 3/5120*a^3*sin(10*d*x + 10*c)/d + 15/8192*a^3*sin(8*d*x + 8*c)/d - 3/1024*a^3*sin(6*d*x + 6*c)/d - 111/8192*a^3*sin(4*d*x + 4*c)/d + 3/512*a^3*sin(2*d*x + 2*c)/d","A",0
607,1,191,0,0.418167," ","integrate(cos(d*x+c)^6*sin(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{19}{256} \, a^{3} x - \frac{a^{3} \cos\left(11 \, d x + 11 \, c\right)}{11264 \, d} + \frac{11 \, a^{3} \cos\left(9 \, d x + 9 \, c\right)}{9216 \, d} + \frac{41 \, a^{3} \cos\left(7 \, d x + 7 \, c\right)}{7168 \, d} + \frac{a^{3} \cos\left(5 \, d x + 5 \, c\right)}{1024 \, d} - \frac{53 \, a^{3} \cos\left(3 \, d x + 3 \, c\right)}{1536 \, d} - \frac{41 \, a^{3} \cos\left(d x + c\right)}{512 \, d} + \frac{3 \, a^{3} \sin\left(10 \, d x + 10 \, c\right)}{5120 \, d} + \frac{a^{3} \sin\left(8 \, d x + 8 \, c\right)}{2048 \, d} - \frac{25 \, a^{3} \sin\left(6 \, d x + 6 \, c\right)}{3072 \, d} - \frac{5 \, a^{3} \sin\left(4 \, d x + 4 \, c\right)}{256 \, d} + \frac{11 \, a^{3} \sin\left(2 \, d x + 2 \, c\right)}{512 \, d}"," ",0,"19/256*a^3*x - 1/11264*a^3*cos(11*d*x + 11*c)/d + 11/9216*a^3*cos(9*d*x + 9*c)/d + 41/7168*a^3*cos(7*d*x + 7*c)/d + 1/1024*a^3*cos(5*d*x + 5*c)/d - 53/1536*a^3*cos(3*d*x + 3*c)/d - 41/512*a^3*cos(d*x + c)/d + 3/5120*a^3*sin(10*d*x + 10*c)/d + 1/2048*a^3*sin(8*d*x + 8*c)/d - 25/3072*a^3*sin(6*d*x + 6*c)/d - 5/256*a^3*sin(4*d*x + 4*c)/d + 11/512*a^3*sin(2*d*x + 2*c)/d","A",0
608,1,174,0,0.361612," ","integrate(cos(d*x+c)^6*sin(d*x+c)*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{33}{256} \, a^{3} x + \frac{a^{3} \cos\left(9 \, d x + 9 \, c\right)}{768 \, d} + \frac{5 \, a^{3} \cos\left(7 \, d x + 7 \, c\right)}{1792 \, d} - \frac{a^{3} \cos\left(5 \, d x + 5 \, c\right)}{64 \, d} - \frac{5 \, a^{3} \cos\left(3 \, d x + 3 \, c\right)}{64 \, d} - \frac{19 \, a^{3} \cos\left(d x + c\right)}{128 \, d} + \frac{a^{3} \sin\left(10 \, d x + 10 \, c\right)}{5120 \, d} - \frac{5 \, a^{3} \sin\left(8 \, d x + 8 \, c\right)}{2048 \, d} - \frac{17 \, a^{3} \sin\left(6 \, d x + 6 \, c\right)}{1024 \, d} - \frac{7 \, a^{3} \sin\left(4 \, d x + 4 \, c\right)}{256 \, d} + \frac{25 \, a^{3} \sin\left(2 \, d x + 2 \, c\right)}{512 \, d}"," ",0,"33/256*a^3*x + 1/768*a^3*cos(9*d*x + 9*c)/d + 5/1792*a^3*cos(7*d*x + 7*c)/d - 1/64*a^3*cos(5*d*x + 5*c)/d - 5/64*a^3*cos(3*d*x + 3*c)/d - 19/128*a^3*cos(d*x + c)/d + 1/5120*a^3*sin(10*d*x + 10*c)/d - 5/2048*a^3*sin(8*d*x + 8*c)/d - 17/1024*a^3*sin(6*d*x + 6*c)/d - 7/256*a^3*sin(4*d*x + 4*c)/d + 25/512*a^3*sin(2*d*x + 2*c)/d","A",0
609,1,277,0,0.313234," ","integrate(cos(d*x+c)^6*csc(d*x+c)*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{13125 \, {\left(d x + c\right)} a^{3} + 13440 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{2 \, {\left(27195 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} + 65135 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 161280 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 63595 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 286720 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 133175 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 519680 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 133175 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 544768 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 63595 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 254464 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 65135 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 118784 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 27195 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 14848 \, a^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{8}}}{13440 \, d}"," ",0,"1/13440*(13125*(d*x + c)*a^3 + 13440*a^3*log(abs(tan(1/2*d*x + 1/2*c))) - 2*(27195*a^3*tan(1/2*d*x + 1/2*c)^15 + 65135*a^3*tan(1/2*d*x + 1/2*c)^13 - 161280*a^3*tan(1/2*d*x + 1/2*c)^12 + 63595*a^3*tan(1/2*d*x + 1/2*c)^11 - 286720*a^3*tan(1/2*d*x + 1/2*c)^10 + 133175*a^3*tan(1/2*d*x + 1/2*c)^9 - 519680*a^3*tan(1/2*d*x + 1/2*c)^8 - 133175*a^3*tan(1/2*d*x + 1/2*c)^7 - 544768*a^3*tan(1/2*d*x + 1/2*c)^6 - 63595*a^3*tan(1/2*d*x + 1/2*c)^5 - 254464*a^3*tan(1/2*d*x + 1/2*c)^4 - 65135*a^3*tan(1/2*d*x + 1/2*c)^3 - 118784*a^3*tan(1/2*d*x + 1/2*c)^2 - 27195*a^3*tan(1/2*d*x + 1/2*c) - 14848*a^3)/(tan(1/2*d*x + 1/2*c)^2 + 1)^8)/d","A",0
610,1,290,0,0.330428," ","integrate(cos(d*x+c)^6*csc(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{525 \, {\left(d x + c\right)} a^{3} - 1680 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 280 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{280 \, {\left(6 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)} + \frac{2 \, {\left(525 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 4480 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 980 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 20160 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 945 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 38080 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 49280 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 945 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 32256 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 980 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12992 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 525 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2496 \, a^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{7}}}{560 \, d}"," ",0,"-1/560*(525*(d*x + c)*a^3 - 1680*a^3*log(abs(tan(1/2*d*x + 1/2*c))) - 280*a^3*tan(1/2*d*x + 1/2*c) + 280*(6*a^3*tan(1/2*d*x + 1/2*c) + a^3)/tan(1/2*d*x + 1/2*c) + 2*(525*a^3*tan(1/2*d*x + 1/2*c)^13 - 4480*a^3*tan(1/2*d*x + 1/2*c)^12 - 980*a^3*tan(1/2*d*x + 1/2*c)^11 - 20160*a^3*tan(1/2*d*x + 1/2*c)^10 + 945*a^3*tan(1/2*d*x + 1/2*c)^9 - 38080*a^3*tan(1/2*d*x + 1/2*c)^8 - 49280*a^3*tan(1/2*d*x + 1/2*c)^6 - 945*a^3*tan(1/2*d*x + 1/2*c)^5 - 32256*a^3*tan(1/2*d*x + 1/2*c)^4 + 980*a^3*tan(1/2*d*x + 1/2*c)^3 - 12992*a^3*tan(1/2*d*x + 1/2*c)^2 - 525*a^3*tan(1/2*d*x + 1/2*c) - 2496*a^3)/(tan(1/2*d*x + 1/2*c)^2 + 1)^7)/d","A",0
611,1,306,0,0.370484," ","integrate(cos(d*x+c)^6*csc(d*x+c)^3*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{30 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1275 \, {\left(d x + c\right)} a^{3} + 120 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 360 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{30 \, {\left(6 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}} + \frac{2 \, {\left(645 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 1440 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 1735 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 3360 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 450 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 5440 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 450 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4800 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1735 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1824 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 645 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 544 \, a^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(30*a^3*tan(1/2*d*x + 1/2*c)^2 - 1275*(d*x + c)*a^3 + 120*a^3*log(abs(tan(1/2*d*x + 1/2*c))) + 360*a^3*tan(1/2*d*x + 1/2*c) - 30*(6*a^3*tan(1/2*d*x + 1/2*c)^2 + 12*a^3*tan(1/2*d*x + 1/2*c) + a^3)/tan(1/2*d*x + 1/2*c)^2 + 2*(645*a^3*tan(1/2*d*x + 1/2*c)^11 + 1440*a^3*tan(1/2*d*x + 1/2*c)^10 + 1735*a^3*tan(1/2*d*x + 1/2*c)^9 + 3360*a^3*tan(1/2*d*x + 1/2*c)^8 + 450*a^3*tan(1/2*d*x + 1/2*c)^7 + 5440*a^3*tan(1/2*d*x + 1/2*c)^6 - 450*a^3*tan(1/2*d*x + 1/2*c)^5 + 4800*a^3*tan(1/2*d*x + 1/2*c)^4 - 1735*a^3*tan(1/2*d*x + 1/2*c)^3 + 1824*a^3*tan(1/2*d*x + 1/2*c)^2 - 645*a^3*tan(1/2*d*x + 1/2*c) + 544*a^3)/(tan(1/2*d*x + 1/2*c)^2 + 1)^6)/d","A",0
612,1,292,0,0.381044," ","integrate(cos(d*x+c)^6*csc(d*x+c)^4*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{5 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 45 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 375 \, {\left(d x + c\right)} a^{3} - 780 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 45 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{5 \, {\left(286 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{3}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}} + \frac{2 \, {\left(345 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 720 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 330 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2880 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 3680 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 330 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2560 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 345 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 656 \, a^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(5*a^3*tan(1/2*d*x + 1/2*c)^3 + 45*a^3*tan(1/2*d*x + 1/2*c)^2 - 375*(d*x + c)*a^3 - 780*a^3*log(abs(tan(1/2*d*x + 1/2*c))) + 45*a^3*tan(1/2*d*x + 1/2*c) + 5*(286*a^3*tan(1/2*d*x + 1/2*c)^3 - 9*a^3*tan(1/2*d*x + 1/2*c)^2 - 9*a^3*tan(1/2*d*x + 1/2*c) - a^3)/tan(1/2*d*x + 1/2*c)^3 + 2*(345*a^3*tan(1/2*d*x + 1/2*c)^9 - 720*a^3*tan(1/2*d*x + 1/2*c)^8 + 330*a^3*tan(1/2*d*x + 1/2*c)^7 - 2880*a^3*tan(1/2*d*x + 1/2*c)^6 - 3680*a^3*tan(1/2*d*x + 1/2*c)^4 - 330*a^3*tan(1/2*d*x + 1/2*c)^3 - 2560*a^3*tan(1/2*d*x + 1/2*c)^2 - 345*a^3*tan(1/2*d*x + 1/2*c) - 656*a^3)/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","A",0
613,1,313,0,0.397017," ","integrate(cos(d*x+c)^6*csc(d*x+c)^5*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 8 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 360 \, {\left(d x + c\right)} a^{3} - 360 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 184 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{250 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 136 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 32 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 552 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 837 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 1248 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1100 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 736 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 556 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 152 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{3}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}^{4}}}{64 \, d}"," ",0,"1/64*(a^3*tan(1/2*d*x + 1/2*c)^4 + 8*a^3*tan(1/2*d*x + 1/2*c)^3 + 8*a^3*tan(1/2*d*x + 1/2*c)^2 + 360*(d*x + c)*a^3 - 360*a^3*log(abs(tan(1/2*d*x + 1/2*c))) - 184*a^3*tan(1/2*d*x + 1/2*c) + (250*a^3*tan(1/2*d*x + 1/2*c)^12 + 136*a^3*tan(1/2*d*x + 1/2*c)^11 - 32*a^3*tan(1/2*d*x + 1/2*c)^10 + 552*a^3*tan(1/2*d*x + 1/2*c)^9 - 837*a^3*tan(1/2*d*x + 1/2*c)^8 + 1248*a^3*tan(1/2*d*x + 1/2*c)^7 - 1100*a^3*tan(1/2*d*x + 1/2*c)^6 + 736*a^3*tan(1/2*d*x + 1/2*c)^5 - 556*a^3*tan(1/2*d*x + 1/2*c)^4 + 152*a^3*tan(1/2*d*x + 1/2*c)^3 - 12*a^3*tan(1/2*d*x + 1/2*c)^2 - 8*a^3*tan(1/2*d*x + 1/2*c) - a^3)/(tan(1/2*d*x + 1/2*c)^3 + tan(1/2*d*x + 1/2*c))^4)/d","A",0
614,1,276,0,0.393554," ","integrate(cos(d*x+c)^6*csc(d*x+c)^6*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{6 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 45 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 50 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 600 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 6240 \, {\left(d x + c\right)} a^{3} + 3000 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 2580 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{320 \, {\left(9 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, a^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}} - \frac{6850 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 2580 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 600 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 50 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 45 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{960 \, d}"," ",0,"1/960*(6*a^3*tan(1/2*d*x + 1/2*c)^5 + 45*a^3*tan(1/2*d*x + 1/2*c)^4 + 50*a^3*tan(1/2*d*x + 1/2*c)^3 - 600*a^3*tan(1/2*d*x + 1/2*c)^2 + 6240*(d*x + c)*a^3 + 3000*a^3*log(abs(tan(1/2*d*x + 1/2*c))) - 2580*a^3*tan(1/2*d*x + 1/2*c) - 320*(9*a^3*tan(1/2*d*x + 1/2*c)^5 - 12*a^3*tan(1/2*d*x + 1/2*c)^2 - 9*a^3*tan(1/2*d*x + 1/2*c) - 4*a^3)/(tan(1/2*d*x + 1/2*c)^2 + 1)^3 - (6850*a^3*tan(1/2*d*x + 1/2*c)^5 - 2580*a^3*tan(1/2*d*x + 1/2*c)^4 - 600*a^3*tan(1/2*d*x + 1/2*c)^3 + 50*a^3*tan(1/2*d*x + 1/2*c)^2 + 45*a^3*tan(1/2*d*x + 1/2*c) + 6*a^3)/tan(1/2*d*x + 1/2*c)^5)/d","A",0
615,1,307,0,0.426539," ","integrate(cos(d*x+c)^6*csc(d*x+c)^7*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{5 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 36 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 45 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 340 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1215 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 960 \, {\left(d x + c\right)} a^{3} + 10200 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 1800 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{1920 \, {\left(a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, a^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}} - \frac{24990 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 1800 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1215 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 340 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 45 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 36 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6}}}{1920 \, d}"," ",0,"1/1920*(5*a^3*tan(1/2*d*x + 1/2*c)^6 + 36*a^3*tan(1/2*d*x + 1/2*c)^5 + 45*a^3*tan(1/2*d*x + 1/2*c)^4 - 340*a^3*tan(1/2*d*x + 1/2*c)^3 - 1215*a^3*tan(1/2*d*x + 1/2*c)^2 - 960*(d*x + c)*a^3 + 10200*a^3*log(abs(tan(1/2*d*x + 1/2*c))) + 1800*a^3*tan(1/2*d*x + 1/2*c) - 1920*(a^3*tan(1/2*d*x + 1/2*c)^3 - 6*a^3*tan(1/2*d*x + 1/2*c)^2 - a^3*tan(1/2*d*x + 1/2*c) - 6*a^3)/(tan(1/2*d*x + 1/2*c)^2 + 1)^2 - (24990*a^3*tan(1/2*d*x + 1/2*c)^6 + 1800*a^3*tan(1/2*d*x + 1/2*c)^5 - 1215*a^3*tan(1/2*d*x + 1/2*c)^4 - 340*a^3*tan(1/2*d*x + 1/2*c)^3 + 45*a^3*tan(1/2*d*x + 1/2*c)^2 + 36*a^3*tan(1/2*d*x + 1/2*c) + 5*a^3)/tan(1/2*d*x + 1/2*c)^6)/d","A",0
616,1,291,0,0.421038," ","integrate(cos(d*x+c)^6*csc(d*x+c)^8*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{5 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 35 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 49 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 245 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 875 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 455 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 13440 \, {\left(d x + c\right)} a^{3} + 4200 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 9065 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{8960 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} - \frac{10890 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 9065 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 455 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 875 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 245 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 49 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 35 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7}}}{4480 \, d}"," ",0,"1/4480*(5*a^3*tan(1/2*d*x + 1/2*c)^7 + 35*a^3*tan(1/2*d*x + 1/2*c)^6 + 49*a^3*tan(1/2*d*x + 1/2*c)^5 - 245*a^3*tan(1/2*d*x + 1/2*c)^4 - 875*a^3*tan(1/2*d*x + 1/2*c)^3 + 455*a^3*tan(1/2*d*x + 1/2*c)^2 - 13440*(d*x + c)*a^3 + 4200*a^3*log(abs(tan(1/2*d*x + 1/2*c))) + 9065*a^3*tan(1/2*d*x + 1/2*c) + 8960*a^3/(tan(1/2*d*x + 1/2*c)^2 + 1) - (10890*a^3*tan(1/2*d*x + 1/2*c)^7 + 9065*a^3*tan(1/2*d*x + 1/2*c)^6 + 455*a^3*tan(1/2*d*x + 1/2*c)^5 - 875*a^3*tan(1/2*d*x + 1/2*c)^4 - 245*a^3*tan(1/2*d*x + 1/2*c)^3 + 49*a^3*tan(1/2*d*x + 1/2*c)^2 + 35*a^3*tan(1/2*d*x + 1/2*c) + 5*a^3)/tan(1/2*d*x + 1/2*c)^7)/d","A",0
617,1,302,0,0.467711," ","integrate(cos(d*x+c)^6*csc(d*x+c)^9*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{105 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 720 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1120 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 3696 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 14280 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 560 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 77280 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 215040 \, {\left(d x + c\right)} a^{3} - 210000 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 122640 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{570750 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 122640 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 77280 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 560 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 14280 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 3696 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1120 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 720 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 105 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8}}}{215040 \, d}"," ",0,"1/215040*(105*a^3*tan(1/2*d*x + 1/2*c)^8 + 720*a^3*tan(1/2*d*x + 1/2*c)^7 + 1120*a^3*tan(1/2*d*x + 1/2*c)^6 - 3696*a^3*tan(1/2*d*x + 1/2*c)^5 - 14280*a^3*tan(1/2*d*x + 1/2*c)^4 - 560*a^3*tan(1/2*d*x + 1/2*c)^3 + 77280*a^3*tan(1/2*d*x + 1/2*c)^2 - 215040*(d*x + c)*a^3 - 210000*a^3*log(abs(tan(1/2*d*x + 1/2*c))) + 122640*a^3*tan(1/2*d*x + 1/2*c) + (570750*a^3*tan(1/2*d*x + 1/2*c)^8 - 122640*a^3*tan(1/2*d*x + 1/2*c)^7 - 77280*a^3*tan(1/2*d*x + 1/2*c)^6 + 560*a^3*tan(1/2*d*x + 1/2*c)^5 + 14280*a^3*tan(1/2*d*x + 1/2*c)^4 + 3696*a^3*tan(1/2*d*x + 1/2*c)^3 - 1120*a^3*tan(1/2*d*x + 1/2*c)^2 - 720*a^3*tan(1/2*d*x + 1/2*c) - 105*a^3)/tan(1/2*d*x + 1/2*c)^8)/d","A",0
618,1,324,0,0.424931," ","integrate(cos(d*x+c)^6*csc(d*x+c)^10*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{28 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 189 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 324 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 672 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 3024 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1512 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 9744 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18144 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 55440 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 16632 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{156838 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 16632 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 18144 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 9744 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 1512 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3024 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 672 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 324 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 189 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 28 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9}}}{129024 \, d}"," ",0,"1/129024*(28*a^3*tan(1/2*d*x + 1/2*c)^9 + 189*a^3*tan(1/2*d*x + 1/2*c)^8 + 324*a^3*tan(1/2*d*x + 1/2*c)^7 - 672*a^3*tan(1/2*d*x + 1/2*c)^6 - 3024*a^3*tan(1/2*d*x + 1/2*c)^5 - 1512*a^3*tan(1/2*d*x + 1/2*c)^4 + 9744*a^3*tan(1/2*d*x + 1/2*c)^3 + 18144*a^3*tan(1/2*d*x + 1/2*c)^2 - 55440*a^3*log(abs(tan(1/2*d*x + 1/2*c))) - 16632*a^3*tan(1/2*d*x + 1/2*c) + (156838*a^3*tan(1/2*d*x + 1/2*c)^9 + 16632*a^3*tan(1/2*d*x + 1/2*c)^8 - 18144*a^3*tan(1/2*d*x + 1/2*c)^7 - 9744*a^3*tan(1/2*d*x + 1/2*c)^6 + 1512*a^3*tan(1/2*d*x + 1/2*c)^5 + 3024*a^3*tan(1/2*d*x + 1/2*c)^4 + 672*a^3*tan(1/2*d*x + 1/2*c)^3 - 324*a^3*tan(1/2*d*x + 1/2*c)^2 - 189*a^3*tan(1/2*d*x + 1/2*c) - 28*a^3)/tan(1/2*d*x + 1/2*c)^9)/d","A",0
619,1,356,0,0.468850," ","integrate(cos(d*x+c)^6*csc(d*x+c)^11*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{42 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 280 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 525 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 600 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 3570 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 3360 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 5880 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 16800 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 10500 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 55440 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 31920 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{162382 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 31920 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 10500 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 16800 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 5880 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 3360 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3570 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 600 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 525 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 280 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 42 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10}}}{430080 \, d}"," ",0,"1/430080*(42*a^3*tan(1/2*d*x + 1/2*c)^10 + 280*a^3*tan(1/2*d*x + 1/2*c)^9 + 525*a^3*tan(1/2*d*x + 1/2*c)^8 - 600*a^3*tan(1/2*d*x + 1/2*c)^7 - 3570*a^3*tan(1/2*d*x + 1/2*c)^6 - 3360*a^3*tan(1/2*d*x + 1/2*c)^5 + 5880*a^3*tan(1/2*d*x + 1/2*c)^4 + 16800*a^3*tan(1/2*d*x + 1/2*c)^3 + 10500*a^3*tan(1/2*d*x + 1/2*c)^2 - 55440*a^3*log(abs(tan(1/2*d*x + 1/2*c))) - 31920*a^3*tan(1/2*d*x + 1/2*c) + (162382*a^3*tan(1/2*d*x + 1/2*c)^10 + 31920*a^3*tan(1/2*d*x + 1/2*c)^9 - 10500*a^3*tan(1/2*d*x + 1/2*c)^8 - 16800*a^3*tan(1/2*d*x + 1/2*c)^7 - 5880*a^3*tan(1/2*d*x + 1/2*c)^6 + 3360*a^3*tan(1/2*d*x + 1/2*c)^5 + 3570*a^3*tan(1/2*d*x + 1/2*c)^4 + 600*a^3*tan(1/2*d*x + 1/2*c)^3 - 525*a^3*tan(1/2*d*x + 1/2*c)^2 - 280*a^3*tan(1/2*d*x + 1/2*c) - 42*a^3)/tan(1/2*d*x + 1/2*c)^10)/d","A",0
620,1,388,0,0.457914," ","integrate(cos(d*x+c)^6*csc(d*x+c)^12*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{630 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 4158 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 8470 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 3465 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 40590 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 57750 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 6930 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 138600 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 244860 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 152460 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1053360 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 568260 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{3181018 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 568260 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 152460 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 244860 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 138600 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 6930 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 57750 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 40590 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 3465 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 8470 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4158 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 630 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11}}}{14192640 \, d}"," ",0,"1/14192640*(630*a^3*tan(1/2*d*x + 1/2*c)^11 + 4158*a^3*tan(1/2*d*x + 1/2*c)^10 + 8470*a^3*tan(1/2*d*x + 1/2*c)^9 - 3465*a^3*tan(1/2*d*x + 1/2*c)^8 - 40590*a^3*tan(1/2*d*x + 1/2*c)^7 - 57750*a^3*tan(1/2*d*x + 1/2*c)^6 + 6930*a^3*tan(1/2*d*x + 1/2*c)^5 + 138600*a^3*tan(1/2*d*x + 1/2*c)^4 + 244860*a^3*tan(1/2*d*x + 1/2*c)^3 + 152460*a^3*tan(1/2*d*x + 1/2*c)^2 - 1053360*a^3*log(abs(tan(1/2*d*x + 1/2*c))) - 568260*a^3*tan(1/2*d*x + 1/2*c) + (3181018*a^3*tan(1/2*d*x + 1/2*c)^11 + 568260*a^3*tan(1/2*d*x + 1/2*c)^10 - 152460*a^3*tan(1/2*d*x + 1/2*c)^9 - 244860*a^3*tan(1/2*d*x + 1/2*c)^8 - 138600*a^3*tan(1/2*d*x + 1/2*c)^7 - 6930*a^3*tan(1/2*d*x + 1/2*c)^6 + 57750*a^3*tan(1/2*d*x + 1/2*c)^5 + 40590*a^3*tan(1/2*d*x + 1/2*c)^4 + 3465*a^3*tan(1/2*d*x + 1/2*c)^3 - 8470*a^3*tan(1/2*d*x + 1/2*c)^2 - 4158*a^3*tan(1/2*d*x + 1/2*c) - 630*a^3)/tan(1/2*d*x + 1/2*c)^11)/d","A",0
621,1,420,0,0.544208," ","integrate(cos(d*x+c)^6*csc(d*x+c)^13*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{1155 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 7560 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 16632 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 3080 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 51975 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 106920 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 83160 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 83160 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 384615 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 572880 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 166320 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2273040 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 1496880 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{7053722 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 1496880 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 166320 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 572880 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 384615 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 83160 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 83160 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 106920 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 51975 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 3080 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 16632 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 7560 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1155 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12}}}{56770560 \, d}"," ",0,"1/56770560*(1155*a^3*tan(1/2*d*x + 1/2*c)^12 + 7560*a^3*tan(1/2*d*x + 1/2*c)^11 + 16632*a^3*tan(1/2*d*x + 1/2*c)^10 + 3080*a^3*tan(1/2*d*x + 1/2*c)^9 - 51975*a^3*tan(1/2*d*x + 1/2*c)^8 - 106920*a^3*tan(1/2*d*x + 1/2*c)^7 - 83160*a^3*tan(1/2*d*x + 1/2*c)^6 + 83160*a^3*tan(1/2*d*x + 1/2*c)^5 + 384615*a^3*tan(1/2*d*x + 1/2*c)^4 + 572880*a^3*tan(1/2*d*x + 1/2*c)^3 + 166320*a^3*tan(1/2*d*x + 1/2*c)^2 - 2273040*a^3*log(abs(tan(1/2*d*x + 1/2*c))) - 1496880*a^3*tan(1/2*d*x + 1/2*c) + (7053722*a^3*tan(1/2*d*x + 1/2*c)^12 + 1496880*a^3*tan(1/2*d*x + 1/2*c)^11 - 166320*a^3*tan(1/2*d*x + 1/2*c)^10 - 572880*a^3*tan(1/2*d*x + 1/2*c)^9 - 384615*a^3*tan(1/2*d*x + 1/2*c)^8 - 83160*a^3*tan(1/2*d*x + 1/2*c)^7 + 83160*a^3*tan(1/2*d*x + 1/2*c)^6 + 106920*a^3*tan(1/2*d*x + 1/2*c)^5 + 51975*a^3*tan(1/2*d*x + 1/2*c)^4 - 3080*a^3*tan(1/2*d*x + 1/2*c)^3 - 16632*a^3*tan(1/2*d*x + 1/2*c)^2 - 7560*a^3*tan(1/2*d*x + 1/2*c) - 1155*a^3)/tan(1/2*d*x + 1/2*c)^12)/d","A",0
622,1,452,0,0.496438," ","integrate(cos(d*x+c)^6*csc(d*x+c)^14*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{770 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 5005 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 11830 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 8008 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 20020 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 65065 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 94380 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 40040 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 150150 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 385385 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 450450 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 80080 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2162160 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 1401400 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{6875958 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 1401400 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 80080 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 450450 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 385385 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 150150 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 40040 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 94380 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 65065 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 20020 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 8008 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 11830 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 5005 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 770 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13}}}{82001920 \, d}"," ",0,"1/82001920*(770*a^3*tan(1/2*d*x + 1/2*c)^13 + 5005*a^3*tan(1/2*d*x + 1/2*c)^12 + 11830*a^3*tan(1/2*d*x + 1/2*c)^11 + 8008*a^3*tan(1/2*d*x + 1/2*c)^10 - 20020*a^3*tan(1/2*d*x + 1/2*c)^9 - 65065*a^3*tan(1/2*d*x + 1/2*c)^8 - 94380*a^3*tan(1/2*d*x + 1/2*c)^7 - 40040*a^3*tan(1/2*d*x + 1/2*c)^6 + 150150*a^3*tan(1/2*d*x + 1/2*c)^5 + 385385*a^3*tan(1/2*d*x + 1/2*c)^4 + 450450*a^3*tan(1/2*d*x + 1/2*c)^3 + 80080*a^3*tan(1/2*d*x + 1/2*c)^2 - 2162160*a^3*log(abs(tan(1/2*d*x + 1/2*c))) - 1401400*a^3*tan(1/2*d*x + 1/2*c) + (6875958*a^3*tan(1/2*d*x + 1/2*c)^13 + 1401400*a^3*tan(1/2*d*x + 1/2*c)^12 - 80080*a^3*tan(1/2*d*x + 1/2*c)^11 - 450450*a^3*tan(1/2*d*x + 1/2*c)^10 - 385385*a^3*tan(1/2*d*x + 1/2*c)^9 - 150150*a^3*tan(1/2*d*x + 1/2*c)^8 + 40040*a^3*tan(1/2*d*x + 1/2*c)^7 + 94380*a^3*tan(1/2*d*x + 1/2*c)^6 + 65065*a^3*tan(1/2*d*x + 1/2*c)^5 + 20020*a^3*tan(1/2*d*x + 1/2*c)^4 - 8008*a^3*tan(1/2*d*x + 1/2*c)^3 - 11830*a^3*tan(1/2*d*x + 1/2*c)^2 - 5005*a^3*tan(1/2*d*x + 1/2*c) - 770*a^3)/tan(1/2*d*x + 1/2*c)^13)/d","A",0
623,1,324,0,0.485151," ","integrate(cos(d*x+c)^6*csc(d*x+c)^4*(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{10 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2025 \, {\left(d x + c\right)} a^{4} - 1440 \, a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 450 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{10 \, {\left(264 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 45 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{4}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}} + \frac{2 \, {\left(1335 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 3085 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 3840 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 1110 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 7680 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 1110 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 7680 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 3085 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4608 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1335 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 768 \, a^{4}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(10*a^4*tan(1/2*d*x + 1/2*c)^3 + 120*a^4*tan(1/2*d*x + 1/2*c)^2 - 2025*(d*x + c)*a^4 - 1440*a^4*log(abs(tan(1/2*d*x + 1/2*c))) + 450*a^4*tan(1/2*d*x + 1/2*c) + 10*(264*a^4*tan(1/2*d*x + 1/2*c)^3 - 45*a^4*tan(1/2*d*x + 1/2*c)^2 - 12*a^4*tan(1/2*d*x + 1/2*c) - a^4)/tan(1/2*d*x + 1/2*c)^3 + 2*(1335*a^4*tan(1/2*d*x + 1/2*c)^11 + 3085*a^4*tan(1/2*d*x + 1/2*c)^9 - 3840*a^4*tan(1/2*d*x + 1/2*c)^8 + 1110*a^4*tan(1/2*d*x + 1/2*c)^7 - 7680*a^4*tan(1/2*d*x + 1/2*c)^6 - 1110*a^4*tan(1/2*d*x + 1/2*c)^5 - 7680*a^4*tan(1/2*d*x + 1/2*c)^4 - 3085*a^4*tan(1/2*d*x + 1/2*c)^3 - 4608*a^4*tan(1/2*d*x + 1/2*c)^2 - 1335*a^4*tan(1/2*d*x + 1/2*c) - 768*a^4)/(tan(1/2*d*x + 1/2*c)^2 + 1)^6)/d","A",0
624,1,218,0,0.205180," ","integrate(cos(d*x+c)^6*sin(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{945 \, {\left(d x + c\right)}}{a} + \frac{2 \, {\left(945 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{17} + 8190 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} - 97650 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 215040 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 106470 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 322560 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 451584 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 106470 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 129024 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 97650 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36864 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 8190 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9216 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 945 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1024\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{9} a}}{40320 \, d}"," ",0,"1/40320*(945*(d*x + c)/a + 2*(945*tan(1/2*d*x + 1/2*c)^17 + 8190*tan(1/2*d*x + 1/2*c)^15 - 97650*tan(1/2*d*x + 1/2*c)^13 + 215040*tan(1/2*d*x + 1/2*c)^12 + 106470*tan(1/2*d*x + 1/2*c)^11 - 322560*tan(1/2*d*x + 1/2*c)^10 + 451584*tan(1/2*d*x + 1/2*c)^8 - 106470*tan(1/2*d*x + 1/2*c)^7 - 129024*tan(1/2*d*x + 1/2*c)^6 + 97650*tan(1/2*d*x + 1/2*c)^5 + 36864*tan(1/2*d*x + 1/2*c)^4 - 8190*tan(1/2*d*x + 1/2*c)^3 + 9216*tan(1/2*d*x + 1/2*c)^2 - 945*tan(1/2*d*x + 1/2*c) + 1024)/((tan(1/2*d*x + 1/2*c)^2 + 1)^9*a))/d","A",0
625,1,205,0,0.171802," ","integrate(cos(d*x+c)^6*sin(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{105 \, {\left(d x + c\right)}}{a} + \frac{2 \, {\left(105 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} + 805 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 8960 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 11655 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 23485 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 8960 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 23485 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 14336 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 11655 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1792 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 805 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2048 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 105 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 256\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{8} a}}{4480 \, d}"," ",0,"-1/4480*(105*(d*x + c)/a + 2*(105*tan(1/2*d*x + 1/2*c)^15 + 805*tan(1/2*d*x + 1/2*c)^13 + 8960*tan(1/2*d*x + 1/2*c)^12 - 11655*tan(1/2*d*x + 1/2*c)^11 + 23485*tan(1/2*d*x + 1/2*c)^9 + 8960*tan(1/2*d*x + 1/2*c)^8 - 23485*tan(1/2*d*x + 1/2*c)^7 + 14336*tan(1/2*d*x + 1/2*c)^6 + 11655*tan(1/2*d*x + 1/2*c)^5 - 1792*tan(1/2*d*x + 1/2*c)^4 - 805*tan(1/2*d*x + 1/2*c)^3 + 2048*tan(1/2*d*x + 1/2*c)^2 - 105*tan(1/2*d*x + 1/2*c) + 256)/((tan(1/2*d*x + 1/2*c)^2 + 1)^8*a))/d","A",0
626,1,179,0,0.156831," ","integrate(cos(d*x+c)^6*sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{105 \, {\left(d x + c\right)}}{a} + \frac{2 \, {\left(105 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 1540 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 3360 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 1085 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 3360 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 6720 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 1085 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1344 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 1540 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 672 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 105 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 96\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{7} a}}{1680 \, d}"," ",0,"1/1680*(105*(d*x + c)/a + 2*(105*tan(1/2*d*x + 1/2*c)^13 - 1540*tan(1/2*d*x + 1/2*c)^11 + 3360*tan(1/2*d*x + 1/2*c)^10 + 1085*tan(1/2*d*x + 1/2*c)^9 - 3360*tan(1/2*d*x + 1/2*c)^8 + 6720*tan(1/2*d*x + 1/2*c)^6 - 1085*tan(1/2*d*x + 1/2*c)^5 - 1344*tan(1/2*d*x + 1/2*c)^4 + 1540*tan(1/2*d*x + 1/2*c)^3 + 672*tan(1/2*d*x + 1/2*c)^2 - 105*tan(1/2*d*x + 1/2*c) + 96)/((tan(1/2*d*x + 1/2*c)^2 + 1)^7*a))/d","A",0
627,1,179,0,0.147544," ","integrate(cos(d*x+c)^6*sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{15 \, {\left(d x + c\right)}}{a} + \frac{2 \, {\left(15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 240 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 235 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 240 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 390 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 480 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 390 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 480 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 235 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 48 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 48\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6} a}}{240 \, d}"," ",0,"-1/240*(15*(d*x + c)/a + 2*(15*tan(1/2*d*x + 1/2*c)^11 + 240*tan(1/2*d*x + 1/2*c)^10 - 235*tan(1/2*d*x + 1/2*c)^9 + 240*tan(1/2*d*x + 1/2*c)^8 + 390*tan(1/2*d*x + 1/2*c)^7 + 480*tan(1/2*d*x + 1/2*c)^6 - 390*tan(1/2*d*x + 1/2*c)^5 + 480*tan(1/2*d*x + 1/2*c)^4 + 235*tan(1/2*d*x + 1/2*c)^3 + 48*tan(1/2*d*x + 1/2*c)^2 - 15*tan(1/2*d*x + 1/2*c) + 48)/((tan(1/2*d*x + 1/2*c)^2 + 1)^6*a))/d","B",0
628,1,143,0,0.160600," ","integrate(cos(d*x+c)^6*csc(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{9 \, {\left(d x + c\right)}}{a} - \frac{24 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a} - \frac{2 \, {\left(15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 48 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 96 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 80 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 32\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4} a}}{24 \, d}"," ",0,"-1/24*(9*(d*x + c)/a - 24*log(abs(tan(1/2*d*x + 1/2*c)))/a - 2*(15*tan(1/2*d*x + 1/2*c)^7 + 48*tan(1/2*d*x + 1/2*c)^6 - 9*tan(1/2*d*x + 1/2*c)^5 + 96*tan(1/2*d*x + 1/2*c)^4 + 9*tan(1/2*d*x + 1/2*c)^3 + 80*tan(1/2*d*x + 1/2*c)^2 - 15*tan(1/2*d*x + 1/2*c) + 32)/((tan(1/2*d*x + 1/2*c)^2 + 1)^4*a))/d","A",0
629,1,147,0,0.170878," ","integrate(cos(d*x+c)^6*csc(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{9 \, {\left(d x + c\right)}}{a} + \frac{6 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a} - \frac{3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a} - \frac{3 \, {\left(2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)} - \frac{2 \, {\left(3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 12 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 12 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} a}}{6 \, d}"," ",0,"-1/6*(9*(d*x + c)/a + 6*log(abs(tan(1/2*d*x + 1/2*c)))/a - 3*tan(1/2*d*x + 1/2*c)/a - 3*(2*tan(1/2*d*x + 1/2*c) - 1)/(a*tan(1/2*d*x + 1/2*c)) - 2*(3*tan(1/2*d*x + 1/2*c)^5 - 12*tan(1/2*d*x + 1/2*c)^4 - 12*tan(1/2*d*x + 1/2*c)^2 - 3*tan(1/2*d*x + 1/2*c) - 8)/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*a))/d","A",0
630,1,167,0,0.183317," ","integrate(cos(d*x+c)^6*csc(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{12 \, {\left(d x + c\right)}}{a} - \frac{12 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a} + \frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{2}} + \frac{6 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 4 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 5 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 16 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 4 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}^{2} a}}{8 \, d}"," ",0,"1/8*(12*(d*x + c)/a - 12*log(abs(tan(1/2*d*x + 1/2*c)))/a + (a*tan(1/2*d*x + 1/2*c)^2 - 4*a*tan(1/2*d*x + 1/2*c))/a^2 + (6*tan(1/2*d*x + 1/2*c)^6 - 4*tan(1/2*d*x + 1/2*c)^5 - 5*tan(1/2*d*x + 1/2*c)^4 + 16*tan(1/2*d*x + 1/2*c)^3 - 12*tan(1/2*d*x + 1/2*c)^2 + 4*tan(1/2*d*x + 1/2*c) - 1)/((tan(1/2*d*x + 1/2*c)^3 + tan(1/2*d*x + 1/2*c))^2*a))/d","A",0
631,1,157,0,0.187787," ","integrate(cos(d*x+c)^6*csc(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{24 \, {\left(d x + c\right)}}{a} + \frac{36 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a} + \frac{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3}} + \frac{48}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a} - \frac{66 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{24 \, d}"," ",0,"1/24*(24*(d*x + c)/a + 36*log(abs(tan(1/2*d*x + 1/2*c)))/a + (a^2*tan(1/2*d*x + 1/2*c)^3 - 3*a^2*tan(1/2*d*x + 1/2*c)^2 - 15*a^2*tan(1/2*d*x + 1/2*c))/a^3 + 48/((tan(1/2*d*x + 1/2*c)^2 + 1)*a) - (66*tan(1/2*d*x + 1/2*c)^3 - 15*tan(1/2*d*x + 1/2*c)^2 - 3*tan(1/2*d*x + 1/2*c) + 1)/(a*tan(1/2*d*x + 1/2*c)^3))/d","A",0
632,1,167,0,0.203663," ","integrate(cos(d*x+c)^6*csc(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{192 \, {\left(d x + c\right)}}{a} - \frac{72 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a} - \frac{3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 8 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 120 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{4}} + \frac{150 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 120 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}}}{192 \, d}"," ",0,"-1/192*(192*(d*x + c)/a - 72*log(abs(tan(1/2*d*x + 1/2*c)))/a - (3*a^3*tan(1/2*d*x + 1/2*c)^4 - 8*a^3*tan(1/2*d*x + 1/2*c)^3 - 24*a^3*tan(1/2*d*x + 1/2*c)^2 + 120*a^3*tan(1/2*d*x + 1/2*c))/a^4 + (150*tan(1/2*d*x + 1/2*c)^4 + 120*tan(1/2*d*x + 1/2*c)^3 - 24*tan(1/2*d*x + 1/2*c)^2 - 8*tan(1/2*d*x + 1/2*c) + 3)/(a*tan(1/2*d*x + 1/2*c)^4))/d","A",0
633,1,187,0,0.202372," ","integrate(cos(d*x+c)^6*csc(d*x+c)^6/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{120 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a} - \frac{2 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 5 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 10 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 20 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{5}} - \frac{274 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 20 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 40 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 10 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 5 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{320 \, d}"," ",0,"-1/320*(120*log(abs(tan(1/2*d*x + 1/2*c)))/a - (2*a^4*tan(1/2*d*x + 1/2*c)^5 - 5*a^4*tan(1/2*d*x + 1/2*c)^4 - 10*a^4*tan(1/2*d*x + 1/2*c)^3 + 40*a^4*tan(1/2*d*x + 1/2*c)^2 + 20*a^4*tan(1/2*d*x + 1/2*c))/a^5 - (274*tan(1/2*d*x + 1/2*c)^5 - 20*tan(1/2*d*x + 1/2*c)^4 - 40*tan(1/2*d*x + 1/2*c)^3 + 10*tan(1/2*d*x + 1/2*c)^2 + 5*tan(1/2*d*x + 1/2*c) - 2)/(a*tan(1/2*d*x + 1/2*c)^5))/d","B",0
634,1,179,0,0.212748," ","integrate(cos(d*x+c)^6*sin(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{105 \, {\left(d x + c\right)}}{a^{2}} + \frac{2 \, {\left(105 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 700 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 1680 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 3395 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 7280 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 1120 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 3395 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2016 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 700 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1232 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 105 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 176\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{7} a^{2}}}{840 \, d}"," ",0,"-1/840*(105*(d*x + c)/a^2 + 2*(105*tan(1/2*d*x + 1/2*c)^13 + 700*tan(1/2*d*x + 1/2*c)^11 + 1680*tan(1/2*d*x + 1/2*c)^10 - 3395*tan(1/2*d*x + 1/2*c)^9 + 7280*tan(1/2*d*x + 1/2*c)^8 - 1120*tan(1/2*d*x + 1/2*c)^6 + 3395*tan(1/2*d*x + 1/2*c)^5 + 2016*tan(1/2*d*x + 1/2*c)^4 - 700*tan(1/2*d*x + 1/2*c)^3 + 1232*tan(1/2*d*x + 1/2*c)^2 - 105*tan(1/2*d*x + 1/2*c) + 176)/((tan(1/2*d*x + 1/2*c)^2 + 1)^7*a^2))/d","A",0
635,1,153,0,0.179642," ","integrate(cos(d*x+c)^6*sin(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{45 \, {\left(d x + c\right)}}{a^{2}} + \frac{2 \, {\left(45 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 65 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 960 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 750 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 640 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 750 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 65 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 384 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 45 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 64\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6} a^{2}}}{240 \, d}"," ",0,"1/240*(45*(d*x + c)/a^2 + 2*(45*tan(1/2*d*x + 1/2*c)^11 - 65*tan(1/2*d*x + 1/2*c)^9 + 960*tan(1/2*d*x + 1/2*c)^8 - 750*tan(1/2*d*x + 1/2*c)^7 + 640*tan(1/2*d*x + 1/2*c)^6 + 750*tan(1/2*d*x + 1/2*c)^5 + 65*tan(1/2*d*x + 1/2*c)^3 + 384*tan(1/2*d*x + 1/2*c)^2 - 45*tan(1/2*d*x + 1/2*c) + 64)/((tan(1/2*d*x + 1/2*c)^2 + 1)^6*a^2))/d","A",0
636,1,140,0,0.191437," ","integrate(cos(d*x+c)^6*sin(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{15 \, {\left(d x + c\right)}}{a^{2}} + \frac{2 \, {\left(15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 60 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 90 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 240 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 40 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 90 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 80 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 28\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5} a^{2}}}{60 \, d}"," ",0,"-1/60*(15*(d*x + c)/a^2 + 2*(15*tan(1/2*d*x + 1/2*c)^9 + 60*tan(1/2*d*x + 1/2*c)^8 - 90*tan(1/2*d*x + 1/2*c)^7 + 240*tan(1/2*d*x + 1/2*c)^6 + 40*tan(1/2*d*x + 1/2*c)^4 + 90*tan(1/2*d*x + 1/2*c)^3 + 80*tan(1/2*d*x + 1/2*c)^2 - 15*tan(1/2*d*x + 1/2*c) + 28)/((tan(1/2*d*x + 1/2*c)^2 + 1)^5*a^2))/d","A",0
637,1,91,0,0.173072," ","integrate(cos(d*x+c)^6*csc(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(d x + c\right)}}{a^{2}} - \frac{3 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} - \frac{2 \, {\left(3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} a^{2}}}{3 \, d}"," ",0,"-1/3*(3*(d*x + c)/a^2 - 3*log(abs(tan(1/2*d*x + 1/2*c)))/a^2 - 2*(3*tan(1/2*d*x + 1/2*c)^5 + 6*tan(1/2*d*x + 1/2*c)^2 - 3*tan(1/2*d*x + 1/2*c) + 2)/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*a^2))/d","A",0
638,1,131,0,0.209591," ","integrate(cos(d*x+c)^6*csc(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{d x + c}{a^{2}} + \frac{4 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} - \frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{2}} - \frac{4 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1}{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)} + \frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{2}}}{2 \, d}"," ",0,"-1/2*((d*x + c)/a^2 + 4*log(abs(tan(1/2*d*x + 1/2*c)))/a^2 - tan(1/2*d*x + 1/2*c)/a^2 - (4*tan(1/2*d*x + 1/2*c) - 1)/(a^2*tan(1/2*d*x + 1/2*c)) + 2*(tan(1/2*d*x + 1/2*c)^3 + 4*tan(1/2*d*x + 1/2*c)^2 - tan(1/2*d*x + 1/2*c) + 4)/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^2))/d","A",0
639,1,128,0,0.208774," ","integrate(cos(d*x+c)^6*csc(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{16 \, {\left(d x + c\right)}}{a^{2}} + \frac{4 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} + \frac{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{4}} + \frac{16}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a^{2}} - \frac{6 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1}{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}}{8 \, d}"," ",0,"1/8*(16*(d*x + c)/a^2 + 4*log(abs(tan(1/2*d*x + 1/2*c)))/a^2 + (a^2*tan(1/2*d*x + 1/2*c)^2 - 8*a^2*tan(1/2*d*x + 1/2*c))/a^4 + 16/((tan(1/2*d*x + 1/2*c)^2 + 1)*a^2) - (6*tan(1/2*d*x + 1/2*c)^2 - 8*tan(1/2*d*x + 1/2*c) + 1)/(a^2*tan(1/2*d*x + 1/2*c)^2))/d","A",0
640,1,137,0,0.241454," ","integrate(cos(d*x+c)^6*csc(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{24 \, {\left(d x + c\right)}}{a^{2}} - \frac{24 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} + \frac{44 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 6 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1}{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}} - \frac{a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 9 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{24 \, d}"," ",0,"-1/24*(24*(d*x + c)/a^2 - 24*log(abs(tan(1/2*d*x + 1/2*c)))/a^2 + (44*tan(1/2*d*x + 1/2*c)^3 + 9*tan(1/2*d*x + 1/2*c)^2 - 6*tan(1/2*d*x + 1/2*c) + 1)/(a^2*tan(1/2*d*x + 1/2*c)^3) - (a^4*tan(1/2*d*x + 1/2*c)^3 - 6*a^4*tan(1/2*d*x + 1/2*c)^2 + 9*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
641,1,158,0,0.251156," ","integrate(cos(d*x+c)^6*csc(d*x+c)^5/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{120 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} - \frac{250 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 48 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 16 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3}{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}} - \frac{3 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 16 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 24 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 48 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{8}}}{192 \, d}"," ",0,"-1/192*(120*log(abs(tan(1/2*d*x + 1/2*c)))/a^2 - (250*tan(1/2*d*x + 1/2*c)^4 - 48*tan(1/2*d*x + 1/2*c)^3 - 24*tan(1/2*d*x + 1/2*c)^2 + 16*tan(1/2*d*x + 1/2*c) - 3)/(a^2*tan(1/2*d*x + 1/2*c)^4) - (3*a^6*tan(1/2*d*x + 1/2*c)^4 - 16*a^6*tan(1/2*d*x + 1/2*c)^3 + 24*a^6*tan(1/2*d*x + 1/2*c)^2 + 48*a^6*tan(1/2*d*x + 1/2*c))/a^8)/d","B",0
642,1,157,0,0.254416," ","integrate(cos(d*x+c)^6*csc(d*x+c)^6/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{120 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} - \frac{274 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 90 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 25 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3}{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}} + \frac{3 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 25 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 90 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{10}}}{480 \, d}"," ",0,"1/480*(120*log(abs(tan(1/2*d*x + 1/2*c)))/a^2 - (274*tan(1/2*d*x + 1/2*c)^5 - 90*tan(1/2*d*x + 1/2*c)^4 + 25*tan(1/2*d*x + 1/2*c)^2 - 15*tan(1/2*d*x + 1/2*c) + 3)/(a^2*tan(1/2*d*x + 1/2*c)^5) + (3*a^8*tan(1/2*d*x + 1/2*c)^5 - 15*a^8*tan(1/2*d*x + 1/2*c)^4 + 25*a^8*tan(1/2*d*x + 1/2*c)^3 - 90*a^8*tan(1/2*d*x + 1/2*c))/a^10)/d","A",0
643,1,216,0,0.285032," ","integrate(cos(d*x+c)^6*csc(d*x+c)^7/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{360 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} - \frac{882 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 240 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 40 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 45 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5}{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6}} - \frac{5 \, a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 24 \, a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 45 \, a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 40 \, a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 240 \, a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{12}}}{1920 \, d}"," ",0,"-1/1920*(360*log(abs(tan(1/2*d*x + 1/2*c)))/a^2 - (882*tan(1/2*d*x + 1/2*c)^6 - 240*tan(1/2*d*x + 1/2*c)^5 + 15*tan(1/2*d*x + 1/2*c)^4 + 40*tan(1/2*d*x + 1/2*c)^3 - 45*tan(1/2*d*x + 1/2*c)^2 + 24*tan(1/2*d*x + 1/2*c) - 5)/(a^2*tan(1/2*d*x + 1/2*c)^6) - (5*a^10*tan(1/2*d*x + 1/2*c)^6 - 24*a^10*tan(1/2*d*x + 1/2*c)^5 + 45*a^10*tan(1/2*d*x + 1/2*c)^4 - 40*a^10*tan(1/2*d*x + 1/2*c)^3 - 15*a^10*tan(1/2*d*x + 1/2*c)^2 + 240*a^10*tan(1/2*d*x + 1/2*c))/a^12)/d","A",0
644,1,166,0,0.260636," ","integrate(cos(d*x+c)^6*sin(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{345 \, {\left(d x + c\right)}}{a^{3}} + \frac{2 \, {\left(345 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 1955 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 480 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 2250 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 5440 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 2250 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 7680 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1955 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3264 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 345 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 544\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6} a^{3}}}{240 \, d}"," ",0,"-1/240*(345*(d*x + c)/a^3 + 2*(345*tan(1/2*d*x + 1/2*c)^11 + 1955*tan(1/2*d*x + 1/2*c)^9 + 480*tan(1/2*d*x + 1/2*c)^8 + 2250*tan(1/2*d*x + 1/2*c)^7 + 5440*tan(1/2*d*x + 1/2*c)^6 - 2250*tan(1/2*d*x + 1/2*c)^5 + 7680*tan(1/2*d*x + 1/2*c)^4 - 1955*tan(1/2*d*x + 1/2*c)^3 + 3264*tan(1/2*d*x + 1/2*c)^2 - 345*tan(1/2*d*x + 1/2*c) + 544)/((tan(1/2*d*x + 1/2*c)^2 + 1)^6*a^3))/d","A",0
645,1,127,0,0.212549," ","integrate(cos(d*x+c)^6*sin(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{195 \, {\left(d x + c\right)}}{a^{3}} + \frac{2 \, {\left(195 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 750 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 720 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 2320 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 750 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1520 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 195 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 304\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5} a^{3}}}{120 \, d}"," ",0,"1/120*(195*(d*x + c)/a^3 + 2*(195*tan(1/2*d*x + 1/2*c)^9 + 750*tan(1/2*d*x + 1/2*c)^7 + 720*tan(1/2*d*x + 1/2*c)^6 + 2320*tan(1/2*d*x + 1/2*c)^4 - 750*tan(1/2*d*x + 1/2*c)^3 + 1520*tan(1/2*d*x + 1/2*c)^2 - 195*tan(1/2*d*x + 1/2*c) + 304)/((tan(1/2*d*x + 1/2*c)^2 + 1)^5*a^3))/d","A",0
646,1,127,0,0.193757," ","integrate(cos(d*x+c)^6*sin(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{15 \, {\left(d x + c\right)}}{a^{3}} + \frac{2 \, {\left(15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 8 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 23 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 23 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 88 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4} a^{3}}}{8 \, d}"," ",0,"-1/8*(15*(d*x + c)/a^3 + 2*(15*tan(1/2*d*x + 1/2*c)^7 + 8*tan(1/2*d*x + 1/2*c)^6 + 23*tan(1/2*d*x + 1/2*c)^5 + 72*tan(1/2*d*x + 1/2*c)^4 - 23*tan(1/2*d*x + 1/2*c)^3 + 88*tan(1/2*d*x + 1/2*c)^2 - 15*tan(1/2*d*x + 1/2*c) + 24)/((tan(1/2*d*x + 1/2*c)^2 + 1)^4*a^3))/d","A",0
647,1,89,0,0.202706," ","integrate(cos(d*x+c)^6*csc(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{7 \, {\left(d x + c\right)}}{a^{3}} - \frac{2 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} + \frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{3}}}{2 \, d}"," ",0,"-1/2*(7*(d*x + c)/a^3 - 2*log(abs(tan(1/2*d*x + 1/2*c)))/a^3 + 2*(tan(1/2*d*x + 1/2*c)^3 + 6*tan(1/2*d*x + 1/2*c)^2 - tan(1/2*d*x + 1/2*c) + 6)/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^3))/d","A",0
648,1,111,0,0.210501," ","integrate(cos(d*x+c)^6*csc(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{6 \, {\left(d x + c\right)}}{a^{3}} - \frac{6 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} + \frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3}} + \frac{2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 6 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} a^{3}}}{2 \, d}"," ",0,"1/2*(6*(d*x + c)/a^3 - 6*log(abs(tan(1/2*d*x + 1/2*c)))/a^3 + tan(1/2*d*x + 1/2*c)/a^3 + (2*tan(1/2*d*x + 1/2*c)^3 - tan(1/2*d*x + 1/2*c)^2 + 6*tan(1/2*d*x + 1/2*c) - 1)/((tan(1/2*d*x + 1/2*c)^3 + tan(1/2*d*x + 1/2*c))*a^3))/d","B",0
649,1,108,0,0.252461," ","integrate(cos(d*x+c)^6*csc(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{8 \, {\left(d x + c\right)}}{a^{3}} - \frac{28 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} + \frac{42 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1}{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}} - \frac{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{8 \, d}"," ",0,"-1/8*(8*(d*x + c)/a^3 - 28*log(abs(tan(1/2*d*x + 1/2*c)))/a^3 + (42*tan(1/2*d*x + 1/2*c)^2 - 12*tan(1/2*d*x + 1/2*c) + 1)/(a^3*tan(1/2*d*x + 1/2*c)^2) - (a^3*tan(1/2*d*x + 1/2*c)^2 - 12*a^3*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
650,1,128,0,0.241225," ","integrate(cos(d*x+c)^6*csc(d*x+c)^4/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{60 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} - \frac{110 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 45 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1}{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}} - \frac{a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 45 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{9}}}{24 \, d}"," ",0,"-1/24*(60*log(abs(tan(1/2*d*x + 1/2*c)))/a^3 - (110*tan(1/2*d*x + 1/2*c)^3 - 45*tan(1/2*d*x + 1/2*c)^2 + 9*tan(1/2*d*x + 1/2*c) - 1)/(a^3*tan(1/2*d*x + 1/2*c)^3) - (a^6*tan(1/2*d*x + 1/2*c)^3 - 9*a^6*tan(1/2*d*x + 1/2*c)^2 + 45*a^6*tan(1/2*d*x + 1/2*c))/a^9)/d","A",0
651,1,156,0,0.261388," ","integrate(cos(d*x+c)^6*csc(d*x+c)^5/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{120 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} - \frac{250 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 104 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 32 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1}{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}} + \frac{a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 8 \, a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 32 \, a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 104 \, a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{12}}}{64 \, d}"," ",0,"1/64*(120*log(abs(tan(1/2*d*x + 1/2*c)))/a^3 - (250*tan(1/2*d*x + 1/2*c)^4 - 104*tan(1/2*d*x + 1/2*c)^3 + 32*tan(1/2*d*x + 1/2*c)^2 - 8*tan(1/2*d*x + 1/2*c) + 1)/(a^3*tan(1/2*d*x + 1/2*c)^4) + (a^9*tan(1/2*d*x + 1/2*c)^4 - 8*a^9*tan(1/2*d*x + 1/2*c)^3 + 32*a^9*tan(1/2*d*x + 1/2*c)^2 - 104*a^9*tan(1/2*d*x + 1/2*c))/a^12)/d","A",0
652,1,187,0,0.276923," ","integrate(cos(d*x+c)^6*csc(d*x+c)^6/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{1560 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} - \frac{3562 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1380 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 480 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 170 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 45 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6}{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}} - \frac{6 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 45 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 170 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 480 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1380 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{960 \, d}"," ",0,"-1/960*(1560*log(abs(tan(1/2*d*x + 1/2*c)))/a^3 - (3562*tan(1/2*d*x + 1/2*c)^5 - 1380*tan(1/2*d*x + 1/2*c)^4 + 480*tan(1/2*d*x + 1/2*c)^3 - 170*tan(1/2*d*x + 1/2*c)^2 + 45*tan(1/2*d*x + 1/2*c) - 6)/(a^3*tan(1/2*d*x + 1/2*c)^5) - (6*a^12*tan(1/2*d*x + 1/2*c)^5 - 45*a^12*tan(1/2*d*x + 1/2*c)^4 + 170*a^12*tan(1/2*d*x + 1/2*c)^3 - 480*a^12*tan(1/2*d*x + 1/2*c)^2 + 1380*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
653,0,0,0,0.000000," ","integrate(cos(d*x+c)^6*sin(d*x+c)^n*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{3} \sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{6}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^3*sin(d*x + c)^n*cos(d*x + c)^6, x)","F",0
654,0,0,0,0.000000," ","integrate(cos(d*x+c)^6*sin(d*x+c)^n*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{2} \sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{6}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^2*sin(d*x + c)^n*cos(d*x + c)^6, x)","F",0
655,0,0,0,0.000000," ","integrate(cos(d*x+c)^6*sin(d*x+c)^n*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\int {\left(a \sin\left(d x + c\right) + a\right)} \sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{6}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)*sin(d*x + c)^n*cos(d*x + c)^6, x)","F",0
656,1,163,0,0.405916," ","integrate(cos(d*x+c)^7*sin(d*x+c)^6*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{a \cos\left(14 \, d x + 14 \, c\right)}{114688 \, d} - \frac{7 \, a \cos\left(10 \, d x + 10 \, c\right)}{81920 \, d} + \frac{7 \, a \cos\left(6 \, d x + 6 \, c\right)}{16384 \, d} - \frac{35 \, a \cos\left(2 \, d x + 2 \, c\right)}{16384 \, d} - \frac{a \sin\left(13 \, d x + 13 \, c\right)}{53248 \, d} - \frac{a \sin\left(11 \, d x + 11 \, c\right)}{45056 \, d} + \frac{a \sin\left(9 \, d x + 9 \, c\right)}{6144 \, d} + \frac{3 \, a \sin\left(7 \, d x + 7 \, c\right)}{14336 \, d} - \frac{3 \, a \sin\left(5 \, d x + 5 \, c\right)}{4096 \, d} - \frac{5 \, a \sin\left(3 \, d x + 3 \, c\right)}{4096 \, d} + \frac{5 \, a \sin\left(d x + c\right)}{1024 \, d}"," ",0,"1/114688*a*cos(14*d*x + 14*c)/d - 7/81920*a*cos(10*d*x + 10*c)/d + 7/16384*a*cos(6*d*x + 6*c)/d - 35/16384*a*cos(2*d*x + 2*c)/d - 1/53248*a*sin(13*d*x + 13*c)/d - 1/45056*a*sin(11*d*x + 11*c)/d + 1/6144*a*sin(9*d*x + 9*c)/d + 3/14336*a*sin(7*d*x + 7*c)/d - 3/4096*a*sin(5*d*x + 5*c)/d - 5/4096*a*sin(3*d*x + 3*c)/d + 5/1024*a*sin(d*x + c)/d","A",0
657,1,193,0,0.368066," ","integrate(cos(d*x+c)^7*sin(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{a \cos\left(12 \, d x + 12 \, c\right)}{24576 \, d} - \frac{a \cos\left(10 \, d x + 10 \, c\right)}{10240 \, d} + \frac{a \cos\left(8 \, d x + 8 \, c\right)}{4096 \, d} + \frac{5 \, a \cos\left(6 \, d x + 6 \, c\right)}{6144 \, d} - \frac{5 \, a \cos\left(4 \, d x + 4 \, c\right)}{8192 \, d} - \frac{5 \, a \cos\left(2 \, d x + 2 \, c\right)}{1024 \, d} - \frac{a \sin\left(13 \, d x + 13 \, c\right)}{53248 \, d} - \frac{a \sin\left(11 \, d x + 11 \, c\right)}{45056 \, d} + \frac{a \sin\left(9 \, d x + 9 \, c\right)}{6144 \, d} + \frac{3 \, a \sin\left(7 \, d x + 7 \, c\right)}{14336 \, d} - \frac{3 \, a \sin\left(5 \, d x + 5 \, c\right)}{4096 \, d} - \frac{5 \, a \sin\left(3 \, d x + 3 \, c\right)}{4096 \, d} + \frac{5 \, a \sin\left(d x + c\right)}{1024 \, d}"," ",0,"-1/24576*a*cos(12*d*x + 12*c)/d - 1/10240*a*cos(10*d*x + 10*c)/d + 1/4096*a*cos(8*d*x + 8*c)/d + 5/6144*a*cos(6*d*x + 6*c)/d - 5/8192*a*cos(4*d*x + 4*c)/d - 5/1024*a*cos(2*d*x + 2*c)/d - 1/53248*a*sin(13*d*x + 13*c)/d - 1/45056*a*sin(11*d*x + 11*c)/d + 1/6144*a*sin(9*d*x + 9*c)/d + 3/14336*a*sin(7*d*x + 7*c)/d - 3/4096*a*sin(5*d*x + 5*c)/d - 5/4096*a*sin(3*d*x + 3*c)/d + 5/1024*a*sin(d*x + c)/d","A",0
658,1,178,0,0.322851," ","integrate(cos(d*x+c)^7*sin(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{a \cos\left(12 \, d x + 12 \, c\right)}{24576 \, d} - \frac{a \cos\left(10 \, d x + 10 \, c\right)}{10240 \, d} + \frac{a \cos\left(8 \, d x + 8 \, c\right)}{4096 \, d} + \frac{5 \, a \cos\left(6 \, d x + 6 \, c\right)}{6144 \, d} - \frac{5 \, a \cos\left(4 \, d x + 4 \, c\right)}{8192 \, d} - \frac{5 \, a \cos\left(2 \, d x + 2 \, c\right)}{1024 \, d} + \frac{a \sin\left(11 \, d x + 11 \, c\right)}{11264 \, d} + \frac{a \sin\left(9 \, d x + 9 \, c\right)}{3072 \, d} - \frac{a \sin\left(7 \, d x + 7 \, c\right)}{7168 \, d} - \frac{11 \, a \sin\left(5 \, d x + 5 \, c\right)}{5120 \, d} - \frac{a \sin\left(3 \, d x + 3 \, c\right)}{512 \, d} + \frac{7 \, a \sin\left(d x + c\right)}{512 \, d}"," ",0,"-1/24576*a*cos(12*d*x + 12*c)/d - 1/10240*a*cos(10*d*x + 10*c)/d + 1/4096*a*cos(8*d*x + 8*c)/d + 5/6144*a*cos(6*d*x + 6*c)/d - 5/8192*a*cos(4*d*x + 4*c)/d - 5/1024*a*cos(2*d*x + 2*c)/d + 1/11264*a*sin(11*d*x + 11*c)/d + 1/3072*a*sin(9*d*x + 9*c)/d - 1/7168*a*sin(7*d*x + 7*c)/d - 11/5120*a*sin(5*d*x + 5*c)/d - 1/512*a*sin(3*d*x + 3*c)/d + 7/512*a*sin(d*x + c)/d","A",0
659,1,163,0,0.290717," ","integrate(cos(d*x+c)^7*sin(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{a \cos\left(10 \, d x + 10 \, c\right)}{5120 \, d} + \frac{a \cos\left(8 \, d x + 8 \, c\right)}{1024 \, d} + \frac{a \cos\left(6 \, d x + 6 \, c\right)}{1024 \, d} - \frac{a \cos\left(4 \, d x + 4 \, c\right)}{256 \, d} - \frac{7 \, a \cos\left(2 \, d x + 2 \, c\right)}{512 \, d} + \frac{a \sin\left(11 \, d x + 11 \, c\right)}{11264 \, d} + \frac{a \sin\left(9 \, d x + 9 \, c\right)}{3072 \, d} - \frac{a \sin\left(7 \, d x + 7 \, c\right)}{7168 \, d} - \frac{11 \, a \sin\left(5 \, d x + 5 \, c\right)}{5120 \, d} - \frac{a \sin\left(3 \, d x + 3 \, c\right)}{512 \, d} + \frac{7 \, a \sin\left(d x + c\right)}{512 \, d}"," ",0,"1/5120*a*cos(10*d*x + 10*c)/d + 1/1024*a*cos(8*d*x + 8*c)/d + 1/1024*a*cos(6*d*x + 6*c)/d - 1/256*a*cos(4*d*x + 4*c)/d - 7/512*a*cos(2*d*x + 2*c)/d + 1/11264*a*sin(11*d*x + 11*c)/d + 1/3072*a*sin(9*d*x + 9*c)/d - 1/7168*a*sin(7*d*x + 7*c)/d - 11/5120*a*sin(5*d*x + 5*c)/d - 1/512*a*sin(3*d*x + 3*c)/d + 7/512*a*sin(d*x + c)/d","A",0
660,1,133,0,0.258270," ","integrate(cos(d*x+c)^7*sin(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{a \cos\left(10 \, d x + 10 \, c\right)}{5120 \, d} + \frac{a \cos\left(8 \, d x + 8 \, c\right)}{1024 \, d} + \frac{a \cos\left(6 \, d x + 6 \, c\right)}{1024 \, d} - \frac{a \cos\left(4 \, d x + 4 \, c\right)}{256 \, d} - \frac{7 \, a \cos\left(2 \, d x + 2 \, c\right)}{512 \, d} - \frac{a \sin\left(9 \, d x + 9 \, c\right)}{2304 \, d} - \frac{5 \, a \sin\left(7 \, d x + 7 \, c\right)}{1792 \, d} - \frac{a \sin\left(5 \, d x + 5 \, c\right)}{160 \, d} + \frac{7 \, a \sin\left(d x + c\right)}{128 \, d}"," ",0,"1/5120*a*cos(10*d*x + 10*c)/d + 1/1024*a*cos(8*d*x + 8*c)/d + 1/1024*a*cos(6*d*x + 6*c)/d - 1/256*a*cos(4*d*x + 4*c)/d - 7/512*a*cos(2*d*x + 2*c)/d - 1/2304*a*sin(9*d*x + 9*c)/d - 5/1792*a*sin(7*d*x + 7*c)/d - 1/160*a*sin(5*d*x + 5*c)/d + 7/128*a*sin(d*x + c)/d","A",0
661,1,118,0,0.228516," ","integrate(cos(d*x+c)^7*sin(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{a \cos\left(8 \, d x + 8 \, c\right)}{1024 \, d} - \frac{a \cos\left(6 \, d x + 6 \, c\right)}{128 \, d} - \frac{7 \, a \cos\left(4 \, d x + 4 \, c\right)}{256 \, d} - \frac{7 \, a \cos\left(2 \, d x + 2 \, c\right)}{128 \, d} - \frac{a \sin\left(9 \, d x + 9 \, c\right)}{2304 \, d} - \frac{5 \, a \sin\left(7 \, d x + 7 \, c\right)}{1792 \, d} - \frac{a \sin\left(5 \, d x + 5 \, c\right)}{160 \, d} + \frac{7 \, a \sin\left(d x + c\right)}{128 \, d}"," ",0,"-1/1024*a*cos(8*d*x + 8*c)/d - 1/128*a*cos(6*d*x + 6*c)/d - 7/256*a*cos(4*d*x + 4*c)/d - 7/128*a*cos(2*d*x + 2*c)/d - 1/2304*a*sin(9*d*x + 9*c)/d - 5/1792*a*sin(7*d*x + 7*c)/d - 1/160*a*sin(5*d*x + 5*c)/d + 7/128*a*sin(d*x + c)/d","A",0
662,1,92,0,0.269081," ","integrate(cos(d*x+c)^7*csc(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{60 \, a \sin\left(d x + c\right)^{7} + 70 \, a \sin\left(d x + c\right)^{6} - 252 \, a \sin\left(d x + c\right)^{5} - 315 \, a \sin\left(d x + c\right)^{4} + 420 \, a \sin\left(d x + c\right)^{3} + 630 \, a \sin\left(d x + c\right)^{2} - 420 \, a \log\left({\left| \sin\left(d x + c\right) \right|}\right) - 420 \, a \sin\left(d x + c\right)}{420 \, d}"," ",0,"-1/420*(60*a*sin(d*x + c)^7 + 70*a*sin(d*x + c)^6 - 252*a*sin(d*x + c)^5 - 315*a*sin(d*x + c)^4 + 420*a*sin(d*x + c)^3 + 630*a*sin(d*x + c)^2 - 420*a*log(abs(sin(d*x + c))) - 420*a*sin(d*x + c))/d","A",0
663,1,101,0,0.206297," ","integrate(cos(d*x+c)^7*csc(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{10 \, a \sin\left(d x + c\right)^{6} + 12 \, a \sin\left(d x + c\right)^{5} - 45 \, a \sin\left(d x + c\right)^{4} - 60 \, a \sin\left(d x + c\right)^{3} + 90 \, a \sin\left(d x + c\right)^{2} - 60 \, a \log\left({\left| \sin\left(d x + c\right) \right|}\right) + 180 \, a \sin\left(d x + c\right) + \frac{60 \, {\left(a \sin\left(d x + c\right) + a\right)}}{\sin\left(d x + c\right)}}{60 \, d}"," ",0,"-1/60*(10*a*sin(d*x + c)^6 + 12*a*sin(d*x + c)^5 - 45*a*sin(d*x + c)^4 - 60*a*sin(d*x + c)^3 + 90*a*sin(d*x + c)^2 - 60*a*log(abs(sin(d*x + c))) + 180*a*sin(d*x + c) + 60*(a*sin(d*x + c) + a)/sin(d*x + c))/d","A",0
664,1,104,0,0.236630," ","integrate(cos(d*x+c)^7*csc(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{4 \, a \sin\left(d x + c\right)^{5} + 5 \, a \sin\left(d x + c\right)^{4} - 20 \, a \sin\left(d x + c\right)^{3} - 30 \, a \sin\left(d x + c\right)^{2} + 60 \, a \log\left({\left| \sin\left(d x + c\right) \right|}\right) + 60 \, a \sin\left(d x + c\right) - \frac{10 \, {\left(9 \, a \sin\left(d x + c\right)^{2} - 2 \, a \sin\left(d x + c\right) - a\right)}}{\sin\left(d x + c\right)^{2}}}{20 \, d}"," ",0,"-1/20*(4*a*sin(d*x + c)^5 + 5*a*sin(d*x + c)^4 - 20*a*sin(d*x + c)^3 - 30*a*sin(d*x + c)^2 + 60*a*log(abs(sin(d*x + c))) + 60*a*sin(d*x + c) - 10*(9*a*sin(d*x + c)^2 - 2*a*sin(d*x + c) - a)/sin(d*x + c)^2)/d","A",0
665,1,104,0,0.223475," ","integrate(cos(d*x+c)^7*csc(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{3 \, a \sin\left(d x + c\right)^{4} + 4 \, a \sin\left(d x + c\right)^{3} - 18 \, a \sin\left(d x + c\right)^{2} + 36 \, a \log\left({\left| \sin\left(d x + c\right) \right|}\right) - 36 \, a \sin\left(d x + c\right) - \frac{2 \, {\left(33 \, a \sin\left(d x + c\right)^{3} + 18 \, a \sin\left(d x + c\right)^{2} - 3 \, a \sin\left(d x + c\right) - 2 \, a\right)}}{\sin\left(d x + c\right)^{3}}}{12 \, d}"," ",0,"-1/12*(3*a*sin(d*x + c)^4 + 4*a*sin(d*x + c)^3 - 18*a*sin(d*x + c)^2 + 36*a*log(abs(sin(d*x + c))) - 36*a*sin(d*x + c) - 2*(33*a*sin(d*x + c)^3 + 18*a*sin(d*x + c)^2 - 3*a*sin(d*x + c) - 2*a)/sin(d*x + c)^3)/d","A",0
666,1,103,0,0.245408," ","integrate(cos(d*x+c)^7*csc(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{4 \, a \sin\left(d x + c\right)^{3} + 6 \, a \sin\left(d x + c\right)^{2} - 36 \, a \log\left({\left| \sin\left(d x + c\right) \right|}\right) - 36 \, a \sin\left(d x + c\right) + \frac{75 \, a \sin\left(d x + c\right)^{4} - 36 \, a \sin\left(d x + c\right)^{3} - 18 \, a \sin\left(d x + c\right)^{2} + 4 \, a \sin\left(d x + c\right) + 3 \, a}{\sin\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"-1/12*(4*a*sin(d*x + c)^3 + 6*a*sin(d*x + c)^2 - 36*a*log(abs(sin(d*x + c))) - 36*a*sin(d*x + c) + (75*a*sin(d*x + c)^4 - 36*a*sin(d*x + c)^3 - 18*a*sin(d*x + c)^2 + 4*a*sin(d*x + c) + 3*a)/sin(d*x + c)^4)/d","A",0
667,1,103,0,0.237831," ","integrate(cos(d*x+c)^7*csc(d*x+c)^6*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{10 \, a \sin\left(d x + c\right)^{2} - 60 \, a \log\left({\left| \sin\left(d x + c\right) \right|}\right) + 20 \, a \sin\left(d x + c\right) + \frac{137 \, a \sin\left(d x + c\right)^{5} + 60 \, a \sin\left(d x + c\right)^{4} - 30 \, a \sin\left(d x + c\right)^{3} - 20 \, a \sin\left(d x + c\right)^{2} + 5 \, a \sin\left(d x + c\right) + 4 \, a}{\sin\left(d x + c\right)^{5}}}{20 \, d}"," ",0,"-1/20*(10*a*sin(d*x + c)^2 - 60*a*log(abs(sin(d*x + c))) + 20*a*sin(d*x + c) + (137*a*sin(d*x + c)^5 + 60*a*sin(d*x + c)^4 - 30*a*sin(d*x + c)^3 - 20*a*sin(d*x + c)^2 + 5*a*sin(d*x + c) + 4*a)/sin(d*x + c)^5)/d","A",0
668,1,104,0,0.276705," ","integrate(cos(d*x+c)^7*csc(d*x+c)^7*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{60 \, a \log\left({\left| \sin\left(d x + c\right) \right|}\right) + 60 \, a \sin\left(d x + c\right) - \frac{147 \, a \sin\left(d x + c\right)^{6} - 180 \, a \sin\left(d x + c\right)^{5} - 90 \, a \sin\left(d x + c\right)^{4} + 60 \, a \sin\left(d x + c\right)^{3} + 45 \, a \sin\left(d x + c\right)^{2} - 12 \, a \sin\left(d x + c\right) - 10 \, a}{\sin\left(d x + c\right)^{6}}}{60 \, d}"," ",0,"-1/60*(60*a*log(abs(sin(d*x + c))) + 60*a*sin(d*x + c) - (147*a*sin(d*x + c)^6 - 180*a*sin(d*x + c)^5 - 90*a*sin(d*x + c)^4 + 60*a*sin(d*x + c)^3 + 45*a*sin(d*x + c)^2 - 12*a*sin(d*x + c) - 10*a)/sin(d*x + c)^6)/d","A",0
669,1,106,0,0.262074," ","integrate(cos(d*x+c)^7*csc(d*x+c)^8*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{420 \, a \log\left({\left| \sin\left(d x + c\right) \right|}\right) - \frac{1089 \, a \sin\left(d x + c\right)^{7} + 420 \, a \sin\left(d x + c\right)^{6} - 630 \, a \sin\left(d x + c\right)^{5} - 420 \, a \sin\left(d x + c\right)^{4} + 315 \, a \sin\left(d x + c\right)^{3} + 252 \, a \sin\left(d x + c\right)^{2} - 70 \, a \sin\left(d x + c\right) - 60 \, a}{\sin\left(d x + c\right)^{7}}}{420 \, d}"," ",0,"-1/420*(420*a*log(abs(sin(d*x + c))) - (1089*a*sin(d*x + c)^7 + 420*a*sin(d*x + c)^6 - 630*a*sin(d*x + c)^5 - 420*a*sin(d*x + c)^4 + 315*a*sin(d*x + c)^3 + 252*a*sin(d*x + c)^2 - 70*a*sin(d*x + c) - 60*a)/sin(d*x + c)^7)/d","A",0
670,1,92,0,0.275393," ","integrate(cos(d*x+c)^7*csc(d*x+c)^9*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{280 \, a \sin\left(d x + c\right)^{7} + 140 \, a \sin\left(d x + c\right)^{6} - 280 \, a \sin\left(d x + c\right)^{5} - 210 \, a \sin\left(d x + c\right)^{4} + 168 \, a \sin\left(d x + c\right)^{3} + 140 \, a \sin\left(d x + c\right)^{2} - 40 \, a \sin\left(d x + c\right) - 35 \, a}{280 \, d \sin\left(d x + c\right)^{8}}"," ",0,"1/280*(280*a*sin(d*x + c)^7 + 140*a*sin(d*x + c)^6 - 280*a*sin(d*x + c)^5 - 210*a*sin(d*x + c)^4 + 168*a*sin(d*x + c)^3 + 140*a*sin(d*x + c)^2 - 40*a*sin(d*x + c) - 35*a)/(d*sin(d*x + c)^8)","A",0
671,1,92,0,0.277479," ","integrate(cos(d*x+c)^7*csc(d*x+c)^10*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{1260 \, a \sin\left(d x + c\right)^{7} + 840 \, a \sin\left(d x + c\right)^{6} - 1890 \, a \sin\left(d x + c\right)^{5} - 1512 \, a \sin\left(d x + c\right)^{4} + 1260 \, a \sin\left(d x + c\right)^{3} + 1080 \, a \sin\left(d x + c\right)^{2} - 315 \, a \sin\left(d x + c\right) - 280 \, a}{2520 \, d \sin\left(d x + c\right)^{9}}"," ",0,"1/2520*(1260*a*sin(d*x + c)^7 + 840*a*sin(d*x + c)^6 - 1890*a*sin(d*x + c)^5 - 1512*a*sin(d*x + c)^4 + 1260*a*sin(d*x + c)^3 + 1080*a*sin(d*x + c)^2 - 315*a*sin(d*x + c) - 280*a)/(d*sin(d*x + c)^9)","A",0
672,1,92,0,0.288124," ","integrate(cos(d*x+c)^7*csc(d*x+c)^11*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{840 \, a \sin\left(d x + c\right)^{7} + 630 \, a \sin\left(d x + c\right)^{6} - 1512 \, a \sin\left(d x + c\right)^{5} - 1260 \, a \sin\left(d x + c\right)^{4} + 1080 \, a \sin\left(d x + c\right)^{3} + 945 \, a \sin\left(d x + c\right)^{2} - 280 \, a \sin\left(d x + c\right) - 252 \, a}{2520 \, d \sin\left(d x + c\right)^{10}}"," ",0,"1/2520*(840*a*sin(d*x + c)^7 + 630*a*sin(d*x + c)^6 - 1512*a*sin(d*x + c)^5 - 1260*a*sin(d*x + c)^4 + 1080*a*sin(d*x + c)^3 + 945*a*sin(d*x + c)^2 - 280*a*sin(d*x + c) - 252*a)/(d*sin(d*x + c)^10)","A",0
673,1,92,0,0.280113," ","integrate(cos(d*x+c)^7*csc(d*x+c)^12*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{2310 \, a \sin\left(d x + c\right)^{7} + 1848 \, a \sin\left(d x + c\right)^{6} - 4620 \, a \sin\left(d x + c\right)^{5} - 3960 \, a \sin\left(d x + c\right)^{4} + 3465 \, a \sin\left(d x + c\right)^{3} + 3080 \, a \sin\left(d x + c\right)^{2} - 924 \, a \sin\left(d x + c\right) - 840 \, a}{9240 \, d \sin\left(d x + c\right)^{11}}"," ",0,"1/9240*(2310*a*sin(d*x + c)^7 + 1848*a*sin(d*x + c)^6 - 4620*a*sin(d*x + c)^5 - 3960*a*sin(d*x + c)^4 + 3465*a*sin(d*x + c)^3 + 3080*a*sin(d*x + c)^2 - 924*a*sin(d*x + c) - 840*a)/(d*sin(d*x + c)^11)","A",0
674,1,92,0,0.298313," ","integrate(cos(d*x+c)^7*csc(d*x+c)^13*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{1848 \, a \sin\left(d x + c\right)^{7} + 1540 \, a \sin\left(d x + c\right)^{6} - 3960 \, a \sin\left(d x + c\right)^{5} - 3465 \, a \sin\left(d x + c\right)^{4} + 3080 \, a \sin\left(d x + c\right)^{3} + 2772 \, a \sin\left(d x + c\right)^{2} - 840 \, a \sin\left(d x + c\right) - 770 \, a}{9240 \, d \sin\left(d x + c\right)^{12}}"," ",0,"1/9240*(1848*a*sin(d*x + c)^7 + 1540*a*sin(d*x + c)^6 - 3960*a*sin(d*x + c)^5 - 3465*a*sin(d*x + c)^4 + 3080*a*sin(d*x + c)^3 + 2772*a*sin(d*x + c)^2 - 840*a*sin(d*x + c) - 770*a)/(d*sin(d*x + c)^12)","A",0
675,1,92,0,0.317327," ","integrate(cos(d*x+c)^7*csc(d*x+c)^14*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{20020 \, a \sin\left(d x + c\right)^{7} + 17160 \, a \sin\left(d x + c\right)^{6} - 45045 \, a \sin\left(d x + c\right)^{5} - 40040 \, a \sin\left(d x + c\right)^{4} + 36036 \, a \sin\left(d x + c\right)^{3} + 32760 \, a \sin\left(d x + c\right)^{2} - 10010 \, a \sin\left(d x + c\right) - 9240 \, a}{120120 \, d \sin\left(d x + c\right)^{13}}"," ",0,"1/120120*(20020*a*sin(d*x + c)^7 + 17160*a*sin(d*x + c)^6 - 45045*a*sin(d*x + c)^5 - 40040*a*sin(d*x + c)^4 + 36036*a*sin(d*x + c)^3 + 32760*a*sin(d*x + c)^2 - 10010*a*sin(d*x + c) - 9240*a)/(d*sin(d*x + c)^13)","A",0
676,1,92,0,0.340363," ","integrate(cos(d*x+c)^7*csc(d*x+c)^15*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{17160 \, a \sin\left(d x + c\right)^{7} + 15015 \, a \sin\left(d x + c\right)^{6} - 40040 \, a \sin\left(d x + c\right)^{5} - 36036 \, a \sin\left(d x + c\right)^{4} + 32760 \, a \sin\left(d x + c\right)^{3} + 30030 \, a \sin\left(d x + c\right)^{2} - 9240 \, a \sin\left(d x + c\right) - 8580 \, a}{120120 \, d \sin\left(d x + c\right)^{14}}"," ",0,"1/120120*(17160*a*sin(d*x + c)^7 + 15015*a*sin(d*x + c)^6 - 40040*a*sin(d*x + c)^5 - 36036*a*sin(d*x + c)^4 + 32760*a*sin(d*x + c)^3 + 30030*a*sin(d*x + c)^2 - 9240*a*sin(d*x + c) - 8580*a)/(d*sin(d*x + c)^14)","A",0
677,1,69,0,0.208906," ","integrate(cos(d*x+c)^7*sin(d*x+c)^6/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{2310 \, \sin\left(d x + c\right)^{12} - 2520 \, \sin\left(d x + c\right)^{11} - 5544 \, \sin\left(d x + c\right)^{10} + 6160 \, \sin\left(d x + c\right)^{9} + 3465 \, \sin\left(d x + c\right)^{8} - 3960 \, \sin\left(d x + c\right)^{7}}{27720 \, a d}"," ",0,"-1/27720*(2310*sin(d*x + c)^12 - 2520*sin(d*x + c)^11 - 5544*sin(d*x + c)^10 + 6160*sin(d*x + c)^9 + 3465*sin(d*x + c)^8 - 3960*sin(d*x + c)^7)/(a*d)","A",0
678,1,69,0,0.225965," ","integrate(cos(d*x+c)^7*sin(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{1260 \, \sin\left(d x + c\right)^{11} - 1386 \, \sin\left(d x + c\right)^{10} - 3080 \, \sin\left(d x + c\right)^{9} + 3465 \, \sin\left(d x + c\right)^{8} + 1980 \, \sin\left(d x + c\right)^{7} - 2310 \, \sin\left(d x + c\right)^{6}}{13860 \, a d}"," ",0,"-1/13860*(1260*sin(d*x + c)^11 - 1386*sin(d*x + c)^10 - 3080*sin(d*x + c)^9 + 3465*sin(d*x + c)^8 + 1980*sin(d*x + c)^7 - 2310*sin(d*x + c)^6)/(a*d)","A",0
679,1,69,0,0.202513," ","integrate(cos(d*x+c)^7*sin(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{126 \, \sin\left(d x + c\right)^{10} - 140 \, \sin\left(d x + c\right)^{9} - 315 \, \sin\left(d x + c\right)^{8} + 360 \, \sin\left(d x + c\right)^{7} + 210 \, \sin\left(d x + c\right)^{6} - 252 \, \sin\left(d x + c\right)^{5}}{1260 \, a d}"," ",0,"-1/1260*(126*sin(d*x + c)^10 - 140*sin(d*x + c)^9 - 315*sin(d*x + c)^8 + 360*sin(d*x + c)^7 + 210*sin(d*x + c)^6 - 252*sin(d*x + c)^5)/(a*d)","A",0
680,1,69,0,0.199671," ","integrate(cos(d*x+c)^7*sin(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{280 \, \sin\left(d x + c\right)^{9} - 315 \, \sin\left(d x + c\right)^{8} - 720 \, \sin\left(d x + c\right)^{7} + 840 \, \sin\left(d x + c\right)^{6} + 504 \, \sin\left(d x + c\right)^{5} - 630 \, \sin\left(d x + c\right)^{4}}{2520 \, a d}"," ",0,"-1/2520*(280*sin(d*x + c)^9 - 315*sin(d*x + c)^8 - 720*sin(d*x + c)^7 + 840*sin(d*x + c)^6 + 504*sin(d*x + c)^5 - 630*sin(d*x + c)^4)/(a*d)","A",0
681,1,69,0,0.183116," ","integrate(cos(d*x+c)^7*sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{105 \, \sin\left(d x + c\right)^{8} - 120 \, \sin\left(d x + c\right)^{7} - 280 \, \sin\left(d x + c\right)^{6} + 336 \, \sin\left(d x + c\right)^{5} + 210 \, \sin\left(d x + c\right)^{4} - 280 \, \sin\left(d x + c\right)^{3}}{840 \, a d}"," ",0,"-1/840*(105*sin(d*x + c)^8 - 120*sin(d*x + c)^7 - 280*sin(d*x + c)^6 + 336*sin(d*x + c)^5 + 210*sin(d*x + c)^4 - 280*sin(d*x + c)^3)/(a*d)","A",0
682,1,69,0,0.172518," ","integrate(cos(d*x+c)^7*sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{30 \, \sin\left(d x + c\right)^{7} - 35 \, \sin\left(d x + c\right)^{6} - 84 \, \sin\left(d x + c\right)^{5} + 105 \, \sin\left(d x + c\right)^{4} + 70 \, \sin\left(d x + c\right)^{3} - 105 \, \sin\left(d x + c\right)^{2}}{210 \, a d}"," ",0,"-1/210*(30*sin(d*x + c)^7 - 35*sin(d*x + c)^6 - 84*sin(d*x + c)^5 + 105*sin(d*x + c)^4 + 70*sin(d*x + c)^3 - 105*sin(d*x + c)^2)/(a*d)","A",0
683,1,67,0,0.148197," ","integrate(cos(d*x+c)^7/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{5 \, \sin\left(d x + c\right)^{6} - 6 \, \sin\left(d x + c\right)^{5} - 15 \, \sin\left(d x + c\right)^{4} + 20 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)^{2} - 30 \, \sin\left(d x + c\right)}{30 \, a d}"," ",0,"-1/30*(5*sin(d*x + c)^6 - 6*sin(d*x + c)^5 - 15*sin(d*x + c)^4 + 20*sin(d*x + c)^3 + 15*sin(d*x + c)^2 - 30*sin(d*x + c))/(a*d)","A",0
684,1,88,0,0.192575," ","integrate(cos(d*x+c)^7*csc(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{60 \, \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a} - \frac{12 \, a^{4} \sin\left(d x + c\right)^{5} - 15 \, a^{4} \sin\left(d x + c\right)^{4} - 40 \, a^{4} \sin\left(d x + c\right)^{3} + 60 \, a^{4} \sin\left(d x + c\right)^{2} + 60 \, a^{4} \sin\left(d x + c\right)}{a^{5}}}{60 \, d}"," ",0,"1/60*(60*log(abs(sin(d*x + c)))/a - (12*a^4*sin(d*x + c)^5 - 15*a^4*sin(d*x + c)^4 - 40*a^4*sin(d*x + c)^3 + 60*a^4*sin(d*x + c)^2 + 60*a^4*sin(d*x + c))/a^5)/d","A",0
685,1,95,0,0.212980," ","integrate(cos(d*x+c)^7*csc(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{12 \, \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a} - \frac{12 \, {\left(\sin\left(d x + c\right) - 1\right)}}{a \sin\left(d x + c\right)} + \frac{3 \, a^{3} \sin\left(d x + c\right)^{4} - 4 \, a^{3} \sin\left(d x + c\right)^{3} - 12 \, a^{3} \sin\left(d x + c\right)^{2} + 24 \, a^{3} \sin\left(d x + c\right)}{a^{4}}}{12 \, d}"," ",0,"-1/12*(12*log(abs(sin(d*x + c)))/a - 12*(sin(d*x + c) - 1)/(a*sin(d*x + c)) + (3*a^3*sin(d*x + c)^4 - 4*a^3*sin(d*x + c)^3 - 12*a^3*sin(d*x + c)^2 + 24*a^3*sin(d*x + c))/a^4)/d","A",0
686,1,94,0,0.213881," ","integrate(cos(d*x+c)^7*csc(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{12 \, \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a} + \frac{2 \, a^{2} \sin\left(d x + c\right)^{3} - 3 \, a^{2} \sin\left(d x + c\right)^{2} - 12 \, a^{2} \sin\left(d x + c\right)}{a^{3}} - \frac{3 \, {\left(6 \, \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) - 1\right)}}{a \sin\left(d x + c\right)^{2}}}{6 \, d}"," ",0,"-1/6*(12*log(abs(sin(d*x + c)))/a + (2*a^2*sin(d*x + c)^3 - 3*a^2*sin(d*x + c)^2 - 12*a^2*sin(d*x + c))/a^3 - 3*(6*sin(d*x + c)^2 + 2*sin(d*x + c) - 1)/(a*sin(d*x + c)^2))/d","A",0
687,1,87,0,0.286964," ","integrate(cos(d*x+c)^7*csc(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{12 \, \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a} - \frac{3 \, {\left(a \sin\left(d x + c\right)^{2} - 2 \, a \sin\left(d x + c\right)\right)}}{a^{2}} - \frac{22 \, \sin\left(d x + c\right)^{3} - 12 \, \sin\left(d x + c\right)^{2} - 3 \, \sin\left(d x + c\right) + 2}{a \sin\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(12*log(abs(sin(d*x + c)))/a - 3*(a*sin(d*x + c)^2 - 2*a*sin(d*x + c))/a^2 - (22*sin(d*x + c)^3 - 12*sin(d*x + c)^2 - 3*sin(d*x + c) + 2)/(a*sin(d*x + c)^3))/d","A",0
688,1,83,0,0.235683," ","integrate(cos(d*x+c)^7*csc(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{12 \, \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a} - \frac{12 \, \sin\left(d x + c\right)}{a} - \frac{25 \, \sin\left(d x + c\right)^{4} + 24 \, \sin\left(d x + c\right)^{3} - 12 \, \sin\left(d x + c\right)^{2} - 4 \, \sin\left(d x + c\right) + 3}{a \sin\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"1/12*(12*log(abs(sin(d*x + c)))/a - 12*sin(d*x + c)/a - (25*sin(d*x + c)^4 + 24*sin(d*x + c)^3 - 12*sin(d*x + c)^2 - 4*sin(d*x + c) + 3)/(a*sin(d*x + c)^4))/d","A",0
689,1,82,0,0.223141," ","integrate(cos(d*x+c)^7*csc(d*x+c)^6/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{60 \, \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a} - \frac{137 \, \sin\left(d x + c\right)^{5} - 60 \, \sin\left(d x + c\right)^{4} - 60 \, \sin\left(d x + c\right)^{3} + 40 \, \sin\left(d x + c\right)^{2} + 15 \, \sin\left(d x + c\right) - 12}{a \sin\left(d x + c\right)^{5}}}{60 \, d}"," ",0,"-1/60*(60*log(abs(sin(d*x + c)))/a - (137*sin(d*x + c)^5 - 60*sin(d*x + c)^4 - 60*sin(d*x + c)^3 + 40*sin(d*x + c)^2 + 15*sin(d*x + c) - 12)/(a*sin(d*x + c)^5))/d","A",0
690,1,66,0,0.219743," ","integrate(cos(d*x+c)^7*csc(d*x+c)^7/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{30 \, \sin\left(d x + c\right)^{5} - 15 \, \sin\left(d x + c\right)^{4} - 20 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)^{2} + 6 \, \sin\left(d x + c\right) - 5}{30 \, a d \sin\left(d x + c\right)^{6}}"," ",0,"1/30*(30*sin(d*x + c)^5 - 15*sin(d*x + c)^4 - 20*sin(d*x + c)^3 + 15*sin(d*x + c)^2 + 6*sin(d*x + c) - 5)/(a*d*sin(d*x + c)^6)","A",0
691,1,66,0,0.239284," ","integrate(cos(d*x+c)^7*csc(d*x+c)^8/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{105 \, \sin\left(d x + c\right)^{5} - 70 \, \sin\left(d x + c\right)^{4} - 105 \, \sin\left(d x + c\right)^{3} + 84 \, \sin\left(d x + c\right)^{2} + 35 \, \sin\left(d x + c\right) - 30}{210 \, a d \sin\left(d x + c\right)^{7}}"," ",0,"1/210*(105*sin(d*x + c)^5 - 70*sin(d*x + c)^4 - 105*sin(d*x + c)^3 + 84*sin(d*x + c)^2 + 35*sin(d*x + c) - 30)/(a*d*sin(d*x + c)^7)","A",0
692,1,66,0,0.245790," ","integrate(cos(d*x+c)^7*csc(d*x+c)^9/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{280 \, \sin\left(d x + c\right)^{5} - 210 \, \sin\left(d x + c\right)^{4} - 336 \, \sin\left(d x + c\right)^{3} + 280 \, \sin\left(d x + c\right)^{2} + 120 \, \sin\left(d x + c\right) - 105}{840 \, a d \sin\left(d x + c\right)^{8}}"," ",0,"1/840*(280*sin(d*x + c)^5 - 210*sin(d*x + c)^4 - 336*sin(d*x + c)^3 + 280*sin(d*x + c)^2 + 120*sin(d*x + c) - 105)/(a*d*sin(d*x + c)^8)","A",0
693,1,66,0,0.234225," ","integrate(cos(d*x+c)^7*csc(d*x+c)^10/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{630 \, \sin\left(d x + c\right)^{5} - 504 \, \sin\left(d x + c\right)^{4} - 840 \, \sin\left(d x + c\right)^{3} + 720 \, \sin\left(d x + c\right)^{2} + 315 \, \sin\left(d x + c\right) - 280}{2520 \, a d \sin\left(d x + c\right)^{9}}"," ",0,"1/2520*(630*sin(d*x + c)^5 - 504*sin(d*x + c)^4 - 840*sin(d*x + c)^3 + 720*sin(d*x + c)^2 + 315*sin(d*x + c) - 280)/(a*d*sin(d*x + c)^9)","A",0
694,1,66,0,0.259717," ","integrate(cos(d*x+c)^7*csc(d*x+c)^11/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{252 \, \sin\left(d x + c\right)^{5} - 210 \, \sin\left(d x + c\right)^{4} - 360 \, \sin\left(d x + c\right)^{3} + 315 \, \sin\left(d x + c\right)^{2} + 140 \, \sin\left(d x + c\right) - 126}{1260 \, a d \sin\left(d x + c\right)^{10}}"," ",0,"1/1260*(252*sin(d*x + c)^5 - 210*sin(d*x + c)^4 - 360*sin(d*x + c)^3 + 315*sin(d*x + c)^2 + 140*sin(d*x + c) - 126)/(a*d*sin(d*x + c)^10)","A",0
695,1,66,0,0.250421," ","integrate(cos(d*x+c)^7*csc(d*x+c)^12/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{2310 \, \sin\left(d x + c\right)^{5} - 1980 \, \sin\left(d x + c\right)^{4} - 3465 \, \sin\left(d x + c\right)^{3} + 3080 \, \sin\left(d x + c\right)^{2} + 1386 \, \sin\left(d x + c\right) - 1260}{13860 \, a d \sin\left(d x + c\right)^{11}}"," ",0,"1/13860*(2310*sin(d*x + c)^5 - 1980*sin(d*x + c)^4 - 3465*sin(d*x + c)^3 + 3080*sin(d*x + c)^2 + 1386*sin(d*x + c) - 1260)/(a*d*sin(d*x + c)^11)","A",0
696,1,66,0,0.269769," ","integrate(cos(d*x+c)^7*csc(d*x+c)^13/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{3960 \, \sin\left(d x + c\right)^{5} - 3465 \, \sin\left(d x + c\right)^{4} - 6160 \, \sin\left(d x + c\right)^{3} + 5544 \, \sin\left(d x + c\right)^{2} + 2520 \, \sin\left(d x + c\right) - 2310}{27720 \, a d \sin\left(d x + c\right)^{12}}"," ",0,"1/27720*(3960*sin(d*x + c)^5 - 3465*sin(d*x + c)^4 - 6160*sin(d*x + c)^3 + 5544*sin(d*x + c)^2 + 2520*sin(d*x + c) - 2310)/(a*d*sin(d*x + c)^12)","A",0
697,-2,0,0,0.000000," ","integrate(cos(d*x+c)^7*sin(d*x+c)^n*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 39.12Not invertible Error: Bad Argument Value","F(-2)",0
698,-1,0,0,0.000000," ","integrate(cos(d*x+c)^7*sin(d*x+c)^n*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
699,-1,0,0,0.000000," ","integrate(cos(d*x+c)^7*sin(d*x+c)^n*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
700,0,0,0,0.000000," ","integrate(cos(d*x+c)^7*sin(d*x+c)^n/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\int \frac{\sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{7}}{a \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sin(d*x + c)^n*cos(d*x + c)^7/(a*sin(d*x + c) + a), x)","F",0
701,0,0,0,0.000000," ","integrate(cos(d*x+c)^7*sin(d*x+c)^n/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{7}}{{\left(a \sin\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sin(d*x + c)^n*cos(d*x + c)^7/(a*sin(d*x + c) + a)^2, x)","F",0
702,0,0,0,0.000000," ","integrate(cos(d*x+c)^7*sin(d*x+c)^n/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\int \frac{\sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{7}}{{\left(a \sin\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(sin(d*x + c)^n*cos(d*x + c)^7/(a*sin(d*x + c) + a)^3, x)","F",0
703,0,0,0,0.000000," ","integrate(cos(d*x+c)^7*sin(d*x+c)^n/(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","\int \frac{\sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{7}}{{\left(a \sin\left(d x + c\right) + a\right)}^{4}}\,{d x}"," ",0,"integrate(sin(d*x + c)^n*cos(d*x + c)^7/(a*sin(d*x + c) + a)^4, x)","F",0
704,0,0,0,0.000000," ","integrate(cos(d*x+c)^7*sin(d*x+c)^n/(a+a*sin(d*x+c))^5,x, algorithm=""giac"")","\int \frac{\sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{7}}{{\left(a \sin\left(d x + c\right) + a\right)}^{5}}\,{d x}"," ",0,"integrate(sin(d*x + c)^n*cos(d*x + c)^7/(a*sin(d*x + c) + a)^5, x)","F",0
705,1,309,0,0.232081," ","integrate(cos(d*x+c)^8*sin(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{3465 \, {\left(d x + c\right)}}{a} + \frac{2 \, {\left(3465 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{23} + 40425 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{21} + 215523 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{19} + 3784704 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{18} - 5794173 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{17} - 5677056 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{16} + 19523658 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} + 11354112 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{14} - 35058870 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 3784704 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 35058870 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 4866048 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 19523658 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 9732096 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 5794173 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1982464 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 215523 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 540672 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 40425 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 98304 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3465 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8192\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{12} a}}{709632 \, d}"," ",0,"-1/709632*(3465*(d*x + c)/a + 2*(3465*tan(1/2*d*x + 1/2*c)^23 + 40425*tan(1/2*d*x + 1/2*c)^21 + 215523*tan(1/2*d*x + 1/2*c)^19 + 3784704*tan(1/2*d*x + 1/2*c)^18 - 5794173*tan(1/2*d*x + 1/2*c)^17 - 5677056*tan(1/2*d*x + 1/2*c)^16 + 19523658*tan(1/2*d*x + 1/2*c)^15 + 11354112*tan(1/2*d*x + 1/2*c)^14 - 35058870*tan(1/2*d*x + 1/2*c)^13 + 3784704*tan(1/2*d*x + 1/2*c)^12 + 35058870*tan(1/2*d*x + 1/2*c)^11 - 4866048*tan(1/2*d*x + 1/2*c)^10 - 19523658*tan(1/2*d*x + 1/2*c)^9 + 9732096*tan(1/2*d*x + 1/2*c)^8 + 5794173*tan(1/2*d*x + 1/2*c)^7 - 1982464*tan(1/2*d*x + 1/2*c)^6 - 215523*tan(1/2*d*x + 1/2*c)^5 + 540672*tan(1/2*d*x + 1/2*c)^4 - 40425*tan(1/2*d*x + 1/2*c)^3 + 98304*tan(1/2*d*x + 1/2*c)^2 - 3465*tan(1/2*d*x + 1/2*c) + 8192)/((tan(1/2*d*x + 1/2*c)^2 + 1)^12*a))/d","A",0
706,1,270,0,0.222194," ","integrate(cos(d*x+c)^8*sin(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{10395 \, {\left(d x + c\right)}}{a} + \frac{2 \, {\left(10395 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{21} + 110880 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{19} - 2302839 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{17} + 4730880 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{16} + 4790016 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} - 11827200 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{14} - 5828130 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 26019840 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 21288960 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 5828130 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 15206400 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 4790016 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 3041280 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 2302839 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 563200 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 110880 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 112640 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 10395 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 10240\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{11} a}}{887040 \, d}"," ",0,"1/887040*(10395*(d*x + c)/a + 2*(10395*tan(1/2*d*x + 1/2*c)^21 + 110880*tan(1/2*d*x + 1/2*c)^19 - 2302839*tan(1/2*d*x + 1/2*c)^17 + 4730880*tan(1/2*d*x + 1/2*c)^16 + 4790016*tan(1/2*d*x + 1/2*c)^15 - 11827200*tan(1/2*d*x + 1/2*c)^14 - 5828130*tan(1/2*d*x + 1/2*c)^13 + 26019840*tan(1/2*d*x + 1/2*c)^12 - 21288960*tan(1/2*d*x + 1/2*c)^10 + 5828130*tan(1/2*d*x + 1/2*c)^9 + 15206400*tan(1/2*d*x + 1/2*c)^8 - 4790016*tan(1/2*d*x + 1/2*c)^7 - 3041280*tan(1/2*d*x + 1/2*c)^6 + 2302839*tan(1/2*d*x + 1/2*c)^5 + 563200*tan(1/2*d*x + 1/2*c)^4 - 110880*tan(1/2*d*x + 1/2*c)^3 + 112640*tan(1/2*d*x + 1/2*c)^2 - 10395*tan(1/2*d*x + 1/2*c) + 10240)/((tan(1/2*d*x + 1/2*c)^2 + 1)^11*a))/d","A",0
707,1,257,0,0.207219," ","integrate(cos(d*x+c)^8*sin(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{945 \, {\left(d x + c\right)}}{a} + \frac{2 \, {\left(945 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{19} + 9135 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{17} + 161280 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{16} - 218484 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} - 107520 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{14} + 653940 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 537600 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 1183770 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 322560 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 1183770 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 653940 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 414720 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 218484 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 46080 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 9135 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 25600 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 945 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2560\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{10} a}}{80640 \, d}"," ",0,"-1/80640*(945*(d*x + c)/a + 2*(945*tan(1/2*d*x + 1/2*c)^19 + 9135*tan(1/2*d*x + 1/2*c)^17 + 161280*tan(1/2*d*x + 1/2*c)^16 - 218484*tan(1/2*d*x + 1/2*c)^15 - 107520*tan(1/2*d*x + 1/2*c)^14 + 653940*tan(1/2*d*x + 1/2*c)^13 + 537600*tan(1/2*d*x + 1/2*c)^12 - 1183770*tan(1/2*d*x + 1/2*c)^11 + 322560*tan(1/2*d*x + 1/2*c)^10 + 1183770*tan(1/2*d*x + 1/2*c)^9 - 653940*tan(1/2*d*x + 1/2*c)^7 + 414720*tan(1/2*d*x + 1/2*c)^6 + 218484*tan(1/2*d*x + 1/2*c)^5 - 46080*tan(1/2*d*x + 1/2*c)^4 - 9135*tan(1/2*d*x + 1/2*c)^3 + 25600*tan(1/2*d*x + 1/2*c)^2 - 945*tan(1/2*d*x + 1/2*c) + 2560)/((tan(1/2*d*x + 1/2*c)^2 + 1)^10*a))/d","A",0
708,1,231,0,0.174950," ","integrate(cos(d*x+c)^8*sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{315 \, {\left(d x + c\right)}}{a} + \frac{2 \, {\left(315 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{17} - 8022 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} + 16128 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{14} + 10458 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 26880 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 18270 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 80640 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 48384 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 18270 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 48384 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 10458 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6912 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 8022 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2304 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 315 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 256\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{9} a}}{8064 \, d}"," ",0,"1/8064*(315*(d*x + c)/a + 2*(315*tan(1/2*d*x + 1/2*c)^17 - 8022*tan(1/2*d*x + 1/2*c)^15 + 16128*tan(1/2*d*x + 1/2*c)^14 + 10458*tan(1/2*d*x + 1/2*c)^13 - 26880*tan(1/2*d*x + 1/2*c)^12 - 18270*tan(1/2*d*x + 1/2*c)^11 + 80640*tan(1/2*d*x + 1/2*c)^10 - 48384*tan(1/2*d*x + 1/2*c)^8 + 18270*tan(1/2*d*x + 1/2*c)^7 + 48384*tan(1/2*d*x + 1/2*c)^6 - 10458*tan(1/2*d*x + 1/2*c)^5 - 6912*tan(1/2*d*x + 1/2*c)^4 + 8022*tan(1/2*d*x + 1/2*c)^3 + 2304*tan(1/2*d*x + 1/2*c)^2 - 315*tan(1/2*d*x + 1/2*c) + 256)/((tan(1/2*d*x + 1/2*c)^2 + 1)^9*a))/d","A",0
709,1,231,0,0.161310," ","integrate(cos(d*x+c)^8*sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{105 \, {\left(d x + c\right)}}{a} + \frac{2 \, {\left(105 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} + 2688 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{14} - 2779 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 2688 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 6265 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 13440 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 12355 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 13440 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 12355 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 8064 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 6265 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 8064 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2779 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 384 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 105 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 384\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{8} a}}{2688 \, d}"," ",0,"-1/2688*(105*(d*x + c)/a + 2*(105*tan(1/2*d*x + 1/2*c)^15 + 2688*tan(1/2*d*x + 1/2*c)^14 - 2779*tan(1/2*d*x + 1/2*c)^13 + 2688*tan(1/2*d*x + 1/2*c)^12 + 6265*tan(1/2*d*x + 1/2*c)^11 + 13440*tan(1/2*d*x + 1/2*c)^10 - 12355*tan(1/2*d*x + 1/2*c)^9 + 13440*tan(1/2*d*x + 1/2*c)^8 + 12355*tan(1/2*d*x + 1/2*c)^7 + 8064*tan(1/2*d*x + 1/2*c)^6 - 6265*tan(1/2*d*x + 1/2*c)^5 + 8064*tan(1/2*d*x + 1/2*c)^4 + 2779*tan(1/2*d*x + 1/2*c)^3 + 384*tan(1/2*d*x + 1/2*c)^2 - 105*tan(1/2*d*x + 1/2*c) + 384)/((tan(1/2*d*x + 1/2*c)^2 + 1)^8*a))/d","B",0
710,1,195,0,0.173438," ","integrate(cos(d*x+c)^8*csc(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{75 \, {\left(d x + c\right)}}{a} - \frac{240 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a} - \frac{2 \, {\left(165 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 720 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 25 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 2160 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 450 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 3680 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 450 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3360 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 25 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1488 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 165 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 368\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6} a}}{240 \, d}"," ",0,"-1/240*(75*(d*x + c)/a - 240*log(abs(tan(1/2*d*x + 1/2*c)))/a - 2*(165*tan(1/2*d*x + 1/2*c)^11 + 720*tan(1/2*d*x + 1/2*c)^10 - 25*tan(1/2*d*x + 1/2*c)^9 + 2160*tan(1/2*d*x + 1/2*c)^8 + 450*tan(1/2*d*x + 1/2*c)^7 + 3680*tan(1/2*d*x + 1/2*c)^6 - 450*tan(1/2*d*x + 1/2*c)^5 + 3360*tan(1/2*d*x + 1/2*c)^4 + 25*tan(1/2*d*x + 1/2*c)^3 + 1488*tan(1/2*d*x + 1/2*c)^2 - 165*tan(1/2*d*x + 1/2*c) + 368)/((tan(1/2*d*x + 1/2*c)^2 + 1)^6*a))/d","A",0
711,1,199,0,0.194581," ","integrate(cos(d*x+c)^8*csc(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{225 \, {\left(d x + c\right)}}{a} + \frac{120 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a} - \frac{60 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a} - \frac{60 \, {\left(2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)} - \frac{2 \, {\left(135 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 360 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 150 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 720 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 1120 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 150 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 560 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 135 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 184\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5} a}}{120 \, d}"," ",0,"-1/120*(225*(d*x + c)/a + 120*log(abs(tan(1/2*d*x + 1/2*c)))/a - 60*tan(1/2*d*x + 1/2*c)/a - 60*(2*tan(1/2*d*x + 1/2*c) - 1)/(a*tan(1/2*d*x + 1/2*c)) - 2*(135*tan(1/2*d*x + 1/2*c)^9 - 360*tan(1/2*d*x + 1/2*c)^8 + 150*tan(1/2*d*x + 1/2*c)^7 - 720*tan(1/2*d*x + 1/2*c)^6 - 1120*tan(1/2*d*x + 1/2*c)^4 - 150*tan(1/2*d*x + 1/2*c)^3 - 560*tan(1/2*d*x + 1/2*c)^2 - 135*tan(1/2*d*x + 1/2*c) - 184)/((tan(1/2*d*x + 1/2*c)^2 + 1)^5*a))/d","A",0
712,1,216,0,0.213298," ","integrate(cos(d*x+c)^8*csc(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{45 \, {\left(d x + c\right)}}{a} - \frac{60 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a} + \frac{3 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a^{2}} + \frac{3 \, {\left(30 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 4 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}} - \frac{2 \, {\left(27 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 72 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 168 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 152 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 27 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 56\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4} a}}{24 \, d}"," ",0,"1/24*(45*(d*x + c)/a - 60*log(abs(tan(1/2*d*x + 1/2*c)))/a + 3*(a*tan(1/2*d*x + 1/2*c)^2 - 4*a*tan(1/2*d*x + 1/2*c))/a^2 + 3*(30*tan(1/2*d*x + 1/2*c)^2 + 4*tan(1/2*d*x + 1/2*c) - 1)/(a*tan(1/2*d*x + 1/2*c)^2) - 2*(27*tan(1/2*d*x + 1/2*c)^7 + 72*tan(1/2*d*x + 1/2*c)^6 + 3*tan(1/2*d*x + 1/2*c)^5 + 168*tan(1/2*d*x + 1/2*c)^4 - 3*tan(1/2*d*x + 1/2*c)^3 + 152*tan(1/2*d*x + 1/2*c)^2 - 27*tan(1/2*d*x + 1/2*c) + 56)/((tan(1/2*d*x + 1/2*c)^2 + 1)^4*a))/d","A",0
713,1,228,0,0.379848," ","integrate(cos(d*x+c)^8*csc(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{180 \, {\left(d x + c\right)}}{a} + \frac{180 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a} + \frac{3 \, {\left(a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 27 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a^{3}} - \frac{110 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 111 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 240 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 273 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 306 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 253 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}^{3} a}}{72 \, d}"," ",0,"1/72*(180*(d*x + c)/a + 180*log(abs(tan(1/2*d*x + 1/2*c)))/a + 3*(a^2*tan(1/2*d*x + 1/2*c)^3 - 3*a^2*tan(1/2*d*x + 1/2*c)^2 - 27*a^2*tan(1/2*d*x + 1/2*c))/a^3 - (110*tan(1/2*d*x + 1/2*c)^9 - 9*tan(1/2*d*x + 1/2*c)^8 - 111*tan(1/2*d*x + 1/2*c)^7 - 240*tan(1/2*d*x + 1/2*c)^6 - 273*tan(1/2*d*x + 1/2*c)^5 - 306*tan(1/2*d*x + 1/2*c)^4 - 253*tan(1/2*d*x + 1/2*c)^3 - 72*tan(1/2*d*x + 1/2*c)^2 - 9*tan(1/2*d*x + 1/2*c) + 3)/((tan(1/2*d*x + 1/2*c)^3 + tan(1/2*d*x + 1/2*c))^3*a))/d","A",0
714,1,224,0,0.219617," ","integrate(cos(d*x+c)^8*csc(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{480 \, {\left(d x + c\right)}}{a} - \frac{360 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a} - \frac{192 \, {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a} - \frac{3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 8 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 48 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 216 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{4}} + \frac{750 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 216 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 48 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}}}{192 \, d}"," ",0,"-1/192*(480*(d*x + c)/a - 360*log(abs(tan(1/2*d*x + 1/2*c)))/a - 192*(tan(1/2*d*x + 1/2*c)^3 + 2*tan(1/2*d*x + 1/2*c)^2 - tan(1/2*d*x + 1/2*c) + 2)/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a) - (3*a^3*tan(1/2*d*x + 1/2*c)^4 - 8*a^3*tan(1/2*d*x + 1/2*c)^3 - 48*a^3*tan(1/2*d*x + 1/2*c)^2 + 216*a^3*tan(1/2*d*x + 1/2*c))/a^4 + (750*tan(1/2*d*x + 1/2*c)^4 + 216*tan(1/2*d*x + 1/2*c)^3 - 48*tan(1/2*d*x + 1/2*c)^2 - 8*tan(1/2*d*x + 1/2*c) + 3)/(a*tan(1/2*d*x + 1/2*c)^4))/d","A",0
715,1,217,0,0.220935," ","integrate(cos(d*x+c)^8*csc(d*x+c)^6/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{960 \, {\left(d x + c\right)}}{a} + \frac{1800 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a} + \frac{1920}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a} - \frac{6 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 70 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 240 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 660 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{5}} - \frac{4110 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 660 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 240 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 70 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{960 \, d}"," ",0,"-1/960*(960*(d*x + c)/a + 1800*log(abs(tan(1/2*d*x + 1/2*c)))/a + 1920/((tan(1/2*d*x + 1/2*c)^2 + 1)*a) - (6*a^4*tan(1/2*d*x + 1/2*c)^5 - 15*a^4*tan(1/2*d*x + 1/2*c)^4 - 70*a^4*tan(1/2*d*x + 1/2*c)^3 + 240*a^4*tan(1/2*d*x + 1/2*c)^2 + 660*a^4*tan(1/2*d*x + 1/2*c))/a^5 - (4110*tan(1/2*d*x + 1/2*c)^5 - 660*tan(1/2*d*x + 1/2*c)^4 - 240*tan(1/2*d*x + 1/2*c)^3 + 70*tan(1/2*d*x + 1/2*c)^2 + 15*tan(1/2*d*x + 1/2*c) - 6)/(a*tan(1/2*d*x + 1/2*c)^5))/d","A",0
716,1,224,0,0.243358," ","integrate(cos(d*x+c)^8*csc(d*x+c)^7/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{1920 \, {\left(d x + c\right)}}{a} - \frac{600 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a} + \frac{5 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 12 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 45 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 140 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 225 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1320 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}} + \frac{1470 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 1320 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 225 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 140 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 45 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6}}}{1920 \, d}"," ",0,"1/1920*(1920*(d*x + c)/a - 600*log(abs(tan(1/2*d*x + 1/2*c)))/a + (5*a^5*tan(1/2*d*x + 1/2*c)^6 - 12*a^5*tan(1/2*d*x + 1/2*c)^5 - 45*a^5*tan(1/2*d*x + 1/2*c)^4 + 140*a^5*tan(1/2*d*x + 1/2*c)^3 + 225*a^5*tan(1/2*d*x + 1/2*c)^2 - 1320*a^5*tan(1/2*d*x + 1/2*c))/a^6 + (1470*tan(1/2*d*x + 1/2*c)^6 + 1320*tan(1/2*d*x + 1/2*c)^5 - 225*tan(1/2*d*x + 1/2*c)^4 - 140*tan(1/2*d*x + 1/2*c)^3 + 45*tan(1/2*d*x + 1/2*c)^2 + 12*tan(1/2*d*x + 1/2*c) - 5)/(a*tan(1/2*d*x + 1/2*c)^6))/d","A",0
717,1,244,0,0.230274," ","integrate(cos(d*x+c)^8*csc(d*x+c)^8/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{840 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a} + \frac{3 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 7 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 21 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 63 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 63 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 315 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 105 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{7}} - \frac{2178 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 105 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 315 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 63 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 63 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 21 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 7 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7}}}{2688 \, d}"," ",0,"1/2688*(840*log(abs(tan(1/2*d*x + 1/2*c)))/a + (3*a^6*tan(1/2*d*x + 1/2*c)^7 - 7*a^6*tan(1/2*d*x + 1/2*c)^6 - 21*a^6*tan(1/2*d*x + 1/2*c)^5 + 63*a^6*tan(1/2*d*x + 1/2*c)^4 + 63*a^6*tan(1/2*d*x + 1/2*c)^3 - 315*a^6*tan(1/2*d*x + 1/2*c)^2 - 105*a^6*tan(1/2*d*x + 1/2*c))/a^7 - (2178*tan(1/2*d*x + 1/2*c)^7 - 105*tan(1/2*d*x + 1/2*c)^6 - 315*tan(1/2*d*x + 1/2*c)^5 + 63*tan(1/2*d*x + 1/2*c)^4 + 63*tan(1/2*d*x + 1/2*c)^3 - 21*tan(1/2*d*x + 1/2*c)^2 - 7*tan(1/2*d*x + 1/2*c) + 3)/(a*tan(1/2*d*x + 1/2*c)^7))/d","B",0
718,1,274,0,0.262728," ","integrate(cos(d*x+c)^8*csc(d*x+c)^9/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{1680 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a} - \frac{21 \, a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 48 \, a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 112 \, a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 336 \, a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 168 \, a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1008 \, a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 336 \, a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1680 \, a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{8}} - \frac{4566 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 1680 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 336 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 1008 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 168 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 336 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 112 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 48 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 21}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8}}}{43008 \, d}"," ",0,"-1/43008*(1680*log(abs(tan(1/2*d*x + 1/2*c)))/a - (21*a^7*tan(1/2*d*x + 1/2*c)^8 - 48*a^7*tan(1/2*d*x + 1/2*c)^7 - 112*a^7*tan(1/2*d*x + 1/2*c)^6 + 336*a^7*tan(1/2*d*x + 1/2*c)^5 + 168*a^7*tan(1/2*d*x + 1/2*c)^4 - 1008*a^7*tan(1/2*d*x + 1/2*c)^3 + 336*a^7*tan(1/2*d*x + 1/2*c)^2 + 1680*a^7*tan(1/2*d*x + 1/2*c))/a^8 - (4566*tan(1/2*d*x + 1/2*c)^8 - 1680*tan(1/2*d*x + 1/2*c)^7 - 336*tan(1/2*d*x + 1/2*c)^6 + 1008*tan(1/2*d*x + 1/2*c)^5 - 168*tan(1/2*d*x + 1/2*c)^4 - 336*tan(1/2*d*x + 1/2*c)^3 + 112*tan(1/2*d*x + 1/2*c)^2 + 48*tan(1/2*d*x + 1/2*c) - 21)/(a*tan(1/2*d*x + 1/2*c)^8))/d","B",0
719,1,273,0,0.243378," ","integrate(cos(d*x+c)^8*csc(d*x+c)^10/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{5040 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a} + \frac{28 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 63 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 108 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 336 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 504 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 672 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1008 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1512 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{9}} - \frac{14258 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1512 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 1008 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 672 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 504 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 336 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 108 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 63 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 28}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9}}}{129024 \, d}"," ",0,"1/129024*(5040*log(abs(tan(1/2*d*x + 1/2*c)))/a + (28*a^8*tan(1/2*d*x + 1/2*c)^9 - 63*a^8*tan(1/2*d*x + 1/2*c)^8 - 108*a^8*tan(1/2*d*x + 1/2*c)^7 + 336*a^8*tan(1/2*d*x + 1/2*c)^6 - 504*a^8*tan(1/2*d*x + 1/2*c)^4 + 672*a^8*tan(1/2*d*x + 1/2*c)^3 - 1008*a^8*tan(1/2*d*x + 1/2*c)^2 - 1512*a^8*tan(1/2*d*x + 1/2*c))/a^9 - (14258*tan(1/2*d*x + 1/2*c)^9 - 1512*tan(1/2*d*x + 1/2*c)^8 - 1008*tan(1/2*d*x + 1/2*c)^7 + 672*tan(1/2*d*x + 1/2*c)^6 - 504*tan(1/2*d*x + 1/2*c)^5 + 336*tan(1/2*d*x + 1/2*c)^3 - 108*tan(1/2*d*x + 1/2*c)^2 - 63*tan(1/2*d*x + 1/2*c) + 28)/(a*tan(1/2*d*x + 1/2*c)^9))/d","A",0
720,1,303,0,0.285304," ","integrate(cos(d*x+c)^8*csc(d*x+c)^11/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{15120 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a} - \frac{126 \, a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 280 \, a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 315 \, a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 1080 \, a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 630 \, a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 2520 \, a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 6720 \, a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1260 \, a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 15120 \, a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{10}} - \frac{44286 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 15120 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1260 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 6720 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2520 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 630 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1080 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 315 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 280 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 126}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10}}}{1290240 \, d}"," ",0,"-1/1290240*(15120*log(abs(tan(1/2*d*x + 1/2*c)))/a - (126*a^9*tan(1/2*d*x + 1/2*c)^10 - 280*a^9*tan(1/2*d*x + 1/2*c)^9 - 315*a^9*tan(1/2*d*x + 1/2*c)^8 + 1080*a^9*tan(1/2*d*x + 1/2*c)^7 - 630*a^9*tan(1/2*d*x + 1/2*c)^6 + 2520*a^9*tan(1/2*d*x + 1/2*c)^4 - 6720*a^9*tan(1/2*d*x + 1/2*c)^3 + 1260*a^9*tan(1/2*d*x + 1/2*c)^2 + 15120*a^9*tan(1/2*d*x + 1/2*c))/a^10 - (44286*tan(1/2*d*x + 1/2*c)^10 - 15120*tan(1/2*d*x + 1/2*c)^9 - 1260*tan(1/2*d*x + 1/2*c)^8 + 6720*tan(1/2*d*x + 1/2*c)^7 - 2520*tan(1/2*d*x + 1/2*c)^6 + 630*tan(1/2*d*x + 1/2*c)^4 - 1080*tan(1/2*d*x + 1/2*c)^3 + 315*tan(1/2*d*x + 1/2*c)^2 + 280*tan(1/2*d*x + 1/2*c) - 126)/(a*tan(1/2*d*x + 1/2*c)^10))/d","A",0
721,1,360,0,0.269150," ","integrate(cos(d*x+c)^8*csc(d*x+c)^12/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{166320 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a} + \frac{630 \, a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 1386 \, a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 770 \, a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 3465 \, a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 4950 \, a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 6930 \, a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 6930 \, a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27720 \, a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 23100 \, a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 13860 \, a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 69300 \, a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{11}} - \frac{502266 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 69300 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 13860 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 23100 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 27720 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 6930 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 6930 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4950 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 3465 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 770 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1386 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 630}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11}}}{14192640 \, d}"," ",0,"1/14192640*(166320*log(abs(tan(1/2*d*x + 1/2*c)))/a + (630*a^10*tan(1/2*d*x + 1/2*c)^11 - 1386*a^10*tan(1/2*d*x + 1/2*c)^10 - 770*a^10*tan(1/2*d*x + 1/2*c)^9 + 3465*a^10*tan(1/2*d*x + 1/2*c)^8 - 4950*a^10*tan(1/2*d*x + 1/2*c)^7 + 6930*a^10*tan(1/2*d*x + 1/2*c)^6 + 6930*a^10*tan(1/2*d*x + 1/2*c)^5 - 27720*a^10*tan(1/2*d*x + 1/2*c)^4 + 23100*a^10*tan(1/2*d*x + 1/2*c)^3 - 13860*a^10*tan(1/2*d*x + 1/2*c)^2 - 69300*a^10*tan(1/2*d*x + 1/2*c))/a^11 - (502266*tan(1/2*d*x + 1/2*c)^11 - 69300*tan(1/2*d*x + 1/2*c)^10 - 13860*tan(1/2*d*x + 1/2*c)^9 + 23100*tan(1/2*d*x + 1/2*c)^8 - 27720*tan(1/2*d*x + 1/2*c)^7 + 6930*tan(1/2*d*x + 1/2*c)^6 + 6930*tan(1/2*d*x + 1/2*c)^5 - 4950*tan(1/2*d*x + 1/2*c)^4 + 3465*tan(1/2*d*x + 1/2*c)^3 - 770*tan(1/2*d*x + 1/2*c)^2 - 1386*tan(1/2*d*x + 1/2*c) + 630)/(a*tan(1/2*d*x + 1/2*c)^11))/d","B",0
722,1,270,0,0.313214," ","integrate(cos(d*x+c)^8*sin(d*x+c)^5/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{10395 \, {\left(d x + c\right)}}{a^{2}} + \frac{2 \, {\left(10395 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{21} + 110880 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{19} + 535689 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{17} + 2365440 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{16} - 6564096 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} + 8279040 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{14} + 8364510 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 12536832 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 20579328 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 8364510 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 2534400 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 6564096 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 506880 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 535689 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 957440 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 110880 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 191488 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 10395 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 17408\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{11} a^{2}}}{443520 \, d}"," ",0,"-1/443520*(10395*(d*x + c)/a^2 + 2*(10395*tan(1/2*d*x + 1/2*c)^21 + 110880*tan(1/2*d*x + 1/2*c)^19 + 535689*tan(1/2*d*x + 1/2*c)^17 + 2365440*tan(1/2*d*x + 1/2*c)^16 - 6564096*tan(1/2*d*x + 1/2*c)^15 + 8279040*tan(1/2*d*x + 1/2*c)^14 + 8364510*tan(1/2*d*x + 1/2*c)^13 - 12536832*tan(1/2*d*x + 1/2*c)^12 + 20579328*tan(1/2*d*x + 1/2*c)^10 - 8364510*tan(1/2*d*x + 1/2*c)^9 - 2534400*tan(1/2*d*x + 1/2*c)^8 + 6564096*tan(1/2*d*x + 1/2*c)^7 + 506880*tan(1/2*d*x + 1/2*c)^6 - 535689*tan(1/2*d*x + 1/2*c)^5 + 957440*tan(1/2*d*x + 1/2*c)^4 - 110880*tan(1/2*d*x + 1/2*c)^3 + 191488*tan(1/2*d*x + 1/2*c)^2 - 10395*tan(1/2*d*x + 1/2*c) + 17408)/((tan(1/2*d*x + 1/2*c)^2 + 1)^11*a^2))/d","A",0
723,1,257,0,0.257837," ","integrate(cos(d*x+c)^8*sin(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2835 \, {\left(d x + c\right)}}{a^{2}} + \frac{2 \, {\left(2835 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{19} + 27405 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{17} - 139356 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} + 860160 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{14} - 618660 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 430080 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 1609650 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 516096 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 1609650 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1290240 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 618660 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 368640 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 139356 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 184320 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 27405 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40960 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2835 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4096\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{10} a^{2}}}{80640 \, d}"," ",0,"1/80640*(2835*(d*x + c)/a^2 + 2*(2835*tan(1/2*d*x + 1/2*c)^19 + 27405*tan(1/2*d*x + 1/2*c)^17 - 139356*tan(1/2*d*x + 1/2*c)^15 + 860160*tan(1/2*d*x + 1/2*c)^14 - 618660*tan(1/2*d*x + 1/2*c)^13 - 430080*tan(1/2*d*x + 1/2*c)^12 + 1609650*tan(1/2*d*x + 1/2*c)^11 + 516096*tan(1/2*d*x + 1/2*c)^10 - 1609650*tan(1/2*d*x + 1/2*c)^9 + 1290240*tan(1/2*d*x + 1/2*c)^8 + 618660*tan(1/2*d*x + 1/2*c)^7 - 368640*tan(1/2*d*x + 1/2*c)^6 + 139356*tan(1/2*d*x + 1/2*c)^5 + 184320*tan(1/2*d*x + 1/2*c)^4 - 27405*tan(1/2*d*x + 1/2*c)^3 + 40960*tan(1/2*d*x + 1/2*c)^2 - 2835*tan(1/2*d*x + 1/2*c) + 4096)/((tan(1/2*d*x + 1/2*c)^2 + 1)^10*a^2))/d","A",0
724,1,231,0,0.289056," ","integrate(cos(d*x+c)^8*sin(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{945 \, {\left(d x + c\right)}}{a^{2}} + \frac{2 \, {\left(945 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{17} + 8190 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} + 40320 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{14} - 97650 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 147840 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 106470 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 120960 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 330624 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 106470 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 8064 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 97650 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 19584 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 8190 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 14976 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 945 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1664\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{9} a^{2}}}{20160 \, d}"," ",0,"-1/20160*(945*(d*x + c)/a^2 + 2*(945*tan(1/2*d*x + 1/2*c)^17 + 8190*tan(1/2*d*x + 1/2*c)^15 + 40320*tan(1/2*d*x + 1/2*c)^14 - 97650*tan(1/2*d*x + 1/2*c)^13 + 147840*tan(1/2*d*x + 1/2*c)^12 + 106470*tan(1/2*d*x + 1/2*c)^11 - 120960*tan(1/2*d*x + 1/2*c)^10 + 330624*tan(1/2*d*x + 1/2*c)^8 - 106470*tan(1/2*d*x + 1/2*c)^7 - 8064*tan(1/2*d*x + 1/2*c)^6 + 97650*tan(1/2*d*x + 1/2*c)^5 + 19584*tan(1/2*d*x + 1/2*c)^4 - 8190*tan(1/2*d*x + 1/2*c)^3 + 14976*tan(1/2*d*x + 1/2*c)^2 - 945*tan(1/2*d*x + 1/2*c) + 1664)/((tan(1/2*d*x + 1/2*c)^2 + 1)^9*a^2))/d","A",0
725,1,205,0,0.235003," ","integrate(cos(d*x+c)^8*sin(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{1155 \, {\left(d x + c\right)}}{a^{2}} + \frac{2 \, {\left(1155 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} - 9065 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 53760 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 38605 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 79135 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 53760 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 79135 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 86016 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 38605 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 10752 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 9065 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12288 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1155 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1536\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{8} a^{2}}}{13440 \, d}"," ",0,"1/13440*(1155*(d*x + c)/a^2 + 2*(1155*tan(1/2*d*x + 1/2*c)^15 - 9065*tan(1/2*d*x + 1/2*c)^13 + 53760*tan(1/2*d*x + 1/2*c)^12 - 38605*tan(1/2*d*x + 1/2*c)^11 + 79135*tan(1/2*d*x + 1/2*c)^9 + 53760*tan(1/2*d*x + 1/2*c)^8 - 79135*tan(1/2*d*x + 1/2*c)^7 + 86016*tan(1/2*d*x + 1/2*c)^6 + 38605*tan(1/2*d*x + 1/2*c)^5 - 10752*tan(1/2*d*x + 1/2*c)^4 + 9065*tan(1/2*d*x + 1/2*c)^3 + 12288*tan(1/2*d*x + 1/2*c)^2 - 1155*tan(1/2*d*x + 1/2*c) + 1536)/((tan(1/2*d*x + 1/2*c)^2 + 1)^8*a^2))/d","A",0
726,1,192,0,0.191974," ","integrate(cos(d*x+c)^8*sin(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{105 \, {\left(d x + c\right)}}{a^{2}} + \frac{2 \, {\left(105 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 840 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 1540 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 3360 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 1085 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 840 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 6720 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 1085 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1176 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 1540 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 672 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 105 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 216\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{7} a^{2}}}{840 \, d}"," ",0,"-1/840*(105*(d*x + c)/a^2 + 2*(105*tan(1/2*d*x + 1/2*c)^13 + 840*tan(1/2*d*x + 1/2*c)^12 - 1540*tan(1/2*d*x + 1/2*c)^11 + 3360*tan(1/2*d*x + 1/2*c)^10 + 1085*tan(1/2*d*x + 1/2*c)^9 + 840*tan(1/2*d*x + 1/2*c)^8 + 6720*tan(1/2*d*x + 1/2*c)^6 - 1085*tan(1/2*d*x + 1/2*c)^5 + 1176*tan(1/2*d*x + 1/2*c)^4 + 1540*tan(1/2*d*x + 1/2*c)^3 + 672*tan(1/2*d*x + 1/2*c)^2 - 105*tan(1/2*d*x + 1/2*c) + 216)/((tan(1/2*d*x + 1/2*c)^2 + 1)^7*a^2))/d","A",0
727,1,156,0,0.215969," ","integrate(cos(d*x+c)^8*csc(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{45 \, {\left(d x + c\right)}}{a^{2}} - \frac{60 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} - \frac{2 \, {\left(75 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 60 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 30 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 360 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 320 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 30 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 280 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 75 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 68\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5} a^{2}}}{60 \, d}"," ",0,"-1/60*(45*(d*x + c)/a^2 - 60*log(abs(tan(1/2*d*x + 1/2*c)))/a^2 - 2*(75*tan(1/2*d*x + 1/2*c)^9 + 60*tan(1/2*d*x + 1/2*c)^8 + 30*tan(1/2*d*x + 1/2*c)^7 + 360*tan(1/2*d*x + 1/2*c)^6 + 320*tan(1/2*d*x + 1/2*c)^4 - 30*tan(1/2*d*x + 1/2*c)^3 + 280*tan(1/2*d*x + 1/2*c)^2 - 75*tan(1/2*d*x + 1/2*c) + 68)/((tan(1/2*d*x + 1/2*c)^2 + 1)^5*a^2))/d","A",0
728,1,186,0,0.217237," ","integrate(cos(d*x+c)^8*csc(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{27 \, {\left(d x + c\right)}}{a^{2}} + \frac{48 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} - \frac{12 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{2}} - \frac{12 \, {\left(4 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}}{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)} + \frac{2 \, {\left(3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 96 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 21 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 192 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 21 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 160 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 64\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4} a^{2}}}{24 \, d}"," ",0,"-1/24*(27*(d*x + c)/a^2 + 48*log(abs(tan(1/2*d*x + 1/2*c)))/a^2 - 12*tan(1/2*d*x + 1/2*c)/a^2 - 12*(4*tan(1/2*d*x + 1/2*c) - 1)/(a^2*tan(1/2*d*x + 1/2*c)) + 2*(3*tan(1/2*d*x + 1/2*c)^7 + 96*tan(1/2*d*x + 1/2*c)^6 - 21*tan(1/2*d*x + 1/2*c)^5 + 192*tan(1/2*d*x + 1/2*c)^4 + 21*tan(1/2*d*x + 1/2*c)^3 + 160*tan(1/2*d*x + 1/2*c)^2 - 3*tan(1/2*d*x + 1/2*c) + 64)/((tan(1/2*d*x + 1/2*c)^2 + 1)^4*a^2))/d","A",0
729,1,168,0,0.230862," ","integrate(cos(d*x+c)^8*csc(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{72 \, {\left(d x + c\right)}}{a^{2}} - \frac{12 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} + \frac{3 \, {\left(a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a^{4}} + \frac{3 \, {\left(6 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 8 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}}{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}} - \frac{16 \, {\left(3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} a^{2}}}{24 \, d}"," ",0,"1/24*(72*(d*x + c)/a^2 - 12*log(abs(tan(1/2*d*x + 1/2*c)))/a^2 + 3*(a^2*tan(1/2*d*x + 1/2*c)^2 - 8*a^2*tan(1/2*d*x + 1/2*c))/a^4 + 3*(6*tan(1/2*d*x + 1/2*c)^2 + 8*tan(1/2*d*x + 1/2*c) - 1)/(a^2*tan(1/2*d*x + 1/2*c)^2) - 16*(3*tan(1/2*d*x + 1/2*c)^5 - 3*tan(1/2*d*x + 1/2*c)^4 - 3*tan(1/2*d*x + 1/2*c) - 1)/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*a^2))/d","A",0
730,1,194,0,0.233310," ","integrate(cos(d*x+c)^8*csc(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{12 \, {\left(d x + c\right)}}{a^{2}} - \frac{72 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} - \frac{24 \, {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{2}} + \frac{132 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 6 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1}{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}} - \frac{a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{24 \, d}"," ",0,"-1/24*(12*(d*x + c)/a^2 - 72*log(abs(tan(1/2*d*x + 1/2*c)))/a^2 - 24*(tan(1/2*d*x + 1/2*c)^3 + 4*tan(1/2*d*x + 1/2*c)^2 - tan(1/2*d*x + 1/2*c) + 4)/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^2) + (132*tan(1/2*d*x + 1/2*c)^3 - 3*tan(1/2*d*x + 1/2*c)^2 - 6*tan(1/2*d*x + 1/2*c) + 1)/(a^2*tan(1/2*d*x + 1/2*c)^3) - (a^4*tan(1/2*d*x + 1/2*c)^3 - 6*a^4*tan(1/2*d*x + 1/2*c)^2 - 3*a^4*tan(1/2*d*x + 1/2*c))/a^6)/d","B",0
731,1,159,0,0.247077," ","integrate(cos(d*x+c)^8*csc(d*x+c)^5/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{384 \, {\left(d x + c\right)}}{a^{2}} + \frac{216 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} + \frac{384}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a^{2}} - \frac{450 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 240 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 16 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3}{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}} - \frac{3 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 16 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 240 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{8}}}{192 \, d}"," ",0,"-1/192*(384*(d*x + c)/a^2 + 216*log(abs(tan(1/2*d*x + 1/2*c)))/a^2 + 384/((tan(1/2*d*x + 1/2*c)^2 + 1)*a^2) - (450*tan(1/2*d*x + 1/2*c)^4 - 240*tan(1/2*d*x + 1/2*c)^3 + 16*tan(1/2*d*x + 1/2*c) - 3)/(a^2*tan(1/2*d*x + 1/2*c)^4) - (3*a^6*tan(1/2*d*x + 1/2*c)^4 - 16*a^6*tan(1/2*d*x + 1/2*c)^3 + 240*a^6*tan(1/2*d*x + 1/2*c))/a^8)/d","A",0
732,1,195,0,0.264389," ","integrate(cos(d*x+c)^8*csc(d*x+c)^6/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{480 \, {\left(d x + c\right)}}{a^{2}} - \frac{360 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} + \frac{822 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 270 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 120 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3}{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}} + \frac{3 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 5 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 270 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{10}}}{480 \, d}"," ",0,"1/480*(480*(d*x + c)/a^2 - 360*log(abs(tan(1/2*d*x + 1/2*c)))/a^2 + (822*tan(1/2*d*x + 1/2*c)^5 + 270*tan(1/2*d*x + 1/2*c)^4 - 120*tan(1/2*d*x + 1/2*c)^3 - 5*tan(1/2*d*x + 1/2*c)^2 + 15*tan(1/2*d*x + 1/2*c) - 3)/(a^2*tan(1/2*d*x + 1/2*c)^5) + (3*a^8*tan(1/2*d*x + 1/2*c)^5 - 15*a^8*tan(1/2*d*x + 1/2*c)^4 + 5*a^8*tan(1/2*d*x + 1/2*c)^3 + 120*a^8*tan(1/2*d*x + 1/2*c)^2 - 270*a^8*tan(1/2*d*x + 1/2*c))/a^10)/d","A",0
733,1,215,0,0.301499," ","integrate(cos(d*x+c)^8*csc(d*x+c)^7/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{840 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} - \frac{2058 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 240 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 255 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 120 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 24 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5}{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6}} + \frac{5 \, a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 24 \, a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 120 \, a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 255 \, a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 240 \, a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{12}}}{1920 \, d}"," ",0,"1/1920*(840*log(abs(tan(1/2*d*x + 1/2*c)))/a^2 - (2058*tan(1/2*d*x + 1/2*c)^6 - 240*tan(1/2*d*x + 1/2*c)^5 - 255*tan(1/2*d*x + 1/2*c)^4 + 120*tan(1/2*d*x + 1/2*c)^3 + 15*tan(1/2*d*x + 1/2*c)^2 - 24*tan(1/2*d*x + 1/2*c) + 5)/(a^2*tan(1/2*d*x + 1/2*c)^6) + (5*a^10*tan(1/2*d*x + 1/2*c)^6 - 24*a^10*tan(1/2*d*x + 1/2*c)^5 + 15*a^10*tan(1/2*d*x + 1/2*c)^4 + 120*a^10*tan(1/2*d*x + 1/2*c)^3 - 255*a^10*tan(1/2*d*x + 1/2*c)^2 - 240*a^10*tan(1/2*d*x + 1/2*c))/a^12)/d","A",0
734,1,245,0,0.279231," ","integrate(cos(d*x+c)^8*csc(d*x+c)^8/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{1680 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} - \frac{4356 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1155 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 210 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 525 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 210 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 63 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 70 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15}{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7}} - \frac{15 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 70 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 63 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 210 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 525 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 210 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1155 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{14}}}{13440 \, d}"," ",0,"-1/13440*(1680*log(abs(tan(1/2*d*x + 1/2*c)))/a^2 - (4356*tan(1/2*d*x + 1/2*c)^7 - 1155*tan(1/2*d*x + 1/2*c)^6 - 210*tan(1/2*d*x + 1/2*c)^5 + 525*tan(1/2*d*x + 1/2*c)^4 - 210*tan(1/2*d*x + 1/2*c)^3 - 63*tan(1/2*d*x + 1/2*c)^2 + 70*tan(1/2*d*x + 1/2*c) - 15)/(a^2*tan(1/2*d*x + 1/2*c)^7) - (15*a^12*tan(1/2*d*x + 1/2*c)^7 - 70*a^12*tan(1/2*d*x + 1/2*c)^6 + 63*a^12*tan(1/2*d*x + 1/2*c)^5 + 210*a^12*tan(1/2*d*x + 1/2*c)^4 - 525*a^12*tan(1/2*d*x + 1/2*c)^3 + 210*a^12*tan(1/2*d*x + 1/2*c)^2 + 1155*a^12*tan(1/2*d*x + 1/2*c))/a^14)/d","B",0
735,1,273,0,0.310966," ","integrate(cos(d*x+c)^8*csc(d*x+c)^9/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{18480 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} - \frac{50226 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 10080 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1680 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 3360 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 2520 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 672 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 560 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 480 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 105}{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8}} + \frac{105 \, a^{14} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 480 \, a^{14} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 560 \, a^{14} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 672 \, a^{14} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 2520 \, a^{14} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 3360 \, a^{14} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1680 \, a^{14} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 10080 \, a^{14} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{16}}}{215040 \, d}"," ",0,"1/215040*(18480*log(abs(tan(1/2*d*x + 1/2*c)))/a^2 - (50226*tan(1/2*d*x + 1/2*c)^8 - 10080*tan(1/2*d*x + 1/2*c)^7 - 1680*tan(1/2*d*x + 1/2*c)^6 + 3360*tan(1/2*d*x + 1/2*c)^5 - 2520*tan(1/2*d*x + 1/2*c)^4 + 672*tan(1/2*d*x + 1/2*c)^3 + 560*tan(1/2*d*x + 1/2*c)^2 - 480*tan(1/2*d*x + 1/2*c) + 105)/(a^2*tan(1/2*d*x + 1/2*c)^8) + (105*a^14*tan(1/2*d*x + 1/2*c)^8 - 480*a^14*tan(1/2*d*x + 1/2*c)^7 + 560*a^14*tan(1/2*d*x + 1/2*c)^6 + 672*a^14*tan(1/2*d*x + 1/2*c)^5 - 2520*a^14*tan(1/2*d*x + 1/2*c)^4 + 3360*a^14*tan(1/2*d*x + 1/2*c)^3 - 1680*a^14*tan(1/2*d*x + 1/2*c)^2 - 10080*a^14*tan(1/2*d*x + 1/2*c))/a^16)/d","A",0
736,1,245,0,0.300002," ","integrate(cos(d*x+c)^8*csc(d*x+c)^10/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{15120 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} - \frac{42774 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 11340 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 3360 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 2520 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1008 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 450 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 315 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 70}{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9}} - \frac{70 \, a^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 315 \, a^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 450 \, a^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1008 \, a^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2520 \, a^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 3360 \, a^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 11340 \, a^{16} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{18}}}{322560 \, d}"," ",0,"-1/322560*(15120*log(abs(tan(1/2*d*x + 1/2*c)))/a^2 - (42774*tan(1/2*d*x + 1/2*c)^9 - 11340*tan(1/2*d*x + 1/2*c)^8 + 3360*tan(1/2*d*x + 1/2*c)^6 - 2520*tan(1/2*d*x + 1/2*c)^5 + 1008*tan(1/2*d*x + 1/2*c)^4 - 450*tan(1/2*d*x + 1/2*c)^2 + 315*tan(1/2*d*x + 1/2*c) - 70)/(a^2*tan(1/2*d*x + 1/2*c)^9) - (70*a^16*tan(1/2*d*x + 1/2*c)^9 - 315*a^16*tan(1/2*d*x + 1/2*c)^8 + 450*a^16*tan(1/2*d*x + 1/2*c)^7 - 1008*a^16*tan(1/2*d*x + 1/2*c)^5 + 2520*a^16*tan(1/2*d*x + 1/2*c)^4 - 3360*a^16*tan(1/2*d*x + 1/2*c)^3 + 11340*a^16*tan(1/2*d*x + 1/2*c))/a^18)/d","A",0
737,1,331,0,0.340034," ","integrate(cos(d*x+c)^8*csc(d*x+c)^11/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{45360 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} - \frac{132858 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 30240 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1260 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 6720 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 7560 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 4032 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 630 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 720 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 945 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 560 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 126}{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10}} + \frac{126 \, a^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 560 \, a^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 945 \, a^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 720 \, a^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 630 \, a^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 4032 \, a^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 7560 \, a^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 6720 \, a^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1260 \, a^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 30240 \, a^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{20}}}{1290240 \, d}"," ",0,"1/1290240*(45360*log(abs(tan(1/2*d*x + 1/2*c)))/a^2 - (132858*tan(1/2*d*x + 1/2*c)^10 - 30240*tan(1/2*d*x + 1/2*c)^9 + 1260*tan(1/2*d*x + 1/2*c)^8 + 6720*tan(1/2*d*x + 1/2*c)^7 - 7560*tan(1/2*d*x + 1/2*c)^6 + 4032*tan(1/2*d*x + 1/2*c)^5 - 630*tan(1/2*d*x + 1/2*c)^4 - 720*tan(1/2*d*x + 1/2*c)^3 + 945*tan(1/2*d*x + 1/2*c)^2 - 560*tan(1/2*d*x + 1/2*c) + 126)/(a^2*tan(1/2*d*x + 1/2*c)^10) + (126*a^18*tan(1/2*d*x + 1/2*c)^10 - 560*a^18*tan(1/2*d*x + 1/2*c)^9 + 945*a^18*tan(1/2*d*x + 1/2*c)^8 - 720*a^18*tan(1/2*d*x + 1/2*c)^7 - 630*a^18*tan(1/2*d*x + 1/2*c)^6 + 4032*a^18*tan(1/2*d*x + 1/2*c)^5 - 7560*a^18*tan(1/2*d*x + 1/2*c)^4 + 6720*a^18*tan(1/2*d*x + 1/2*c)^3 + 1260*a^18*tan(1/2*d*x + 1/2*c)^2 - 30240*a^18*tan(1/2*d*x + 1/2*c))/a^20)/d","A",0
738,1,361,0,0.335709," ","integrate(cos(d*x+c)^8*csc(d*x+c)^12/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{166320 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} - \frac{502266 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 131670 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 13860 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 25410 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 27720 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 18711 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 6930 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1485 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 3465 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2695 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1386 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 315}{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11}} - \frac{315 \, a^{20} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 1386 \, a^{20} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 2695 \, a^{20} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 3465 \, a^{20} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 1485 \, a^{20} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 6930 \, a^{20} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 18711 \, a^{20} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 27720 \, a^{20} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 25410 \, a^{20} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 13860 \, a^{20} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 131670 \, a^{20} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{22}}}{7096320 \, d}"," ",0,"-1/7096320*(166320*log(abs(tan(1/2*d*x + 1/2*c)))/a^2 - (502266*tan(1/2*d*x + 1/2*c)^11 - 131670*tan(1/2*d*x + 1/2*c)^10 + 13860*tan(1/2*d*x + 1/2*c)^9 + 25410*tan(1/2*d*x + 1/2*c)^8 - 27720*tan(1/2*d*x + 1/2*c)^7 + 18711*tan(1/2*d*x + 1/2*c)^6 - 6930*tan(1/2*d*x + 1/2*c)^5 - 1485*tan(1/2*d*x + 1/2*c)^4 + 3465*tan(1/2*d*x + 1/2*c)^3 - 2695*tan(1/2*d*x + 1/2*c)^2 + 1386*tan(1/2*d*x + 1/2*c) - 315)/(a^2*tan(1/2*d*x + 1/2*c)^11) - (315*a^20*tan(1/2*d*x + 1/2*c)^11 - 1386*a^20*tan(1/2*d*x + 1/2*c)^10 + 2695*a^20*tan(1/2*d*x + 1/2*c)^9 - 3465*a^20*tan(1/2*d*x + 1/2*c)^8 + 1485*a^20*tan(1/2*d*x + 1/2*c)^7 + 6930*a^20*tan(1/2*d*x + 1/2*c)^6 - 18711*a^20*tan(1/2*d*x + 1/2*c)^5 + 27720*a^20*tan(1/2*d*x + 1/2*c)^4 - 25410*a^20*tan(1/2*d*x + 1/2*c)^3 - 13860*a^20*tan(1/2*d*x + 1/2*c)^2 + 131670*a^20*tan(1/2*d*x + 1/2*c))/a^22)/d","A",0
739,1,218,0,0.288535," ","integrate(cos(d*x+c)^8*sin(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{3045 \, {\left(d x + c\right)}}{a^{3}} + \frac{2 \, {\left(3045 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} + 23345 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 26880 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 51275 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 286720 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 179095 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 170240 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 179095 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 14336 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 51275 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 109312 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 23345 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 38912 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3045 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4864\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{8} a^{3}}}{13440 \, d}"," ",0,"-1/13440*(3045*(d*x + c)/a^3 + 2*(3045*tan(1/2*d*x + 1/2*c)^15 + 23345*tan(1/2*d*x + 1/2*c)^13 + 26880*tan(1/2*d*x + 1/2*c)^12 - 51275*tan(1/2*d*x + 1/2*c)^11 + 286720*tan(1/2*d*x + 1/2*c)^10 - 179095*tan(1/2*d*x + 1/2*c)^9 + 170240*tan(1/2*d*x + 1/2*c)^8 + 179095*tan(1/2*d*x + 1/2*c)^7 - 14336*tan(1/2*d*x + 1/2*c)^6 + 51275*tan(1/2*d*x + 1/2*c)^5 + 109312*tan(1/2*d*x + 1/2*c)^4 - 23345*tan(1/2*d*x + 1/2*c)^3 + 38912*tan(1/2*d*x + 1/2*c)^2 - 3045*tan(1/2*d*x + 1/2*c) + 4864)/((tan(1/2*d*x + 1/2*c)^2 + 1)^8*a^3))/d","A",0
740,1,179,0,0.240518," ","integrate(cos(d*x+c)^8*sin(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{105 \, {\left(d x + c\right)}}{a^{3}} + \frac{2 \, {\left(105 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 252 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 2016 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 2499 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 5152 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 448 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 2499 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1344 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 252 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1120 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 105 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 160\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{7} a^{3}}}{336 \, d}"," ",0,"1/336*(105*(d*x + c)/a^3 + 2*(105*tan(1/2*d*x + 1/2*c)^13 + 252*tan(1/2*d*x + 1/2*c)^11 + 2016*tan(1/2*d*x + 1/2*c)^10 - 2499*tan(1/2*d*x + 1/2*c)^9 + 5152*tan(1/2*d*x + 1/2*c)^8 + 448*tan(1/2*d*x + 1/2*c)^6 + 2499*tan(1/2*d*x + 1/2*c)^5 + 1344*tan(1/2*d*x + 1/2*c)^4 - 252*tan(1/2*d*x + 1/2*c)^3 + 1120*tan(1/2*d*x + 1/2*c)^2 - 105*tan(1/2*d*x + 1/2*c) + 160)/((tan(1/2*d*x + 1/2*c)^2 + 1)^7*a^3))/d","A",0
741,1,179,0,0.240502," ","integrate(cos(d*x+c)^8*sin(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{105 \, {\left(d x + c\right)}}{a^{3}} + \frac{2 \, {\left(105 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 240 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 365 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 2160 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 1110 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1760 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 1110 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 480 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 365 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 816 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 105 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 176\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6} a^{3}}}{240 \, d}"," ",0,"-1/240*(105*(d*x + c)/a^3 + 2*(105*tan(1/2*d*x + 1/2*c)^11 + 240*tan(1/2*d*x + 1/2*c)^10 - 365*tan(1/2*d*x + 1/2*c)^9 + 2160*tan(1/2*d*x + 1/2*c)^8 - 1110*tan(1/2*d*x + 1/2*c)^7 + 1760*tan(1/2*d*x + 1/2*c)^6 + 1110*tan(1/2*d*x + 1/2*c)^5 + 480*tan(1/2*d*x + 1/2*c)^4 + 365*tan(1/2*d*x + 1/2*c)^3 + 816*tan(1/2*d*x + 1/2*c)^2 - 105*tan(1/2*d*x + 1/2*c) + 176)/((tan(1/2*d*x + 1/2*c)^2 + 1)^6*a^3))/d","A",0
742,1,129,0,0.246699," ","integrate(cos(d*x+c)^8*csc(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{13 \, {\left(d x + c\right)}}{a^{3}} - \frac{8 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} - \frac{2 \, {\left(11 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 16 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 19 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 19 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 16 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 11 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4} a^{3}}}{8 \, d}"," ",0,"-1/8*(13*(d*x + c)/a^3 - 8*log(abs(tan(1/2*d*x + 1/2*c)))/a^3 - 2*(11*tan(1/2*d*x + 1/2*c)^7 - 16*tan(1/2*d*x + 1/2*c)^6 + 19*tan(1/2*d*x + 1/2*c)^5 - 19*tan(1/2*d*x + 1/2*c)^3 + 16*tan(1/2*d*x + 1/2*c)^2 - 11*tan(1/2*d*x + 1/2*c))/((tan(1/2*d*x + 1/2*c)^2 + 1)^4*a^3))/d","A",0
743,1,147,0,0.252736," ","integrate(cos(d*x+c)^8*csc(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(d x + c\right)}}{a^{3}} - \frac{18 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} + \frac{3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3}} + \frac{3 \, {\left(6 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}}{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)} - \frac{2 \, {\left(9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 36 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 16\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} a^{3}}}{6 \, d}"," ",0,"1/6*(3*(d*x + c)/a^3 - 18*log(abs(tan(1/2*d*x + 1/2*c)))/a^3 + 3*tan(1/2*d*x + 1/2*c)/a^3 + 3*(6*tan(1/2*d*x + 1/2*c) - 1)/(a^3*tan(1/2*d*x + 1/2*c)) - 2*(9*tan(1/2*d*x + 1/2*c)^5 + 12*tan(1/2*d*x + 1/2*c)^4 + 36*tan(1/2*d*x + 1/2*c)^2 - 9*tan(1/2*d*x + 1/2*c) + 16)/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*a^3))/d","A",0
744,1,172,0,0.261530," ","integrate(cos(d*x+c)^8*csc(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{20 \, {\left(d x + c\right)}}{a^{3}} + \frac{20 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} - \frac{10 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 20 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 16 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}^{2} a^{3}} + \frac{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{8 \, d}"," ",0,"1/8*(20*(d*x + c)/a^3 + 20*log(abs(tan(1/2*d*x + 1/2*c)))/a^3 - (10*tan(1/2*d*x + 1/2*c)^6 - 20*tan(1/2*d*x + 1/2*c)^5 - 27*tan(1/2*d*x + 1/2*c)^4 - 16*tan(1/2*d*x + 1/2*c)^3 - 36*tan(1/2*d*x + 1/2*c)^2 - 12*tan(1/2*d*x + 1/2*c) + 1)/((tan(1/2*d*x + 1/2*c)^3 + tan(1/2*d*x + 1/2*c))^2*a^3) + (a^3*tan(1/2*d*x + 1/2*c)^2 - 12*a^3*tan(1/2*d*x + 1/2*c))/a^6)/d","A",0
745,1,157,0,0.267274," ","integrate(cos(d*x+c)^8*csc(d*x+c)^4/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{72 \, {\left(d x + c\right)}}{a^{3}} - \frac{12 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} + \frac{48}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a^{3}} + \frac{22 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 33 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1}{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}} - \frac{a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 33 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{9}}}{24 \, d}"," ",0,"-1/24*(72*(d*x + c)/a^3 - 12*log(abs(tan(1/2*d*x + 1/2*c)))/a^3 + 48/((tan(1/2*d*x + 1/2*c)^2 + 1)*a^3) + (22*tan(1/2*d*x + 1/2*c)^3 + 33*tan(1/2*d*x + 1/2*c)^2 - 9*tan(1/2*d*x + 1/2*c) + 1)/(a^3*tan(1/2*d*x + 1/2*c)^3) - (a^6*tan(1/2*d*x + 1/2*c)^3 - 9*a^6*tan(1/2*d*x + 1/2*c)^2 + 33*a^6*tan(1/2*d*x + 1/2*c))/a^9)/d","A",0
746,1,166,0,0.312128," ","integrate(cos(d*x+c)^8*csc(d*x+c)^5/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{192 \, {\left(d x + c\right)}}{a^{3}} - \frac{312 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} + \frac{650 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 24 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3}{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}} + \frac{3 \, {\left(a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 8 \, a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 24 \, a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a^{12}}}{192 \, d}"," ",0,"1/192*(192*(d*x + c)/a^3 - 312*log(abs(tan(1/2*d*x + 1/2*c)))/a^3 + (650*tan(1/2*d*x + 1/2*c)^4 + 24*tan(1/2*d*x + 1/2*c)^3 - 72*tan(1/2*d*x + 1/2*c)^2 + 24*tan(1/2*d*x + 1/2*c) - 3)/(a^3*tan(1/2*d*x + 1/2*c)^4) + 3*(a^9*tan(1/2*d*x + 1/2*c)^4 - 8*a^9*tan(1/2*d*x + 1/2*c)^3 + 24*a^9*tan(1/2*d*x + 1/2*c)^2 - 8*a^9*tan(1/2*d*x + 1/2*c))/a^12)/d","A",0
747,1,186,0,0.310585," ","integrate(cos(d*x+c)^8*csc(d*x+c)^6/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{840 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} - \frac{1918 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 420 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 120 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 130 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 45 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6}{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}} + \frac{6 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 45 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 130 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 420 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{960 \, d}"," ",0,"1/960*(840*log(abs(tan(1/2*d*x + 1/2*c)))/a^3 - (1918*tan(1/2*d*x + 1/2*c)^5 - 420*tan(1/2*d*x + 1/2*c)^4 - 120*tan(1/2*d*x + 1/2*c)^3 + 130*tan(1/2*d*x + 1/2*c)^2 - 45*tan(1/2*d*x + 1/2*c) + 6)/(a^3*tan(1/2*d*x + 1/2*c)^5) + (6*a^12*tan(1/2*d*x + 1/2*c)^5 - 45*a^12*tan(1/2*d*x + 1/2*c)^4 + 130*a^12*tan(1/2*d*x + 1/2*c)^3 - 120*a^12*tan(1/2*d*x + 1/2*c)^2 - 420*a^12*tan(1/2*d*x + 1/2*c))/a^15)/d","B",0
748,1,216,0,0.331253," ","integrate(cos(d*x+c)^8*csc(d*x+c)^7/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{840 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} - \frac{2058 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 600 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 140 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 105 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 36 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5}{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6}} - \frac{5 \, a^{15} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 36 \, a^{15} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 105 \, a^{15} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 140 \, a^{15} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, a^{15} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 600 \, a^{15} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{18}}}{1920 \, d}"," ",0,"-1/1920*(840*log(abs(tan(1/2*d*x + 1/2*c)))/a^3 - (2058*tan(1/2*d*x + 1/2*c)^6 - 600*tan(1/2*d*x + 1/2*c)^5 + 15*tan(1/2*d*x + 1/2*c)^4 + 140*tan(1/2*d*x + 1/2*c)^3 - 105*tan(1/2*d*x + 1/2*c)^2 + 36*tan(1/2*d*x + 1/2*c) - 5)/(a^3*tan(1/2*d*x + 1/2*c)^6) - (5*a^15*tan(1/2*d*x + 1/2*c)^6 - 36*a^15*tan(1/2*d*x + 1/2*c)^5 + 105*a^15*tan(1/2*d*x + 1/2*c)^4 - 140*a^15*tan(1/2*d*x + 1/2*c)^3 - 15*a^15*tan(1/2*d*x + 1/2*c)^2 + 600*a^15*tan(1/2*d*x + 1/2*c))/a^18)/d","A",0
749,1,244,0,0.354603," ","integrate(cos(d*x+c)^8*csc(d*x+c)^8/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{840 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} - \frac{2178 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 609 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 63 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 91 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 105 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 63 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 21 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3}{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7}} + \frac{3 \, a^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 21 \, a^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 63 \, a^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 105 \, a^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 91 \, a^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 63 \, a^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 609 \, a^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{21}}}{2688 \, d}"," ",0,"1/2688*(840*log(abs(tan(1/2*d*x + 1/2*c)))/a^3 - (2178*tan(1/2*d*x + 1/2*c)^7 - 609*tan(1/2*d*x + 1/2*c)^6 + 63*tan(1/2*d*x + 1/2*c)^5 + 91*tan(1/2*d*x + 1/2*c)^4 - 105*tan(1/2*d*x + 1/2*c)^3 + 63*tan(1/2*d*x + 1/2*c)^2 - 21*tan(1/2*d*x + 1/2*c) + 3)/(a^3*tan(1/2*d*x + 1/2*c)^7) + (3*a^18*tan(1/2*d*x + 1/2*c)^7 - 21*a^18*tan(1/2*d*x + 1/2*c)^6 + 63*a^18*tan(1/2*d*x + 1/2*c)^5 - 105*a^18*tan(1/2*d*x + 1/2*c)^4 + 91*a^18*tan(1/2*d*x + 1/2*c)^3 + 63*a^18*tan(1/2*d*x + 1/2*c)^2 - 609*a^18*tan(1/2*d*x + 1/2*c))/a^21)/d","A",0
750,1,274,0,0.361985," ","integrate(cos(d*x+c)^8*csc(d*x+c)^9/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{48720 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} - \frac{132414 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 38640 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 6720 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 3920 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 5880 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 4368 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2240 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 720 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 105}{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8}} - \frac{105 \, a^{21} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 720 \, a^{21} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 2240 \, a^{21} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 4368 \, a^{21} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 5880 \, a^{21} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 3920 \, a^{21} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6720 \, a^{21} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 38640 \, a^{21} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{24}}}{215040 \, d}"," ",0,"-1/215040*(48720*log(abs(tan(1/2*d*x + 1/2*c)))/a^3 - (132414*tan(1/2*d*x + 1/2*c)^8 - 38640*tan(1/2*d*x + 1/2*c)^7 + 6720*tan(1/2*d*x + 1/2*c)^6 + 3920*tan(1/2*d*x + 1/2*c)^5 - 5880*tan(1/2*d*x + 1/2*c)^4 + 4368*tan(1/2*d*x + 1/2*c)^3 - 2240*tan(1/2*d*x + 1/2*c)^2 + 720*tan(1/2*d*x + 1/2*c) - 105)/(a^3*tan(1/2*d*x + 1/2*c)^8) - (105*a^21*tan(1/2*d*x + 1/2*c)^8 - 720*a^21*tan(1/2*d*x + 1/2*c)^7 + 2240*a^21*tan(1/2*d*x + 1/2*c)^6 - 4368*a^21*tan(1/2*d*x + 1/2*c)^5 + 5880*a^21*tan(1/2*d*x + 1/2*c)^4 - 3920*a^21*tan(1/2*d*x + 1/2*c)^3 - 6720*a^21*tan(1/2*d*x + 1/2*c)^2 + 38640*a^21*tan(1/2*d*x + 1/2*c))/a^24)/d","A",0
751,1,105,0,0.178916," ","integrate(sec(d*x+c)^2*sin(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{9 \, {\left(d x + c\right)} a + \frac{12 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1} + \frac{2 \, {\left(3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 24 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 10 \, a\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"-1/6*(9*(d*x + c)*a + 12*a/(tan(1/2*d*x + 1/2*c) - 1) + 2*(3*a*tan(1/2*d*x + 1/2*c)^5 - 6*a*tan(1/2*d*x + 1/2*c)^4 - 24*a*tan(1/2*d*x + 1/2*c)^2 - 3*a*tan(1/2*d*x + 1/2*c) - 10*a)/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
752,1,90,0,0.168431," ","integrate(sec(d*x+c)^2*sin(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{3 \, {\left(d x + c\right)} a + \frac{4 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1} + \frac{2 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, a\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"-1/2*(3*(d*x + c)*a + 4*a/(tan(1/2*d*x + 1/2*c) - 1) + 2*(a*tan(1/2*d*x + 1/2*c)^3 - 2*a*tan(1/2*d*x + 1/2*c)^2 - a*tan(1/2*d*x + 1/2*c) - 2*a)/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","A",0
753,1,81,0,0.174961," ","integrate(sec(d*x+c)^2*sin(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{{\left(d x + c\right)} a + \frac{2 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, a\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1}}{d}"," ",0,"-((d*x + c)*a + 2*(a*tan(1/2*d*x + 1/2*c)^2 - a*tan(1/2*d*x + 1/2*c) + 2*a)/(tan(1/2*d*x + 1/2*c)^3 - tan(1/2*d*x + 1/2*c)^2 + tan(1/2*d*x + 1/2*c) - 1))/d","B",0
754,1,29,0,0.159894," ","integrate(sec(d*x+c)^2*sin(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{{\left(d x + c\right)} a + \frac{2 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1}}{d}"," ",0,"-((d*x + c)*a + 2*a/(tan(1/2*d*x + 1/2*c) - 1))/d","A",0
755,1,34,0,0.174656," ","integrate(csc(d*x+c)*sec(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{2 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1}}{d}"," ",0,"(a*log(abs(tan(1/2*d*x + 1/2*c))) - 2*a/(tan(1/2*d*x + 1/2*c) - 1))/d","A",0
756,1,87,0,0.205117," ","integrate(csc(d*x+c)^2*sec(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{2 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 4 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}}{2 \, d}"," ",0,"1/2*(2*a*log(abs(tan(1/2*d*x + 1/2*c))) + a*tan(1/2*d*x + 1/2*c) - (a*tan(1/2*d*x + 1/2*c)^2 + 4*a*tan(1/2*d*x + 1/2*c) - a)/(tan(1/2*d*x + 1/2*c)^2 - tan(1/2*d*x + 1/2*c)))/d","A",0
757,1,102,0,0.213245," ","integrate(csc(d*x+c)^3*sec(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 4 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{16 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1} - \frac{18 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 4 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}}{8 \, d}"," ",0,"1/8*(a*tan(1/2*d*x + 1/2*c)^2 + 12*a*log(abs(tan(1/2*d*x + 1/2*c))) + 4*a*tan(1/2*d*x + 1/2*c) - 16*a/(tan(1/2*d*x + 1/2*c) - 1) - (18*a*tan(1/2*d*x + 1/2*c)^2 + 4*a*tan(1/2*d*x + 1/2*c) + a)/tan(1/2*d*x + 1/2*c)^2)/d","A",0
758,1,130,0,0.213454," ","integrate(csc(d*x+c)^4*sec(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 36 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 21 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{48 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1} - \frac{66 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 21 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{24 \, d}"," ",0,"1/24*(a*tan(1/2*d*x + 1/2*c)^3 + 3*a*tan(1/2*d*x + 1/2*c)^2 + 36*a*log(abs(tan(1/2*d*x + 1/2*c))) + 21*a*tan(1/2*d*x + 1/2*c) - 48*a/(tan(1/2*d*x + 1/2*c) - 1) - (66*a*tan(1/2*d*x + 1/2*c)^3 + 21*a*tan(1/2*d*x + 1/2*c)^2 + 3*a*tan(1/2*d*x + 1/2*c) + a)/tan(1/2*d*x + 1/2*c)^3)/d","A",0
759,1,119,0,0.195852," ","integrate(sec(d*x+c)^2*sin(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{9 \, {\left(d x + c\right)} a^{2} + \frac{12 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1} + \frac{2 \, {\left(3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 18 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, a^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{3 \, d}"," ",0,"-1/3*(9*(d*x + c)*a^2 + 12*a^2/(tan(1/2*d*x + 1/2*c) - 1) + 2*(3*a^2*tan(1/2*d*x + 1/2*c)^5 - 6*a^2*tan(1/2*d*x + 1/2*c)^4 - 18*a^2*tan(1/2*d*x + 1/2*c)^2 - 3*a^2*tan(1/2*d*x + 1/2*c) - 8*a^2)/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
760,1,102,0,0.200984," ","integrate(sec(d*x+c)^2*sin(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{5 \, {\left(d x + c\right)} a^{2} + \frac{8 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1} + \frac{2 \, {\left(a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, a^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"-1/2*(5*(d*x + c)*a^2 + 8*a^2/(tan(1/2*d*x + 1/2*c) - 1) + 2*(a^2*tan(1/2*d*x + 1/2*c)^3 - 4*a^2*tan(1/2*d*x + 1/2*c)^2 - a^2*tan(1/2*d*x + 1/2*c) - 4*a^2)/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","A",0
761,1,89,0,0.190353," ","integrate(sec(d*x+c)^2*sin(d*x+c)*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{2 \, {\left({\left(d x + c\right)} a^{2} + \frac{2 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1}\right)}}{d}"," ",0,"-2*((d*x + c)*a^2 + (2*a^2*tan(1/2*d*x + 1/2*c)^2 - a^2*tan(1/2*d*x + 1/2*c) + 3*a^2)/(tan(1/2*d*x + 1/2*c)^3 - tan(1/2*d*x + 1/2*c)^2 + tan(1/2*d*x + 1/2*c) - 1))/d","B",0
762,1,38,0,0.201889," ","integrate(csc(d*x+c)*sec(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{4 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1}}{d}"," ",0,"(a^2*log(abs(tan(1/2*d*x + 1/2*c))) - 4*a^2/(tan(1/2*d*x + 1/2*c) - 1))/d","A",0
763,1,98,0,0.200190," ","integrate(csc(d*x+c)^2*sec(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{4 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{2 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 7 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}}{2 \, d}"," ",0,"1/2*(4*a^2*log(abs(tan(1/2*d*x + 1/2*c))) + a^2*tan(1/2*d*x + 1/2*c) - (2*a^2*tan(1/2*d*x + 1/2*c)^2 + 7*a^2*tan(1/2*d*x + 1/2*c) - a^2)/(tan(1/2*d*x + 1/2*c)^2 - tan(1/2*d*x + 1/2*c)))/d","A",0
764,1,116,0,0.227450," ","integrate(csc(d*x+c)^3*sec(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 20 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 8 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{32 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1} - \frac{30 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 8 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}}{8 \, d}"," ",0,"1/8*(a^2*tan(1/2*d*x + 1/2*c)^2 + 20*a^2*log(abs(tan(1/2*d*x + 1/2*c))) + 8*a^2*tan(1/2*d*x + 1/2*c) - 32*a^2/(tan(1/2*d*x + 1/2*c) - 1) - (30*a^2*tan(1/2*d*x + 1/2*c)^2 + 8*a^2*tan(1/2*d*x + 1/2*c) + a^2)/tan(1/2*d*x + 1/2*c)^2)/d","A",0
765,1,167,0,0.211662," ","integrate(sec(d*x+c)^2*sin(d*x+c)^3*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{51 \, {\left(d x + c\right)} a^{3} + \frac{64 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1} + \frac{2 \, {\left(19 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 32 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 27 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 144 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 27 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 160 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 19 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 48 \, a^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{8 \, d}"," ",0,"-1/8*(51*(d*x + c)*a^3 + 64*a^3/(tan(1/2*d*x + 1/2*c) - 1) + 2*(19*a^3*tan(1/2*d*x + 1/2*c)^7 - 32*a^3*tan(1/2*d*x + 1/2*c)^6 + 27*a^3*tan(1/2*d*x + 1/2*c)^5 - 144*a^3*tan(1/2*d*x + 1/2*c)^4 - 27*a^3*tan(1/2*d*x + 1/2*c)^3 - 160*a^3*tan(1/2*d*x + 1/2*c)^2 - 19*a^3*tan(1/2*d*x + 1/2*c) - 48*a^3)/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","A",0
766,1,119,0,0.215332," ","integrate(sec(d*x+c)^2*sin(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{33 \, {\left(d x + c\right)} a^{3} + \frac{48 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1} + \frac{2 \, {\left(9 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 24 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 60 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 28 \, a^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"-1/6*(33*(d*x + c)*a^3 + 48*a^3/(tan(1/2*d*x + 1/2*c) - 1) + 2*(9*a^3*tan(1/2*d*x + 1/2*c)^5 - 24*a^3*tan(1/2*d*x + 1/2*c)^4 - 60*a^3*tan(1/2*d*x + 1/2*c)^2 - 9*a^3*tan(1/2*d*x + 1/2*c) - 28*a^3)/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
767,1,102,0,0.184284," ","integrate(sec(d*x+c)^2*sin(d*x+c)*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{9 \, {\left(d x + c\right)} a^{3} + \frac{16 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1} + \frac{2 \, {\left(a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, a^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"-1/2*(9*(d*x + c)*a^3 + 16*a^3/(tan(1/2*d*x + 1/2*c) - 1) + 2*(a^3*tan(1/2*d*x + 1/2*c)^3 - 6*a^3*tan(1/2*d*x + 1/2*c)^2 - a^3*tan(1/2*d*x + 1/2*c) - 6*a^3)/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","A",0
768,1,49,0,0.193409," ","integrate(csc(d*x+c)*sec(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{{\left(d x + c\right)} a^{3} - a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + \frac{8 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1}}{d}"," ",0,"-((d*x + c)*a^3 - a^3*log(abs(tan(1/2*d*x + 1/2*c))) + 8*a^3/(tan(1/2*d*x + 1/2*c) - 1))/d","A",0
769,1,98,0,0.211733," ","integrate(csc(d*x+c)^2*sec(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{6 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 14 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}}{2 \, d}"," ",0,"1/2*(6*a^3*log(abs(tan(1/2*d*x + 1/2*c))) + a^3*tan(1/2*d*x + 1/2*c) - (3*a^3*tan(1/2*d*x + 1/2*c)^2 + 14*a^3*tan(1/2*d*x + 1/2*c) - a^3)/(tan(1/2*d*x + 1/2*c)^2 - tan(1/2*d*x + 1/2*c)))/d","A",0
770,1,116,0,0.227724," ","integrate(csc(d*x+c)^3*sec(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 36 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 12 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{64 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1} - \frac{54 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}}{8 \, d}"," ",0,"1/8*(a^3*tan(1/2*d*x + 1/2*c)^2 + 36*a^3*log(abs(tan(1/2*d*x + 1/2*c))) + 12*a^3*tan(1/2*d*x + 1/2*c) - 64*a^3/(tan(1/2*d*x + 1/2*c) - 1) - (54*a^3*tan(1/2*d*x + 1/2*c)^2 + 12*a^3*tan(1/2*d*x + 1/2*c) + a^3)/tan(1/2*d*x + 1/2*c)^2)/d","A",0
771,1,148,0,0.230742," ","integrate(csc(d*x+c)^4*sec(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 132 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 57 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{192 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1} - \frac{242 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 57 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 9 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{24 \, d}"," ",0,"1/24*(a^3*tan(1/2*d*x + 1/2*c)^3 + 9*a^3*tan(1/2*d*x + 1/2*c)^2 + 132*a^3*log(abs(tan(1/2*d*x + 1/2*c))) + 57*a^3*tan(1/2*d*x + 1/2*c) - 192*a^3/(tan(1/2*d*x + 1/2*c) - 1) - (242*a^3*tan(1/2*d*x + 1/2*c)^3 + 57*a^3*tan(1/2*d*x + 1/2*c)^2 + 9*a^3*tan(1/2*d*x + 1/2*c) + a^3)/tan(1/2*d*x + 1/2*c)^3)/d","A",0
772,1,125,0,0.192652," ","integrate(sec(d*x+c)^2*sin(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{6 \, {\left(d x + c\right)}}{a} - \frac{3 \, {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)} a} + \frac{15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 36 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 17}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(6*(d*x + c)/a - 3*(tan(1/2*d*x + 1/2*c)^2 - 4*tan(1/2*d*x + 1/2*c) + 5)/((tan(1/2*d*x + 1/2*c)^3 - tan(1/2*d*x + 1/2*c)^2 + tan(1/2*d*x + 1/2*c) - 1)*a) + (15*tan(1/2*d*x + 1/2*c)^2 + 36*tan(1/2*d*x + 1/2*c) + 17)/(a*(tan(1/2*d*x + 1/2*c) + 1)^3))/d","A",0
773,1,77,0,0.230451," ","integrate(sec(d*x+c)^2*sin(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{6 \, {\left(d x + c\right)}}{a} + \frac{3}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}} + \frac{9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 11}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{3}}}{6 \, d}"," ",0,"-1/6*(6*(d*x + c)/a + 3/(a*(tan(1/2*d*x + 1/2*c) - 1)) + (9*tan(1/2*d*x + 1/2*c)^2 + 24*tan(1/2*d*x + 1/2*c) + 11)/(a*(tan(1/2*d*x + 1/2*c) + 1)^3))/d","A",0
774,1,68,0,0.202170," ","integrate(sec(d*x+c)^2*sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{3}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}} - \frac{3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{3}}}{6 \, d}"," ",0,"-1/6*(3/(a*(tan(1/2*d*x + 1/2*c) - 1)) - (3*tan(1/2*d*x + 1/2*c)^2 + 12*tan(1/2*d*x + 1/2*c) + 5)/(a*(tan(1/2*d*x + 1/2*c) + 1)^3))/d","A",0
775,1,57,0,0.187389," ","integrate(sec(d*x+c)^2*sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{3}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}} - \frac{3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{3}}}{6 \, d}"," ",0,"-1/6*(3/(a*(tan(1/2*d*x + 1/2*c) - 1)) - (3*tan(1/2*d*x + 1/2*c)^2 + 1)/(a*(tan(1/2*d*x + 1/2*c) + 1)^3))/d","A",0
776,1,83,0,0.177319," ","integrate(csc(d*x+c)*sec(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{6 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a} - \frac{3}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}} + \frac{15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 13}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(6*log(abs(tan(1/2*d*x + 1/2*c)))/a - 3/(a*(tan(1/2*d*x + 1/2*c) - 1)) + (15*tan(1/2*d*x + 1/2*c)^2 + 24*tan(1/2*d*x + 1/2*c) + 13)/(a*(tan(1/2*d*x + 1/2*c) + 1)^3))/d","A",0
777,1,133,0,0.184186," ","integrate(csc(d*x+c)^2*sec(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{6 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a} - \frac{3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a} - \frac{3 \, {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} a} + \frac{21 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 36 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 19}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{3}}}{6 \, d}"," ",0,"-1/6*(6*log(abs(tan(1/2*d*x + 1/2*c)))/a - 3*tan(1/2*d*x + 1/2*c)/a - 3*(tan(1/2*d*x + 1/2*c)^2 - 3*tan(1/2*d*x + 1/2*c) + 1)/((tan(1/2*d*x + 1/2*c)^2 - tan(1/2*d*x + 1/2*c))*a) + (21*tan(1/2*d*x + 1/2*c)^2 + 36*tan(1/2*d*x + 1/2*c) + 19)/(a*(tan(1/2*d*x + 1/2*c) + 1)^3))/d","A",0
778,1,160,0,0.232570," ","integrate(sec(d*x+c)^2*sin(d*x+c)^6/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{90 \, {\left(d x + c\right)}}{a^{2}} + \frac{20 \, {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} a^{2}} + \frac{5}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}} + \frac{155 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 690 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1120 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 750 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 181}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{5}}}{20 \, d}"," ",0,"-1/20*(90*(d*x + c)/a^2 + 20*(tan(1/2*d*x + 1/2*c)^3 + 4*tan(1/2*d*x + 1/2*c)^2 - tan(1/2*d*x + 1/2*c) + 4)/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*a^2) + 5/(a^2*(tan(1/2*d*x + 1/2*c) - 1)) + (155*tan(1/2*d*x + 1/2*c)^4 + 690*tan(1/2*d*x + 1/2*c)^3 + 1120*tan(1/2*d*x + 1/2*c)^2 + 750*tan(1/2*d*x + 1/2*c) + 181)/(a^2*(tan(1/2*d*x + 1/2*c) + 1)^5))/d","A",0
779,1,151,0,0.231274," ","integrate(sec(d*x+c)^2*sin(d*x+c)^5/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{120 \, {\left(d x + c\right)}}{a^{2}} - \frac{15 \, {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)} a^{2}} + \frac{255 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 1170 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1960 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1310 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 313}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{5}}}{60 \, d}"," ",0,"1/60*(120*(d*x + c)/a^2 - 15*(tan(1/2*d*x + 1/2*c)^2 - 8*tan(1/2*d*x + 1/2*c) + 9)/((tan(1/2*d*x + 1/2*c)^3 - tan(1/2*d*x + 1/2*c)^2 + tan(1/2*d*x + 1/2*c) - 1)*a^2) + (255*tan(1/2*d*x + 1/2*c)^4 + 1170*tan(1/2*d*x + 1/2*c)^3 + 1960*tan(1/2*d*x + 1/2*c)^2 + 1310*tan(1/2*d*x + 1/2*c) + 313)/(a^2*(tan(1/2*d*x + 1/2*c) + 1)^5))/d","A",0
780,1,103,0,0.218651," ","integrate(sec(d*x+c)^2*sin(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{60 \, {\left(d x + c\right)}}{a^{2}} + \frac{15}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}} + \frac{105 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 510 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 920 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 610 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 143}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{5}}}{60 \, d}"," ",0,"-1/60*(60*(d*x + c)/a^2 + 15/(a^2*(tan(1/2*d*x + 1/2*c) - 1)) + (105*tan(1/2*d*x + 1/2*c)^4 + 510*tan(1/2*d*x + 1/2*c)^3 + 920*tan(1/2*d*x + 1/2*c)^2 + 610*tan(1/2*d*x + 1/2*c) + 143)/(a^2*(tan(1/2*d*x + 1/2*c) + 1)^5))/d","A",0
781,1,94,0,0.217324," ","integrate(sec(d*x+c)^2*sin(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{5}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}} - \frac{5 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 30 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 80 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 50 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 11}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{5}}}{20 \, d}"," ",0,"-1/20*(5/(a^2*(tan(1/2*d*x + 1/2*c) - 1)) - (5*tan(1/2*d*x + 1/2*c)^4 + 30*tan(1/2*d*x + 1/2*c)^3 + 80*tan(1/2*d*x + 1/2*c)^2 + 50*tan(1/2*d*x + 1/2*c) + 11)/(a^2*(tan(1/2*d*x + 1/2*c) + 1)^5))/d","A",0
782,1,94,0,0.211615," ","integrate(sec(d*x+c)^2*sin(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{15}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}} - \frac{15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 90 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 80 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 70 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 17}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{5}}}{60 \, d}"," ",0,"-1/60*(15/(a^2*(tan(1/2*d*x + 1/2*c) - 1)) - (15*tan(1/2*d*x + 1/2*c)^4 + 90*tan(1/2*d*x + 1/2*c)^3 + 80*tan(1/2*d*x + 1/2*c)^2 + 70*tan(1/2*d*x + 1/2*c) + 17)/(a^2*(tan(1/2*d*x + 1/2*c) + 1)^5))/d","A",0
783,1,94,0,0.194594," ","integrate(sec(d*x+c)^2*sin(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{15}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}} - \frac{15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 30 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 50 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 7}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{5}}}{60 \, d}"," ",0,"-1/60*(15/(a^2*(tan(1/2*d*x + 1/2*c) - 1)) - (15*tan(1/2*d*x + 1/2*c)^4 - 30*tan(1/2*d*x + 1/2*c)^3 - 40*tan(1/2*d*x + 1/2*c)^2 - 50*tan(1/2*d*x + 1/2*c) - 7)/(a^2*(tan(1/2*d*x + 1/2*c) + 1)^5))/d","A",0
784,1,109,0,0.187183," ","integrate(csc(d*x+c)*sec(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{60 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} - \frac{15}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}} + \frac{255 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 810 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1120 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 710 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 193}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{5}}}{60 \, d}"," ",0,"1/60*(60*log(abs(tan(1/2*d*x + 1/2*c)))/a^2 - 15/(a^2*(tan(1/2*d*x + 1/2*c) - 1)) + (255*tan(1/2*d*x + 1/2*c)^4 + 810*tan(1/2*d*x + 1/2*c)^3 + 1120*tan(1/2*d*x + 1/2*c)^2 + 710*tan(1/2*d*x + 1/2*c) + 193)/(a^2*(tan(1/2*d*x + 1/2*c) + 1)^5))/d","A",0
785,1,161,0,0.225194," ","integrate(csc(d*x+c)^2*sec(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{120 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} - \frac{30 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{2}} - \frac{15 \, {\left(4 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 7 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} a^{2}} + \frac{465 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 1590 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2240 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1450 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 383}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{5}}}{60 \, d}"," ",0,"-1/60*(120*log(abs(tan(1/2*d*x + 1/2*c)))/a^2 - 30*tan(1/2*d*x + 1/2*c)/a^2 - 15*(4*tan(1/2*d*x + 1/2*c)^2 - 7*tan(1/2*d*x + 1/2*c) + 2)/((tan(1/2*d*x + 1/2*c)^2 - tan(1/2*d*x + 1/2*c))*a^2) + (465*tan(1/2*d*x + 1/2*c)^4 + 1590*tan(1/2*d*x + 1/2*c)^3 + 2240*tan(1/2*d*x + 1/2*c)^2 + 1450*tan(1/2*d*x + 1/2*c) + 383)/(a^2*(tan(1/2*d*x + 1/2*c) + 1)^5))/d","A",0
786,1,187,0,0.231816," ","integrate(csc(d*x+c)^3*sec(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{180 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} + \frac{5 \, {\left(a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a^{4}} - \frac{10}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}} - \frac{5 \, {\left(54 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}} + \frac{2 \, {\left(245 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 870 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1240 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 810 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 211\right)}}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{5}}}{40 \, d}"," ",0,"1/40*(180*log(abs(tan(1/2*d*x + 1/2*c)))/a^2 + 5*(a^2*tan(1/2*d*x + 1/2*c)^2 - 8*a^2*tan(1/2*d*x + 1/2*c))/a^4 - 10/(a^2*(tan(1/2*d*x + 1/2*c) - 1)) - 5*(54*tan(1/2*d*x + 1/2*c)^2 - 8*tan(1/2*d*x + 1/2*c) + 1)/(a^2*tan(1/2*d*x + 1/2*c)^2) + 2*(245*tan(1/2*d*x + 1/2*c)^4 + 870*tan(1/2*d*x + 1/2*c)^3 + 1240*tan(1/2*d*x + 1/2*c)^2 + 810*tan(1/2*d*x + 1/2*c) + 211)/(a^2*(tan(1/2*d*x + 1/2*c) + 1)^5))/d","A",0
787,1,177,0,0.303448," ","integrate(sec(d*x+c)^2*sin(d*x+c)^6/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{840 \, {\left(d x + c\right)}}{a^{3}} - \frac{35 \, {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 16 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 17\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)} a^{3}} + \frac{1715 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 11480 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 31815 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 45920 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 35161 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 13832 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2221}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{7}}}{280 \, d}"," ",0,"1/280*(840*(d*x + c)/a^3 - 35*(tan(1/2*d*x + 1/2*c)^2 - 16*tan(1/2*d*x + 1/2*c) + 17)/((tan(1/2*d*x + 1/2*c)^3 - tan(1/2*d*x + 1/2*c)^2 + tan(1/2*d*x + 1/2*c) - 1)*a^3) + (1715*tan(1/2*d*x + 1/2*c)^6 + 11480*tan(1/2*d*x + 1/2*c)^5 + 31815*tan(1/2*d*x + 1/2*c)^4 + 45920*tan(1/2*d*x + 1/2*c)^3 + 35161*tan(1/2*d*x + 1/2*c)^2 + 13832*tan(1/2*d*x + 1/2*c) + 2221)/(a^3*(tan(1/2*d*x + 1/2*c) + 1)^7))/d","A",0
788,1,129,0,0.298525," ","integrate(sec(d*x+c)^2*sin(d*x+c)^5/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{840 \, {\left(d x + c\right)}}{a^{3}} + \frac{105}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}} + \frac{1575 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 10920 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 31675 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 48160 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36981 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 14392 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2281}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{7}}}{840 \, d}"," ",0,"-1/840*(840*(d*x + c)/a^3 + 105/(a^3*(tan(1/2*d*x + 1/2*c) - 1)) + (1575*tan(1/2*d*x + 1/2*c)^6 + 10920*tan(1/2*d*x + 1/2*c)^5 + 31675*tan(1/2*d*x + 1/2*c)^4 + 48160*tan(1/2*d*x + 1/2*c)^3 + 36981*tan(1/2*d*x + 1/2*c)^2 + 14392*tan(1/2*d*x + 1/2*c) + 2281)/(a^3*(tan(1/2*d*x + 1/2*c) + 1)^7))/d","A",0
789,1,120,0,0.264437," ","integrate(sec(d*x+c)^2*sin(d*x+c)^4/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{35}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}} - \frac{35 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 280 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1015 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2240 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1673 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 616 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 93}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{7}}}{280 \, d}"," ",0,"-1/280*(35/(a^3*(tan(1/2*d*x + 1/2*c) - 1)) - (35*tan(1/2*d*x + 1/2*c)^6 + 280*tan(1/2*d*x + 1/2*c)^5 + 1015*tan(1/2*d*x + 1/2*c)^4 + 2240*tan(1/2*d*x + 1/2*c)^3 + 1673*tan(1/2*d*x + 1/2*c)^2 + 616*tan(1/2*d*x + 1/2*c) + 93)/(a^3*(tan(1/2*d*x + 1/2*c) + 1)^7))/d","A",0
790,1,120,0,0.254224," ","integrate(sec(d*x+c)^2*sin(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{35}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}} - \frac{35 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 280 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1015 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 1120 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1001 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 392 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 61}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{7}}}{280 \, d}"," ",0,"-1/280*(35/(a^3*(tan(1/2*d*x + 1/2*c) - 1)) - (35*tan(1/2*d*x + 1/2*c)^6 + 280*tan(1/2*d*x + 1/2*c)^5 + 1015*tan(1/2*d*x + 1/2*c)^4 + 1120*tan(1/2*d*x + 1/2*c)^3 + 1001*tan(1/2*d*x + 1/2*c)^2 + 392*tan(1/2*d*x + 1/2*c) + 61)/(a^3*(tan(1/2*d*x + 1/2*c) + 1)^7))/d","A",0
791,1,120,0,0.271380," ","integrate(sec(d*x+c)^2*sin(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{21}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}} - \frac{21 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 168 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 161 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 224 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 63 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 56 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 11}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{7}}}{168 \, d}"," ",0,"-1/168*(21/(a^3*(tan(1/2*d*x + 1/2*c) - 1)) - (21*tan(1/2*d*x + 1/2*c)^6 + 168*tan(1/2*d*x + 1/2*c)^5 + 161*tan(1/2*d*x + 1/2*c)^4 + 224*tan(1/2*d*x + 1/2*c)^3 + 63*tan(1/2*d*x + 1/2*c)^2 + 56*tan(1/2*d*x + 1/2*c) + 11)/(a^3*(tan(1/2*d*x + 1/2*c) + 1)^7))/d","A",0
792,1,120,0,0.268581," ","integrate(sec(d*x+c)^2*sin(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{35}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}} - \frac{35 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 280 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 665 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1120 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 791 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 392 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 51}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{7}}}{280 \, d}"," ",0,"-1/280*(35/(a^3*(tan(1/2*d*x + 1/2*c) - 1)) - (35*tan(1/2*d*x + 1/2*c)^6 - 280*tan(1/2*d*x + 1/2*c)^5 - 665*tan(1/2*d*x + 1/2*c)^4 - 1120*tan(1/2*d*x + 1/2*c)^3 - 791*tan(1/2*d*x + 1/2*c)^2 - 392*tan(1/2*d*x + 1/2*c) - 51)/(a^3*(tan(1/2*d*x + 1/2*c) + 1)^7))/d","A",0
793,1,135,0,0.274071," ","integrate(csc(d*x+c)*sec(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{840 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} - \frac{105}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}} + \frac{5145 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 24360 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 54005 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 66080 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 47691 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 18872 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3431}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{7}}}{840 \, d}"," ",0,"1/840*(840*log(abs(tan(1/2*d*x + 1/2*c)))/a^3 - 105/(a^3*(tan(1/2*d*x + 1/2*c) - 1)) + (5145*tan(1/2*d*x + 1/2*c)^6 + 24360*tan(1/2*d*x + 1/2*c)^5 + 54005*tan(1/2*d*x + 1/2*c)^4 + 66080*tan(1/2*d*x + 1/2*c)^3 + 47691*tan(1/2*d*x + 1/2*c)^2 + 18872*tan(1/2*d*x + 1/2*c) + 3431)/(a^3*(tan(1/2*d*x + 1/2*c) + 1)^7))/d","A",0
794,1,187,0,0.220985," ","integrate(csc(d*x+c)^2*sec(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{840 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} - \frac{140 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3}} - \frac{35 \, {\left(12 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 17 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} a^{3}} + \frac{3885 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 19880 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 45465 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 57120 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 41671 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 16632 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2931}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{7}}}{280 \, d}"," ",0,"-1/280*(840*log(abs(tan(1/2*d*x + 1/2*c)))/a^3 - 140*tan(1/2*d*x + 1/2*c)/a^3 - 35*(12*tan(1/2*d*x + 1/2*c)^2 - 17*tan(1/2*d*x + 1/2*c) + 4)/((tan(1/2*d*x + 1/2*c)^2 - tan(1/2*d*x + 1/2*c))*a^3) + (3885*tan(1/2*d*x + 1/2*c)^6 + 19880*tan(1/2*d*x + 1/2*c)^5 + 45465*tan(1/2*d*x + 1/2*c)^4 + 57120*tan(1/2*d*x + 1/2*c)^3 + 41671*tan(1/2*d*x + 1/2*c)^2 + 16632*tan(1/2*d*x + 1/2*c) + 2931)/(a^3*(tan(1/2*d*x + 1/2*c) + 1)^7))/d","A",0
795,1,182,0,0.201450," ","integrate(sec(d*x+c)^4*sin(d*x+c)^6*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{15 \, {\left(d x + c\right)} a - \frac{3 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1} + \frac{33 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 102 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 200 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 330 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 402 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 410 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 264 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 150 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 61 \, a}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(15*(d*x + c)*a - 3*a/(tan(1/2*d*x + 1/2*c) + 1) + (33*a*tan(1/2*d*x + 1/2*c)^8 - 102*a*tan(1/2*d*x + 1/2*c)^7 + 200*a*tan(1/2*d*x + 1/2*c)^6 - 330*a*tan(1/2*d*x + 1/2*c)^5 + 402*a*tan(1/2*d*x + 1/2*c)^4 - 410*a*tan(1/2*d*x + 1/2*c)^3 + 264*a*tan(1/2*d*x + 1/2*c)^2 - 150*a*tan(1/2*d*x + 1/2*c) + 61*a)/(tan(1/2*d*x + 1/2*c)^3 - tan(1/2*d*x + 1/2*c)^2 + tan(1/2*d*x + 1/2*c) - 1)^3)/d","A",0
796,1,134,0,0.200756," ","integrate(sec(d*x+c)^4*sin(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{15 \, {\left(d x + c\right)} a + \frac{3 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1} + \frac{6 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, a\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}} + \frac{21 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 48 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 23 \, a}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(15*(d*x + c)*a + 3*a/(tan(1/2*d*x + 1/2*c) + 1) + 6*(a*tan(1/2*d*x + 1/2*c)^3 - 2*a*tan(1/2*d*x + 1/2*c)^2 - a*tan(1/2*d*x + 1/2*c) - 2*a)/(tan(1/2*d*x + 1/2*c)^2 + 1)^2 + (21*a*tan(1/2*d*x + 1/2*c)^2 - 48*a*tan(1/2*d*x + 1/2*c) + 23*a)/(tan(1/2*d*x + 1/2*c) - 1)^3)/d","A",0
797,1,124,0,0.194335," ","integrate(sec(d*x+c)^4*sin(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{6 \, {\left(d x + c\right)} a - \frac{3 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 4 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, a\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1} + \frac{15 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 36 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 17 \, a}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(6*(d*x + c)*a - 3*(a*tan(1/2*d*x + 1/2*c)^2 + 4*a*tan(1/2*d*x + 1/2*c) + 5*a)/(tan(1/2*d*x + 1/2*c)^3 + tan(1/2*d*x + 1/2*c)^2 + tan(1/2*d*x + 1/2*c) + 1) + (15*a*tan(1/2*d*x + 1/2*c)^2 - 36*a*tan(1/2*d*x + 1/2*c) + 17*a)/(tan(1/2*d*x + 1/2*c) - 1)^3)/d","A",0
798,1,74,0,0.182259," ","integrate(sec(d*x+c)^4*sin(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{6 \, {\left(d x + c\right)} a + \frac{3 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1} + \frac{9 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 24 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 11 \, a}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(6*(d*x + c)*a + 3*a/(tan(1/2*d*x + 1/2*c) + 1) + (9*a*tan(1/2*d*x + 1/2*c)^2 - 24*a*tan(1/2*d*x + 1/2*c) + 11*a)/(tan(1/2*d*x + 1/2*c) - 1)^3)/d","A",0
799,1,67,0,0.177691," ","integrate(sec(d*x+c)^4*sin(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{3 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1} - \frac{3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, a}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}}}{6 \, d}"," ",0,"-1/6*(3*a/(tan(1/2*d*x + 1/2*c) + 1) - (3*a*tan(1/2*d*x + 1/2*c)^2 - 12*a*tan(1/2*d*x + 1/2*c) + 5*a)/(tan(1/2*d*x + 1/2*c) - 1)^3)/d","A",0
800,1,53,0,0.168504," ","integrate(sec(d*x+c)^4*sin(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{3 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1} - \frac{3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*a/(tan(1/2*d*x + 1/2*c) + 1) - (3*a*tan(1/2*d*x + 1/2*c)^2 + a)/(tan(1/2*d*x + 1/2*c) - 1)^3)/d","A",0
801,1,81,0,0.204520," ","integrate(csc(d*x+c)*sec(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{6 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + \frac{3 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1} - \frac{15 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 24 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 13 \, a}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(6*a*log(abs(tan(1/2*d*x + 1/2*c))) + 3*a/(tan(1/2*d*x + 1/2*c) + 1) - (15*a*tan(1/2*d*x + 1/2*c)^2 - 24*a*tan(1/2*d*x + 1/2*c) + 13*a)/(tan(1/2*d*x + 1/2*c) - 1)^3)/d","A",0
802,1,129,0,0.210661," ","integrate(csc(d*x+c)^2*sec(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{6 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{3 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)} - \frac{21 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 36 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 19 \, a}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(6*a*log(abs(tan(1/2*d*x + 1/2*c))) + 3*a*tan(1/2*d*x + 1/2*c) - 3*(a*tan(1/2*d*x + 1/2*c)^2 + 3*a*tan(1/2*d*x + 1/2*c) + a)/(tan(1/2*d*x + 1/2*c)^2 + tan(1/2*d*x + 1/2*c)) - (21*a*tan(1/2*d*x + 1/2*c)^2 - 36*a*tan(1/2*d*x + 1/2*c) + 19*a)/(tan(1/2*d*x + 1/2*c) - 1)^3)/d","A",0
803,1,148,0,0.225286," ","integrate(csc(d*x+c)^3*sec(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 60 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 12 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{12 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1} - \frac{3 \, {\left(30 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 4 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}} - \frac{4 \, {\left(27 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 48 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 25 \, a\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}}}{24 \, d}"," ",0,"1/24*(3*a*tan(1/2*d*x + 1/2*c)^2 + 60*a*log(abs(tan(1/2*d*x + 1/2*c))) + 12*a*tan(1/2*d*x + 1/2*c) + 12*a/(tan(1/2*d*x + 1/2*c) + 1) - 3*(30*a*tan(1/2*d*x + 1/2*c)^2 + 4*a*tan(1/2*d*x + 1/2*c) + a)/tan(1/2*d*x + 1/2*c)^2 - 4*(27*a*tan(1/2*d*x + 1/2*c)^2 - 48*a*tan(1/2*d*x + 1/2*c) + 25*a)/(tan(1/2*d*x + 1/2*c) - 1)^3)/d","A",0
804,1,135,0,0.209844," ","integrate(sec(d*x+c)^4*sin(d*x+c)^4*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{21 \, {\left(d x + c\right)} a^{2} + \frac{6 \, {\left(a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, a^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}} + \frac{4 \, {\left(9 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 21 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 10 \, a^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(21*(d*x + c)*a^2 + 6*(a^2*tan(1/2*d*x + 1/2*c)^3 - 4*a^2*tan(1/2*d*x + 1/2*c)^2 - a^2*tan(1/2*d*x + 1/2*c) - 4*a^2)/(tan(1/2*d*x + 1/2*c)^2 + 1)^2 + 4*(9*a^2*tan(1/2*d*x + 1/2*c)^2 - 21*a^2*tan(1/2*d*x + 1/2*c) + 10*a^2)/(tan(1/2*d*x + 1/2*c) - 1)^3)/d","A",0
805,1,86,0,0.214999," ","integrate(sec(d*x+c)^4*sin(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{2 \, {\left(3 \, {\left(d x + c\right)} a^{2} - \frac{3 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + \frac{6 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 7 \, a^{2}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}}\right)}}{3 \, d}"," ",0,"2/3*(3*(d*x + c)*a^2 - 3*a^2/(tan(1/2*d*x + 1/2*c)^2 + 1) + (6*a^2*tan(1/2*d*x + 1/2*c)^2 - 15*a^2*tan(1/2*d*x + 1/2*c) + 7*a^2)/(tan(1/2*d*x + 1/2*c) - 1)^3)/d","A",0
806,1,67,0,0.205034," ","integrate(sec(d*x+c)^4*sin(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{3 \, {\left(d x + c\right)} a^{2} + \frac{2 \, {\left(3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, a^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*(d*x + c)*a^2 + 2*(3*a^2*tan(1/2*d*x + 1/2*c)^2 - 9*a^2*tan(1/2*d*x + 1/2*c) + 4*a^2)/(tan(1/2*d*x + 1/2*c) - 1)^3)/d","A",0
807,1,38,0,0.196601," ","integrate(sec(d*x+c)^4*sin(d*x+c)*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{2 \, {\left(3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{2}\right)}}{3 \, d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}}"," ",0,"-2/3*(3*a^2*tan(1/2*d*x + 1/2*c) - a^2)/(d*(tan(1/2*d*x + 1/2*c) - 1)^3)","A",0
808,1,73,0,0.198706," ","integrate(csc(d*x+c)*sec(d*x+c)^4*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{3 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{2 \, {\left(6 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, a^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*a^2*log(abs(tan(1/2*d*x + 1/2*c))) - 2*(6*a^2*tan(1/2*d*x + 1/2*c)^2 - 9*a^2*tan(1/2*d*x + 1/2*c) + 5*a^2)/(tan(1/2*d*x + 1/2*c) - 1)^3)/d","A",0
809,1,118,0,0.223736," ","integrate(csc(d*x+c)^2*sec(d*x+c)^4*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{12 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{3 \, {\left(4 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)} - \frac{4 \, {\left(9 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8 \, a^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(12*a^2*log(abs(tan(1/2*d*x + 1/2*c))) + 3*a^2*tan(1/2*d*x + 1/2*c) - 3*(4*a^2*tan(1/2*d*x + 1/2*c) + a^2)/tan(1/2*d*x + 1/2*c) - 4*(9*a^2*tan(1/2*d*x + 1/2*c)^2 - 15*a^2*tan(1/2*d*x + 1/2*c) + 8*a^2)/(tan(1/2*d*x + 1/2*c) - 1)^3)/d","A",0
810,1,150,0,0.247497," ","integrate(csc(d*x+c)^3*sec(d*x+c)^4*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 84 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 24 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{3 \, {\left(42 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 8 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}} - \frac{16 \, {\left(12 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 21 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 11 \, a^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}}}{24 \, d}"," ",0,"1/24*(3*a^2*tan(1/2*d*x + 1/2*c)^2 + 84*a^2*log(abs(tan(1/2*d*x + 1/2*c))) + 24*a^2*tan(1/2*d*x + 1/2*c) - 3*(42*a^2*tan(1/2*d*x + 1/2*c)^2 + 8*a^2*tan(1/2*d*x + 1/2*c) + a^2)/tan(1/2*d*x + 1/2*c)^2 - 16*(12*a^2*tan(1/2*d*x + 1/2*c)^2 - 21*a^2*tan(1/2*d*x + 1/2*c) + 11*a^2)/(tan(1/2*d*x + 1/2*c) - 1)^3)/d","A",0
811,1,187,0,0.258824," ","integrate(sec(d*x+c)^4*sin(d*x+c)^4*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{51 \, {\left(d x + c\right)} a^{3} + \frac{2 \, {\left(51 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 153 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 289 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 459 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 501 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 511 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 327 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 189 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 80 \, a^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(51*(d*x + c)*a^3 + 2*(51*a^3*tan(1/2*d*x + 1/2*c)^8 - 153*a^3*tan(1/2*d*x + 1/2*c)^7 + 289*a^3*tan(1/2*d*x + 1/2*c)^6 - 459*a^3*tan(1/2*d*x + 1/2*c)^5 + 501*a^3*tan(1/2*d*x + 1/2*c)^4 - 511*a^3*tan(1/2*d*x + 1/2*c)^3 + 327*a^3*tan(1/2*d*x + 1/2*c)^2 - 189*a^3*tan(1/2*d*x + 1/2*c) + 80*a^3)/(tan(1/2*d*x + 1/2*c)^3 - tan(1/2*d*x + 1/2*c)^2 + tan(1/2*d*x + 1/2*c) - 1)^3)/d","A",0
812,1,135,0,0.261758," ","integrate(sec(d*x+c)^4*sin(d*x+c)^3*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{33 \, {\left(d x + c\right)} a^{3} + \frac{6 \, {\left(a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, a^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}} + \frac{4 \, {\left(15 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 36 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 17 \, a^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(33*(d*x + c)*a^3 + 6*(a^3*tan(1/2*d*x + 1/2*c)^3 - 6*a^3*tan(1/2*d*x + 1/2*c)^2 - a^3*tan(1/2*d*x + 1/2*c) - 6*a^3)/(tan(1/2*d*x + 1/2*c)^2 + 1)^2 + 4*(15*a^3*tan(1/2*d*x + 1/2*c)^2 - 36*a^3*tan(1/2*d*x + 1/2*c) + 17*a^3)/(tan(1/2*d*x + 1/2*c) - 1)^3)/d","A",0
813,1,87,0,0.231980," ","integrate(sec(d*x+c)^4*sin(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{9 \, {\left(d x + c\right)} a^{3} - \frac{6 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + \frac{2 \, {\left(9 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 24 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 11 \, a^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}}}{3 \, d}"," ",0,"1/3*(9*(d*x + c)*a^3 - 6*a^3/(tan(1/2*d*x + 1/2*c)^2 + 1) + 2*(9*a^3*tan(1/2*d*x + 1/2*c)^2 - 24*a^3*tan(1/2*d*x + 1/2*c) + 11*a^3)/(tan(1/2*d*x + 1/2*c) - 1)^3)/d","A",0
814,1,67,0,0.201071," ","integrate(sec(d*x+c)^4*sin(d*x+c)*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{3 \, {\left(d x + c\right)} a^{3} + \frac{2 \, {\left(3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, a^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*(d*x + c)*a^3 + 2*(3*a^3*tan(1/2*d*x + 1/2*c)^2 - 12*a^3*tan(1/2*d*x + 1/2*c) + 5*a^3)/(tan(1/2*d*x + 1/2*c) - 1)^3)/d","A",0
815,1,73,0,0.248711," ","integrate(csc(d*x+c)*sec(d*x+c)^4*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{3 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{2 \, {\left(9 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 7 \, a^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*a^3*log(abs(tan(1/2*d*x + 1/2*c))) - 2*(9*a^3*tan(1/2*d*x + 1/2*c)^2 - 12*a^3*tan(1/2*d*x + 1/2*c) + 7*a^3)/(tan(1/2*d*x + 1/2*c) - 1)^3)/d","A",0
816,1,118,0,0.250460," ","integrate(csc(d*x+c)^2*sec(d*x+c)^4*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{18 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{3 \, {\left(6 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)} - \frac{4 \, {\left(15 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 24 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 13 \, a^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(18*a^3*log(abs(tan(1/2*d*x + 1/2*c))) + 3*a^3*tan(1/2*d*x + 1/2*c) - 3*(6*a^3*tan(1/2*d*x + 1/2*c) + a^3)/tan(1/2*d*x + 1/2*c) - 4*(15*a^3*tan(1/2*d*x + 1/2*c)^2 - 24*a^3*tan(1/2*d*x + 1/2*c) + 13*a^3)/(tan(1/2*d*x + 1/2*c) - 1)^3)/d","A",0
817,1,150,0,0.272931," ","integrate(csc(d*x+c)^3*sec(d*x+c)^4*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 132 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 36 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{3 \, {\left(66 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}} - \frac{16 \, {\left(21 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 36 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 19 \, a^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}}}{24 \, d}"," ",0,"1/24*(3*a^3*tan(1/2*d*x + 1/2*c)^2 + 132*a^3*log(abs(tan(1/2*d*x + 1/2*c))) + 36*a^3*tan(1/2*d*x + 1/2*c) - 3*(66*a^3*tan(1/2*d*x + 1/2*c)^2 + 12*a^3*tan(1/2*d*x + 1/2*c) + a^3)/tan(1/2*d*x + 1/2*c)^2 - 16*(21*a^3*tan(1/2*d*x + 1/2*c)^2 - 36*a^3*tan(1/2*d*x + 1/2*c) + 19*a^3)/(tan(1/2*d*x + 1/2*c) - 1)^3)/d","A",0
818,1,194,0,0.307033," ","integrate(csc(d*x+c)^4*sec(d*x+c)^4*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 204 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 69 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{187 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 60 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 405 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 394 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 45 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 6 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{3}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}^{3}}}{24 \, d}"," ",0,"1/24*(a^3*tan(1/2*d*x + 1/2*c)^3 + 9*a^3*tan(1/2*d*x + 1/2*c)^2 + 204*a^3*log(abs(tan(1/2*d*x + 1/2*c))) + 69*a^3*tan(1/2*d*x + 1/2*c) - (187*a^3*tan(1/2*d*x + 1/2*c)^6 - 60*a^3*tan(1/2*d*x + 1/2*c)^5 - 405*a^3*tan(1/2*d*x + 1/2*c)^4 + 394*a^3*tan(1/2*d*x + 1/2*c)^3 - 45*a^3*tan(1/2*d*x + 1/2*c)^2 - 6*a^3*tan(1/2*d*x + 1/2*c) - a^3)/(tan(1/2*d*x + 1/2*c)^2 - tan(1/2*d*x + 1/2*c))^3)/d","A",0
819,1,200,0,0.272036," ","integrate(sec(d*x+c)^4*sin(d*x+c)^4*(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{489 \, {\left(d x + c\right)} a^{4} + \frac{64 \, {\left(12 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 27 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 13 \, a^{4}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}} + \frac{2 \, {\left(105 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 288 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 129 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1056 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 129 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1120 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 105 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 352 \, a^{4}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(489*(d*x + c)*a^4 + 64*(12*a^4*tan(1/2*d*x + 1/2*c)^2 - 27*a^4*tan(1/2*d*x + 1/2*c) + 13*a^4)/(tan(1/2*d*x + 1/2*c) - 1)^3 + 2*(105*a^4*tan(1/2*d*x + 1/2*c)^7 - 288*a^4*tan(1/2*d*x + 1/2*c)^6 + 129*a^4*tan(1/2*d*x + 1/2*c)^5 - 1056*a^4*tan(1/2*d*x + 1/2*c)^4 - 129*a^4*tan(1/2*d*x + 1/2*c)^3 - 1120*a^4*tan(1/2*d*x + 1/2*c)^2 - 105*a^4*tan(1/2*d*x + 1/2*c) - 352*a^4)/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","A",0
820,1,135,0,0.240271," ","integrate(sec(d*x+c)^4*sin(d*x+c)^2*(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{51 \, {\left(d x + c\right)} a^{4} + \frac{6 \, {\left(a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 8 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, a^{4}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}} + \frac{16 \, {\left(6 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 7 \, a^{4}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(51*(d*x + c)*a^4 + 6*(a^4*tan(1/2*d*x + 1/2*c)^3 - 8*a^4*tan(1/2*d*x + 1/2*c)^2 - a^4*tan(1/2*d*x + 1/2*c) - 8*a^4)/(tan(1/2*d*x + 1/2*c)^2 + 1)^2 + 16*(6*a^4*tan(1/2*d*x + 1/2*c)^2 - 15*a^4*tan(1/2*d*x + 1/2*c) + 7*a^4)/(tan(1/2*d*x + 1/2*c) - 1)^3)/d","A",0
821,1,149,0,0.249982," ","integrate(sec(d*x+c)^4*sin(d*x+c)^6/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{120 \, {\left(d x + c\right)}}{a} + \frac{240}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a} - \frac{5 \, {\left(21 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 48 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 23\right)}}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}} + \frac{345 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 1560 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2570 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1720 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 413}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{5}}}{120 \, d}"," ",0,"-1/120*(120*(d*x + c)/a + 240/((tan(1/2*d*x + 1/2*c)^2 + 1)*a) - 5*(21*tan(1/2*d*x + 1/2*c)^2 - 48*tan(1/2*d*x + 1/2*c) + 23)/(a*(tan(1/2*d*x + 1/2*c) - 1)^3) + (345*tan(1/2*d*x + 1/2*c)^4 + 1560*tan(1/2*d*x + 1/2*c)^3 + 2570*tan(1/2*d*x + 1/2*c)^2 + 1720*tan(1/2*d*x + 1/2*c) + 413)/(a*(tan(1/2*d*x + 1/2*c) + 1)^5))/d","A",0
822,1,130,0,0.232275," ","integrate(sec(d*x+c)^4*sin(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{120 \, {\left(d x + c\right)}}{a} + \frac{5 \, {\left(15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 36 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 17\right)}}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}} + \frac{3 \, {\left(55 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 260 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 450 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 300 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 71\right)}}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(120*(d*x + c)/a + 5*(15*tan(1/2*d*x + 1/2*c)^2 - 36*tan(1/2*d*x + 1/2*c) + 17)/(a*(tan(1/2*d*x + 1/2*c) - 1)^3) + 3*(55*tan(1/2*d*x + 1/2*c)^4 + 260*tan(1/2*d*x + 1/2*c)^3 + 450*tan(1/2*d*x + 1/2*c)^2 + 300*tan(1/2*d*x + 1/2*c) + 71)/(a*(tan(1/2*d*x + 1/2*c) + 1)^5))/d","A",0
823,1,120,0,0.236106," ","integrate(sec(d*x+c)^4*sin(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{5 \, {\left(9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 24 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 11\right)}}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}} - \frac{45 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 240 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 490 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 320 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 73}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(5*(9*tan(1/2*d*x + 1/2*c)^2 - 24*tan(1/2*d*x + 1/2*c) + 11)/(a*(tan(1/2*d*x + 1/2*c) - 1)^3) - (45*tan(1/2*d*x + 1/2*c)^4 + 240*tan(1/2*d*x + 1/2*c)^3 + 490*tan(1/2*d*x + 1/2*c)^2 + 320*tan(1/2*d*x + 1/2*c) + 73)/(a*(tan(1/2*d*x + 1/2*c) + 1)^5))/d","A",0
824,1,120,0,0.212868," ","integrate(sec(d*x+c)^4*sin(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{5 \, {\left(3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5\right)}}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}} - \frac{15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 60 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 10 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 20 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 7}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(5*(3*tan(1/2*d*x + 1/2*c)^2 - 12*tan(1/2*d*x + 1/2*c) + 5)/(a*(tan(1/2*d*x + 1/2*c) - 1)^3) - (15*tan(1/2*d*x + 1/2*c)^4 + 60*tan(1/2*d*x + 1/2*c)^3 + 10*tan(1/2*d*x + 1/2*c)^2 + 20*tan(1/2*d*x + 1/2*c) + 7)/(a*(tan(1/2*d*x + 1/2*c) + 1)^5))/d","B",0
825,1,109,0,0.232888," ","integrate(sec(d*x+c)^4*sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{5 \, {\left(3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}} - \frac{3 \, {\left(5 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 40 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 50 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 40 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9\right)}}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{5}}}{120 \, d}"," ",0,"-1/120*(5*(3*tan(1/2*d*x + 1/2*c)^2 + 1)/(a*(tan(1/2*d*x + 1/2*c) - 1)^3) - 3*(5*tan(1/2*d*x + 1/2*c)^4 + 40*tan(1/2*d*x + 1/2*c)^3 + 50*tan(1/2*d*x + 1/2*c)^2 + 40*tan(1/2*d*x + 1/2*c) + 9)/(a*(tan(1/2*d*x + 1/2*c) + 1)^5))/d","A",0
826,1,120,0,0.243673," ","integrate(sec(d*x+c)^4*sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{5 \, {\left(9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 7\right)}}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}} - \frac{45 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 60 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 70 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 20 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 13}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{5}}}{120 \, d}"," ",0,"-1/120*(5*(9*tan(1/2*d*x + 1/2*c)^2 - 12*tan(1/2*d*x + 1/2*c) + 7)/(a*(tan(1/2*d*x + 1/2*c) - 1)^3) - (45*tan(1/2*d*x + 1/2*c)^4 + 60*tan(1/2*d*x + 1/2*c)^3 + 70*tan(1/2*d*x + 1/2*c)^2 + 20*tan(1/2*d*x + 1/2*c) + 13)/(a*(tan(1/2*d*x + 1/2*c) + 1)^5))/d","B",0
827,1,136,0,0.207395," ","integrate(csc(d*x+c)*sec(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{120 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a} - \frac{5 \, {\left(21 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 36 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 19\right)}}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}} + \frac{3 \, {\left(115 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 380 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 530 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 340 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 91\right)}}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(120*log(abs(tan(1/2*d*x + 1/2*c)))/a - 5*(21*tan(1/2*d*x + 1/2*c)^2 - 36*tan(1/2*d*x + 1/2*c) + 19)/(a*(tan(1/2*d*x + 1/2*c) - 1)^3) + 3*(115*tan(1/2*d*x + 1/2*c)^4 + 380*tan(1/2*d*x + 1/2*c)^3 + 530*tan(1/2*d*x + 1/2*c)^2 + 340*tan(1/2*d*x + 1/2*c) + 91)/(a*(tan(1/2*d*x + 1/2*c) + 1)^5))/d","A",0
828,1,178,0,0.220666," ","integrate(csc(d*x+c)^2*sec(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{120 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a} - \frac{60 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a} - \frac{60 \, {\left(2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}}{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)} + \frac{5 \, {\left(27 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 48 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 25\right)}}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}} + \frac{585 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2040 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2890 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1880 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 493}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{5}}}{120 \, d}"," ",0,"-1/120*(120*log(abs(tan(1/2*d*x + 1/2*c)))/a - 60*tan(1/2*d*x + 1/2*c)/a - 60*(2*tan(1/2*d*x + 1/2*c) - 1)/(a*tan(1/2*d*x + 1/2*c)) + 5*(27*tan(1/2*d*x + 1/2*c)^2 - 48*tan(1/2*d*x + 1/2*c) + 25)/(a*(tan(1/2*d*x + 1/2*c) - 1)^3) + (585*tan(1/2*d*x + 1/2*c)^4 + 2040*tan(1/2*d*x + 1/2*c)^3 + 2890*tan(1/2*d*x + 1/2*c)^2 + 1880*tan(1/2*d*x + 1/2*c) + 493)/(a*(tan(1/2*d*x + 1/2*c) + 1)^5))/d","A",0
829,1,175,0,0.303517," ","integrate(sec(d*x+c)^4*sin(d*x+c)^7/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{1680 \, {\left(d x + c\right)}}{a^{2}} + \frac{1680}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} a^{2}} - \frac{35 \, {\left(12 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 27 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 13\right)}}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}} + \frac{3780 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 25095 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 68845 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 98350 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 75222 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 29659 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4777}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{7}}}{840 \, d}"," ",0,"-1/840*(1680*(d*x + c)/a^2 + 1680/((tan(1/2*d*x + 1/2*c)^2 + 1)*a^2) - 35*(12*tan(1/2*d*x + 1/2*c)^2 - 27*tan(1/2*d*x + 1/2*c) + 13)/(a^2*(tan(1/2*d*x + 1/2*c) - 1)^3) + (3780*tan(1/2*d*x + 1/2*c)^6 + 25095*tan(1/2*d*x + 1/2*c)^5 + 68845*tan(1/2*d*x + 1/2*c)^4 + 98350*tan(1/2*d*x + 1/2*c)^3 + 75222*tan(1/2*d*x + 1/2*c)^2 + 29659*tan(1/2*d*x + 1/2*c) + 4777)/(a^2*(tan(1/2*d*x + 1/2*c) + 1)^7))/d","A",0
830,1,155,0,0.289160," ","integrate(sec(d*x+c)^4*sin(d*x+c)^6/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{840 \, {\left(d x + c\right)}}{a^{2}} + \frac{35 \, {\left(9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 21 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 10\right)}}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}} + \frac{1365 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 9345 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 26600 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 39410 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30261 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 11837 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1886}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{7}}}{840 \, d}"," ",0,"1/840*(840*(d*x + c)/a^2 + 35*(9*tan(1/2*d*x + 1/2*c)^2 - 21*tan(1/2*d*x + 1/2*c) + 10)/(a^2*(tan(1/2*d*x + 1/2*c) - 1)^3) + (1365*tan(1/2*d*x + 1/2*c)^6 + 9345*tan(1/2*d*x + 1/2*c)^5 + 26600*tan(1/2*d*x + 1/2*c)^4 + 39410*tan(1/2*d*x + 1/2*c)^3 + 30261*tan(1/2*d*x + 1/2*c)^2 + 11837*tan(1/2*d*x + 1/2*c) + 1886)/(a^2*(tan(1/2*d*x + 1/2*c) + 1)^7))/d","A",0
831,1,146,0,0.295357," ","integrate(sec(d*x+c)^4*sin(d*x+c)^5/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{7 \, {\left(6 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 7\right)}}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}} - \frac{42 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 315 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1015 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 1750 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1344 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 511 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 79}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{7}}}{168 \, d}"," ",0,"1/168*(7*(6*tan(1/2*d*x + 1/2*c)^2 - 15*tan(1/2*d*x + 1/2*c) + 7)/(a^2*(tan(1/2*d*x + 1/2*c) - 1)^3) - (42*tan(1/2*d*x + 1/2*c)^6 + 315*tan(1/2*d*x + 1/2*c)^5 + 1015*tan(1/2*d*x + 1/2*c)^4 + 1750*tan(1/2*d*x + 1/2*c)^3 + 1344*tan(1/2*d*x + 1/2*c)^2 + 511*tan(1/2*d*x + 1/2*c) + 79)/(a^2*(tan(1/2*d*x + 1/2*c) + 1)^7))/d","A",0
832,1,146,0,0.272697," ","integrate(sec(d*x+c)^4*sin(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{35 \, {\left(3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4\right)}}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}} - \frac{105 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 735 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2030 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2030 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1701 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 707 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 116}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{7}}}{840 \, d}"," ",0,"1/840*(35*(3*tan(1/2*d*x + 1/2*c)^2 - 9*tan(1/2*d*x + 1/2*c) + 4)/(a^2*(tan(1/2*d*x + 1/2*c) - 1)^3) - (105*tan(1/2*d*x + 1/2*c)^6 + 735*tan(1/2*d*x + 1/2*c)^5 + 2030*tan(1/2*d*x + 1/2*c)^4 + 2030*tan(1/2*d*x + 1/2*c)^3 + 1701*tan(1/2*d*x + 1/2*c)^2 + 707*tan(1/2*d*x + 1/2*c) + 116)/(a^2*(tan(1/2*d*x + 1/2*c) + 1)^7))/d","A",0
833,1,120,0,0.275959," ","integrate(sec(d*x+c)^4*sin(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{35 \, {\left(3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}} - \frac{105 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1015 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 1330 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1302 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 469 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 67}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{7}}}{840 \, d}"," ",0,"-1/840*(35*(3*tan(1/2*d*x + 1/2*c) - 1)/(a^2*(tan(1/2*d*x + 1/2*c) - 1)^3) - (105*tan(1/2*d*x + 1/2*c)^5 + 1015*tan(1/2*d*x + 1/2*c)^4 + 1330*tan(1/2*d*x + 1/2*c)^3 + 1302*tan(1/2*d*x + 1/2*c)^2 + 469*tan(1/2*d*x + 1/2*c) + 67)/(a^2*(tan(1/2*d*x + 1/2*c) + 1)^7))/d","A",0
834,1,146,0,0.262817," ","integrate(sec(d*x+c)^4*sin(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{35 \, {\left(3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)}}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}} - \frac{105 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 945 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1820 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2450 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1617 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 749 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 122}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{7}}}{840 \, d}"," ",0,"-1/840*(35*(3*tan(1/2*d*x + 1/2*c)^2 - 3*tan(1/2*d*x + 1/2*c) + 2)/(a^2*(tan(1/2*d*x + 1/2*c) - 1)^3) - (105*tan(1/2*d*x + 1/2*c)^6 + 945*tan(1/2*d*x + 1/2*c)^5 + 1820*tan(1/2*d*x + 1/2*c)^4 + 2450*tan(1/2*d*x + 1/2*c)^3 + 1617*tan(1/2*d*x + 1/2*c)^2 + 749*tan(1/2*d*x + 1/2*c) + 122)/(a^2*(tan(1/2*d*x + 1/2*c) + 1)^7))/d","A",0
835,1,146,0,0.263470," ","integrate(sec(d*x+c)^4*sin(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{35 \, {\left(6 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5\right)}}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}} - \frac{210 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 105 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 175 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 910 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 756 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 427 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 31}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{7}}}{840 \, d}"," ",0,"-1/840*(35*(6*tan(1/2*d*x + 1/2*c)^2 - 9*tan(1/2*d*x + 1/2*c) + 5)/(a^2*(tan(1/2*d*x + 1/2*c) - 1)^3) - (210*tan(1/2*d*x + 1/2*c)^6 + 105*tan(1/2*d*x + 1/2*c)^5 - 175*tan(1/2*d*x + 1/2*c)^4 - 910*tan(1/2*d*x + 1/2*c)^3 - 756*tan(1/2*d*x + 1/2*c)^2 - 427*tan(1/2*d*x + 1/2*c) - 31)/(a^2*(tan(1/2*d*x + 1/2*c) + 1)^7))/d","A",0
836,1,161,0,0.215888," ","integrate(csc(d*x+c)*sec(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{840 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} - \frac{35 \, {\left(12 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 21 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 11\right)}}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}} + \frac{3780 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 18585 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 41755 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 51730 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 37506 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 14917 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2671}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{7}}}{840 \, d}"," ",0,"1/840*(840*log(abs(tan(1/2*d*x + 1/2*c)))/a^2 - 35*(12*tan(1/2*d*x + 1/2*c)^2 - 21*tan(1/2*d*x + 1/2*c) + 11)/(a^2*(tan(1/2*d*x + 1/2*c) - 1)^3) + (3780*tan(1/2*d*x + 1/2*c)^6 + 18585*tan(1/2*d*x + 1/2*c)^5 + 41755*tan(1/2*d*x + 1/2*c)^4 + 51730*tan(1/2*d*x + 1/2*c)^3 + 37506*tan(1/2*d*x + 1/2*c)^2 + 14917*tan(1/2*d*x + 1/2*c) + 2671)/(a^2*(tan(1/2*d*x + 1/2*c) + 1)^7))/d","A",0
837,1,204,0,0.245793," ","integrate(csc(d*x+c)^2*sec(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{1680 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} - \frac{420 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{2}} - \frac{420 \, {\left(4 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}}{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)} + \frac{35 \, {\left(15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 27 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 14\right)}}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}} + \frac{7875 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 41055 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 94640 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 119630 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 87507 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 34979 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6122}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{7}}}{840 \, d}"," ",0,"-1/840*(1680*log(abs(tan(1/2*d*x + 1/2*c)))/a^2 - 420*tan(1/2*d*x + 1/2*c)/a^2 - 420*(4*tan(1/2*d*x + 1/2*c) - 1)/(a^2*tan(1/2*d*x + 1/2*c)) + 35*(15*tan(1/2*d*x + 1/2*c)^2 - 27*tan(1/2*d*x + 1/2*c) + 14)/(a^2*(tan(1/2*d*x + 1/2*c) - 1)^3) + (7875*tan(1/2*d*x + 1/2*c)^6 + 41055*tan(1/2*d*x + 1/2*c)^5 + 94640*tan(1/2*d*x + 1/2*c)^4 + 119630*tan(1/2*d*x + 1/2*c)^3 + 87507*tan(1/2*d*x + 1/2*c)^2 + 34979*tan(1/2*d*x + 1/2*c) + 6122)/(a^2*(tan(1/2*d*x + 1/2*c) + 1)^7))/d","A",0
838,1,238,0,0.265809," ","integrate(csc(d*x+c)^3*sec(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{4620 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} + \frac{105 \, {\left(a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a^{4}} - \frac{105 \, {\left(66 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}} - \frac{35 \, {\left(18 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 33 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 17\right)}}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}} + \frac{14070 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 75705 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 177205 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 226450 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 166488 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 66661 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 11533}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{7}}}{840 \, d}"," ",0,"1/840*(4620*log(abs(tan(1/2*d*x + 1/2*c)))/a^2 + 105*(a^2*tan(1/2*d*x + 1/2*c)^2 - 8*a^2*tan(1/2*d*x + 1/2*c))/a^4 - 105*(66*tan(1/2*d*x + 1/2*c)^2 - 8*tan(1/2*d*x + 1/2*c) + 1)/(a^2*tan(1/2*d*x + 1/2*c)^2) - 35*(18*tan(1/2*d*x + 1/2*c)^2 - 33*tan(1/2*d*x + 1/2*c) + 17)/(a^2*(tan(1/2*d*x + 1/2*c) - 1)^3) + (14070*tan(1/2*d*x + 1/2*c)^6 + 75705*tan(1/2*d*x + 1/2*c)^5 + 177205*tan(1/2*d*x + 1/2*c)^4 + 226450*tan(1/2*d*x + 1/2*c)^3 + 166488*tan(1/2*d*x + 1/2*c)^2 + 66661*tan(1/2*d*x + 1/2*c) + 11533)/(a^2*(tan(1/2*d*x + 1/2*c) + 1)^7))/d","A",0
839,1,181,0,0.405864," ","integrate(sec(d*x+c)^4*sin(d*x+c)^7/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{10080 \, {\left(d x + c\right)}}{a^{3}} + \frac{105 \, {\left(21 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 48 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 23\right)}}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}} + \frac{17955 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 160020 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 624960 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 1387260 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1884582 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 1556268 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 774792 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 215748 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 25967}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{9}}}{10080 \, d}"," ",0,"1/10080*(10080*(d*x + c)/a^3 + 105*(21*tan(1/2*d*x + 1/2*c)^2 - 48*tan(1/2*d*x + 1/2*c) + 23)/(a^3*(tan(1/2*d*x + 1/2*c) - 1)^3) + (17955*tan(1/2*d*x + 1/2*c)^8 + 160020*tan(1/2*d*x + 1/2*c)^7 + 624960*tan(1/2*d*x + 1/2*c)^6 + 1387260*tan(1/2*d*x + 1/2*c)^5 + 1884582*tan(1/2*d*x + 1/2*c)^4 + 1556268*tan(1/2*d*x + 1/2*c)^3 + 774792*tan(1/2*d*x + 1/2*c)^2 + 215748*tan(1/2*d*x + 1/2*c) + 25967)/(a^3*(tan(1/2*d*x + 1/2*c) + 1)^9))/d","A",0
840,1,172,0,0.388322," ","integrate(sec(d*x+c)^4*sin(d*x+c)^6/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{21 \, {\left(15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 36 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 17\right)}}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}} - \frac{315 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 3024 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 13020 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 32760 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 51282 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 43008 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 20988 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 5688 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 667}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{9}}}{2016 \, d}"," ",0,"1/2016*(21*(15*tan(1/2*d*x + 1/2*c)^2 - 36*tan(1/2*d*x + 1/2*c) + 17)/(a^3*(tan(1/2*d*x + 1/2*c) - 1)^3) - (315*tan(1/2*d*x + 1/2*c)^8 + 3024*tan(1/2*d*x + 1/2*c)^7 + 13020*tan(1/2*d*x + 1/2*c)^6 + 32760*tan(1/2*d*x + 1/2*c)^5 + 51282*tan(1/2*d*x + 1/2*c)^4 + 43008*tan(1/2*d*x + 1/2*c)^3 + 20988*tan(1/2*d*x + 1/2*c)^2 + 5688*tan(1/2*d*x + 1/2*c) + 667)/(a^3*(tan(1/2*d*x + 1/2*c) + 1)^9))/d","A",0
841,1,172,0,0.387448," ","integrate(sec(d*x+c)^4*sin(d*x+c)^5/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{21 \, {\left(9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 24 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 11\right)}}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}} - \frac{189 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 1764 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 7224 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 16380 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 19026 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 16380 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8352 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2340 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 281}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{9}}}{2016 \, d}"," ",0,"1/2016*(21*(9*tan(1/2*d*x + 1/2*c)^2 - 24*tan(1/2*d*x + 1/2*c) + 11)/(a^3*(tan(1/2*d*x + 1/2*c) - 1)^3) - (189*tan(1/2*d*x + 1/2*c)^8 + 1764*tan(1/2*d*x + 1/2*c)^7 + 7224*tan(1/2*d*x + 1/2*c)^6 + 16380*tan(1/2*d*x + 1/2*c)^5 + 19026*tan(1/2*d*x + 1/2*c)^4 + 16380*tan(1/2*d*x + 1/2*c)^3 + 8352*tan(1/2*d*x + 1/2*c)^2 + 2340*tan(1/2*d*x + 1/2*c) + 281)/(a^3*(tan(1/2*d*x + 1/2*c) + 1)^9))/d","A",0
842,1,159,0,0.351994," ","integrate(sec(d*x+c)^4*sin(d*x+c)^4/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{105 \, {\left(3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5\right)}}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}} - \frac{315 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 2520 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 7140 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 1638 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 8232 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2988 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 432 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 13}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{9}}}{10080 \, d}"," ",0,"1/10080*(105*(3*tan(1/2*d*x + 1/2*c)^2 - 12*tan(1/2*d*x + 1/2*c) + 5)/(a^3*(tan(1/2*d*x + 1/2*c) - 1)^3) - (315*tan(1/2*d*x + 1/2*c)^8 + 2520*tan(1/2*d*x + 1/2*c)^7 + 7140*tan(1/2*d*x + 1/2*c)^6 - 1638*tan(1/2*d*x + 1/2*c)^4 - 8232*tan(1/2*d*x + 1/2*c)^3 - 2988*tan(1/2*d*x + 1/2*c)^2 - 432*tan(1/2*d*x + 1/2*c) - 13)/(a^3*(tan(1/2*d*x + 1/2*c) + 1)^9))/d","A",0
843,1,161,0,0.349257," ","integrate(sec(d*x+c)^4*sin(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{15 \, {\left(3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}} - \frac{45 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 540 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 3120 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 5940 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 8298 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 6372 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3528 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 972 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 113}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{9}}}{1440 \, d}"," ",0,"-1/1440*(15*(3*tan(1/2*d*x + 1/2*c)^2 + 1)/(a^3*(tan(1/2*d*x + 1/2*c) - 1)^3) - (45*tan(1/2*d*x + 1/2*c)^8 + 540*tan(1/2*d*x + 1/2*c)^7 + 3120*tan(1/2*d*x + 1/2*c)^6 + 5940*tan(1/2*d*x + 1/2*c)^5 + 8298*tan(1/2*d*x + 1/2*c)^4 + 6372*tan(1/2*d*x + 1/2*c)^3 + 3528*tan(1/2*d*x + 1/2*c)^2 + 972*tan(1/2*d*x + 1/2*c) + 113)/(a^3*(tan(1/2*d*x + 1/2*c) + 1)^9))/d","A",0
844,1,172,0,0.335435," ","integrate(sec(d*x+c)^4*sin(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{105 \, {\left(9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 7\right)}}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}} - \frac{945 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 10080 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 23940 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 42840 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 41958 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 32592 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 14148 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 5112 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 673}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{9}}}{10080 \, d}"," ",0,"-1/10080*(105*(9*tan(1/2*d*x + 1/2*c)^2 - 12*tan(1/2*d*x + 1/2*c) + 7)/(a^3*(tan(1/2*d*x + 1/2*c) - 1)^3) - (945*tan(1/2*d*x + 1/2*c)^8 + 10080*tan(1/2*d*x + 1/2*c)^7 + 23940*tan(1/2*d*x + 1/2*c)^6 + 42840*tan(1/2*d*x + 1/2*c)^5 + 41958*tan(1/2*d*x + 1/2*c)^4 + 32592*tan(1/2*d*x + 1/2*c)^3 + 14148*tan(1/2*d*x + 1/2*c)^2 + 5112*tan(1/2*d*x + 1/2*c) + 673)/(a^3*(tan(1/2*d*x + 1/2*c) + 1)^9))/d","A",0
845,1,172,0,0.328152," ","integrate(sec(d*x+c)^4*sin(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{21 \, {\left(15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 24 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 13\right)}}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}} - \frac{315 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 756 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 4200 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 11340 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 14994 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 13356 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6768 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2196 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 209}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{9}}}{2016 \, d}"," ",0,"-1/2016*(21*(15*tan(1/2*d*x + 1/2*c)^2 - 24*tan(1/2*d*x + 1/2*c) + 13)/(a^3*(tan(1/2*d*x + 1/2*c) - 1)^3) - (315*tan(1/2*d*x + 1/2*c)^8 - 756*tan(1/2*d*x + 1/2*c)^7 - 4200*tan(1/2*d*x + 1/2*c)^6 - 11340*tan(1/2*d*x + 1/2*c)^5 - 14994*tan(1/2*d*x + 1/2*c)^4 - 13356*tan(1/2*d*x + 1/2*c)^3 - 6768*tan(1/2*d*x + 1/2*c)^2 - 2196*tan(1/2*d*x + 1/2*c) - 209)/(a^3*(tan(1/2*d*x + 1/2*c) + 1)^9))/d","A",0
846,1,187,0,0.237131," ","integrate(csc(d*x+c)*sec(d*x+c)^4/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{10080 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} - \frac{105 \, {\left(27 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 48 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 25\right)}}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}} + \frac{63315 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 412020 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1273440 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 2324700 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2731302 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2097228 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1032552 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 297828 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 40127}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{9}}}{10080 \, d}"," ",0,"1/10080*(10080*log(abs(tan(1/2*d*x + 1/2*c)))/a^3 - 105*(27*tan(1/2*d*x + 1/2*c)^2 - 48*tan(1/2*d*x + 1/2*c) + 25)/(a^3*(tan(1/2*d*x + 1/2*c) - 1)^3) + (63315*tan(1/2*d*x + 1/2*c)^8 + 412020*tan(1/2*d*x + 1/2*c)^7 + 1273440*tan(1/2*d*x + 1/2*c)^6 + 2324700*tan(1/2*d*x + 1/2*c)^5 + 2731302*tan(1/2*d*x + 1/2*c)^4 + 2097228*tan(1/2*d*x + 1/2*c)^3 + 1032552*tan(1/2*d*x + 1/2*c)^2 + 297828*tan(1/2*d*x + 1/2*c) + 40127)/(a^3*(tan(1/2*d*x + 1/2*c) + 1)^9))/d","A",0
847,1,230,0,0.281928," ","integrate(csc(d*x+c)^2*sec(d*x+c)^4/(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{30240 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} - \frac{5040 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3}} - \frac{5040 \, {\left(6 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}}{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)} + \frac{105 \, {\left(33 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 60 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 31\right)}}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}} + \frac{157815 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 1093680 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 3488940 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 6524280 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 7788186 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 6052704 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2995596 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 864504 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 113591}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{9}}}{10080 \, d}"," ",0,"-1/10080*(30240*log(abs(tan(1/2*d*x + 1/2*c)))/a^3 - 5040*tan(1/2*d*x + 1/2*c)/a^3 - 5040*(6*tan(1/2*d*x + 1/2*c) - 1)/(a^3*tan(1/2*d*x + 1/2*c)) + 105*(33*tan(1/2*d*x + 1/2*c)^2 - 60*tan(1/2*d*x + 1/2*c) + 31)/(a^3*(tan(1/2*d*x + 1/2*c) - 1)^3) + (157815*tan(1/2*d*x + 1/2*c)^8 + 1093680*tan(1/2*d*x + 1/2*c)^7 + 3488940*tan(1/2*d*x + 1/2*c)^6 + 6524280*tan(1/2*d*x + 1/2*c)^5 + 7788186*tan(1/2*d*x + 1/2*c)^4 + 6052704*tan(1/2*d*x + 1/2*c)^3 + 2995596*tan(1/2*d*x + 1/2*c)^2 + 864504*tan(1/2*d*x + 1/2*c) + 113591)/(a^3*(tan(1/2*d*x + 1/2*c) + 1)^9))/d","A",0
848,1,172,0,0.460608," ","integrate(sec(d*x+c)^4*sin(d*x+c)^4/(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{1155 \, {\left(3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}}{a^{4} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}} - \frac{3465 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 47355 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 309540 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 588588 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 891198 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 747450 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 481140 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 172700 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 35233 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3203}{a^{4} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{11}}}{110880 \, d}"," ",0,"-1/110880*(1155*(3*tan(1/2*d*x + 1/2*c) - 1)/(a^4*(tan(1/2*d*x + 1/2*c) - 1)^3) - (3465*tan(1/2*d*x + 1/2*c)^9 + 47355*tan(1/2*d*x + 1/2*c)^8 + 309540*tan(1/2*d*x + 1/2*c)^7 + 588588*tan(1/2*d*x + 1/2*c)^6 + 891198*tan(1/2*d*x + 1/2*c)^5 + 747450*tan(1/2*d*x + 1/2*c)^4 + 481140*tan(1/2*d*x + 1/2*c)^3 + 172700*tan(1/2*d*x + 1/2*c)^2 + 35233*tan(1/2*d*x + 1/2*c) + 3203)/(a^4*(tan(1/2*d*x + 1/2*c) + 1)^11))/d","A",0
849,1,198,0,0.438995," ","integrate(sec(d*x+c)^4*sin(d*x+c)^3/(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{1155 \, {\left(3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)}}{a^{4} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}} - \frac{3465 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 45045 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 279510 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 669900 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1205358 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 1334718 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1144440 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 627660 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 257345 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 57013 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5498}{a^{4} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{11}}}{110880 \, d}"," ",0,"-1/110880*(1155*(3*tan(1/2*d*x + 1/2*c)^2 - 3*tan(1/2*d*x + 1/2*c) + 2)/(a^4*(tan(1/2*d*x + 1/2*c) - 1)^3) - (3465*tan(1/2*d*x + 1/2*c)^10 + 45045*tan(1/2*d*x + 1/2*c)^9 + 279510*tan(1/2*d*x + 1/2*c)^8 + 669900*tan(1/2*d*x + 1/2*c)^7 + 1205358*tan(1/2*d*x + 1/2*c)^6 + 1334718*tan(1/2*d*x + 1/2*c)^5 + 1144440*tan(1/2*d*x + 1/2*c)^4 + 627660*tan(1/2*d*x + 1/2*c)^3 + 257345*tan(1/2*d*x + 1/2*c)^2 + 57013*tan(1/2*d*x + 1/2*c) + 5498)/(a^4*(tan(1/2*d*x + 1/2*c) + 1)^11))/d","A",0
850,1,198,0,0.400018," ","integrate(sec(d*x+c)^4*sin(d*x+c)^2/(a+a*sin(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{77 \, {\left(6 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5\right)}}{a^{4} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}} - \frac{462 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 5775 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 14399 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 29260 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 30800 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 27874 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12650 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 6556 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1210 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 935 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 127}{a^{4} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{11}}}{7392 \, d}"," ",0,"-1/7392*(77*(6*tan(1/2*d*x + 1/2*c)^2 - 9*tan(1/2*d*x + 1/2*c) + 5)/(a^4*(tan(1/2*d*x + 1/2*c) - 1)^3) - (462*tan(1/2*d*x + 1/2*c)^10 + 5775*tan(1/2*d*x + 1/2*c)^9 + 14399*tan(1/2*d*x + 1/2*c)^8 + 29260*tan(1/2*d*x + 1/2*c)^7 + 30800*tan(1/2*d*x + 1/2*c)^6 + 27874*tan(1/2*d*x + 1/2*c)^5 + 12650*tan(1/2*d*x + 1/2*c)^4 + 6556*tan(1/2*d*x + 1/2*c)^3 + 1210*tan(1/2*d*x + 1/2*c)^2 + 935*tan(1/2*d*x + 1/2*c) + 127)/(a^4*(tan(1/2*d*x + 1/2*c) + 1)^11))/d","A",0
851,1,113,0,0.255834," ","integrate(sec(d*x+c)^5*sin(d*x+c)^6*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{16 \, a \sin\left(d x + c\right)^{2} + 18 \, a \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) + 78 \, a \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) + 32 \, a \sin\left(d x + c\right) - \frac{2 \, {\left(9 \, a \sin\left(d x + c\right) + 7 \, a\right)}}{\sin\left(d x + c\right) + 1} - \frac{117 \, a \sin\left(d x + c\right)^{2} - 194 \, a \sin\left(d x + c\right) + 81 \, a}{{\left(\sin\left(d x + c\right) - 1\right)}^{2}}}{32 \, d}"," ",0,"-1/32*(16*a*sin(d*x + c)^2 + 18*a*log(abs(sin(d*x + c) + 1)) + 78*a*log(abs(sin(d*x + c) - 1)) + 32*a*sin(d*x + c) - 2*(9*a*sin(d*x + c) + 7*a)/(sin(d*x + c) + 1) - (117*a*sin(d*x + c)^2 - 194*a*sin(d*x + c) + 81*a)/(sin(d*x + c) - 1)^2)/d","A",0
852,1,101,0,0.253822," ","integrate(sec(d*x+c)^5*sin(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{14 \, a \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - 46 \, a \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - 32 \, a \sin\left(d x + c\right) - \frac{2 \, {\left(7 \, a \sin\left(d x + c\right) + 5 \, a\right)}}{\sin\left(d x + c\right) + 1} + \frac{69 \, a \sin\left(d x + c\right)^{2} - 106 \, a \sin\left(d x + c\right) + 41 \, a}{{\left(\sin\left(d x + c\right) - 1\right)}^{2}}}{32 \, d}"," ",0,"1/32*(14*a*log(abs(sin(d*x + c) + 1)) - 46*a*log(abs(sin(d*x + c) - 1)) - 32*a*sin(d*x + c) - 2*(7*a*sin(d*x + c) + 5*a)/(sin(d*x + c) + 1) + (69*a*sin(d*x + c)^2 - 106*a*sin(d*x + c) + 41*a)/(sin(d*x + c) - 1)^2)/d","A",0
853,1,93,0,0.226241," ","integrate(sec(d*x+c)^5*sin(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{10 \, a \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) + 22 \, a \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - \frac{2 \, {\left(5 \, a \sin\left(d x + c\right) + 3 \, a\right)}}{\sin\left(d x + c\right) + 1} - \frac{33 \, a \sin\left(d x + c\right)^{2} - 42 \, a \sin\left(d x + c\right) + 13 \, a}{{\left(\sin\left(d x + c\right) - 1\right)}^{2}}}{32 \, d}"," ",0,"-1/32*(10*a*log(abs(sin(d*x + c) + 1)) + 22*a*log(abs(sin(d*x + c) - 1)) - 2*(5*a*sin(d*x + c) + 3*a)/(sin(d*x + c) + 1) - (33*a*sin(d*x + c)^2 - 42*a*sin(d*x + c) + 13*a)/(sin(d*x + c) - 1)^2)/d","A",0
854,1,90,0,0.223087," ","integrate(sec(d*x+c)^5*sin(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{6 \, a \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - 6 \, a \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - \frac{2 \, {\left(3 \, a \sin\left(d x + c\right) + a\right)}}{\sin\left(d x + c\right) + 1} + \frac{9 \, a \sin\left(d x + c\right)^{2} - 2 \, a \sin\left(d x + c\right) - 3 \, a}{{\left(\sin\left(d x + c\right) - 1\right)}^{2}}}{32 \, d}"," ",0,"1/32*(6*a*log(abs(sin(d*x + c) + 1)) - 6*a*log(abs(sin(d*x + c) - 1)) - 2*(3*a*sin(d*x + c) + a)/(sin(d*x + c) + 1) + (9*a*sin(d*x + c)^2 - 2*a*sin(d*x + c) - 3*a)/(sin(d*x + c) - 1)^2)/d","A",0
855,1,91,0,0.223449," ","integrate(sec(d*x+c)^5*sin(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{2 \, a \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - 2 \, a \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - \frac{2 \, {\left(a \sin\left(d x + c\right) - a\right)}}{\sin\left(d x + c\right) + 1} + \frac{3 \, a \sin\left(d x + c\right)^{2} - 14 \, a \sin\left(d x + c\right) + 7 \, a}{{\left(\sin\left(d x + c\right) - 1\right)}^{2}}}{32 \, d}"," ",0,"-1/32*(2*a*log(abs(sin(d*x + c) + 1)) - 2*a*log(abs(sin(d*x + c) - 1)) - 2*(a*sin(d*x + c) - a)/(sin(d*x + c) + 1) + (3*a*sin(d*x + c)^2 - 14*a*sin(d*x + c) + 7*a)/(sin(d*x + c) - 1)^2)/d","A",0
856,1,91,0,0.204867," ","integrate(sec(d*x+c)^5*sin(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{2 \, a \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - 2 \, a \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - \frac{2 \, {\left(a \sin\left(d x + c\right) + 3 \, a\right)}}{\sin\left(d x + c\right) + 1} + \frac{3 \, a \sin\left(d x + c\right)^{2} - 6 \, a \sin\left(d x + c\right) - a}{{\left(\sin\left(d x + c\right) - 1\right)}^{2}}}{32 \, d}"," ",0,"-1/32*(2*a*log(abs(sin(d*x + c) + 1)) - 2*a*log(abs(sin(d*x + c) - 1)) - 2*(a*sin(d*x + c) + 3*a)/(sin(d*x + c) + 1) + (3*a*sin(d*x + c)^2 - 6*a*sin(d*x + c) - a)/(sin(d*x + c) - 1)^2)/d","A",0
857,1,104,0,0.239870," ","integrate(csc(d*x+c)*sec(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{10 \, a \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) + 22 \, a \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - 32 \, a \log\left({\left| \sin\left(d x + c\right) \right|}\right) - \frac{2 \, {\left(5 \, a \sin\left(d x + c\right) + 7 \, a\right)}}{\sin\left(d x + c\right) + 1} - \frac{33 \, a \sin\left(d x + c\right)^{2} - 82 \, a \sin\left(d x + c\right) + 53 \, a}{{\left(\sin\left(d x + c\right) - 1\right)}^{2}}}{32 \, d}"," ",0,"-1/32*(10*a*log(abs(sin(d*x + c) + 1)) + 22*a*log(abs(sin(d*x + c) - 1)) - 32*a*log(abs(sin(d*x + c))) - 2*(5*a*sin(d*x + c) + 7*a)/(sin(d*x + c) + 1) - (33*a*sin(d*x + c)^2 - 82*a*sin(d*x + c) + 53*a)/(sin(d*x + c) - 1)^2)/d","A",0
858,1,121,0,0.284876," ","integrate(csc(d*x+c)^2*sec(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{14 \, a \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - 46 \, a \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) + 32 \, a \log\left({\left| \sin\left(d x + c\right) \right|}\right) - \frac{23 \, a \sin\left(d x + c\right)^{2} + 59 \, a \sin\left(d x + c\right) + 32 \, a}{\sin\left(d x + c\right)^{2} + \sin\left(d x + c\right)} + \frac{69 \, a \sin\left(d x + c\right)^{2} - 162 \, a \sin\left(d x + c\right) + 97 \, a}{{\left(\sin\left(d x + c\right) - 1\right)}^{2}}}{32 \, d}"," ",0,"1/32*(14*a*log(abs(sin(d*x + c) + 1)) - 46*a*log(abs(sin(d*x + c) - 1)) + 32*a*log(abs(sin(d*x + c))) - (23*a*sin(d*x + c)^2 + 59*a*sin(d*x + c) + 32*a)/(sin(d*x + c)^2 + sin(d*x + c)) + (69*a*sin(d*x + c)^2 - 162*a*sin(d*x + c) + 97*a)/(sin(d*x + c) - 1)^2)/d","A",0
859,1,125,0,0.282899," ","integrate(csc(d*x+c)^3*sec(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{36 \, a \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) + 156 \, a \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - 192 \, a \log\left({\left| \sin\left(d x + c\right) \right|}\right) - \frac{4 \, {\left(9 \, a \sin\left(d x + c\right) + 11 \, a\right)}}{\sin\left(d x + c\right) + 1} + \frac{27 \, a \sin\left(d x + c\right)^{4} + 74 \, a \sin\left(d x + c\right)^{3} - 141 \, a \sin\left(d x + c\right)^{2} + 32 \, a}{{\left(\sin\left(d x + c\right)^{2} - \sin\left(d x + c\right)\right)}^{2}}}{64 \, d}"," ",0,"-1/64*(36*a*log(abs(sin(d*x + c) + 1)) + 156*a*log(abs(sin(d*x + c) - 1)) - 192*a*log(abs(sin(d*x + c))) - 4*(9*a*sin(d*x + c) + 11*a)/(sin(d*x + c) + 1) + (27*a*sin(d*x + c)^4 + 74*a*sin(d*x + c)^3 - 141*a*sin(d*x + c)^2 + 32*a)/(sin(d*x + c)^2 - sin(d*x + c))^2)/d","A",0
860,1,149,0,0.288192," ","integrate(csc(d*x+c)^4*sec(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{66 \, a \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - 354 \, a \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) + 288 \, a \log\left({\left| \sin\left(d x + c\right) \right|}\right) - \frac{6 \, {\left(11 \, a \sin\left(d x + c\right) + 13 \, a\right)}}{\sin\left(d x + c\right) + 1} + \frac{3 \, {\left(177 \, a \sin\left(d x + c\right)^{2} - 394 \, a \sin\left(d x + c\right) + 221 \, a\right)}}{{\left(\sin\left(d x + c\right) - 1\right)}^{2}} - \frac{16 \, {\left(33 \, a \sin\left(d x + c\right)^{3} + 18 \, a \sin\left(d x + c\right)^{2} + 3 \, a \sin\left(d x + c\right) + 2 \, a\right)}}{\sin\left(d x + c\right)^{3}}}{96 \, d}"," ",0,"1/96*(66*a*log(abs(sin(d*x + c) + 1)) - 354*a*log(abs(sin(d*x + c) - 1)) + 288*a*log(abs(sin(d*x + c))) - 6*(11*a*sin(d*x + c) + 13*a)/(sin(d*x + c) + 1) + 3*(177*a*sin(d*x + c)^2 - 394*a*sin(d*x + c) + 221*a)/(sin(d*x + c) - 1)^2 - 16*(33*a*sin(d*x + c)^3 + 18*a*sin(d*x + c)^2 + 3*a*sin(d*x + c) + 2*a)/sin(d*x + c)^3)/d","A",0
861,1,102,0,0.294226," ","integrate(sec(d*x+c)^5*sin(d*x+c)^5*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{8 \, a^{2} \sin\left(d x + c\right)^{2} + 2 \, a^{2} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) + 62 \, a^{2} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) + 32 \, a^{2} \sin\left(d x + c\right) - \frac{93 \, a^{2} \sin\left(d x + c\right)^{2} - 150 \, a^{2} \sin\left(d x + c\right) + 61 \, a^{2}}{{\left(\sin\left(d x + c\right) - 1\right)}^{2}}}{16 \, d}"," ",0,"-1/16*(8*a^2*sin(d*x + c)^2 + 2*a^2*log(abs(sin(d*x + c) + 1)) + 62*a^2*log(abs(sin(d*x + c) - 1)) + 32*a^2*sin(d*x + c) - (93*a^2*sin(d*x + c)^2 - 150*a^2*sin(d*x + c) + 61*a^2)/(sin(d*x + c) - 1)^2)/d","A",0
862,1,88,0,0.292113," ","integrate(sec(d*x+c)^5*sin(d*x+c)^4*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{2 \, a^{2} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - 34 \, a^{2} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - 16 \, a^{2} \sin\left(d x + c\right) + \frac{51 \, a^{2} \sin\left(d x + c\right)^{2} - 74 \, a^{2} \sin\left(d x + c\right) + 27 \, a^{2}}{{\left(\sin\left(d x + c\right) - 1\right)}^{2}}}{16 \, d}"," ",0,"1/16*(2*a^2*log(abs(sin(d*x + c) + 1)) - 34*a^2*log(abs(sin(d*x + c) - 1)) - 16*a^2*sin(d*x + c) + (51*a^2*sin(d*x + c)^2 - 74*a^2*sin(d*x + c) + 27*a^2)/(sin(d*x + c) - 1)^2)/d","A",0
863,1,78,0,0.255214," ","integrate(sec(d*x+c)^5*sin(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{2 \, a^{2} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) + 14 \, a^{2} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - \frac{21 \, a^{2} \sin\left(d x + c\right)^{2} - 22 \, a^{2} \sin\left(d x + c\right) + 5 \, a^{2}}{{\left(\sin\left(d x + c\right) - 1\right)}^{2}}}{16 \, d}"," ",0,"-1/16*(2*a^2*log(abs(sin(d*x + c) + 1)) + 14*a^2*log(abs(sin(d*x + c) - 1)) - (21*a^2*sin(d*x + c)^2 - 22*a^2*sin(d*x + c) + 5*a^2)/(sin(d*x + c) - 1)^2)/d","A",0
864,1,77,0,0.231319," ","integrate(sec(d*x+c)^5*sin(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{2 \, a^{2} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - 2 \, a^{2} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) + \frac{3 \, a^{2} \sin\left(d x + c\right)^{2} + 6 \, a^{2} \sin\left(d x + c\right) - 5 \, a^{2}}{{\left(\sin\left(d x + c\right) - 1\right)}^{2}}}{16 \, d}"," ",0,"1/16*(2*a^2*log(abs(sin(d*x + c) + 1)) - 2*a^2*log(abs(sin(d*x + c) - 1)) + (3*a^2*sin(d*x + c)^2 + 6*a^2*sin(d*x + c) - 5*a^2)/(sin(d*x + c) - 1)^2)/d","A",0
865,1,95,0,0.223443," ","integrate(sec(d*x+c)^5*sin(d*x+c)*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{a^{2} \log\left({\left| \frac{1}{\sin\left(d x + c\right)} + \sin\left(d x + c\right) + 2 \right|}\right) - a^{2} \log\left({\left| \frac{1}{\sin\left(d x + c\right)} + \sin\left(d x + c\right) - 2 \right|}\right) + \frac{a^{2} {\left(\frac{1}{\sin\left(d x + c\right)} + \sin\left(d x + c\right)\right)} - 6 \, a^{2}}{\frac{1}{\sin\left(d x + c\right)} + \sin\left(d x + c\right) - 2}}{16 \, d}"," ",0,"-1/16*(a^2*log(abs(1/sin(d*x + c) + sin(d*x + c) + 2)) - a^2*log(abs(1/sin(d*x + c) + sin(d*x + c) - 2)) + (a^2*(1/sin(d*x + c) + sin(d*x + c)) - 6*a^2)/(1/sin(d*x + c) + sin(d*x + c) - 2))/d","A",0
866,1,91,0,0.275829," ","integrate(csc(d*x+c)*sec(d*x+c)^5*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{2 \, a^{2} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) + 14 \, a^{2} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - 16 \, a^{2} \log\left({\left| \sin\left(d x + c\right) \right|}\right) - \frac{21 \, a^{2} \sin\left(d x + c\right)^{2} - 54 \, a^{2} \sin\left(d x + c\right) + 37 \, a^{2}}{{\left(\sin\left(d x + c\right) - 1\right)}^{2}}}{16 \, d}"," ",0,"-1/16*(2*a^2*log(abs(sin(d*x + c) + 1)) + 14*a^2*log(abs(sin(d*x + c) - 1)) - 16*a^2*log(abs(sin(d*x + c))) - (21*a^2*sin(d*x + c)^2 - 54*a^2*sin(d*x + c) + 37*a^2)/(sin(d*x + c) - 1)^2)/d","A",0
867,1,115,0,0.300193," ","integrate(csc(d*x+c)^2*sec(d*x+c)^5*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{2 \, a^{2} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - 34 \, a^{2} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) + 32 \, a^{2} \log\left({\left| \sin\left(d x + c\right) \right|}\right) - \frac{16 \, {\left(2 \, a^{2} \sin\left(d x + c\right) + a^{2}\right)}}{\sin\left(d x + c\right)} + \frac{51 \, a^{2} \sin\left(d x + c\right)^{2} - 122 \, a^{2} \sin\left(d x + c\right) + 75 \, a^{2}}{{\left(\sin\left(d x + c\right) - 1\right)}^{2}}}{16 \, d}"," ",0,"1/16*(2*a^2*log(abs(sin(d*x + c) + 1)) - 34*a^2*log(abs(sin(d*x + c) - 1)) + 32*a^2*log(abs(sin(d*x + c))) - 16*(2*a^2*sin(d*x + c) + a^2)/sin(d*x + c) + (51*a^2*sin(d*x + c)^2 - 122*a^2*sin(d*x + c) + 75*a^2)/(sin(d*x + c) - 1)^2)/d","A",0
868,1,125,0,0.298004," ","integrate(csc(d*x+c)^3*sec(d*x+c)^5*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{4 \, a^{2} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) + 124 \, a^{2} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - 128 \, a^{2} \log\left({\left| \sin\left(d x + c\right) \right|}\right) + \frac{3 \, a^{2} \sin\left(d x + c\right)^{4} + 114 \, a^{2} \sin\left(d x + c\right)^{3} - 173 \, a^{2} \sin\left(d x + c\right)^{2} + 32 \, a^{2} \sin\left(d x + c\right) + 16 \, a^{2}}{{\left(\sin\left(d x + c\right)^{2} - \sin\left(d x + c\right)\right)}^{2}}}{32 \, d}"," ",0,"-1/32*(4*a^2*log(abs(sin(d*x + c) + 1)) + 124*a^2*log(abs(sin(d*x + c) - 1)) - 128*a^2*log(abs(sin(d*x + c))) + (3*a^2*sin(d*x + c)^4 + 114*a^2*sin(d*x + c)^3 - 173*a^2*sin(d*x + c)^2 + 32*a^2*sin(d*x + c) + 16*a^2)/(sin(d*x + c)^2 - sin(d*x + c))^2)/d","A",0
869,1,142,0,0.346174," ","integrate(csc(d*x+c)^4*sec(d*x+c)^5*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{6 \, a^{2} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - 294 \, a^{2} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) + 288 \, a^{2} \log\left({\left| \sin\left(d x + c\right) \right|}\right) + \frac{3 \, {\left(147 \, a^{2} \sin\left(d x + c\right)^{2} - 330 \, a^{2} \sin\left(d x + c\right) + 187 \, a^{2}\right)}}{{\left(\sin\left(d x + c\right) - 1\right)}^{2}} - \frac{16 \, {\left(33 \, a^{2} \sin\left(d x + c\right)^{3} + 12 \, a^{2} \sin\left(d x + c\right)^{2} + 3 \, a^{2} \sin\left(d x + c\right) + a^{2}\right)}}{\sin\left(d x + c\right)^{3}}}{48 \, d}"," ",0,"1/48*(6*a^2*log(abs(sin(d*x + c) + 1)) - 294*a^2*log(abs(sin(d*x + c) - 1)) + 288*a^2*log(abs(sin(d*x + c))) + 3*(147*a^2*sin(d*x + c)^2 - 330*a^2*sin(d*x + c) + 187*a^2)/(sin(d*x + c) - 1)^2 - 16*(33*a^2*sin(d*x + c)^3 + 12*a^2*sin(d*x + c)^2 + 3*a^2*sin(d*x + c) + a^2)/sin(d*x + c)^3)/d","A",0
870,1,242,0,0.285511," ","integrate(sec(d*x+c)^5*sin(d*x+c)^5*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{30 \, a^{3} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right) - 60 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{55 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 36 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 183 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 80 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 183 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 36 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 55 \, a^{3}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}} + \frac{125 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 524 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 804 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 524 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 125 \, a^{3}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{4}}}{3 \, d}"," ",0,"1/3*(30*a^3*log(tan(1/2*d*x + 1/2*c)^2 + 1) - 60*a^3*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - (55*a^3*tan(1/2*d*x + 1/2*c)^6 + 36*a^3*tan(1/2*d*x + 1/2*c)^5 + 183*a^3*tan(1/2*d*x + 1/2*c)^4 + 80*a^3*tan(1/2*d*x + 1/2*c)^3 + 183*a^3*tan(1/2*d*x + 1/2*c)^2 + 36*a^3*tan(1/2*d*x + 1/2*c) + 55*a^3)/(tan(1/2*d*x + 1/2*c)^2 + 1)^3 + (125*a^3*tan(1/2*d*x + 1/2*c)^4 - 524*a^3*tan(1/2*d*x + 1/2*c)^3 + 804*a^3*tan(1/2*d*x + 1/2*c)^2 - 524*a^3*tan(1/2*d*x + 1/2*c) + 125*a^3)/(tan(1/2*d*x + 1/2*c) - 1)^4)/d","B",0
871,1,209,0,0.302887," ","integrate(sec(d*x+c)^5*sin(d*x+c)^4*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{6 \, a^{3} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right) - 12 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{9 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 6 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 20 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 6 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, a^{3}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}} + \frac{25 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 106 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 164 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 106 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 25 \, a^{3}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{4}}}{d}"," ",0,"(6*a^3*log(tan(1/2*d*x + 1/2*c)^2 + 1) - 12*a^3*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - (9*a^3*tan(1/2*d*x + 1/2*c)^4 + 6*a^3*tan(1/2*d*x + 1/2*c)^3 + 20*a^3*tan(1/2*d*x + 1/2*c)^2 + 6*a^3*tan(1/2*d*x + 1/2*c) + 9*a^3)/(tan(1/2*d*x + 1/2*c)^2 + 1)^2 + (25*a^3*tan(1/2*d*x + 1/2*c)^4 - 106*a^3*tan(1/2*d*x + 1/2*c)^3 + 164*a^3*tan(1/2*d*x + 1/2*c)^2 - 106*a^3*tan(1/2*d*x + 1/2*c) + 25*a^3)/(tan(1/2*d*x + 1/2*c) - 1)^4)/d","B",0
872,1,178,0,0.273988," ","integrate(sec(d*x+c)^5*sin(d*x+c)^3*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{6 \, a^{3} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right) - 12 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, {\left(3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a^{3}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + \frac{25 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 108 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 170 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 108 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 25 \, a^{3}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{4}}}{2 \, d}"," ",0,"1/2*(6*a^3*log(tan(1/2*d*x + 1/2*c)^2 + 1) - 12*a^3*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*(3*a^3*tan(1/2*d*x + 1/2*c)^2 + 2*a^3*tan(1/2*d*x + 1/2*c) + 3*a^3)/(tan(1/2*d*x + 1/2*c)^2 + 1) + (25*a^3*tan(1/2*d*x + 1/2*c)^4 - 108*a^3*tan(1/2*d*x + 1/2*c)^3 + 170*a^3*tan(1/2*d*x + 1/2*c)^2 - 108*a^3*tan(1/2*d*x + 1/2*c) + 25*a^3)/(tan(1/2*d*x + 1/2*c) - 1)^4)/d","B",0
873,1,125,0,0.267558," ","integrate(sec(d*x+c)^5*sin(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{6 \, a^{3} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right) - 12 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{25 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 112 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 186 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 112 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 25 \, a^{3}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{4}}}{6 \, d}"," ",0,"1/6*(6*a^3*log(tan(1/2*d*x + 1/2*c)^2 + 1) - 12*a^3*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + (25*a^3*tan(1/2*d*x + 1/2*c)^4 - 112*a^3*tan(1/2*d*x + 1/2*c)^3 + 186*a^3*tan(1/2*d*x + 1/2*c)^2 - 112*a^3*tan(1/2*d*x + 1/2*c) + 25*a^3)/(tan(1/2*d*x + 1/2*c) - 1)^4)/d","A",0
874,1,32,0,0.232657," ","integrate(sec(d*x+c)^5*sin(d*x+c)*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{2 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{4}}"," ",0,"2*a^3*tan(1/2*d*x + 1/2*c)^2/(d*(tan(1/2*d*x + 1/2*c) - 1)^4)","A",0
875,1,123,0,0.268746," ","integrate(csc(d*x+c)*sec(d*x+c)^5*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{12 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - 6 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{25 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 76 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 114 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 76 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 25 \, a^{3}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{4}}}{6 \, d}"," ",0,"-1/6*(12*a^3*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 6*a^3*log(abs(tan(1/2*d*x + 1/2*c))) - (25*a^3*tan(1/2*d*x + 1/2*c)^4 - 76*a^3*tan(1/2*d*x + 1/2*c)^3 + 114*a^3*tan(1/2*d*x + 1/2*c)^2 - 76*a^3*tan(1/2*d*x + 1/2*c) + 25*a^3)/(tan(1/2*d*x + 1/2*c) - 1)^4)/d","A",0
876,1,166,0,0.314710," ","integrate(csc(d*x+c)^2*sec(d*x+c)^5*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{12 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - 6 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{6 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)} - \frac{25 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 88 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 130 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 88 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 25 \, a^{3}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{4}}}{2 \, d}"," ",0,"-1/2*(12*a^3*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 6*a^3*log(abs(tan(1/2*d*x + 1/2*c))) + a^3*tan(1/2*d*x + 1/2*c) + (6*a^3*tan(1/2*d*x + 1/2*c) + a^3)/tan(1/2*d*x + 1/2*c) - (25*a^3*tan(1/2*d*x + 1/2*c)^4 - 88*a^3*tan(1/2*d*x + 1/2*c)^3 + 130*a^3*tan(1/2*d*x + 1/2*c)^2 - 88*a^3*tan(1/2*d*x + 1/2*c) + 25*a^3)/(tan(1/2*d*x + 1/2*c) - 1)^4)/d","A",0
877,1,198,0,0.328432," ","integrate(csc(d*x+c)^3*sec(d*x+c)^5*(a+a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 96 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - 48 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 12 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{72 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}} - \frac{8 \, {\left(25 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 92 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 136 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 92 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 25 \, a^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{4}}}{8 \, d}"," ",0,"-1/8*(a^3*tan(1/2*d*x + 1/2*c)^2 + 96*a^3*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 48*a^3*log(abs(tan(1/2*d*x + 1/2*c))) + 12*a^3*tan(1/2*d*x + 1/2*c) + (72*a^3*tan(1/2*d*x + 1/2*c)^2 + 12*a^3*tan(1/2*d*x + 1/2*c) + a^3)/tan(1/2*d*x + 1/2*c)^2 - 8*(25*a^3*tan(1/2*d*x + 1/2*c)^4 - 92*a^3*tan(1/2*d*x + 1/2*c)^3 + 136*a^3*tan(1/2*d*x + 1/2*c)^2 - 92*a^3*tan(1/2*d*x + 1/2*c) + 25*a^3)/(tan(1/2*d*x + 1/2*c) - 1)^4)/d","A",0
878,1,179,0,0.360349," ","integrate(sec(d*x+c)^7*sin(d*x+c)^11/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{21540 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} - \frac{6180 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a} - \frac{512 \, {\left(2 \, a^{2} \sin\left(d x + c\right)^{3} - 3 \, a^{2} \sin\left(d x + c\right)^{2} + 30 \, a^{2} \sin\left(d x + c\right)\right)}}{a^{3}} + \frac{2 \, {\left(5665 \, \sin\left(d x + c\right)^{3} - 15495 \, \sin\left(d x + c\right)^{2} + 14199 \, \sin\left(d x + c\right) - 4353\right)}}{a {\left(\sin\left(d x + c\right) - 1\right)}^{3}} - \frac{44875 \, \sin\left(d x + c\right)^{4} + 164140 \, \sin\left(d x + c\right)^{3} + 226578 \, \sin\left(d x + c\right)^{2} + 139660 \, \sin\left(d x + c\right) + 32395}{a {\left(\sin\left(d x + c\right) + 1\right)}^{4}}}{3072 \, d}"," ",0,"-1/3072*(21540*log(abs(sin(d*x + c) + 1))/a - 6180*log(abs(sin(d*x + c) - 1))/a - 512*(2*a^2*sin(d*x + c)^3 - 3*a^2*sin(d*x + c)^2 + 30*a^2*sin(d*x + c))/a^3 + 2*(5665*sin(d*x + c)^3 - 15495*sin(d*x + c)^2 + 14199*sin(d*x + c) - 4353)/(a*(sin(d*x + c) - 1)^3) - (44875*sin(d*x + c)^4 + 164140*sin(d*x + c)^3 + 226578*sin(d*x + c)^2 + 139660*sin(d*x + c) + 32395)/(a*(sin(d*x + c) + 1)^4))/d","A",0
879,1,161,0,0.361412," ","integrate(sec(d*x+c)^7*sin(d*x+c)^10/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{11460 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} + \frac{3900 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a} + \frac{1536 \, {\left(a \sin\left(d x + c\right)^{2} - 2 \, a \sin\left(d x + c\right)\right)}}{a^{2}} - \frac{2 \, {\left(3575 \, \sin\left(d x + c\right)^{3} - 9585 \, \sin\left(d x + c\right)^{2} + 8625 \, \sin\left(d x + c\right) - 2599\right)}}{a {\left(\sin\left(d x + c\right) - 1\right)}^{3}} - \frac{23875 \, \sin\left(d x + c\right)^{4} + 85420 \, \sin\left(d x + c\right)^{3} + 115650 \, \sin\left(d x + c\right)^{2} + 70028 \, \sin\left(d x + c\right) + 15971}{a {\left(\sin\left(d x + c\right) + 1\right)}^{4}}}{3072 \, d}"," ",0,"1/3072*(11460*log(abs(sin(d*x + c) + 1))/a + 3900*log(abs(sin(d*x + c) - 1))/a + 1536*(a*sin(d*x + c)^2 - 2*a*sin(d*x + c))/a^2 - 2*(3575*sin(d*x + c)^3 - 9585*sin(d*x + c)^2 + 8625*sin(d*x + c) - 2599)/(a*(sin(d*x + c) - 1)^3) - (23875*sin(d*x + c)^4 + 85420*sin(d*x + c)^3 + 115650*sin(d*x + c)^2 + 70028*sin(d*x + c) + 15971)/(a*(sin(d*x + c) + 1)^4))/d","A",0
880,1,147,0,0.413178," ","integrate(sec(d*x+c)^7*sin(d*x+c)^9/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{5316 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} - \frac{2244 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a} - \frac{3072 \, \sin\left(d x + c\right)}{a} + \frac{2 \, {\left(2057 \, \sin\left(d x + c\right)^{3} - 5343 \, \sin\left(d x + c\right)^{2} + 4671 \, \sin\left(d x + c\right) - 1369\right)}}{a {\left(\sin\left(d x + c\right) - 1\right)}^{3}} - \frac{11075 \, \sin\left(d x + c\right)^{4} + 38156 \, \sin\left(d x + c\right)^{3} + 49986 \, \sin\left(d x + c\right)^{2} + 29356 \, \sin\left(d x + c\right) + 6499}{a {\left(\sin\left(d x + c\right) + 1\right)}^{4}}}{3072 \, d}"," ",0,"-1/3072*(5316*log(abs(sin(d*x + c) + 1))/a - 2244*log(abs(sin(d*x + c) - 1))/a - 3072*sin(d*x + c)/a + 2*(2057*sin(d*x + c)^3 - 5343*sin(d*x + c)^2 + 4671*sin(d*x + c) - 1369)/(a*(sin(d*x + c) - 1)^3) - (11075*sin(d*x + c)^4 + 38156*sin(d*x + c)^3 + 49986*sin(d*x + c)^2 + 29356*sin(d*x + c) + 6499)/(a*(sin(d*x + c) + 1)^4))/d","A",0
881,1,136,0,0.363984," ","integrate(sec(d*x+c)^7*sin(d*x+c)^8/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{1956 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} + \frac{1116 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a} - \frac{2 \, {\left(1023 \, \sin\left(d x + c\right)^{3} - 2505 \, \sin\left(d x + c\right)^{2} + 2073 \, \sin\left(d x + c\right) - 575\right)}}{a {\left(\sin\left(d x + c\right) - 1\right)}^{3}} - \frac{4075 \, \sin\left(d x + c\right)^{4} + 12940 \, \sin\left(d x + c\right)^{3} + 15762 \, \sin\left(d x + c\right)^{2} + 8620 \, \sin\left(d x + c\right) + 1771}{a {\left(\sin\left(d x + c\right) + 1\right)}^{4}}}{3072 \, d}"," ",0,"1/3072*(1956*log(abs(sin(d*x + c) + 1))/a + 1116*log(abs(sin(d*x + c) - 1))/a - 2*(1023*sin(d*x + c)^3 - 2505*sin(d*x + c)^2 + 2073*sin(d*x + c) - 575)/(a*(sin(d*x + c) - 1)^3) - (4075*sin(d*x + c)^4 + 12940*sin(d*x + c)^3 + 15762*sin(d*x + c)^2 + 8620*sin(d*x + c) + 1771)/(a*(sin(d*x + c) + 1)^4))/d","A",0
882,1,136,0,0.336873," ","integrate(sec(d*x+c)^7*sin(d*x+c)^7/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{420 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} - \frac{420 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a} + \frac{2 \, {\left(385 \, \sin\left(d x + c\right)^{3} - 807 \, \sin\left(d x + c\right)^{2} + 567 \, \sin\left(d x + c\right) - 129\right)}}{a {\left(\sin\left(d x + c\right) - 1\right)}^{3}} - \frac{875 \, \sin\left(d x + c\right)^{4} + 1964 \, \sin\left(d x + c\right)^{3} + 1554 \, \sin\left(d x + c\right)^{2} + 396 \, \sin\left(d x + c\right) - 21}{a {\left(\sin\left(d x + c\right) + 1\right)}^{4}}}{3072 \, d}"," ",0,"-1/3072*(420*log(abs(sin(d*x + c) + 1))/a - 420*log(abs(sin(d*x + c) - 1))/a + 2*(385*sin(d*x + c)^3 - 807*sin(d*x + c)^2 + 567*sin(d*x + c) - 129)/(a*(sin(d*x + c) - 1)^3) - (875*sin(d*x + c)^4 + 1964*sin(d*x + c)^3 + 1554*sin(d*x + c)^2 + 396*sin(d*x + c) - 21)/(a*(sin(d*x + c) + 1)^4))/d","A",0
883,1,136,0,0.308732," ","integrate(sec(d*x+c)^7*sin(d*x+c)^6/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{60 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} - \frac{60 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a} + \frac{2 \, {\left(55 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)^{2} - 111 \, \sin\left(d x + c\right) + 57\right)}}{a {\left(\sin\left(d x + c\right) - 1\right)}^{3}} - \frac{125 \, \sin\left(d x + c\right)^{4} + 980 \, \sin\left(d x + c\right)^{3} + 1662 \, \sin\left(d x + c\right)^{2} + 1140 \, \sin\left(d x + c\right) + 285}{a {\left(\sin\left(d x + c\right) + 1\right)}^{4}}}{3072 \, d}"," ",0,"-1/3072*(60*log(abs(sin(d*x + c) + 1))/a - 60*log(abs(sin(d*x + c) - 1))/a + 2*(55*sin(d*x + c)^3 + 15*sin(d*x + c)^2 - 111*sin(d*x + c) + 57)/(a*(sin(d*x + c) - 1)^3) - (125*sin(d*x + c)^4 + 980*sin(d*x + c)^3 + 1662*sin(d*x + c)^2 + 1140*sin(d*x + c) + 285)/(a*(sin(d*x + c) + 1)^4))/d","A",0
884,1,136,0,0.330268," ","integrate(sec(d*x+c)^7*sin(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{60 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} - \frac{60 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a} + \frac{2 \, {\left(55 \, \sin\left(d x + c\right)^{3} - 225 \, \sin\left(d x + c\right)^{2} + 225 \, \sin\left(d x + c\right) - 71\right)}}{a {\left(\sin\left(d x + c\right) - 1\right)}^{3}} - \frac{125 \, \sin\left(d x + c\right)^{4} + 500 \, \sin\left(d x + c\right)^{3} + 510 \, \sin\left(d x + c\right)^{2} + 212 \, \sin\left(d x + c\right) + 29}{a {\left(\sin\left(d x + c\right) + 1\right)}^{4}}}{3072 \, d}"," ",0,"1/3072*(60*log(abs(sin(d*x + c) + 1))/a - 60*log(abs(sin(d*x + c) - 1))/a + 2*(55*sin(d*x + c)^3 - 225*sin(d*x + c)^2 + 225*sin(d*x + c) - 71)/(a*(sin(d*x + c) - 1)^3) - (125*sin(d*x + c)^4 + 500*sin(d*x + c)^3 + 510*sin(d*x + c)^2 + 212*sin(d*x + c) + 29)/(a*(sin(d*x + c) + 1)^4))/d","A",0
885,1,136,0,0.312548," ","integrate(sec(d*x+c)^7*sin(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{36 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} - \frac{36 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a} + \frac{2 \, {\left(33 \, \sin\left(d x + c\right)^{3} - 87 \, \sin\left(d x + c\right)^{2} + 39 \, \sin\left(d x + c\right) - 1\right)}}{a {\left(\sin\left(d x + c\right) - 1\right)}^{3}} - \frac{75 \, \sin\left(d x + c\right)^{4} + 396 \, \sin\left(d x + c\right)^{3} + 786 \, \sin\left(d x + c\right)^{2} + 556 \, \sin\left(d x + c\right) + 139}{a {\left(\sin\left(d x + c\right) + 1\right)}^{4}}}{3072 \, d}"," ",0,"1/3072*(36*log(abs(sin(d*x + c) + 1))/a - 36*log(abs(sin(d*x + c) - 1))/a + 2*(33*sin(d*x + c)^3 - 87*sin(d*x + c)^2 + 39*sin(d*x + c) - 1)/(a*(sin(d*x + c) - 1)^3) - (75*sin(d*x + c)^4 + 396*sin(d*x + c)^3 + 786*sin(d*x + c)^2 + 556*sin(d*x + c) + 139)/(a*(sin(d*x + c) + 1)^4))/d","A",0
886,1,136,0,0.310184," ","integrate(sec(d*x+c)^7*sin(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{36 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} - \frac{36 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a} + \frac{2 \, {\left(33 \, \sin\left(d x + c\right)^{3} - 135 \, \sin\left(d x + c\right)^{2} + 183 \, \sin\left(d x + c\right) - 65\right)}}{a {\left(\sin\left(d x + c\right) - 1\right)}^{3}} - \frac{75 \, \sin\left(d x + c\right)^{4} + 300 \, \sin\left(d x + c\right)^{3} + 402 \, \sin\left(d x + c\right)^{2} + 140 \, \sin\left(d x + c\right) + 11}{a {\left(\sin\left(d x + c\right) + 1\right)}^{4}}}{3072 \, d}"," ",0,"-1/3072*(36*log(abs(sin(d*x + c) + 1))/a - 36*log(abs(sin(d*x + c) - 1))/a + 2*(33*sin(d*x + c)^3 - 135*sin(d*x + c)^2 + 183*sin(d*x + c) - 65)/(a*(sin(d*x + c) - 1)^3) - (75*sin(d*x + c)^4 + 300*sin(d*x + c)^3 + 402*sin(d*x + c)^2 + 140*sin(d*x + c) + 11)/(a*(sin(d*x + c) + 1)^4))/d","A",0
887,1,136,0,0.276112," ","integrate(sec(d*x+c)^7*sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{60 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} - \frac{60 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a} + \frac{2 \, {\left(55 \, \sin\left(d x + c\right)^{3} - 177 \, \sin\left(d x + c\right)^{2} + 177 \, \sin\left(d x + c\right) - 39\right)}}{a {\left(\sin\left(d x + c\right) - 1\right)}^{3}} - \frac{125 \, \sin\left(d x + c\right)^{4} + 596 \, \sin\left(d x + c\right)^{3} + 1086 \, \sin\left(d x + c\right)^{2} + 884 \, \sin\left(d x + c\right) + 221}{a {\left(\sin\left(d x + c\right) + 1\right)}^{4}}}{3072 \, d}"," ",0,"-1/3072*(60*log(abs(sin(d*x + c) + 1))/a - 60*log(abs(sin(d*x + c) - 1))/a + 2*(55*sin(d*x + c)^3 - 177*sin(d*x + c)^2 + 177*sin(d*x + c) - 39)/(a*(sin(d*x + c) - 1)^3) - (125*sin(d*x + c)^4 + 596*sin(d*x + c)^3 + 1086*sin(d*x + c)^2 + 884*sin(d*x + c) + 221)/(a*(sin(d*x + c) + 1)^4))/d","A",0
888,1,136,0,0.290184," ","integrate(sec(d*x+c)^7*sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{60 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} - \frac{60 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a} + \frac{2 \, {\left(55 \, \sin\left(d x + c\right)^{3} - 225 \, \sin\left(d x + c\right)^{2} + 321 \, \sin\left(d x + c\right) - 167\right)}}{a {\left(\sin\left(d x + c\right) - 1\right)}^{3}} - \frac{125 \, \sin\left(d x + c\right)^{4} + 500 \, \sin\left(d x + c\right)^{3} + 702 \, \sin\left(d x + c\right)^{2} + 340 \, \sin\left(d x + c\right) - 35}{a {\left(\sin\left(d x + c\right) + 1\right)}^{4}}}{3072 \, d}"," ",0,"1/3072*(60*log(abs(sin(d*x + c) + 1))/a - 60*log(abs(sin(d*x + c) - 1))/a + 2*(55*sin(d*x + c)^3 - 225*sin(d*x + c)^2 + 321*sin(d*x + c) - 167)/(a*(sin(d*x + c) - 1)^3) - (125*sin(d*x + c)^4 + 500*sin(d*x + c)^3 + 702*sin(d*x + c)^2 + 340*sin(d*x + c) - 35)/(a*(sin(d*x + c) + 1)^4))/d","A",0
889,1,136,0,0.258138," ","integrate(sec(d*x+c)^7/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{420 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} - \frac{420 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a} + \frac{2 \, {\left(385 \, \sin\left(d x + c\right)^{3} - 1335 \, \sin\left(d x + c\right)^{2} + 1575 \, \sin\left(d x + c\right) - 641\right)}}{a {\left(\sin\left(d x + c\right) - 1\right)}^{3}} - \frac{875 \, \sin\left(d x + c\right)^{4} + 3980 \, \sin\left(d x + c\right)^{3} + 6930 \, \sin\left(d x + c\right)^{2} + 5548 \, \sin\left(d x + c\right) + 1771}{a {\left(\sin\left(d x + c\right) + 1\right)}^{4}}}{3072 \, d}"," ",0,"1/3072*(420*log(abs(sin(d*x + c) + 1))/a - 420*log(abs(sin(d*x + c) - 1))/a + 2*(385*sin(d*x + c)^3 - 1335*sin(d*x + c)^2 + 1575*sin(d*x + c) - 641)/(a*(sin(d*x + c) - 1)^3) - (875*sin(d*x + c)^4 + 3980*sin(d*x + c)^3 + 6930*sin(d*x + c)^2 + 5548*sin(d*x + c) + 1771)/(a*(sin(d*x + c) + 1)^4))/d","A",0
890,1,149,0,0.274948," ","integrate(csc(d*x+c)*sec(d*x+c)^7/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{1956 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} + \frac{1116 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a} - \frac{3072 \, \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a} - \frac{2 \, {\left(1023 \, \sin\left(d x + c\right)^{3} - 3417 \, \sin\left(d x + c\right)^{2} + 3849 \, \sin\left(d x + c\right) - 1471\right)}}{a {\left(\sin\left(d x + c\right) - 1\right)}^{3}} - \frac{4075 \, \sin\left(d x + c\right)^{4} + 17836 \, \sin\left(d x + c\right)^{3} + 29586 \, \sin\left(d x + c\right)^{2} + 22156 \, \sin\left(d x + c\right) + 6379}{a {\left(\sin\left(d x + c\right) + 1\right)}^{4}}}{3072 \, d}"," ",0,"-1/3072*(1956*log(abs(sin(d*x + c) + 1))/a + 1116*log(abs(sin(d*x + c) - 1))/a - 3072*log(abs(sin(d*x + c)))/a - 2*(1023*sin(d*x + c)^3 - 3417*sin(d*x + c)^2 + 3849*sin(d*x + c) - 1471)/(a*(sin(d*x + c) - 1)^3) - (4075*sin(d*x + c)^4 + 17836*sin(d*x + c)^3 + 29586*sin(d*x + c)^2 + 22156*sin(d*x + c) + 6379)/(a*(sin(d*x + c) + 1)^4))/d","A",0
891,1,170,0,0.264427," ","integrate(csc(d*x+c)^2*sec(d*x+c)^7/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{5316 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} - \frac{2244 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a} - \frac{3072 \, \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a} + \frac{3072 \, {\left(\sin\left(d x + c\right) - 1\right)}}{a \sin\left(d x + c\right)} + \frac{2 \, {\left(2057 \, \sin\left(d x + c\right)^{3} - 6735 \, \sin\left(d x + c\right)^{2} + 7407 \, \sin\left(d x + c\right) - 2745\right)}}{a {\left(\sin\left(d x + c\right) - 1\right)}^{3}} - \frac{11075 \, \sin\left(d x + c\right)^{4} + 47660 \, \sin\left(d x + c\right)^{3} + 77442 \, \sin\left(d x + c\right)^{2} + 56460 \, \sin\left(d x + c\right) + 15651}{a {\left(\sin\left(d x + c\right) + 1\right)}^{4}}}{3072 \, d}"," ",0,"1/3072*(5316*log(abs(sin(d*x + c) + 1))/a - 2244*log(abs(sin(d*x + c) - 1))/a - 3072*log(abs(sin(d*x + c)))/a + 3072*(sin(d*x + c) - 1)/(a*sin(d*x + c)) + 2*(2057*sin(d*x + c)^3 - 6735*sin(d*x + c)^2 + 7407*sin(d*x + c) - 2745)/(a*(sin(d*x + c) - 1)^3) - (11075*sin(d*x + c)^4 + 47660*sin(d*x + c)^3 + 77442*sin(d*x + c)^2 + 56460*sin(d*x + c) + 15651)/(a*(sin(d*x + c) + 1)^4))/d","A",0
892,1,182,0,0.298565," ","integrate(csc(d*x+c)^3*sec(d*x+c)^7/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{11460 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} + \frac{3900 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a} - \frac{15360 \, \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a} + \frac{1536 \, {\left(15 \, \sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1\right)}}{a \sin\left(d x + c\right)^{2}} - \frac{2 \, {\left(3575 \, \sin\left(d x + c\right)^{3} - 11553 \, \sin\left(d x + c\right)^{2} + 12513 \, \sin\left(d x + c\right) - 4551\right)}}{a {\left(\sin\left(d x + c\right) - 1\right)}^{3}} - \frac{23875 \, \sin\left(d x + c\right)^{4} + 101644 \, \sin\left(d x + c\right)^{3} + 163074 \, \sin\left(d x + c\right)^{2} + 117036 \, \sin\left(d x + c\right) + 31779}{a {\left(\sin\left(d x + c\right) + 1\right)}^{4}}}{3072 \, d}"," ",0,"-1/3072*(11460*log(abs(sin(d*x + c) + 1))/a + 3900*log(abs(sin(d*x + c) - 1))/a - 15360*log(abs(sin(d*x + c)))/a + 1536*(15*sin(d*x + c)^2 - 2*sin(d*x + c) + 1)/(a*sin(d*x + c)^2) - 2*(3575*sin(d*x + c)^3 - 11553*sin(d*x + c)^2 + 12513*sin(d*x + c) - 4551)/(a*(sin(d*x + c) - 1)^3) - (23875*sin(d*x + c)^4 + 101644*sin(d*x + c)^3 + 163074*sin(d*x + c)^2 + 117036*sin(d*x + c) + 31779)/(a*(sin(d*x + c) + 1)^4))/d","A",0
893,1,187,0,0.297643," ","integrate(csc(d*x+c)^4*sec(d*x+c)^7/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{21540 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} - \frac{6180 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a} - \frac{15360 \, \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a} + \frac{19745 \, \sin\left(d x + c\right)^{6} - 76875 \, \sin\left(d x + c\right)^{5} + 111723 \, \sin\left(d x + c\right)^{4} - 74081 \, \sin\left(d x + c\right)^{3} + 23040 \, \sin\left(d x + c\right)^{2} - 4608 \, \sin\left(d x + c\right) + 1024}{{\left(\sin\left(d x + c\right)^{2} - \sin\left(d x + c\right)\right)}^{3} a} - \frac{44875 \, \sin\left(d x + c\right)^{4} + 189580 \, \sin\left(d x + c\right)^{3} + 301458 \, \sin\left(d x + c\right)^{2} + 214060 \, \sin\left(d x + c\right) + 57355}{a {\left(\sin\left(d x + c\right) + 1\right)}^{4}}}{3072 \, d}"," ",0,"1/3072*(21540*log(abs(sin(d*x + c) + 1))/a - 6180*log(abs(sin(d*x + c) - 1))/a - 15360*log(abs(sin(d*x + c)))/a + (19745*sin(d*x + c)^6 - 76875*sin(d*x + c)^5 + 111723*sin(d*x + c)^4 - 74081*sin(d*x + c)^3 + 23040*sin(d*x + c)^2 - 4608*sin(d*x + c) + 1024)/((sin(d*x + c)^2 - sin(d*x + c))^3*a) - (44875*sin(d*x + c)^4 + 189580*sin(d*x + c)^3 + 301458*sin(d*x + c)^2 + 214060*sin(d*x + c) + 57355)/(a*(sin(d*x + c) + 1)^4))/d","A",0
894,1,138,0,0.242067," ","integrate(sec(d*x+c)^8*sin(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{35 \, {\left(3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{3}} - \frac{105 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1015 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 1330 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1302 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 469 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 67 \, a^{2}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{7}}}{840 \, d}"," ",0,"-1/840*(35*(3*a^2*tan(1/2*d*x + 1/2*c) + a^2)/(tan(1/2*d*x + 1/2*c) + 1)^3 - (105*a^2*tan(1/2*d*x + 1/2*c)^5 - 1015*a^2*tan(1/2*d*x + 1/2*c)^4 + 1330*a^2*tan(1/2*d*x + 1/2*c)^3 - 1302*a^2*tan(1/2*d*x + 1/2*c)^2 + 469*a^2*tan(1/2*d*x + 1/2*c) - 67*a^2)/(tan(1/2*d*x + 1/2*c) - 1)^7)/d","A",0
895,1,181,0,0.408040," ","integrate(sec(d*x+c)^9*sin(d*x+c)^12/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{44580 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} + \frac{16860 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a} + \frac{5120 \, {\left(a \sin\left(d x + c\right)^{2} - 2 \, a \sin\left(d x + c\right)\right)}}{a^{2}} - \frac{5 \, {\left(7025 \, \sin\left(d x + c\right)^{4} - 25604 \, \sin\left(d x + c\right)^{3} + 35226 \, \sin\left(d x + c\right)^{2} - 21644 \, \sin\left(d x + c\right) + 5005\right)}}{a {\left(\sin\left(d x + c\right) - 1\right)}^{4}} - \frac{101791 \, \sin\left(d x + c\right)^{5} + 462755 \, \sin\left(d x + c\right)^{4} + 848410 \, \sin\left(d x + c\right)^{3} + 782370 \, \sin\left(d x + c\right)^{2} + 362335 \, \sin\left(d x + c\right) + 67347}{a {\left(\sin\left(d x + c\right) + 1\right)}^{5}}}{10240 \, d}"," ",0,"-1/10240*(44580*log(abs(sin(d*x + c) + 1))/a + 16860*log(abs(sin(d*x + c) - 1))/a + 5120*(a*sin(d*x + c)^2 - 2*a*sin(d*x + c))/a^2 - 5*(7025*sin(d*x + c)^4 - 25604*sin(d*x + c)^3 + 35226*sin(d*x + c)^2 - 21644*sin(d*x + c) + 5005)/(a*(sin(d*x + c) - 1)^4) - (101791*sin(d*x + c)^5 + 462755*sin(d*x + c)^4 + 848410*sin(d*x + c)^3 + 782370*sin(d*x + c)^2 + 362335*sin(d*x + c) + 67347)/(a*(sin(d*x + c) + 1)^5))/d","A",0
896,1,167,0,0.398965," ","integrate(sec(d*x+c)^9*sin(d*x+c)^11/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{56940 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} - \frac{26220 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a} - \frac{30720 \, \sin\left(d x + c\right)}{a} + \frac{5 \, {\left(10925 \, \sin\left(d x + c\right)^{4} - 38828 \, \sin\left(d x + c\right)^{3} + 52242 \, \sin\left(d x + c\right)^{2} - 31444 \, \sin\left(d x + c\right) + 7129\right)}}{a {\left(\sin\left(d x + c\right) - 1\right)}^{4}} - \frac{130013 \, \sin\left(d x + c\right)^{5} + 573265 \, \sin\left(d x + c\right)^{4} + 1023830 \, \sin\left(d x + c\right)^{3} + 922030 \, \sin\left(d x + c\right)^{2} + 417605 \, \sin\left(d x + c\right) + 75961}{a {\left(\sin\left(d x + c\right) + 1\right)}^{5}}}{30720 \, d}"," ",0,"1/30720*(56940*log(abs(sin(d*x + c) + 1))/a - 26220*log(abs(sin(d*x + c) - 1))/a - 30720*sin(d*x + c)/a + 5*(10925*sin(d*x + c)^4 - 38828*sin(d*x + c)^3 + 52242*sin(d*x + c)^2 - 31444*sin(d*x + c) + 7129)/(a*(sin(d*x + c) - 1)^4) - (130013*sin(d*x + c)^5 + 573265*sin(d*x + c)^4 + 1023830*sin(d*x + c)^3 + 922030*sin(d*x + c)^2 + 417605*sin(d*x + c) + 75961)/(a*(sin(d*x + c) + 1)^5))/d","A",0
897,1,156,0,0.365136," ","integrate(sec(d*x+c)^9*sin(d*x+c)^10/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{19140 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} + \frac{11580 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a} - \frac{5 \, {\left(4825 \, \sin\left(d x + c\right)^{4} - 16372 \, \sin\left(d x + c\right)^{3} + 21138 \, \sin\left(d x + c\right)^{2} - 12236 \, \sin\left(d x + c\right) + 2669\right)}}{a {\left(\sin\left(d x + c\right) - 1\right)}^{4}} - \frac{43703 \, \sin\left(d x + c\right)^{5} + 180715 \, \sin\left(d x + c\right)^{4} + 305330 \, \sin\left(d x + c\right)^{3} + 261130 \, \sin\left(d x + c\right)^{2} + 112415 \, \sin\left(d x + c\right) + 19411}{a {\left(\sin\left(d x + c\right) + 1\right)}^{5}}}{30720 \, d}"," ",0,"-1/30720*(19140*log(abs(sin(d*x + c) + 1))/a + 11580*log(abs(sin(d*x + c) - 1))/a - 5*(4825*sin(d*x + c)^4 - 16372*sin(d*x + c)^3 + 21138*sin(d*x + c)^2 - 12236*sin(d*x + c) + 2669)/(a*(sin(d*x + c) - 1)^4) - (43703*sin(d*x + c)^5 + 180715*sin(d*x + c)^4 + 305330*sin(d*x + c)^3 + 261130*sin(d*x + c)^2 + 112415*sin(d*x + c) + 19411)/(a*(sin(d*x + c) + 1)^5))/d","A",0
898,1,156,0,0.374506," ","integrate(sec(d*x+c)^9*sin(d*x+c)^9/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{1260 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} - \frac{1260 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a} + \frac{5 \, {\left(525 \, \sin\left(d x + c\right)^{4} - 1580 \, \sin\left(d x + c\right)^{3} + 1818 \, \sin\left(d x + c\right)^{2} - 932 \, \sin\left(d x + c\right) + 177\right)}}{a {\left(\sin\left(d x + c\right) - 1\right)}^{4}} - \frac{2877 \, \sin\left(d x + c\right)^{5} + 9265 \, \sin\left(d x + c\right)^{4} + 12030 \, \sin\left(d x + c\right)^{3} + 7430 \, \sin\left(d x + c\right)^{2} + 1965 \, \sin\left(d x + c\right) + 113}{a {\left(\sin\left(d x + c\right) + 1\right)}^{5}}}{10240 \, d}"," ",0,"1/10240*(1260*log(abs(sin(d*x + c) + 1))/a - 1260*log(abs(sin(d*x + c) - 1))/a + 5*(525*sin(d*x + c)^4 - 1580*sin(d*x + c)^3 + 1818*sin(d*x + c)^2 - 932*sin(d*x + c) + 177)/(a*(sin(d*x + c) - 1)^4) - (2877*sin(d*x + c)^5 + 9265*sin(d*x + c)^4 + 12030*sin(d*x + c)^3 + 7430*sin(d*x + c)^2 + 1965*sin(d*x + c) + 113)/(a*(sin(d*x + c) + 1)^5))/d","A",0
899,1,156,0,0.354565," ","integrate(sec(d*x+c)^9*sin(d*x+c)^8/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{420 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} - \frac{420 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a} + \frac{5 \, {\left(175 \, \sin\left(d x + c\right)^{4} - 28 \, \sin\left(d x + c\right)^{3} - 522 \, \sin\left(d x + c\right)^{2} + 588 \, \sin\left(d x + c\right) - 189\right)}}{a {\left(\sin\left(d x + c\right) - 1\right)}^{4}} - \frac{959 \, \sin\left(d x + c\right)^{5} + 8995 \, \sin\left(d x + c\right)^{4} + 20810 \, \sin\left(d x + c\right)^{3} + 21810 \, \sin\left(d x + c\right)^{2} + 11055 \, \sin\left(d x + c\right) + 2211}{a {\left(\sin\left(d x + c\right) + 1\right)}^{5}}}{30720 \, d}"," ",0,"1/30720*(420*log(abs(sin(d*x + c) + 1))/a - 420*log(abs(sin(d*x + c) - 1))/a + 5*(175*sin(d*x + c)^4 - 28*sin(d*x + c)^3 - 522*sin(d*x + c)^2 + 588*sin(d*x + c) - 189)/(a*(sin(d*x + c) - 1)^4) - (959*sin(d*x + c)^5 + 8995*sin(d*x + c)^4 + 20810*sin(d*x + c)^3 + 21810*sin(d*x + c)^2 + 11055*sin(d*x + c) + 2211)/(a*(sin(d*x + c) + 1)^5))/d","A",0
900,1,156,0,0.351549," ","integrate(sec(d*x+c)^9*sin(d*x+c)^7/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{420 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} - \frac{420 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a} + \frac{5 \, {\left(175 \, \sin\left(d x + c\right)^{4} - 868 \, \sin\left(d x + c\right)^{3} + 1302 \, \sin\left(d x + c\right)^{2} - 828 \, \sin\left(d x + c\right) + 195\right)}}{a {\left(\sin\left(d x + c\right) - 1\right)}^{4}} - \frac{959 \, \sin\left(d x + c\right)^{5} + 4795 \, \sin\left(d x + c\right)^{4} + 7490 \, \sin\left(d x + c\right)^{3} + 5610 \, \sin\left(d x + c\right)^{2} + 2055 \, \sin\left(d x + c\right) + 291}{a {\left(\sin\left(d x + c\right) + 1\right)}^{5}}}{30720 \, d}"," ",0,"-1/30720*(420*log(abs(sin(d*x + c) + 1))/a - 420*log(abs(sin(d*x + c) - 1))/a + 5*(175*sin(d*x + c)^4 - 868*sin(d*x + c)^3 + 1302*sin(d*x + c)^2 - 828*sin(d*x + c) + 195)/(a*(sin(d*x + c) - 1)^4) - (959*sin(d*x + c)^5 + 4795*sin(d*x + c)^4 + 7490*sin(d*x + c)^3 + 5610*sin(d*x + c)^2 + 2055*sin(d*x + c) + 291)/(a*(sin(d*x + c) + 1)^5))/d","A",0
901,1,156,0,0.360052," ","integrate(sec(d*x+c)^9*sin(d*x+c)^6/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{60 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} - \frac{60 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a} + \frac{5 \, {\left(25 \, \sin\left(d x + c\right)^{4} - 84 \, \sin\left(d x + c\right)^{3} + 66 \, \sin\left(d x + c\right)^{2} - 12 \, \sin\left(d x + c\right) - 3\right)}}{a {\left(\sin\left(d x + c\right) - 1\right)}^{4}} - \frac{137 \, \sin\left(d x + c\right)^{5} + 885 \, \sin\left(d x + c\right)^{4} + 2270 \, \sin\left(d x + c\right)^{3} + 2470 \, \sin\left(d x + c\right)^{2} + 1265 \, \sin\left(d x + c\right) + 253}{a {\left(\sin\left(d x + c\right) + 1\right)}^{5}}}{10240 \, d}"," ",0,"-1/10240*(60*log(abs(sin(d*x + c) + 1))/a - 60*log(abs(sin(d*x + c) - 1))/a + 5*(25*sin(d*x + c)^4 - 84*sin(d*x + c)^3 + 66*sin(d*x + c)^2 - 12*sin(d*x + c) - 3)/(a*(sin(d*x + c) - 1)^4) - (137*sin(d*x + c)^5 + 885*sin(d*x + c)^4 + 2270*sin(d*x + c)^3 + 2470*sin(d*x + c)^2 + 1265*sin(d*x + c) + 253)/(a*(sin(d*x + c) + 1)^5))/d","A",0
902,1,156,0,0.324638," ","integrate(sec(d*x+c)^9*sin(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{180 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} - \frac{180 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a} + \frac{5 \, {\left(75 \, \sin\left(d x + c\right)^{4} - 372 \, \sin\left(d x + c\right)^{3} + 678 \, \sin\left(d x + c\right)^{2} - 476 \, \sin\left(d x + c\right) + 119\right)}}{a {\left(\sin\left(d x + c\right) - 1\right)}^{4}} - \frac{411 \, \sin\left(d x + c\right)^{5} + 2055 \, \sin\left(d x + c\right)^{4} + 3810 \, \sin\left(d x + c\right)^{3} + 2810 \, \sin\left(d x + c\right)^{2} + 955 \, \sin\left(d x + c\right) + 119}{a {\left(\sin\left(d x + c\right) + 1\right)}^{5}}}{30720 \, d}"," ",0,"1/30720*(180*log(abs(sin(d*x + c) + 1))/a - 180*log(abs(sin(d*x + c) - 1))/a + 5*(75*sin(d*x + c)^4 - 372*sin(d*x + c)^3 + 678*sin(d*x + c)^2 - 476*sin(d*x + c) + 119)/(a*(sin(d*x + c) - 1)^4) - (411*sin(d*x + c)^5 + 2055*sin(d*x + c)^4 + 3810*sin(d*x + c)^3 + 2810*sin(d*x + c)^2 + 955*sin(d*x + c) + 119)/(a*(sin(d*x + c) + 1)^5))/d","A",0
903,1,156,0,0.320620," ","integrate(sec(d*x+c)^9*sin(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{180 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} - \frac{180 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a} + \frac{5 \, {\left(75 \, \sin\left(d x + c\right)^{4} - 300 \, \sin\left(d x + c\right)^{3} + 414 \, \sin\left(d x + c\right)^{2} - 196 \, \sin\left(d x + c\right) + 31\right)}}{a {\left(\sin\left(d x + c\right) - 1\right)}^{4}} - \frac{411 \, \sin\left(d x + c\right)^{5} + 2415 \, \sin\left(d x + c\right)^{4} + 5730 \, \sin\left(d x + c\right)^{3} + 6730 \, \sin\left(d x + c\right)^{2} + 3515 \, \sin\left(d x + c\right) + 703}{a {\left(\sin\left(d x + c\right) + 1\right)}^{5}}}{30720 \, d}"," ",0,"1/30720*(180*log(abs(sin(d*x + c) + 1))/a - 180*log(abs(sin(d*x + c) - 1))/a + 5*(75*sin(d*x + c)^4 - 300*sin(d*x + c)^3 + 414*sin(d*x + c)^2 - 196*sin(d*x + c) + 31)/(a*(sin(d*x + c) - 1)^4) - (411*sin(d*x + c)^5 + 2415*sin(d*x + c)^4 + 5730*sin(d*x + c)^3 + 6730*sin(d*x + c)^2 + 3515*sin(d*x + c) + 703)/(a*(sin(d*x + c) + 1)^5))/d","A",0
904,1,156,0,0.305795," ","integrate(sec(d*x+c)^9*sin(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{60 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} - \frac{60 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a} + \frac{5 \, {\left(25 \, \sin\left(d x + c\right)^{4} - 124 \, \sin\left(d x + c\right)^{3} + 234 \, \sin\left(d x + c\right)^{2} - 196 \, \sin\left(d x + c\right) + 53\right)}}{a {\left(\sin\left(d x + c\right) - 1\right)}^{4}} - \frac{137 \, \sin\left(d x + c\right)^{5} + 685 \, \sin\left(d x + c\right)^{4} + 1310 \, \sin\left(d x + c\right)^{3} + 1110 \, \sin\left(d x + c\right)^{2} + 305 \, \sin\left(d x + c\right) + 21}{a {\left(\sin\left(d x + c\right) + 1\right)}^{5}}}{10240 \, d}"," ",0,"-1/10240*(60*log(abs(sin(d*x + c) + 1))/a - 60*log(abs(sin(d*x + c) - 1))/a + 5*(25*sin(d*x + c)^4 - 124*sin(d*x + c)^3 + 234*sin(d*x + c)^2 - 196*sin(d*x + c) + 53)/(a*(sin(d*x + c) - 1)^4) - (137*sin(d*x + c)^5 + 685*sin(d*x + c)^4 + 1310*sin(d*x + c)^3 + 1110*sin(d*x + c)^2 + 305*sin(d*x + c) + 21)/(a*(sin(d*x + c) + 1)^5))/d","A",0
905,1,156,0,0.289474," ","integrate(sec(d*x+c)^9*sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{420 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} - \frac{420 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a} + \frac{5 \, {\left(175 \, \sin\left(d x + c\right)^{4} - 748 \, \sin\left(d x + c\right)^{3} + 1182 \, \sin\left(d x + c\right)^{2} - 788 \, \sin\left(d x + c\right) + 155\right)}}{a {\left(\sin\left(d x + c\right) - 1\right)}^{4}} - \frac{959 \, \sin\left(d x + c\right)^{5} + 5395 \, \sin\left(d x + c\right)^{4} + 12290 \, \sin\left(d x + c\right)^{3} + 14170 \, \sin\left(d x + c\right)^{2} + 8135 \, \sin\left(d x + c\right) + 1627}{a {\left(\sin\left(d x + c\right) + 1\right)}^{5}}}{30720 \, d}"," ",0,"-1/30720*(420*log(abs(sin(d*x + c) + 1))/a - 420*log(abs(sin(d*x + c) - 1))/a + 5*(175*sin(d*x + c)^4 - 748*sin(d*x + c)^3 + 1182*sin(d*x + c)^2 - 788*sin(d*x + c) + 155)/(a*(sin(d*x + c) - 1)^4) - (959*sin(d*x + c)^5 + 5395*sin(d*x + c)^4 + 12290*sin(d*x + c)^3 + 14170*sin(d*x + c)^2 + 8135*sin(d*x + c) + 1627)/(a*(sin(d*x + c) + 1)^5))/d","A",0
906,1,156,0,0.305368," ","integrate(sec(d*x+c)^9*sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{420 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} - \frac{420 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a} + \frac{5 \, {\left(175 \, \sin\left(d x + c\right)^{4} - 868 \, \sin\left(d x + c\right)^{3} + 1662 \, \sin\left(d x + c\right)^{2} - 1484 \, \sin\left(d x + c\right) + 539\right)}}{a {\left(\sin\left(d x + c\right) - 1\right)}^{4}} - \frac{959 \, \sin\left(d x + c\right)^{5} + 4795 \, \sin\left(d x + c\right)^{4} + 9290 \, \sin\left(d x + c\right)^{3} + 8290 \, \sin\left(d x + c\right)^{2} + 2735 \, \sin\left(d x + c\right) - 293}{a {\left(\sin\left(d x + c\right) + 1\right)}^{5}}}{30720 \, d}"," ",0,"1/30720*(420*log(abs(sin(d*x + c) + 1))/a - 420*log(abs(sin(d*x + c) - 1))/a + 5*(175*sin(d*x + c)^4 - 868*sin(d*x + c)^3 + 1662*sin(d*x + c)^2 - 1484*sin(d*x + c) + 539)/(a*(sin(d*x + c) - 1)^4) - (959*sin(d*x + c)^5 + 4795*sin(d*x + c)^4 + 9290*sin(d*x + c)^3 + 8290*sin(d*x + c)^2 + 2735*sin(d*x + c) - 293)/(a*(sin(d*x + c) + 1)^5))/d","A",0
907,1,156,0,0.238733," ","integrate(sec(d*x+c)^9/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{1260 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} - \frac{1260 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a} + \frac{5 \, {\left(525 \, \sin\left(d x + c\right)^{4} - 2324 \, \sin\left(d x + c\right)^{3} + 3906 \, \sin\left(d x + c\right)^{2} - 2972 \, \sin\left(d x + c\right) + 873\right)}}{a {\left(\sin\left(d x + c\right) - 1\right)}^{4}} - \frac{2877 \, \sin\left(d x + c\right)^{5} + 15785 \, \sin\left(d x + c\right)^{4} + 35070 \, \sin\left(d x + c\right)^{3} + 39670 \, \sin\left(d x + c\right)^{2} + 23085 \, \sin\left(d x + c\right) + 5641}{a {\left(\sin\left(d x + c\right) + 1\right)}^{5}}}{10240 \, d}"," ",0,"1/10240*(1260*log(abs(sin(d*x + c) + 1))/a - 1260*log(abs(sin(d*x + c) - 1))/a + 5*(525*sin(d*x + c)^4 - 2324*sin(d*x + c)^3 + 3906*sin(d*x + c)^2 - 2972*sin(d*x + c) + 873)/(a*(sin(d*x + c) - 1)^4) - (2877*sin(d*x + c)^5 + 15785*sin(d*x + c)^4 + 35070*sin(d*x + c)^3 + 39670*sin(d*x + c)^2 + 23085*sin(d*x + c) + 5641)/(a*(sin(d*x + c) + 1)^5))/d","A",0
908,1,169,0,0.241493," ","integrate(csc(d*x+c)*sec(d*x+c)^9/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{19140 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} + \frac{11580 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a} - \frac{30720 \, \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a} - \frac{5 \, {\left(4825 \, \sin\left(d x + c\right)^{4} - 20860 \, \sin\left(d x + c\right)^{3} + 34074 \, \sin\left(d x + c\right)^{2} - 24996 \, \sin\left(d x + c\right) + 6981\right)}}{a {\left(\sin\left(d x + c\right) - 1\right)}^{4}} - \frac{43703 \, \sin\left(d x + c\right)^{5} + 233875 \, \sin\left(d x + c\right)^{4} + 504050 \, \sin\left(d x + c\right)^{3} + 548250 \, \sin\left(d x + c\right)^{2} + 302175 \, \sin\left(d x + c\right) + 67995}{a {\left(\sin\left(d x + c\right) + 1\right)}^{5}}}{30720 \, d}"," ",0,"-1/30720*(19140*log(abs(sin(d*x + c) + 1))/a + 11580*log(abs(sin(d*x + c) - 1))/a - 30720*log(abs(sin(d*x + c)))/a - 5*(4825*sin(d*x + c)^4 - 20860*sin(d*x + c)^3 + 34074*sin(d*x + c)^2 - 24996*sin(d*x + c) + 6981)/(a*(sin(d*x + c) - 1)^4) - (43703*sin(d*x + c)^5 + 233875*sin(d*x + c)^4 + 504050*sin(d*x + c)^3 + 548250*sin(d*x + c)^2 + 302175*sin(d*x + c) + 67995)/(a*(sin(d*x + c) + 1)^5))/d","A",0
909,1,190,0,0.271768," ","integrate(csc(d*x+c)^2*sec(d*x+c)^9/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{56940 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} - \frac{26220 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a} - \frac{30720 \, \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a} + \frac{30720 \, {\left(\sin\left(d x + c\right) - 1\right)}}{a \sin\left(d x + c\right)} + \frac{5 \, {\left(10925 \, \sin\left(d x + c\right)^{4} - 46628 \, \sin\left(d x + c\right)^{3} + 75018 \, \sin\left(d x + c\right)^{2} - 54012 \, \sin\left(d x + c\right) + 14721\right)}}{a {\left(\sin\left(d x + c\right) - 1\right)}^{4}} - \frac{130013 \, \sin\left(d x + c\right)^{5} + 687865 \, \sin\left(d x + c\right)^{4} + 1462550 \, \sin\left(d x + c\right)^{3} + 1564350 \, \sin\left(d x + c\right)^{2} + 843525 \, \sin\left(d x + c\right) + 184065}{a {\left(\sin\left(d x + c\right) + 1\right)}^{5}}}{30720 \, d}"," ",0,"1/30720*(56940*log(abs(sin(d*x + c) + 1))/a - 26220*log(abs(sin(d*x + c) - 1))/a - 30720*log(abs(sin(d*x + c)))/a + 30720*(sin(d*x + c) - 1)/(a*sin(d*x + c)) + 5*(10925*sin(d*x + c)^4 - 46628*sin(d*x + c)^3 + 75018*sin(d*x + c)^2 - 54012*sin(d*x + c) + 14721)/(a*(sin(d*x + c) - 1)^4) - (130013*sin(d*x + c)^5 + 687865*sin(d*x + c)^4 + 1462550*sin(d*x + c)^3 + 1564350*sin(d*x + c)^2 + 843525*sin(d*x + c) + 184065)/(a*(sin(d*x + c) + 1)^5))/d","A",0
910,1,202,0,0.286279," ","integrate(csc(d*x+c)^3*sec(d*x+c)^9/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{44580 \, \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} + \frac{16860 \, \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a} - \frac{61440 \, \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a} + \frac{5120 \, {\left(18 \, \sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1\right)}}{a \sin\left(d x + c\right)^{2}} - \frac{5 \, {\left(7025 \, \sin\left(d x + c\right)^{4} - 29724 \, \sin\left(d x + c\right)^{3} + 47346 \, \sin\left(d x + c\right)^{2} - 33684 \, \sin\left(d x + c\right) + 9045\right)}}{a {\left(\sin\left(d x + c\right) - 1\right)}^{4}} - \frac{101791 \, \sin\left(d x + c\right)^{5} + 534555 \, \sin\left(d x + c\right)^{4} + 1126810 \, \sin\left(d x + c\right)^{3} + 1192850 \, \sin\left(d x + c\right)^{2} + 634975 \, \sin\left(d x + c\right) + 136235}{a {\left(\sin\left(d x + c\right) + 1\right)}^{5}}}{10240 \, d}"," ",0,"-1/10240*(44580*log(abs(sin(d*x + c) + 1))/a + 16860*log(abs(sin(d*x + c) - 1))/a - 61440*log(abs(sin(d*x + c)))/a + 5120*(18*sin(d*x + c)^2 - 2*sin(d*x + c) + 1)/(a*sin(d*x + c)^2) - 5*(7025*sin(d*x + c)^4 - 29724*sin(d*x + c)^3 + 47346*sin(d*x + c)^2 - 33684*sin(d*x + c) + 9045)/(a*(sin(d*x + c) - 1)^4) - (101791*sin(d*x + c)^5 + 534555*sin(d*x + c)^4 + 1126810*sin(d*x + c)^3 + 1192850*sin(d*x + c)^2 + 634975*sin(d*x + c) + 136235)/(a*(sin(d*x + c) + 1)^5))/d","A",0
911,0,0,0,0.000000," ","integrate((g*sec(f*x+e))^p*(d*sin(f*x+e))^n*(a+a*sin(f*x+e))^m,x, algorithm=""giac"")","\int \left(g \sec\left(f x + e\right)\right)^{p} {\left(a \sin\left(f x + e\right) + a\right)}^{m} \left(d \sin\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((g*sec(f*x + e))^p*(a*sin(f*x + e) + a)^m*(d*sin(f*x + e))^n, x)","F",0
912,0,0,0,0.000000," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(d*sin(f*x + e) + c)^n*cos(f*x + e), x)","F",0
913,1,1840,0,0.241320," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))^4*(c+d*sin(f*x+e))^n,x, algorithm=""giac"")","\frac{\frac{{\left({\left(d \sin\left(f x + e\right) + c\right)}^{5} {\left(d \sin\left(f x + e\right) + c\right)}^{n} n^{4} - 4 \, {\left(d \sin\left(f x + e\right) + c\right)}^{4} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c n^{4} + 6 \, {\left(d \sin\left(f x + e\right) + c\right)}^{3} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c^{2} n^{4} - 4 \, {\left(d \sin\left(f x + e\right) + c\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c^{3} n^{4} + {\left(d \sin\left(f x + e\right) + c\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c^{4} n^{4} + 10 \, {\left(d \sin\left(f x + e\right) + c\right)}^{5} {\left(d \sin\left(f x + e\right) + c\right)}^{n} n^{3} - 44 \, {\left(d \sin\left(f x + e\right) + c\right)}^{4} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c n^{3} + 72 \, {\left(d \sin\left(f x + e\right) + c\right)}^{3} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c^{2} n^{3} - 52 \, {\left(d \sin\left(f x + e\right) + c\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c^{3} n^{3} + 14 \, {\left(d \sin\left(f x + e\right) + c\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c^{4} n^{3} + 35 \, {\left(d \sin\left(f x + e\right) + c\right)}^{5} {\left(d \sin\left(f x + e\right) + c\right)}^{n} n^{2} - 164 \, {\left(d \sin\left(f x + e\right) + c\right)}^{4} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c n^{2} + 294 \, {\left(d \sin\left(f x + e\right) + c\right)}^{3} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c^{2} n^{2} - 236 \, {\left(d \sin\left(f x + e\right) + c\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c^{3} n^{2} + 71 \, {\left(d \sin\left(f x + e\right) + c\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c^{4} n^{2} + 50 \, {\left(d \sin\left(f x + e\right) + c\right)}^{5} {\left(d \sin\left(f x + e\right) + c\right)}^{n} n - 244 \, {\left(d \sin\left(f x + e\right) + c\right)}^{4} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c n + 468 \, {\left(d \sin\left(f x + e\right) + c\right)}^{3} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c^{2} n - 428 \, {\left(d \sin\left(f x + e\right) + c\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c^{3} n + 154 \, {\left(d \sin\left(f x + e\right) + c\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c^{4} n + 24 \, {\left(d \sin\left(f x + e\right) + c\right)}^{5} {\left(d \sin\left(f x + e\right) + c\right)}^{n} - 120 \, {\left(d \sin\left(f x + e\right) + c\right)}^{4} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c + 240 \, {\left(d \sin\left(f x + e\right) + c\right)}^{3} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c^{2} - 240 \, {\left(d \sin\left(f x + e\right) + c\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c^{3} + 120 \, {\left(d \sin\left(f x + e\right) + c\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c^{4}\right)} a^{4}}{d^{4} n^{5} + 15 \, d^{4} n^{4} + 85 \, d^{4} n^{3} + 225 \, d^{4} n^{2} + 274 \, d^{4} n + 120 \, d^{4}} + \frac{4 \, {\left({\left(d \sin\left(f x + e\right) + c\right)}^{4} {\left(d \sin\left(f x + e\right) + c\right)}^{n} n^{3} - 3 \, {\left(d \sin\left(f x + e\right) + c\right)}^{3} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c n^{3} + 3 \, {\left(d \sin\left(f x + e\right) + c\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c^{2} n^{3} - {\left(d \sin\left(f x + e\right) + c\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c^{3} n^{3} + 6 \, {\left(d \sin\left(f x + e\right) + c\right)}^{4} {\left(d \sin\left(f x + e\right) + c\right)}^{n} n^{2} - 21 \, {\left(d \sin\left(f x + e\right) + c\right)}^{3} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c n^{2} + 24 \, {\left(d \sin\left(f x + e\right) + c\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c^{2} n^{2} - 9 \, {\left(d \sin\left(f x + e\right) + c\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c^{3} n^{2} + 11 \, {\left(d \sin\left(f x + e\right) + c\right)}^{4} {\left(d \sin\left(f x + e\right) + c\right)}^{n} n - 42 \, {\left(d \sin\left(f x + e\right) + c\right)}^{3} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c n + 57 \, {\left(d \sin\left(f x + e\right) + c\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c^{2} n - 26 \, {\left(d \sin\left(f x + e\right) + c\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c^{3} n + 6 \, {\left(d \sin\left(f x + e\right) + c\right)}^{4} {\left(d \sin\left(f x + e\right) + c\right)}^{n} - 24 \, {\left(d \sin\left(f x + e\right) + c\right)}^{3} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c + 36 \, {\left(d \sin\left(f x + e\right) + c\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c^{2} - 24 \, {\left(d \sin\left(f x + e\right) + c\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c^{3}\right)} a^{4}}{d^{3} n^{4} + 10 \, d^{3} n^{3} + 35 \, d^{3} n^{2} + 50 \, d^{3} n + 24 \, d^{3}} + \frac{6 \, {\left({\left(d \sin\left(f x + e\right) + c\right)}^{3} {\left(d \sin\left(f x + e\right) + c\right)}^{n} n^{2} - 2 \, {\left(d \sin\left(f x + e\right) + c\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c n^{2} + {\left(d \sin\left(f x + e\right) + c\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c^{2} n^{2} + 3 \, {\left(d \sin\left(f x + e\right) + c\right)}^{3} {\left(d \sin\left(f x + e\right) + c\right)}^{n} n - 8 \, {\left(d \sin\left(f x + e\right) + c\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c n + 5 \, {\left(d \sin\left(f x + e\right) + c\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c^{2} n + 2 \, {\left(d \sin\left(f x + e\right) + c\right)}^{3} {\left(d \sin\left(f x + e\right) + c\right)}^{n} - 6 \, {\left(d \sin\left(f x + e\right) + c\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c + 6 \, {\left(d \sin\left(f x + e\right) + c\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c^{2}\right)} a^{4}}{d^{2} n^{3} + 6 \, d^{2} n^{2} + 11 \, d^{2} n + 6 \, d^{2}} + \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n + 1} a^{4}}{n + 1} + \frac{4 \, {\left({\left(d \sin\left(f x + e\right) + c\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{n} n - {\left(d \sin\left(f x + e\right) + c\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c n + {\left(d \sin\left(f x + e\right) + c\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{n} - 2 \, {\left(d \sin\left(f x + e\right) + c\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c\right)} a^{4}}{{\left(n^{2} + 3 \, n + 2\right)} d}}{d f}"," ",0,"(((d*sin(f*x + e) + c)^5*(d*sin(f*x + e) + c)^n*n^4 - 4*(d*sin(f*x + e) + c)^4*(d*sin(f*x + e) + c)^n*c*n^4 + 6*(d*sin(f*x + e) + c)^3*(d*sin(f*x + e) + c)^n*c^2*n^4 - 4*(d*sin(f*x + e) + c)^2*(d*sin(f*x + e) + c)^n*c^3*n^4 + (d*sin(f*x + e) + c)*(d*sin(f*x + e) + c)^n*c^4*n^4 + 10*(d*sin(f*x + e) + c)^5*(d*sin(f*x + e) + c)^n*n^3 - 44*(d*sin(f*x + e) + c)^4*(d*sin(f*x + e) + c)^n*c*n^3 + 72*(d*sin(f*x + e) + c)^3*(d*sin(f*x + e) + c)^n*c^2*n^3 - 52*(d*sin(f*x + e) + c)^2*(d*sin(f*x + e) + c)^n*c^3*n^3 + 14*(d*sin(f*x + e) + c)*(d*sin(f*x + e) + c)^n*c^4*n^3 + 35*(d*sin(f*x + e) + c)^5*(d*sin(f*x + e) + c)^n*n^2 - 164*(d*sin(f*x + e) + c)^4*(d*sin(f*x + e) + c)^n*c*n^2 + 294*(d*sin(f*x + e) + c)^3*(d*sin(f*x + e) + c)^n*c^2*n^2 - 236*(d*sin(f*x + e) + c)^2*(d*sin(f*x + e) + c)^n*c^3*n^2 + 71*(d*sin(f*x + e) + c)*(d*sin(f*x + e) + c)^n*c^4*n^2 + 50*(d*sin(f*x + e) + c)^5*(d*sin(f*x + e) + c)^n*n - 244*(d*sin(f*x + e) + c)^4*(d*sin(f*x + e) + c)^n*c*n + 468*(d*sin(f*x + e) + c)^3*(d*sin(f*x + e) + c)^n*c^2*n - 428*(d*sin(f*x + e) + c)^2*(d*sin(f*x + e) + c)^n*c^3*n + 154*(d*sin(f*x + e) + c)*(d*sin(f*x + e) + c)^n*c^4*n + 24*(d*sin(f*x + e) + c)^5*(d*sin(f*x + e) + c)^n - 120*(d*sin(f*x + e) + c)^4*(d*sin(f*x + e) + c)^n*c + 240*(d*sin(f*x + e) + c)^3*(d*sin(f*x + e) + c)^n*c^2 - 240*(d*sin(f*x + e) + c)^2*(d*sin(f*x + e) + c)^n*c^3 + 120*(d*sin(f*x + e) + c)*(d*sin(f*x + e) + c)^n*c^4)*a^4/(d^4*n^5 + 15*d^4*n^4 + 85*d^4*n^3 + 225*d^4*n^2 + 274*d^4*n + 120*d^4) + 4*((d*sin(f*x + e) + c)^4*(d*sin(f*x + e) + c)^n*n^3 - 3*(d*sin(f*x + e) + c)^3*(d*sin(f*x + e) + c)^n*c*n^3 + 3*(d*sin(f*x + e) + c)^2*(d*sin(f*x + e) + c)^n*c^2*n^3 - (d*sin(f*x + e) + c)*(d*sin(f*x + e) + c)^n*c^3*n^3 + 6*(d*sin(f*x + e) + c)^4*(d*sin(f*x + e) + c)^n*n^2 - 21*(d*sin(f*x + e) + c)^3*(d*sin(f*x + e) + c)^n*c*n^2 + 24*(d*sin(f*x + e) + c)^2*(d*sin(f*x + e) + c)^n*c^2*n^2 - 9*(d*sin(f*x + e) + c)*(d*sin(f*x + e) + c)^n*c^3*n^2 + 11*(d*sin(f*x + e) + c)^4*(d*sin(f*x + e) + c)^n*n - 42*(d*sin(f*x + e) + c)^3*(d*sin(f*x + e) + c)^n*c*n + 57*(d*sin(f*x + e) + c)^2*(d*sin(f*x + e) + c)^n*c^2*n - 26*(d*sin(f*x + e) + c)*(d*sin(f*x + e) + c)^n*c^3*n + 6*(d*sin(f*x + e) + c)^4*(d*sin(f*x + e) + c)^n - 24*(d*sin(f*x + e) + c)^3*(d*sin(f*x + e) + c)^n*c + 36*(d*sin(f*x + e) + c)^2*(d*sin(f*x + e) + c)^n*c^2 - 24*(d*sin(f*x + e) + c)*(d*sin(f*x + e) + c)^n*c^3)*a^4/(d^3*n^4 + 10*d^3*n^3 + 35*d^3*n^2 + 50*d^3*n + 24*d^3) + 6*((d*sin(f*x + e) + c)^3*(d*sin(f*x + e) + c)^n*n^2 - 2*(d*sin(f*x + e) + c)^2*(d*sin(f*x + e) + c)^n*c*n^2 + (d*sin(f*x + e) + c)*(d*sin(f*x + e) + c)^n*c^2*n^2 + 3*(d*sin(f*x + e) + c)^3*(d*sin(f*x + e) + c)^n*n - 8*(d*sin(f*x + e) + c)^2*(d*sin(f*x + e) + c)^n*c*n + 5*(d*sin(f*x + e) + c)*(d*sin(f*x + e) + c)^n*c^2*n + 2*(d*sin(f*x + e) + c)^3*(d*sin(f*x + e) + c)^n - 6*(d*sin(f*x + e) + c)^2*(d*sin(f*x + e) + c)^n*c + 6*(d*sin(f*x + e) + c)*(d*sin(f*x + e) + c)^n*c^2)*a^4/(d^2*n^3 + 6*d^2*n^2 + 11*d^2*n + 6*d^2) + (d*sin(f*x + e) + c)^(n + 1)*a^4/(n + 1) + 4*((d*sin(f*x + e) + c)^2*(d*sin(f*x + e) + c)^n*n - (d*sin(f*x + e) + c)*(d*sin(f*x + e) + c)^n*c*n + (d*sin(f*x + e) + c)^2*(d*sin(f*x + e) + c)^n - 2*(d*sin(f*x + e) + c)*(d*sin(f*x + e) + c)^n*c)*a^4/((n^2 + 3*n + 2)*d))/(d*f)","B",0
914,1,1001,0,0.200734," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))^3*(c+d*sin(f*x+e))^n,x, algorithm=""giac"")","\frac{\frac{{\left({\left(d \sin\left(f x + e\right) + c\right)}^{4} {\left(d \sin\left(f x + e\right) + c\right)}^{n} n^{3} - 3 \, {\left(d \sin\left(f x + e\right) + c\right)}^{3} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c n^{3} + 3 \, {\left(d \sin\left(f x + e\right) + c\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c^{2} n^{3} - {\left(d \sin\left(f x + e\right) + c\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c^{3} n^{3} + 6 \, {\left(d \sin\left(f x + e\right) + c\right)}^{4} {\left(d \sin\left(f x + e\right) + c\right)}^{n} n^{2} - 21 \, {\left(d \sin\left(f x + e\right) + c\right)}^{3} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c n^{2} + 24 \, {\left(d \sin\left(f x + e\right) + c\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c^{2} n^{2} - 9 \, {\left(d \sin\left(f x + e\right) + c\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c^{3} n^{2} + 11 \, {\left(d \sin\left(f x + e\right) + c\right)}^{4} {\left(d \sin\left(f x + e\right) + c\right)}^{n} n - 42 \, {\left(d \sin\left(f x + e\right) + c\right)}^{3} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c n + 57 \, {\left(d \sin\left(f x + e\right) + c\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c^{2} n - 26 \, {\left(d \sin\left(f x + e\right) + c\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c^{3} n + 6 \, {\left(d \sin\left(f x + e\right) + c\right)}^{4} {\left(d \sin\left(f x + e\right) + c\right)}^{n} - 24 \, {\left(d \sin\left(f x + e\right) + c\right)}^{3} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c + 36 \, {\left(d \sin\left(f x + e\right) + c\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c^{2} - 24 \, {\left(d \sin\left(f x + e\right) + c\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c^{3}\right)} a^{3}}{d^{3} n^{4} + 10 \, d^{3} n^{3} + 35 \, d^{3} n^{2} + 50 \, d^{3} n + 24 \, d^{3}} + \frac{3 \, {\left({\left(d \sin\left(f x + e\right) + c\right)}^{3} {\left(d \sin\left(f x + e\right) + c\right)}^{n} n^{2} - 2 \, {\left(d \sin\left(f x + e\right) + c\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c n^{2} + {\left(d \sin\left(f x + e\right) + c\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c^{2} n^{2} + 3 \, {\left(d \sin\left(f x + e\right) + c\right)}^{3} {\left(d \sin\left(f x + e\right) + c\right)}^{n} n - 8 \, {\left(d \sin\left(f x + e\right) + c\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c n + 5 \, {\left(d \sin\left(f x + e\right) + c\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c^{2} n + 2 \, {\left(d \sin\left(f x + e\right) + c\right)}^{3} {\left(d \sin\left(f x + e\right) + c\right)}^{n} - 6 \, {\left(d \sin\left(f x + e\right) + c\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c + 6 \, {\left(d \sin\left(f x + e\right) + c\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c^{2}\right)} a^{3}}{d^{2} n^{3} + 6 \, d^{2} n^{2} + 11 \, d^{2} n + 6 \, d^{2}} + \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n + 1} a^{3}}{n + 1} + \frac{3 \, {\left({\left(d \sin\left(f x + e\right) + c\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{n} n - {\left(d \sin\left(f x + e\right) + c\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c n + {\left(d \sin\left(f x + e\right) + c\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{n} - 2 \, {\left(d \sin\left(f x + e\right) + c\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c\right)} a^{3}}{{\left(n^{2} + 3 \, n + 2\right)} d}}{d f}"," ",0,"(((d*sin(f*x + e) + c)^4*(d*sin(f*x + e) + c)^n*n^3 - 3*(d*sin(f*x + e) + c)^3*(d*sin(f*x + e) + c)^n*c*n^3 + 3*(d*sin(f*x + e) + c)^2*(d*sin(f*x + e) + c)^n*c^2*n^3 - (d*sin(f*x + e) + c)*(d*sin(f*x + e) + c)^n*c^3*n^3 + 6*(d*sin(f*x + e) + c)^4*(d*sin(f*x + e) + c)^n*n^2 - 21*(d*sin(f*x + e) + c)^3*(d*sin(f*x + e) + c)^n*c*n^2 + 24*(d*sin(f*x + e) + c)^2*(d*sin(f*x + e) + c)^n*c^2*n^2 - 9*(d*sin(f*x + e) + c)*(d*sin(f*x + e) + c)^n*c^3*n^2 + 11*(d*sin(f*x + e) + c)^4*(d*sin(f*x + e) + c)^n*n - 42*(d*sin(f*x + e) + c)^3*(d*sin(f*x + e) + c)^n*c*n + 57*(d*sin(f*x + e) + c)^2*(d*sin(f*x + e) + c)^n*c^2*n - 26*(d*sin(f*x + e) + c)*(d*sin(f*x + e) + c)^n*c^3*n + 6*(d*sin(f*x + e) + c)^4*(d*sin(f*x + e) + c)^n - 24*(d*sin(f*x + e) + c)^3*(d*sin(f*x + e) + c)^n*c + 36*(d*sin(f*x + e) + c)^2*(d*sin(f*x + e) + c)^n*c^2 - 24*(d*sin(f*x + e) + c)*(d*sin(f*x + e) + c)^n*c^3)*a^3/(d^3*n^4 + 10*d^3*n^3 + 35*d^3*n^2 + 50*d^3*n + 24*d^3) + 3*((d*sin(f*x + e) + c)^3*(d*sin(f*x + e) + c)^n*n^2 - 2*(d*sin(f*x + e) + c)^2*(d*sin(f*x + e) + c)^n*c*n^2 + (d*sin(f*x + e) + c)*(d*sin(f*x + e) + c)^n*c^2*n^2 + 3*(d*sin(f*x + e) + c)^3*(d*sin(f*x + e) + c)^n*n - 8*(d*sin(f*x + e) + c)^2*(d*sin(f*x + e) + c)^n*c*n + 5*(d*sin(f*x + e) + c)*(d*sin(f*x + e) + c)^n*c^2*n + 2*(d*sin(f*x + e) + c)^3*(d*sin(f*x + e) + c)^n - 6*(d*sin(f*x + e) + c)^2*(d*sin(f*x + e) + c)^n*c + 6*(d*sin(f*x + e) + c)*(d*sin(f*x + e) + c)^n*c^2)*a^3/(d^2*n^3 + 6*d^2*n^2 + 11*d^2*n + 6*d^2) + (d*sin(f*x + e) + c)^(n + 1)*a^3/(n + 1) + 3*((d*sin(f*x + e) + c)^2*(d*sin(f*x + e) + c)^n*n - (d*sin(f*x + e) + c)*(d*sin(f*x + e) + c)^n*c*n + (d*sin(f*x + e) + c)^2*(d*sin(f*x + e) + c)^n - 2*(d*sin(f*x + e) + c)*(d*sin(f*x + e) + c)^n*c)*a^3/((n^2 + 3*n + 2)*d))/(d*f)","B",0
915,1,463,0,0.190550," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^n,x, algorithm=""giac"")","\frac{\frac{{\left({\left(d \sin\left(f x + e\right) + c\right)}^{3} {\left(d \sin\left(f x + e\right) + c\right)}^{n} n^{2} - 2 \, {\left(d \sin\left(f x + e\right) + c\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c n^{2} + {\left(d \sin\left(f x + e\right) + c\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c^{2} n^{2} + 3 \, {\left(d \sin\left(f x + e\right) + c\right)}^{3} {\left(d \sin\left(f x + e\right) + c\right)}^{n} n - 8 \, {\left(d \sin\left(f x + e\right) + c\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c n + 5 \, {\left(d \sin\left(f x + e\right) + c\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c^{2} n + 2 \, {\left(d \sin\left(f x + e\right) + c\right)}^{3} {\left(d \sin\left(f x + e\right) + c\right)}^{n} - 6 \, {\left(d \sin\left(f x + e\right) + c\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c + 6 \, {\left(d \sin\left(f x + e\right) + c\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c^{2}\right)} a^{2}}{d^{2} n^{3} + 6 \, d^{2} n^{2} + 11 \, d^{2} n + 6 \, d^{2}} + \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n + 1} a^{2}}{n + 1} + \frac{2 \, {\left({\left(d \sin\left(f x + e\right) + c\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{n} n - {\left(d \sin\left(f x + e\right) + c\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c n + {\left(d \sin\left(f x + e\right) + c\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{n} - 2 \, {\left(d \sin\left(f x + e\right) + c\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c\right)} a^{2}}{{\left(n^{2} + 3 \, n + 2\right)} d}}{d f}"," ",0,"(((d*sin(f*x + e) + c)^3*(d*sin(f*x + e) + c)^n*n^2 - 2*(d*sin(f*x + e) + c)^2*(d*sin(f*x + e) + c)^n*c*n^2 + (d*sin(f*x + e) + c)*(d*sin(f*x + e) + c)^n*c^2*n^2 + 3*(d*sin(f*x + e) + c)^3*(d*sin(f*x + e) + c)^n*n - 8*(d*sin(f*x + e) + c)^2*(d*sin(f*x + e) + c)^n*c*n + 5*(d*sin(f*x + e) + c)*(d*sin(f*x + e) + c)^n*c^2*n + 2*(d*sin(f*x + e) + c)^3*(d*sin(f*x + e) + c)^n - 6*(d*sin(f*x + e) + c)^2*(d*sin(f*x + e) + c)^n*c + 6*(d*sin(f*x + e) + c)*(d*sin(f*x + e) + c)^n*c^2)*a^2/(d^2*n^3 + 6*d^2*n^2 + 11*d^2*n + 6*d^2) + (d*sin(f*x + e) + c)^(n + 1)*a^2/(n + 1) + 2*((d*sin(f*x + e) + c)^2*(d*sin(f*x + e) + c)^n*n - (d*sin(f*x + e) + c)*(d*sin(f*x + e) + c)^n*c*n + (d*sin(f*x + e) + c)^2*(d*sin(f*x + e) + c)^n - 2*(d*sin(f*x + e) + c)*(d*sin(f*x + e) + c)^n*c)*a^2/((n^2 + 3*n + 2)*d))/(d*f)","B",0
916,1,156,0,0.163280," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))*(c+d*sin(f*x+e))^n,x, algorithm=""giac"")","\frac{\frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n + 1} a}{n + 1} + \frac{{\left({\left(d \sin\left(f x + e\right) + c\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{n} n - {\left(d \sin\left(f x + e\right) + c\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c n + {\left(d \sin\left(f x + e\right) + c\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{n} - 2 \, {\left(d \sin\left(f x + e\right) + c\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n} c\right)} a}{{\left(n^{2} + 3 \, n + 2\right)} d}}{d f}"," ",0,"((d*sin(f*x + e) + c)^(n + 1)*a/(n + 1) + ((d*sin(f*x + e) + c)^2*(d*sin(f*x + e) + c)^n*n - (d*sin(f*x + e) + c)*(d*sin(f*x + e) + c)^n*c*n + (d*sin(f*x + e) + c)^2*(d*sin(f*x + e) + c)^n - 2*(d*sin(f*x + e) + c)*(d*sin(f*x + e) + c)^n*c)*a/((n^2 + 3*n + 2)*d))/(d*f)","B",0
917,0,0,0,0.000000," ","integrate(cos(f*x+e)*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)}{a \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^n*cos(f*x + e)/(a*sin(f*x + e) + a), x)","F",0
918,0,0,0,0.000000," ","integrate(cos(f*x+e)*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^2,x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)}{{\left(a \sin\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^n*cos(f*x + e)/(a*sin(f*x + e) + a)^2, x)","F",0
919,0,0,0,0.000000," ","integrate(cos(f*x+e)*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^3,x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)}{{\left(a \sin\left(f x + e\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^n*cos(f*x + e)/(a*sin(f*x + e) + a)^3, x)","F",0
920,1,1845,0,0.280387," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^4,x, algorithm=""giac"")","\frac{\frac{6 \, {\left({\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(a \sin\left(f x + e\right) + a\right)}^{m} m^{2} - 2 \, {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a m^{2} + {\left(a \sin\left(f x + e\right) + a\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{2} m^{2} + 3 \, {\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(a \sin\left(f x + e\right) + a\right)}^{m} m - 8 \, {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a m + 5 \, {\left(a \sin\left(f x + e\right) + a\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{2} m + 2 \, {\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(a \sin\left(f x + e\right) + a\right)}^{m} - 6 \, {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a + 6 \, {\left(a \sin\left(f x + e\right) + a\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{2}\right)} c^{2} d^{2}}{a^{2} m^{3} + 6 \, a^{2} m^{2} + 11 \, a^{2} m + 6 \, a^{2}} + \frac{4 \, {\left({\left(a \sin\left(f x + e\right) + a\right)}^{4} {\left(a \sin\left(f x + e\right) + a\right)}^{m} m^{3} - 3 \, {\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a m^{3} + 3 \, {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{2} m^{3} - {\left(a \sin\left(f x + e\right) + a\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{3} m^{3} + 6 \, {\left(a \sin\left(f x + e\right) + a\right)}^{4} {\left(a \sin\left(f x + e\right) + a\right)}^{m} m^{2} - 21 \, {\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a m^{2} + 24 \, {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{2} m^{2} - 9 \, {\left(a \sin\left(f x + e\right) + a\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{3} m^{2} + 11 \, {\left(a \sin\left(f x + e\right) + a\right)}^{4} {\left(a \sin\left(f x + e\right) + a\right)}^{m} m - 42 \, {\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a m + 57 \, {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{2} m - 26 \, {\left(a \sin\left(f x + e\right) + a\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{3} m + 6 \, {\left(a \sin\left(f x + e\right) + a\right)}^{4} {\left(a \sin\left(f x + e\right) + a\right)}^{m} - 24 \, {\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a + 36 \, {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{2} - 24 \, {\left(a \sin\left(f x + e\right) + a\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{3}\right)} c d^{3}}{a^{3} m^{4} + 10 \, a^{3} m^{3} + 35 \, a^{3} m^{2} + 50 \, a^{3} m + 24 \, a^{3}} + \frac{{\left({\left(a \sin\left(f x + e\right) + a\right)}^{5} {\left(a \sin\left(f x + e\right) + a\right)}^{m} m^{4} - 4 \, {\left(a \sin\left(f x + e\right) + a\right)}^{4} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a m^{4} + 6 \, {\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{2} m^{4} - 4 \, {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{3} m^{4} + {\left(a \sin\left(f x + e\right) + a\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{4} m^{4} + 10 \, {\left(a \sin\left(f x + e\right) + a\right)}^{5} {\left(a \sin\left(f x + e\right) + a\right)}^{m} m^{3} - 44 \, {\left(a \sin\left(f x + e\right) + a\right)}^{4} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a m^{3} + 72 \, {\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{2} m^{3} - 52 \, {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{3} m^{3} + 14 \, {\left(a \sin\left(f x + e\right) + a\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{4} m^{3} + 35 \, {\left(a \sin\left(f x + e\right) + a\right)}^{5} {\left(a \sin\left(f x + e\right) + a\right)}^{m} m^{2} - 164 \, {\left(a \sin\left(f x + e\right) + a\right)}^{4} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a m^{2} + 294 \, {\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{2} m^{2} - 236 \, {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{3} m^{2} + 71 \, {\left(a \sin\left(f x + e\right) + a\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{4} m^{2} + 50 \, {\left(a \sin\left(f x + e\right) + a\right)}^{5} {\left(a \sin\left(f x + e\right) + a\right)}^{m} m - 244 \, {\left(a \sin\left(f x + e\right) + a\right)}^{4} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a m + 468 \, {\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{2} m - 428 \, {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{3} m + 154 \, {\left(a \sin\left(f x + e\right) + a\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{4} m + 24 \, {\left(a \sin\left(f x + e\right) + a\right)}^{5} {\left(a \sin\left(f x + e\right) + a\right)}^{m} - 120 \, {\left(a \sin\left(f x + e\right) + a\right)}^{4} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a + 240 \, {\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{2} - 240 \, {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{3} + 120 \, {\left(a \sin\left(f x + e\right) + a\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{4}\right)} d^{4}}{a^{4} m^{5} + 15 \, a^{4} m^{4} + 85 \, a^{4} m^{3} + 225 \, a^{4} m^{2} + 274 \, a^{4} m + 120 \, a^{4}} + \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m + 1} c^{4}}{m + 1} + \frac{4 \, {\left({\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m} m - {\left(a \sin\left(f x + e\right) + a\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a m + {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m} - 2 \, {\left(a \sin\left(f x + e\right) + a\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a\right)} c^{3} d}{{\left(m^{2} + 3 \, m + 2\right)} a}}{a f}"," ",0,"(6*((a*sin(f*x + e) + a)^3*(a*sin(f*x + e) + a)^m*m^2 - 2*(a*sin(f*x + e) + a)^2*(a*sin(f*x + e) + a)^m*a*m^2 + (a*sin(f*x + e) + a)*(a*sin(f*x + e) + a)^m*a^2*m^2 + 3*(a*sin(f*x + e) + a)^3*(a*sin(f*x + e) + a)^m*m - 8*(a*sin(f*x + e) + a)^2*(a*sin(f*x + e) + a)^m*a*m + 5*(a*sin(f*x + e) + a)*(a*sin(f*x + e) + a)^m*a^2*m + 2*(a*sin(f*x + e) + a)^3*(a*sin(f*x + e) + a)^m - 6*(a*sin(f*x + e) + a)^2*(a*sin(f*x + e) + a)^m*a + 6*(a*sin(f*x + e) + a)*(a*sin(f*x + e) + a)^m*a^2)*c^2*d^2/(a^2*m^3 + 6*a^2*m^2 + 11*a^2*m + 6*a^2) + 4*((a*sin(f*x + e) + a)^4*(a*sin(f*x + e) + a)^m*m^3 - 3*(a*sin(f*x + e) + a)^3*(a*sin(f*x + e) + a)^m*a*m^3 + 3*(a*sin(f*x + e) + a)^2*(a*sin(f*x + e) + a)^m*a^2*m^3 - (a*sin(f*x + e) + a)*(a*sin(f*x + e) + a)^m*a^3*m^3 + 6*(a*sin(f*x + e) + a)^4*(a*sin(f*x + e) + a)^m*m^2 - 21*(a*sin(f*x + e) + a)^3*(a*sin(f*x + e) + a)^m*a*m^2 + 24*(a*sin(f*x + e) + a)^2*(a*sin(f*x + e) + a)^m*a^2*m^2 - 9*(a*sin(f*x + e) + a)*(a*sin(f*x + e) + a)^m*a^3*m^2 + 11*(a*sin(f*x + e) + a)^4*(a*sin(f*x + e) + a)^m*m - 42*(a*sin(f*x + e) + a)^3*(a*sin(f*x + e) + a)^m*a*m + 57*(a*sin(f*x + e) + a)^2*(a*sin(f*x + e) + a)^m*a^2*m - 26*(a*sin(f*x + e) + a)*(a*sin(f*x + e) + a)^m*a^3*m + 6*(a*sin(f*x + e) + a)^4*(a*sin(f*x + e) + a)^m - 24*(a*sin(f*x + e) + a)^3*(a*sin(f*x + e) + a)^m*a + 36*(a*sin(f*x + e) + a)^2*(a*sin(f*x + e) + a)^m*a^2 - 24*(a*sin(f*x + e) + a)*(a*sin(f*x + e) + a)^m*a^3)*c*d^3/(a^3*m^4 + 10*a^3*m^3 + 35*a^3*m^2 + 50*a^3*m + 24*a^3) + ((a*sin(f*x + e) + a)^5*(a*sin(f*x + e) + a)^m*m^4 - 4*(a*sin(f*x + e) + a)^4*(a*sin(f*x + e) + a)^m*a*m^4 + 6*(a*sin(f*x + e) + a)^3*(a*sin(f*x + e) + a)^m*a^2*m^4 - 4*(a*sin(f*x + e) + a)^2*(a*sin(f*x + e) + a)^m*a^3*m^4 + (a*sin(f*x + e) + a)*(a*sin(f*x + e) + a)^m*a^4*m^4 + 10*(a*sin(f*x + e) + a)^5*(a*sin(f*x + e) + a)^m*m^3 - 44*(a*sin(f*x + e) + a)^4*(a*sin(f*x + e) + a)^m*a*m^3 + 72*(a*sin(f*x + e) + a)^3*(a*sin(f*x + e) + a)^m*a^2*m^3 - 52*(a*sin(f*x + e) + a)^2*(a*sin(f*x + e) + a)^m*a^3*m^3 + 14*(a*sin(f*x + e) + a)*(a*sin(f*x + e) + a)^m*a^4*m^3 + 35*(a*sin(f*x + e) + a)^5*(a*sin(f*x + e) + a)^m*m^2 - 164*(a*sin(f*x + e) + a)^4*(a*sin(f*x + e) + a)^m*a*m^2 + 294*(a*sin(f*x + e) + a)^3*(a*sin(f*x + e) + a)^m*a^2*m^2 - 236*(a*sin(f*x + e) + a)^2*(a*sin(f*x + e) + a)^m*a^3*m^2 + 71*(a*sin(f*x + e) + a)*(a*sin(f*x + e) + a)^m*a^4*m^2 + 50*(a*sin(f*x + e) + a)^5*(a*sin(f*x + e) + a)^m*m - 244*(a*sin(f*x + e) + a)^4*(a*sin(f*x + e) + a)^m*a*m + 468*(a*sin(f*x + e) + a)^3*(a*sin(f*x + e) + a)^m*a^2*m - 428*(a*sin(f*x + e) + a)^2*(a*sin(f*x + e) + a)^m*a^3*m + 154*(a*sin(f*x + e) + a)*(a*sin(f*x + e) + a)^m*a^4*m + 24*(a*sin(f*x + e) + a)^5*(a*sin(f*x + e) + a)^m - 120*(a*sin(f*x + e) + a)^4*(a*sin(f*x + e) + a)^m*a + 240*(a*sin(f*x + e) + a)^3*(a*sin(f*x + e) + a)^m*a^2 - 240*(a*sin(f*x + e) + a)^2*(a*sin(f*x + e) + a)^m*a^3 + 120*(a*sin(f*x + e) + a)*(a*sin(f*x + e) + a)^m*a^4)*d^4/(a^4*m^5 + 15*a^4*m^4 + 85*a^4*m^3 + 225*a^4*m^2 + 274*a^4*m + 120*a^4) + (a*sin(f*x + e) + a)^(m + 1)*c^4/(m + 1) + 4*((a*sin(f*x + e) + a)^2*(a*sin(f*x + e) + a)^m*m - (a*sin(f*x + e) + a)*(a*sin(f*x + e) + a)^m*a*m + (a*sin(f*x + e) + a)^2*(a*sin(f*x + e) + a)^m - 2*(a*sin(f*x + e) + a)*(a*sin(f*x + e) + a)^m*a)*c^3*d/((m^2 + 3*m + 2)*a))/(a*f)","B",0
921,1,1003,0,0.242273," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^3,x, algorithm=""giac"")","\frac{\frac{3 \, {\left({\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(a \sin\left(f x + e\right) + a\right)}^{m} m^{2} - 2 \, {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a m^{2} + {\left(a \sin\left(f x + e\right) + a\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{2} m^{2} + 3 \, {\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(a \sin\left(f x + e\right) + a\right)}^{m} m - 8 \, {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a m + 5 \, {\left(a \sin\left(f x + e\right) + a\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{2} m + 2 \, {\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(a \sin\left(f x + e\right) + a\right)}^{m} - 6 \, {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a + 6 \, {\left(a \sin\left(f x + e\right) + a\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{2}\right)} c d^{2}}{a^{2} m^{3} + 6 \, a^{2} m^{2} + 11 \, a^{2} m + 6 \, a^{2}} + \frac{{\left({\left(a \sin\left(f x + e\right) + a\right)}^{4} {\left(a \sin\left(f x + e\right) + a\right)}^{m} m^{3} - 3 \, {\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a m^{3} + 3 \, {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{2} m^{3} - {\left(a \sin\left(f x + e\right) + a\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{3} m^{3} + 6 \, {\left(a \sin\left(f x + e\right) + a\right)}^{4} {\left(a \sin\left(f x + e\right) + a\right)}^{m} m^{2} - 21 \, {\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a m^{2} + 24 \, {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{2} m^{2} - 9 \, {\left(a \sin\left(f x + e\right) + a\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{3} m^{2} + 11 \, {\left(a \sin\left(f x + e\right) + a\right)}^{4} {\left(a \sin\left(f x + e\right) + a\right)}^{m} m - 42 \, {\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a m + 57 \, {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{2} m - 26 \, {\left(a \sin\left(f x + e\right) + a\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{3} m + 6 \, {\left(a \sin\left(f x + e\right) + a\right)}^{4} {\left(a \sin\left(f x + e\right) + a\right)}^{m} - 24 \, {\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a + 36 \, {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{2} - 24 \, {\left(a \sin\left(f x + e\right) + a\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{3}\right)} d^{3}}{a^{3} m^{4} + 10 \, a^{3} m^{3} + 35 \, a^{3} m^{2} + 50 \, a^{3} m + 24 \, a^{3}} + \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m + 1} c^{3}}{m + 1} + \frac{3 \, {\left({\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m} m - {\left(a \sin\left(f x + e\right) + a\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a m + {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m} - 2 \, {\left(a \sin\left(f x + e\right) + a\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a\right)} c^{2} d}{{\left(m^{2} + 3 \, m + 2\right)} a}}{a f}"," ",0,"(3*((a*sin(f*x + e) + a)^3*(a*sin(f*x + e) + a)^m*m^2 - 2*(a*sin(f*x + e) + a)^2*(a*sin(f*x + e) + a)^m*a*m^2 + (a*sin(f*x + e) + a)*(a*sin(f*x + e) + a)^m*a^2*m^2 + 3*(a*sin(f*x + e) + a)^3*(a*sin(f*x + e) + a)^m*m - 8*(a*sin(f*x + e) + a)^2*(a*sin(f*x + e) + a)^m*a*m + 5*(a*sin(f*x + e) + a)*(a*sin(f*x + e) + a)^m*a^2*m + 2*(a*sin(f*x + e) + a)^3*(a*sin(f*x + e) + a)^m - 6*(a*sin(f*x + e) + a)^2*(a*sin(f*x + e) + a)^m*a + 6*(a*sin(f*x + e) + a)*(a*sin(f*x + e) + a)^m*a^2)*c*d^2/(a^2*m^3 + 6*a^2*m^2 + 11*a^2*m + 6*a^2) + ((a*sin(f*x + e) + a)^4*(a*sin(f*x + e) + a)^m*m^3 - 3*(a*sin(f*x + e) + a)^3*(a*sin(f*x + e) + a)^m*a*m^3 + 3*(a*sin(f*x + e) + a)^2*(a*sin(f*x + e) + a)^m*a^2*m^3 - (a*sin(f*x + e) + a)*(a*sin(f*x + e) + a)^m*a^3*m^3 + 6*(a*sin(f*x + e) + a)^4*(a*sin(f*x + e) + a)^m*m^2 - 21*(a*sin(f*x + e) + a)^3*(a*sin(f*x + e) + a)^m*a*m^2 + 24*(a*sin(f*x + e) + a)^2*(a*sin(f*x + e) + a)^m*a^2*m^2 - 9*(a*sin(f*x + e) + a)*(a*sin(f*x + e) + a)^m*a^3*m^2 + 11*(a*sin(f*x + e) + a)^4*(a*sin(f*x + e) + a)^m*m - 42*(a*sin(f*x + e) + a)^3*(a*sin(f*x + e) + a)^m*a*m + 57*(a*sin(f*x + e) + a)^2*(a*sin(f*x + e) + a)^m*a^2*m - 26*(a*sin(f*x + e) + a)*(a*sin(f*x + e) + a)^m*a^3*m + 6*(a*sin(f*x + e) + a)^4*(a*sin(f*x + e) + a)^m - 24*(a*sin(f*x + e) + a)^3*(a*sin(f*x + e) + a)^m*a + 36*(a*sin(f*x + e) + a)^2*(a*sin(f*x + e) + a)^m*a^2 - 24*(a*sin(f*x + e) + a)*(a*sin(f*x + e) + a)^m*a^3)*d^3/(a^3*m^4 + 10*a^3*m^3 + 35*a^3*m^2 + 50*a^3*m + 24*a^3) + (a*sin(f*x + e) + a)^(m + 1)*c^3/(m + 1) + 3*((a*sin(f*x + e) + a)^2*(a*sin(f*x + e) + a)^m*m - (a*sin(f*x + e) + a)*(a*sin(f*x + e) + a)^m*a*m + (a*sin(f*x + e) + a)^2*(a*sin(f*x + e) + a)^m - 2*(a*sin(f*x + e) + a)*(a*sin(f*x + e) + a)^m*a)*c^2*d/((m^2 + 3*m + 2)*a))/(a*f)","B",0
922,1,462,0,0.162421," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^2,x, algorithm=""giac"")","\frac{\frac{{\left({\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(a \sin\left(f x + e\right) + a\right)}^{m} m^{2} - 2 \, {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a m^{2} + {\left(a \sin\left(f x + e\right) + a\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{2} m^{2} + 3 \, {\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(a \sin\left(f x + e\right) + a\right)}^{m} m - 8 \, {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a m + 5 \, {\left(a \sin\left(f x + e\right) + a\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{2} m + 2 \, {\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(a \sin\left(f x + e\right) + a\right)}^{m} - 6 \, {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a + 6 \, {\left(a \sin\left(f x + e\right) + a\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{2}\right)} d^{2}}{a^{2} m^{3} + 6 \, a^{2} m^{2} + 11 \, a^{2} m + 6 \, a^{2}} + \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m + 1} c^{2}}{m + 1} + \frac{2 \, {\left({\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m} m - {\left(a \sin\left(f x + e\right) + a\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a m + {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m} - 2 \, {\left(a \sin\left(f x + e\right) + a\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a\right)} c d}{{\left(m^{2} + 3 \, m + 2\right)} a}}{a f}"," ",0,"(((a*sin(f*x + e) + a)^3*(a*sin(f*x + e) + a)^m*m^2 - 2*(a*sin(f*x + e) + a)^2*(a*sin(f*x + e) + a)^m*a*m^2 + (a*sin(f*x + e) + a)*(a*sin(f*x + e) + a)^m*a^2*m^2 + 3*(a*sin(f*x + e) + a)^3*(a*sin(f*x + e) + a)^m*m - 8*(a*sin(f*x + e) + a)^2*(a*sin(f*x + e) + a)^m*a*m + 5*(a*sin(f*x + e) + a)*(a*sin(f*x + e) + a)^m*a^2*m + 2*(a*sin(f*x + e) + a)^3*(a*sin(f*x + e) + a)^m - 6*(a*sin(f*x + e) + a)^2*(a*sin(f*x + e) + a)^m*a + 6*(a*sin(f*x + e) + a)*(a*sin(f*x + e) + a)^m*a^2)*d^2/(a^2*m^3 + 6*a^2*m^2 + 11*a^2*m + 6*a^2) + (a*sin(f*x + e) + a)^(m + 1)*c^2/(m + 1) + 2*((a*sin(f*x + e) + a)^2*(a*sin(f*x + e) + a)^m*m - (a*sin(f*x + e) + a)*(a*sin(f*x + e) + a)^m*a*m + (a*sin(f*x + e) + a)^2*(a*sin(f*x + e) + a)^m - 2*(a*sin(f*x + e) + a)*(a*sin(f*x + e) + a)^m*a)*c*d/((m^2 + 3*m + 2)*a))/(a*f)","B",0
923,1,156,0,0.146282," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e)),x, algorithm=""giac"")","\frac{\frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m + 1} c}{m + 1} + \frac{{\left({\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m} m - {\left(a \sin\left(f x + e\right) + a\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a m + {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m} - 2 \, {\left(a \sin\left(f x + e\right) + a\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a\right)} d}{{\left(m^{2} + 3 \, m + 2\right)} a}}{a f}"," ",0,"((a*sin(f*x + e) + a)^(m + 1)*c/(m + 1) + ((a*sin(f*x + e) + a)^2*(a*sin(f*x + e) + a)^m*m - (a*sin(f*x + e) + a)*(a*sin(f*x + e) + a)^m*a*m + (a*sin(f*x + e) + a)^2*(a*sin(f*x + e) + a)^m - 2*(a*sin(f*x + e) + a)*(a*sin(f*x + e) + a)^m*a)*d/((m^2 + 3*m + 2)*a))/(a*f)","B",0
924,0,0,0,0.000000," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))^m/(c+d*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)}{d \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*cos(f*x + e)/(d*sin(f*x + e) + c), x)","F",0
925,0,0,0,0.000000," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))^m/(c+d*sin(f*x+e))^2,x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)}{{\left(d \sin\left(f x + e\right) + c\right)}^{2}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*cos(f*x + e)/(d*sin(f*x + e) + c)^2, x)","F",0
926,0,0,0,0.000000," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))^m/(c+d*sin(f*x+e))^3,x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)}{{\left(d \sin\left(f x + e\right) + c\right)}^{3}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*cos(f*x + e)/(d*sin(f*x + e) + c)^3, x)","F",0
927,0,0,0,0.000000," ","integrate(cos(d*x+c)*sin(d*x+c)^n*(a+a*sin(d*x+c))^m,x, algorithm=""giac"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{m} \sin\left(d x + c\right)^{n} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^m*sin(d*x + c)^n*cos(d*x + c), x)","F",0
928,1,402,0,0.273767," ","integrate(cos(d*x+c)*sin(d*x+c)^4*(a+a*sin(d*x+c))^m,x, algorithm=""giac"")","\frac{{\left(a \sin\left(d x + c\right) + a\right)}^{m} m^{4} \sin\left(d x + c\right)^{5} + {\left(a \sin\left(d x + c\right) + a\right)}^{m} m^{4} \sin\left(d x + c\right)^{4} + 10 \, {\left(a \sin\left(d x + c\right) + a\right)}^{m} m^{3} \sin\left(d x + c\right)^{5} + 6 \, {\left(a \sin\left(d x + c\right) + a\right)}^{m} m^{3} \sin\left(d x + c\right)^{4} + 35 \, {\left(a \sin\left(d x + c\right) + a\right)}^{m} m^{2} \sin\left(d x + c\right)^{5} - 4 \, {\left(a \sin\left(d x + c\right) + a\right)}^{m} m^{3} \sin\left(d x + c\right)^{3} + 11 \, {\left(a \sin\left(d x + c\right) + a\right)}^{m} m^{2} \sin\left(d x + c\right)^{4} + 50 \, {\left(a \sin\left(d x + c\right) + a\right)}^{m} m \sin\left(d x + c\right)^{5} - 12 \, {\left(a \sin\left(d x + c\right) + a\right)}^{m} m^{2} \sin\left(d x + c\right)^{3} + 6 \, {\left(a \sin\left(d x + c\right) + a\right)}^{m} m \sin\left(d x + c\right)^{4} + 24 \, {\left(a \sin\left(d x + c\right) + a\right)}^{m} \sin\left(d x + c\right)^{5} + 12 \, {\left(a \sin\left(d x + c\right) + a\right)}^{m} m^{2} \sin\left(d x + c\right)^{2} - 8 \, {\left(a \sin\left(d x + c\right) + a\right)}^{m} m \sin\left(d x + c\right)^{3} + 12 \, {\left(a \sin\left(d x + c\right) + a\right)}^{m} m \sin\left(d x + c\right)^{2} - 24 \, {\left(a \sin\left(d x + c\right) + a\right)}^{m} m \sin\left(d x + c\right) + 24 \, {\left(a \sin\left(d x + c\right) + a\right)}^{m}}{{\left(m^{5} + 15 \, m^{4} + 85 \, m^{3} + 225 \, m^{2} + 274 \, m + 120\right)} d}"," ",0,"((a*sin(d*x + c) + a)^m*m^4*sin(d*x + c)^5 + (a*sin(d*x + c) + a)^m*m^4*sin(d*x + c)^4 + 10*(a*sin(d*x + c) + a)^m*m^3*sin(d*x + c)^5 + 6*(a*sin(d*x + c) + a)^m*m^3*sin(d*x + c)^4 + 35*(a*sin(d*x + c) + a)^m*m^2*sin(d*x + c)^5 - 4*(a*sin(d*x + c) + a)^m*m^3*sin(d*x + c)^3 + 11*(a*sin(d*x + c) + a)^m*m^2*sin(d*x + c)^4 + 50*(a*sin(d*x + c) + a)^m*m*sin(d*x + c)^5 - 12*(a*sin(d*x + c) + a)^m*m^2*sin(d*x + c)^3 + 6*(a*sin(d*x + c) + a)^m*m*sin(d*x + c)^4 + 24*(a*sin(d*x + c) + a)^m*sin(d*x + c)^5 + 12*(a*sin(d*x + c) + a)^m*m^2*sin(d*x + c)^2 - 8*(a*sin(d*x + c) + a)^m*m*sin(d*x + c)^3 + 12*(a*sin(d*x + c) + a)^m*m*sin(d*x + c)^2 - 24*(a*sin(d*x + c) + a)^m*m*sin(d*x + c) + 24*(a*sin(d*x + c) + a)^m)/((m^5 + 15*m^4 + 85*m^3 + 225*m^2 + 274*m + 120)*d)","B",0
929,1,274,0,0.283742," ","integrate(cos(d*x+c)*sin(d*x+c)^3*(a+a*sin(d*x+c))^m,x, algorithm=""giac"")","\frac{{\left(a \sin\left(d x + c\right) + a\right)}^{m} m^{3} \sin\left(d x + c\right)^{4} + {\left(a \sin\left(d x + c\right) + a\right)}^{m} m^{3} \sin\left(d x + c\right)^{3} + 6 \, {\left(a \sin\left(d x + c\right) + a\right)}^{m} m^{2} \sin\left(d x + c\right)^{4} + 3 \, {\left(a \sin\left(d x + c\right) + a\right)}^{m} m^{2} \sin\left(d x + c\right)^{3} + 11 \, {\left(a \sin\left(d x + c\right) + a\right)}^{m} m \sin\left(d x + c\right)^{4} - 3 \, {\left(a \sin\left(d x + c\right) + a\right)}^{m} m^{2} \sin\left(d x + c\right)^{2} + 2 \, {\left(a \sin\left(d x + c\right) + a\right)}^{m} m \sin\left(d x + c\right)^{3} + 6 \, {\left(a \sin\left(d x + c\right) + a\right)}^{m} \sin\left(d x + c\right)^{4} - 3 \, {\left(a \sin\left(d x + c\right) + a\right)}^{m} m \sin\left(d x + c\right)^{2} + 6 \, {\left(a \sin\left(d x + c\right) + a\right)}^{m} m \sin\left(d x + c\right) - 6 \, {\left(a \sin\left(d x + c\right) + a\right)}^{m}}{{\left(m^{4} + 10 \, m^{3} + 35 \, m^{2} + 50 \, m + 24\right)} d}"," ",0,"((a*sin(d*x + c) + a)^m*m^3*sin(d*x + c)^4 + (a*sin(d*x + c) + a)^m*m^3*sin(d*x + c)^3 + 6*(a*sin(d*x + c) + a)^m*m^2*sin(d*x + c)^4 + 3*(a*sin(d*x + c) + a)^m*m^2*sin(d*x + c)^3 + 11*(a*sin(d*x + c) + a)^m*m*sin(d*x + c)^4 - 3*(a*sin(d*x + c) + a)^m*m^2*sin(d*x + c)^2 + 2*(a*sin(d*x + c) + a)^m*m*sin(d*x + c)^3 + 6*(a*sin(d*x + c) + a)^m*sin(d*x + c)^4 - 3*(a*sin(d*x + c) + a)^m*m*sin(d*x + c)^2 + 6*(a*sin(d*x + c) + a)^m*m*sin(d*x + c) - 6*(a*sin(d*x + c) + a)^m)/((m^4 + 10*m^3 + 35*m^2 + 50*m + 24)*d)","B",0
930,1,170,0,0.263607," ","integrate(cos(d*x+c)*sin(d*x+c)^2*(a+a*sin(d*x+c))^m,x, algorithm=""giac"")","\frac{{\left(a \sin\left(d x + c\right) + a\right)}^{m} m^{2} \sin\left(d x + c\right)^{3} + {\left(a \sin\left(d x + c\right) + a\right)}^{m} m^{2} \sin\left(d x + c\right)^{2} + 3 \, {\left(a \sin\left(d x + c\right) + a\right)}^{m} m \sin\left(d x + c\right)^{3} + {\left(a \sin\left(d x + c\right) + a\right)}^{m} m \sin\left(d x + c\right)^{2} + 2 \, {\left(a \sin\left(d x + c\right) + a\right)}^{m} \sin\left(d x + c\right)^{3} - 2 \, {\left(a \sin\left(d x + c\right) + a\right)}^{m} m \sin\left(d x + c\right) + 2 \, {\left(a \sin\left(d x + c\right) + a\right)}^{m}}{{\left(m^{3} + 6 \, m^{2} + 11 \, m + 6\right)} d}"," ",0,"((a*sin(d*x + c) + a)^m*m^2*sin(d*x + c)^3 + (a*sin(d*x + c) + a)^m*m^2*sin(d*x + c)^2 + 3*(a*sin(d*x + c) + a)^m*m*sin(d*x + c)^3 + (a*sin(d*x + c) + a)^m*m*sin(d*x + c)^2 + 2*(a*sin(d*x + c) + a)^m*sin(d*x + c)^3 - 2*(a*sin(d*x + c) + a)^m*m*sin(d*x + c) + 2*(a*sin(d*x + c) + a)^m)/((m^3 + 6*m^2 + 11*m + 6)*d)","B",0
931,1,92,0,0.258473," ","integrate(cos(d*x+c)*sin(d*x+c)*(a+a*sin(d*x+c))^m,x, algorithm=""giac"")","\frac{{\left(a \sin\left(d x + c\right) + a\right)}^{m} m \sin\left(d x + c\right)^{2} + {\left(a \sin\left(d x + c\right) + a\right)}^{m} m \sin\left(d x + c\right) + {\left(a \sin\left(d x + c\right) + a\right)}^{m} \sin\left(d x + c\right)^{2} - {\left(a \sin\left(d x + c\right) + a\right)}^{m}}{{\left(m^{2} + 3 \, m + 2\right)} d}"," ",0,"((a*sin(d*x + c) + a)^m*m*sin(d*x + c)^2 + (a*sin(d*x + c) + a)^m*m*sin(d*x + c) + (a*sin(d*x + c) + a)^m*sin(d*x + c)^2 - (a*sin(d*x + c) + a)^m)/((m^2 + 3*m + 2)*d)","A",0
932,0,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)*(a+a*sin(d*x+c))^m,x, algorithm=""giac"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{m} \cos\left(d x + c\right) \csc\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^m*cos(d*x + c)*csc(d*x + c), x)","F",0
933,0,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)^2*(a+a*sin(d*x+c))^m,x, algorithm=""giac"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{m} \cos\left(d x + c\right) \csc\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^m*cos(d*x + c)*csc(d*x + c)^2, x)","F",0
934,0,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)^3*(a+a*sin(d*x+c))^m,x, algorithm=""giac"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{m} \cos\left(d x + c\right) \csc\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^m*cos(d*x + c)*csc(d*x + c)^3, x)","F",0
935,1,87,0,0.169025," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))*(c+d*sin(f*x+e)),x, algorithm=""giac"")","\frac{1}{8} \, {\left(4 \, a c + a d\right)} x - \frac{a d \sin\left(4 \, f x + 4 \, e\right)}{32 \, f} + \frac{a c \sin\left(2 \, f x + 2 \, e\right)}{4 \, f} - \frac{{\left(a c + a d\right)} \cos\left(3 \, f x + 3 \, e\right)}{12 \, f} - \frac{{\left(a c + a d\right)} \cos\left(f x + e\right)}{4 \, f}"," ",0,"1/8*(4*a*c + a*d)*x - 1/32*a*d*sin(4*f*x + 4*e)/f + 1/4*a*c*sin(2*f*x + 2*e)/f - 1/12*(a*c + a*d)*cos(3*f*x + 3*e)/f - 1/4*(a*c + a*d)*cos(f*x + e)/f","A",0
936,-2,0,0,0.000000," ","integrate(cos(f*x+e)^2/(a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e)),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos((f*t_nostep+exp(1))/2-pi/4))]Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Discontinuities at zeroes of cos((f*t_nostep+exp(1))/2-pi/4) were not checkedUnable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep+1)]Warning, assuming -c^3*d^5-c^2*d^6+c*d^7+d^8-c*d^7-d^8 is positive. Hint: run assume to make assumptions on a variableWarning, assuming -a*c^3*d^5-a*c^2*d^6+a*c*d^7+a*d^8-a*c*d^7-a*d^8 is positive. Hint: run assume to make assumptions on a variableWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0] was discarded and replaced randomly by 0=[-90]Evaluation time: 65.87sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
937,0,0,0,0.000000," ","integrate(cos(f*x+e)^2/(a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\cos\left(f x + e\right)^{2}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} \sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(cos(f*x + e)^2/((a*sin(f*x + e) + a)^(3/2)*sqrt(d*sin(f*x + e) + c)), x)","F",0
938,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(d*sin(f*x + e) + c)^n*cos(f*x + e)^2, x)","F",0
939,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^3*(c+d*sin(f*x+e))^n,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^3*(d*sin(f*x + e) + c)^n*cos(f*x + e)^2, x)","F",0
940,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^n,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^2*(d*sin(f*x + e) + c)^n*cos(f*x + e)^2, x)","F",0
941,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))*(c+d*sin(f*x+e))^n,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^n*cos(f*x + e)^2, x)","F",0
942,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{2}}{a \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^n*cos(f*x + e)^2/(a*sin(f*x + e) + a), x)","F",0
943,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^2,x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{2}}{{\left(a \sin\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^n*cos(f*x + e)^2/(a*sin(f*x + e) + a)^2, x)","F",0
944,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^3,x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{2}}{{\left(a \sin\left(f x + e\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^n*cos(f*x + e)^2/(a*sin(f*x + e) + a)^3, x)","F",0
945,-1,0,0,0.000000," ","integrate(cos(f*x+e)^4*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
946,0,0,0,0.000000," ","integrate(cos(f*x+e)^4*(a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^n,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^2*(d*sin(f*x + e) + c)^n*cos(f*x + e)^4, x)","F",0
947,0,0,0,0.000000," ","integrate(cos(f*x+e)^4*(a+a*sin(f*x+e))*(c+d*sin(f*x+e))^n,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^n*cos(f*x + e)^4, x)","F",0
948,0,0,0,0.000000," ","integrate(cos(f*x+e)^4*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{4}}{a \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^n*cos(f*x + e)^4/(a*sin(f*x + e) + a), x)","F",0
949,0,0,0,0.000000," ","integrate(cos(f*x+e)^4*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^2,x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{4}}{{\left(a \sin\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^n*cos(f*x + e)^4/(a*sin(f*x + e) + a)^2, x)","F",0
950,0,0,0,0.000000," ","integrate(cos(f*x+e)^4*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^3,x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{4}}{{\left(a \sin\left(f x + e\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^n*cos(f*x + e)^4/(a*sin(f*x + e) + a)^3, x)","F",0
951,0,0,0,0.000000," ","integrate(cos(f*x+e)^4*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^4,x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{4}}{{\left(a \sin\left(f x + e\right) + a\right)}^{4}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^n*cos(f*x + e)^4/(a*sin(f*x + e) + a)^4, x)","F",0
952,0,0,0,0.000000," ","integrate(cos(f*x+e)^4*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^5,x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{4}}{{\left(a \sin\left(f x + e\right) + a\right)}^{5}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^n*cos(f*x + e)^4/(a*sin(f*x + e) + a)^5, x)","F",0
953,1,182,0,0.302255," ","integrate(cos(d*x+c)^7*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""giac"")","-\frac{B a \sin\left(9 \, d x + 9 \, c\right)}{2304 \, d} + \frac{7 \, A a \sin\left(3 \, d x + 3 \, c\right)}{64 \, d} - \frac{{\left(A a + B a\right)} \cos\left(8 \, d x + 8 \, c\right)}{1024 \, d} - \frac{{\left(A a + B a\right)} \cos\left(6 \, d x + 6 \, c\right)}{128 \, d} - \frac{7 \, {\left(A a + B a\right)} \cos\left(4 \, d x + 4 \, c\right)}{256 \, d} - \frac{7 \, {\left(A a + B a\right)} \cos\left(2 \, d x + 2 \, c\right)}{128 \, d} + \frac{{\left(4 \, A a - 5 \, B a\right)} \sin\left(7 \, d x + 7 \, c\right)}{1792 \, d} + \frac{{\left(7 \, A a - 2 \, B a\right)} \sin\left(5 \, d x + 5 \, c\right)}{320 \, d} + \frac{7 \, {\left(10 \, A a + B a\right)} \sin\left(d x + c\right)}{128 \, d}"," ",0,"-1/2304*B*a*sin(9*d*x + 9*c)/d + 7/64*A*a*sin(3*d*x + 3*c)/d - 1/1024*(A*a + B*a)*cos(8*d*x + 8*c)/d - 1/128*(A*a + B*a)*cos(6*d*x + 6*c)/d - 7/256*(A*a + B*a)*cos(4*d*x + 4*c)/d - 7/128*(A*a + B*a)*cos(2*d*x + 2*c)/d + 1/1792*(4*A*a - 5*B*a)*sin(7*d*x + 7*c)/d + 1/320*(7*A*a - 2*B*a)*sin(5*d*x + 5*c)/d + 7/128*(10*A*a + B*a)*sin(d*x + c)/d","A",0
954,1,145,0,0.236877," ","integrate(cos(d*x+c)^5*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""giac"")","-\frac{B a \sin\left(7 \, d x + 7 \, c\right)}{448 \, d} - \frac{{\left(A a + B a\right)} \cos\left(6 \, d x + 6 \, c\right)}{192 \, d} - \frac{{\left(A a + B a\right)} \cos\left(4 \, d x + 4 \, c\right)}{32 \, d} - \frac{5 \, {\left(A a + B a\right)} \cos\left(2 \, d x + 2 \, c\right)}{64 \, d} + \frac{{\left(4 \, A a - 3 \, B a\right)} \sin\left(5 \, d x + 5 \, c\right)}{320 \, d} + \frac{{\left(20 \, A a - B a\right)} \sin\left(3 \, d x + 3 \, c\right)}{192 \, d} + \frac{5 \, {\left(8 \, A a + B a\right)} \sin\left(d x + c\right)}{64 \, d}"," ",0,"-1/448*B*a*sin(7*d*x + 7*c)/d - 1/192*(A*a + B*a)*cos(6*d*x + 6*c)/d - 1/32*(A*a + B*a)*cos(4*d*x + 4*c)/d - 5/64*(A*a + B*a)*cos(2*d*x + 2*c)/d + 1/320*(4*A*a - 3*B*a)*sin(5*d*x + 5*c)/d + 1/192*(20*A*a - B*a)*sin(3*d*x + 3*c)/d + 5/64*(8*A*a + B*a)*sin(d*x + c)/d","A",0
955,1,100,0,0.204633," ","integrate(cos(d*x+c)^3*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""giac"")","-\frac{12 \, B a \sin\left(d x + c\right)^{5} + 15 \, A a \sin\left(d x + c\right)^{4} + 15 \, B a \sin\left(d x + c\right)^{4} + 20 \, A a \sin\left(d x + c\right)^{3} - 20 \, B a \sin\left(d x + c\right)^{3} - 30 \, A a \sin\left(d x + c\right)^{2} - 30 \, B a \sin\left(d x + c\right)^{2} - 60 \, A a \sin\left(d x + c\right)}{60 \, d}"," ",0,"-1/60*(12*B*a*sin(d*x + c)^5 + 15*A*a*sin(d*x + c)^4 + 15*B*a*sin(d*x + c)^4 + 20*A*a*sin(d*x + c)^3 - 20*B*a*sin(d*x + c)^3 - 30*A*a*sin(d*x + c)^2 - 30*B*a*sin(d*x + c)^2 - 60*A*a*sin(d*x + c))/d","A",0
956,1,52,0,0.139871," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""giac"")","\frac{2 \, B a \sin\left(d x + c\right)^{3} + 3 \, A a \sin\left(d x + c\right)^{2} + 3 \, B a \sin\left(d x + c\right)^{2} + 6 \, A a \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(2*B*a*sin(d*x + c)^3 + 3*A*a*sin(d*x + c)^2 + 3*B*a*sin(d*x + c)^2 + 6*A*a*sin(d*x + c))/d","A",0
957,1,114,0,0.174346," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""giac"")","\frac{{\left(A a + B a\right)} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right) - 2 \, {\left(A a + B a\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A a + B a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1}}{d}"," ",0,"((A*a + B*a)*log(tan(1/2*d*x + 1/2*c)^2 + 1) - 2*(A*a + B*a)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - (A*a*tan(1/2*d*x + 1/2*c)^2 + B*a*tan(1/2*d*x + 1/2*c)^2 + 2*B*a*tan(1/2*d*x + 1/2*c) + A*a + B*a)/(tan(1/2*d*x + 1/2*c)^2 + 1))/d","B",0
958,1,84,0,0.230637," ","integrate(sec(d*x+c)^3*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""giac"")","\frac{{\left(A a - B a\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - {\left(A a - B a\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) + \frac{A a \sin\left(d x + c\right) - B a \sin\left(d x + c\right) - 3 \, A a - B a}{\sin\left(d x + c\right) - 1}}{4 \, d}"," ",0,"1/4*((A*a - B*a)*log(abs(sin(d*x + c) + 1)) - (A*a - B*a)*log(abs(sin(d*x + c) - 1)) + (A*a*sin(d*x + c) - B*a*sin(d*x + c) - 3*A*a - B*a)/(sin(d*x + c) - 1))/d","A",0
959,1,152,0,0.224346," ","integrate(sec(d*x+c)^5*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""giac"")","\frac{2 \, {\left(3 \, A a - B a\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - 2 \, {\left(3 \, A a - B a\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - \frac{2 \, {\left(3 \, A a \sin\left(d x + c\right) - B a \sin\left(d x + c\right) + 5 \, A a - 3 \, B a\right)}}{\sin\left(d x + c\right) + 1} + \frac{9 \, A a \sin\left(d x + c\right)^{2} - 3 \, B a \sin\left(d x + c\right)^{2} - 26 \, A a \sin\left(d x + c\right) + 6 \, B a \sin\left(d x + c\right) + 21 \, A a + B a}{{\left(\sin\left(d x + c\right) - 1\right)}^{2}}}{32 \, d}"," ",0,"1/32*(2*(3*A*a - B*a)*log(abs(sin(d*x + c) + 1)) - 2*(3*A*a - B*a)*log(abs(sin(d*x + c) - 1)) - 2*(3*A*a*sin(d*x + c) - B*a*sin(d*x + c) + 5*A*a - 3*B*a)/(sin(d*x + c) + 1) + (9*A*a*sin(d*x + c)^2 - 3*B*a*sin(d*x + c)^2 - 26*A*a*sin(d*x + c) + 6*B*a*sin(d*x + c) + 21*A*a + B*a)/(sin(d*x + c) - 1)^2)/d","A",0
960,1,201,0,0.229696," ","integrate(sec(d*x+c)^7*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""giac"")","\frac{6 \, {\left(5 \, A a - B a\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - 6 \, {\left(5 \, A a - B a\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - \frac{3 \, {\left(15 \, A a \sin\left(d x + c\right)^{2} - 3 \, B a \sin\left(d x + c\right)^{2} + 38 \, A a \sin\left(d x + c\right) - 10 \, B a \sin\left(d x + c\right) + 25 \, A a - 9 \, B a\right)}}{{\left(\sin\left(d x + c\right) + 1\right)}^{2}} + \frac{55 \, A a \sin\left(d x + c\right)^{3} - 11 \, B a \sin\left(d x + c\right)^{3} - 201 \, A a \sin\left(d x + c\right)^{2} + 33 \, B a \sin\left(d x + c\right)^{2} + 255 \, A a \sin\left(d x + c\right) - 27 \, B a \sin\left(d x + c\right) - 117 \, A a - 3 \, B a}{{\left(\sin\left(d x + c\right) - 1\right)}^{3}}}{192 \, d}"," ",0,"1/192*(6*(5*A*a - B*a)*log(abs(sin(d*x + c) + 1)) - 6*(5*A*a - B*a)*log(abs(sin(d*x + c) - 1)) - 3*(15*A*a*sin(d*x + c)^2 - 3*B*a*sin(d*x + c)^2 + 38*A*a*sin(d*x + c) - 10*B*a*sin(d*x + c) + 25*A*a - 9*B*a)/(sin(d*x + c) + 1)^2 + (55*A*a*sin(d*x + c)^3 - 11*B*a*sin(d*x + c)^3 - 201*A*a*sin(d*x + c)^2 + 33*B*a*sin(d*x + c)^2 + 255*A*a*sin(d*x + c) - 27*B*a*sin(d*x + c) - 117*A*a - 3*B*a)/(sin(d*x + c) - 1)^3)/d","A",0
961,1,176,0,0.248534," ","integrate(cos(d*x+c)^6*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""giac"")","\frac{5}{128} \, {\left(8 \, A a + B a\right)} x - \frac{B a \sin\left(8 \, d x + 8 \, c\right)}{1024 \, d} - \frac{{\left(A a + B a\right)} \cos\left(7 \, d x + 7 \, c\right)}{448 \, d} - \frac{{\left(A a + B a\right)} \cos\left(5 \, d x + 5 \, c\right)}{64 \, d} - \frac{3 \, {\left(A a + B a\right)} \cos\left(3 \, d x + 3 \, c\right)}{64 \, d} - \frac{5 \, {\left(A a + B a\right)} \cos\left(d x + c\right)}{64 \, d} + \frac{{\left(A a - B a\right)} \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} + \frac{{\left(6 \, A a - B a\right)} \sin\left(4 \, d x + 4 \, c\right)}{128 \, d} + \frac{{\left(15 \, A a + B a\right)} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d}"," ",0,"5/128*(8*A*a + B*a)*x - 1/1024*B*a*sin(8*d*x + 8*c)/d - 1/448*(A*a + B*a)*cos(7*d*x + 7*c)/d - 1/64*(A*a + B*a)*cos(5*d*x + 5*c)/d - 3/64*(A*a + B*a)*cos(3*d*x + 3*c)/d - 5/64*(A*a + B*a)*cos(d*x + c)/d + 1/192*(A*a - B*a)*sin(6*d*x + 6*c)/d + 1/128*(6*A*a - B*a)*sin(4*d*x + 4*c)/d + 1/64*(15*A*a + B*a)*sin(2*d*x + 2*c)/d","A",0
962,1,133,0,0.214770," ","integrate(cos(d*x+c)^4*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""giac"")","\frac{1}{16} \, {\left(6 \, A a + B a\right)} x - \frac{B a \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} - \frac{{\left(A a + B a\right)} \cos\left(5 \, d x + 5 \, c\right)}{80 \, d} - \frac{{\left(A a + B a\right)} \cos\left(3 \, d x + 3 \, c\right)}{16 \, d} - \frac{{\left(A a + B a\right)} \cos\left(d x + c\right)}{8 \, d} + \frac{{\left(2 \, A a - B a\right)} \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{{\left(16 \, A a + B a\right)} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d}"," ",0,"1/16*(6*A*a + B*a)*x - 1/192*B*a*sin(6*d*x + 6*c)/d - 1/80*(A*a + B*a)*cos(5*d*x + 5*c)/d - 1/16*(A*a + B*a)*cos(3*d*x + 3*c)/d - 1/8*(A*a + B*a)*cos(d*x + c)/d + 1/64*(2*A*a - B*a)*sin(4*d*x + 4*c)/d + 1/64*(16*A*a + B*a)*sin(2*d*x + 2*c)/d","A",0
963,1,83,0,0.181596," ","integrate(cos(d*x+c)^2*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""giac"")","\frac{1}{8} \, {\left(4 \, A a + B a\right)} x - \frac{B a \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{A a \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} - \frac{{\left(A a + B a\right)} \cos\left(3 \, d x + 3 \, c\right)}{12 \, d} - \frac{{\left(A a + B a\right)} \cos\left(d x + c\right)}{4 \, d}"," ",0,"1/8*(4*A*a + B*a)*x - 1/32*B*a*sin(4*d*x + 4*c)/d + 1/4*A*a*sin(2*d*x + 2*c)/d - 1/12*(A*a + B*a)*cos(3*d*x + 3*c)/d - 1/4*(A*a + B*a)*cos(d*x + c)/d","A",0
964,1,36,0,0.180092," ","integrate(sec(d*x+c)^2*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""giac"")","-\frac{{\left(d x + c\right)} B a + \frac{2 \, {\left(A a + B a\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1}}{d}"," ",0,"-((d*x + c)*B*a + 2*(A*a + B*a)/(tan(1/2*d*x + 1/2*c) - 1))/d","A",0
965,1,94,0,0.186242," ","integrate(sec(d*x+c)^4*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(A a - B a\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1} + \frac{9 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 7 \, A a + B a}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}}}{6 \, d}"," ",0,"-1/6*(3*(A*a - B*a)/(tan(1/2*d*x + 1/2*c) + 1) + (9*A*a*tan(1/2*d*x + 1/2*c)^2 + 3*B*a*tan(1/2*d*x + 1/2*c)^2 - 12*A*a*tan(1/2*d*x + 1/2*c) + 7*A*a + B*a)/(tan(1/2*d*x + 1/2*c) - 1)^3)/d","B",0
966,1,225,0,0.207334," ","integrate(sec(d*x+c)^6*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{5 \, {\left(15 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 13 \, A a - 7 \, B a\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{3}} + \frac{165 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 45 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 480 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 60 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 650 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 70 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 400 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 20 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 113 \, A a + 13 \, B a}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{5}}}{120 \, d}"," ",0,"-1/120*(5*(15*A*a*tan(1/2*d*x + 1/2*c)^2 - 9*B*a*tan(1/2*d*x + 1/2*c)^2 + 24*A*a*tan(1/2*d*x + 1/2*c) - 12*B*a*tan(1/2*d*x + 1/2*c) + 13*A*a - 7*B*a)/(tan(1/2*d*x + 1/2*c) + 1)^3 + (165*A*a*tan(1/2*d*x + 1/2*c)^4 + 45*B*a*tan(1/2*d*x + 1/2*c)^4 - 480*A*a*tan(1/2*d*x + 1/2*c)^3 - 60*B*a*tan(1/2*d*x + 1/2*c)^3 + 650*A*a*tan(1/2*d*x + 1/2*c)^2 + 70*B*a*tan(1/2*d*x + 1/2*c)^2 - 400*A*a*tan(1/2*d*x + 1/2*c) - 20*B*a*tan(1/2*d*x + 1/2*c) + 113*A*a + 13*B*a)/(tan(1/2*d*x + 1/2*c) - 1)^5)/d","B",0
967,1,345,0,0.214850," ","integrate(sec(d*x+c)^8*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{7 \, {\left(165 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 75 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 540 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 210 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 750 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 280 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 480 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 170 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 129 \, A a - 49 \, B a\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{5}} + \frac{2205 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 525 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 10080 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1470 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 21945 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2555 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 26460 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2240 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18963 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1407 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 7476 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 434 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1383 \, A a + 137 \, B a}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{7}}}{1680 \, d}"," ",0,"-1/1680*(7*(165*A*a*tan(1/2*d*x + 1/2*c)^4 - 75*B*a*tan(1/2*d*x + 1/2*c)^4 + 540*A*a*tan(1/2*d*x + 1/2*c)^3 - 210*B*a*tan(1/2*d*x + 1/2*c)^3 + 750*A*a*tan(1/2*d*x + 1/2*c)^2 - 280*B*a*tan(1/2*d*x + 1/2*c)^2 + 480*A*a*tan(1/2*d*x + 1/2*c) - 170*B*a*tan(1/2*d*x + 1/2*c) + 129*A*a - 49*B*a)/(tan(1/2*d*x + 1/2*c) + 1)^5 + (2205*A*a*tan(1/2*d*x + 1/2*c)^6 + 525*B*a*tan(1/2*d*x + 1/2*c)^6 - 10080*A*a*tan(1/2*d*x + 1/2*c)^5 - 1470*B*a*tan(1/2*d*x + 1/2*c)^5 + 21945*A*a*tan(1/2*d*x + 1/2*c)^4 + 2555*B*a*tan(1/2*d*x + 1/2*c)^4 - 26460*A*a*tan(1/2*d*x + 1/2*c)^3 - 2240*B*a*tan(1/2*d*x + 1/2*c)^3 + 18963*A*a*tan(1/2*d*x + 1/2*c)^2 + 1407*B*a*tan(1/2*d*x + 1/2*c)^2 - 7476*A*a*tan(1/2*d*x + 1/2*c) - 434*B*a*tan(1/2*d*x + 1/2*c) + 1383*A*a + 137*B*a)/(tan(1/2*d*x + 1/2*c) - 1)^7)/d","B",0
968,1,465,0,0.233130," ","integrate(sec(d*x+c)^10*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(9765 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 3675 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 48720 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15960 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 109865 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 33775 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 136640 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 39760 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 99183 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 28161 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 39536 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 11032 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 7043 \, A a - 2101 \, B a\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{7}} + \frac{51345 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 11025 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 322560 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 47880 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 976500 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 117180 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 1753920 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 168840 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2037294 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 165942 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1550976 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 106008 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 760644 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 47772 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 219456 \, A a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12888 \, B a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 30089 \, A a + 2657 \, B a}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{9}}}{40320 \, d}"," ",0,"-1/40320*(3*(9765*A*a*tan(1/2*d*x + 1/2*c)^6 - 3675*B*a*tan(1/2*d*x + 1/2*c)^6 + 48720*A*a*tan(1/2*d*x + 1/2*c)^5 - 15960*B*a*tan(1/2*d*x + 1/2*c)^5 + 109865*A*a*tan(1/2*d*x + 1/2*c)^4 - 33775*B*a*tan(1/2*d*x + 1/2*c)^4 + 136640*A*a*tan(1/2*d*x + 1/2*c)^3 - 39760*B*a*tan(1/2*d*x + 1/2*c)^3 + 99183*A*a*tan(1/2*d*x + 1/2*c)^2 - 28161*B*a*tan(1/2*d*x + 1/2*c)^2 + 39536*A*a*tan(1/2*d*x + 1/2*c) - 11032*B*a*tan(1/2*d*x + 1/2*c) + 7043*A*a - 2101*B*a)/(tan(1/2*d*x + 1/2*c) + 1)^7 + (51345*A*a*tan(1/2*d*x + 1/2*c)^8 + 11025*B*a*tan(1/2*d*x + 1/2*c)^8 - 322560*A*a*tan(1/2*d*x + 1/2*c)^7 - 47880*B*a*tan(1/2*d*x + 1/2*c)^7 + 976500*A*a*tan(1/2*d*x + 1/2*c)^6 + 117180*B*a*tan(1/2*d*x + 1/2*c)^6 - 1753920*A*a*tan(1/2*d*x + 1/2*c)^5 - 168840*B*a*tan(1/2*d*x + 1/2*c)^5 + 2037294*A*a*tan(1/2*d*x + 1/2*c)^4 + 165942*B*a*tan(1/2*d*x + 1/2*c)^4 - 1550976*A*a*tan(1/2*d*x + 1/2*c)^3 - 106008*B*a*tan(1/2*d*x + 1/2*c)^3 + 760644*A*a*tan(1/2*d*x + 1/2*c)^2 + 47772*B*a*tan(1/2*d*x + 1/2*c)^2 - 219456*A*a*tan(1/2*d*x + 1/2*c) - 12888*B*a*tan(1/2*d*x + 1/2*c) + 30089*A*a + 2657*B*a)/(tan(1/2*d*x + 1/2*c) - 1)^9)/d","B",0
969,1,239,0,0.440226," ","integrate(cos(d*x+c)^7*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""giac"")","\frac{B a^{2} \cos\left(10 \, d x + 10 \, c\right)}{5120 \, d} - \frac{A a^{2} \cos\left(8 \, d x + 8 \, c\right)}{512 \, d} + \frac{7 \, A a^{2} \sin\left(3 \, d x + 3 \, c\right)}{64 \, d} - \frac{{\left(16 \, A a^{2} + 7 \, B a^{2}\right)} \cos\left(6 \, d x + 6 \, c\right)}{1024 \, d} - \frac{{\left(7 \, A a^{2} + 4 \, B a^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)}{128 \, d} - \frac{7 \, {\left(8 \, A a^{2} + 5 \, B a^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)}{512 \, d} - \frac{{\left(A a^{2} + 2 \, B a^{2}\right)} \sin\left(9 \, d x + 9 \, c\right)}{2304 \, d} - \frac{{\left(A a^{2} + 10 \, B a^{2}\right)} \sin\left(7 \, d x + 7 \, c\right)}{1792 \, d} + \frac{{\left(5 \, A a^{2} - 4 \, B a^{2}\right)} \sin\left(5 \, d x + 5 \, c\right)}{320 \, d} + \frac{7 \, {\left(11 \, A a^{2} + 2 \, B a^{2}\right)} \sin\left(d x + c\right)}{128 \, d}"," ",0,"1/5120*B*a^2*cos(10*d*x + 10*c)/d - 1/512*A*a^2*cos(8*d*x + 8*c)/d + 7/64*A*a^2*sin(3*d*x + 3*c)/d - 1/1024*(16*A*a^2 + 7*B*a^2)*cos(6*d*x + 6*c)/d - 1/128*(7*A*a^2 + 4*B*a^2)*cos(4*d*x + 4*c)/d - 7/512*(8*A*a^2 + 5*B*a^2)*cos(2*d*x + 2*c)/d - 1/2304*(A*a^2 + 2*B*a^2)*sin(9*d*x + 9*c)/d - 1/1792*(A*a^2 + 10*B*a^2)*sin(7*d*x + 7*c)/d + 1/320*(5*A*a^2 - 4*B*a^2)*sin(5*d*x + 5*c)/d + 7/128*(11*A*a^2 + 2*B*a^2)*sin(d*x + c)/d","A",0
970,1,202,0,0.328584," ","integrate(cos(d*x+c)^5*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""giac"")","\frac{B a^{2} \cos\left(8 \, d x + 8 \, c\right)}{1024 \, d} - \frac{{\left(4 \, A a^{2} + B a^{2}\right)} \cos\left(6 \, d x + 6 \, c\right)}{384 \, d} - \frac{{\left(16 \, A a^{2} + 9 \, B a^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)}{256 \, d} - \frac{{\left(20 \, A a^{2} + 13 \, B a^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)}{128 \, d} - \frac{{\left(A a^{2} + 2 \, B a^{2}\right)} \sin\left(7 \, d x + 7 \, c\right)}{448 \, d} + \frac{{\left(A a^{2} - 6 \, B a^{2}\right)} \sin\left(5 \, d x + 5 \, c\right)}{320 \, d} + \frac{{\left(19 \, A a^{2} - 2 \, B a^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)}{192 \, d} + \frac{5 \, {\left(9 \, A a^{2} + 2 \, B a^{2}\right)} \sin\left(d x + c\right)}{64 \, d}"," ",0,"1/1024*B*a^2*cos(8*d*x + 8*c)/d - 1/384*(4*A*a^2 + B*a^2)*cos(6*d*x + 6*c)/d - 1/256*(16*A*a^2 + 9*B*a^2)*cos(4*d*x + 4*c)/d - 1/128*(20*A*a^2 + 13*B*a^2)*cos(2*d*x + 2*c)/d - 1/448*(A*a^2 + 2*B*a^2)*sin(7*d*x + 7*c)/d + 1/320*(A*a^2 - 6*B*a^2)*sin(5*d*x + 5*c)/d + 1/192*(19*A*a^2 - 2*B*a^2)*sin(3*d*x + 3*c)/d + 5/64*(9*A*a^2 + 2*B*a^2)*sin(d*x + c)/d","B",0
971,1,116,0,0.246468," ","integrate(cos(d*x+c)^3*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""giac"")","-\frac{5 \, B a^{2} \sin\left(d x + c\right)^{6} + 6 \, A a^{2} \sin\left(d x + c\right)^{5} + 12 \, B a^{2} \sin\left(d x + c\right)^{5} + 15 \, A a^{2} \sin\left(d x + c\right)^{4} - 20 \, B a^{2} \sin\left(d x + c\right)^{3} - 30 \, A a^{2} \sin\left(d x + c\right)^{2} - 15 \, B a^{2} \sin\left(d x + c\right)^{2} - 30 \, A a^{2} \sin\left(d x + c\right)}{30 \, d}"," ",0,"-1/30*(5*B*a^2*sin(d*x + c)^6 + 6*A*a^2*sin(d*x + c)^5 + 12*B*a^2*sin(d*x + c)^5 + 15*A*a^2*sin(d*x + c)^4 - 20*B*a^2*sin(d*x + c)^3 - 30*A*a^2*sin(d*x + c)^2 - 15*B*a^2*sin(d*x + c)^2 - 30*A*a^2*sin(d*x + c))/d","A",0
972,1,88,0,0.161484," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""giac"")","\frac{3 \, B a^{2} \sin\left(d x + c\right)^{4} + 4 \, A a^{2} \sin\left(d x + c\right)^{3} + 8 \, B a^{2} \sin\left(d x + c\right)^{3} + 12 \, A a^{2} \sin\left(d x + c\right)^{2} + 6 \, B a^{2} \sin\left(d x + c\right)^{2} + 12 \, A a^{2} \sin\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(3*B*a^2*sin(d*x + c)^4 + 4*A*a^2*sin(d*x + c)^3 + 8*B*a^2*sin(d*x + c)^3 + 12*A*a^2*sin(d*x + c)^2 + 6*B*a^2*sin(d*x + c)^2 + 12*A*a^2*sin(d*x + c))/d","A",0
973,1,220,0,0.203422," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""giac"")","\frac{2 \, {\left(A a^{2} + B a^{2}\right)} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right) - 4 \, {\left(A a^{2} + B a^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{3 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 3 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 8 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, A a^{2} + 3 \, B a^{2}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{d}"," ",0,"(2*(A*a^2 + B*a^2)*log(tan(1/2*d*x + 1/2*c)^2 + 1) - 4*(A*a^2 + B*a^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - (3*A*a^2*tan(1/2*d*x + 1/2*c)^4 + 3*B*a^2*tan(1/2*d*x + 1/2*c)^4 + 2*A*a^2*tan(1/2*d*x + 1/2*c)^3 + 4*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 6*A*a^2*tan(1/2*d*x + 1/2*c)^2 + 8*B*a^2*tan(1/2*d*x + 1/2*c)^2 + 2*A*a^2*tan(1/2*d*x + 1/2*c) + 4*B*a^2*tan(1/2*d*x + 1/2*c) + 3*A*a^2 + 3*B*a^2)/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","B",0
974,1,112,0,0.213219," ","integrate(sec(d*x+c)^3*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""giac"")","-\frac{B a^{2} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right) - 2 \, B a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{3 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a^{2}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{2}}}{d}"," ",0,"-(B*a^2*log(tan(1/2*d*x + 1/2*c)^2 + 1) - 2*B*a^2*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + (3*B*a^2*tan(1/2*d*x + 1/2*c)^2 - 2*A*a^2*tan(1/2*d*x + 1/2*c) - 8*B*a^2*tan(1/2*d*x + 1/2*c) + 3*B*a^2)/(tan(1/2*d*x + 1/2*c) - 1)^2)/d","B",0
975,1,130,0,0.241520," ","integrate(sec(d*x+c)^5*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""giac"")","\frac{2 \, {\left(A a^{2} - B a^{2}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - 2 \, {\left(A a^{2} - B a^{2}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) + \frac{3 \, A a^{2} \sin\left(d x + c\right)^{2} - 3 \, B a^{2} \sin\left(d x + c\right)^{2} - 10 \, A a^{2} \sin\left(d x + c\right) + 10 \, B a^{2} \sin\left(d x + c\right) + 11 \, A a^{2} - 3 \, B a^{2}}{{\left(\sin\left(d x + c\right) - 1\right)}^{2}}}{16 \, d}"," ",0,"1/16*(2*(A*a^2 - B*a^2)*log(abs(sin(d*x + c) + 1)) - 2*(A*a^2 - B*a^2)*log(abs(sin(d*x + c) - 1)) + (3*A*a^2*sin(d*x + c)^2 - 3*B*a^2*sin(d*x + c)^2 - 10*A*a^2*sin(d*x + c) + 10*B*a^2*sin(d*x + c) + 11*A*a^2 - 3*B*a^2)/(sin(d*x + c) - 1)^2)/d","A",0
976,1,209,0,0.267658," ","integrate(sec(d*x+c)^7*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""giac"")","\frac{6 \, {\left(2 \, A a^{2} - B a^{2}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - 6 \, {\left(2 \, A a^{2} - B a^{2}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - \frac{6 \, {\left(2 \, A a^{2} \sin\left(d x + c\right) - B a^{2} \sin\left(d x + c\right) + 3 \, A a^{2} - 2 \, B a^{2}\right)}}{\sin\left(d x + c\right) + 1} + \frac{22 \, A a^{2} \sin\left(d x + c\right)^{3} - 11 \, B a^{2} \sin\left(d x + c\right)^{3} - 84 \, A a^{2} \sin\left(d x + c\right)^{2} + 39 \, B a^{2} \sin\left(d x + c\right)^{2} + 114 \, A a^{2} \sin\left(d x + c\right) - 45 \, B a^{2} \sin\left(d x + c\right) - 60 \, A a^{2} + 9 \, B a^{2}}{{\left(\sin\left(d x + c\right) - 1\right)}^{3}}}{96 \, d}"," ",0,"1/96*(6*(2*A*a^2 - B*a^2)*log(abs(sin(d*x + c) + 1)) - 6*(2*A*a^2 - B*a^2)*log(abs(sin(d*x + c) - 1)) - 6*(2*A*a^2*sin(d*x + c) - B*a^2*sin(d*x + c) + 3*A*a^2 - 2*B*a^2)/(sin(d*x + c) + 1) + (22*A*a^2*sin(d*x + c)^3 - 11*B*a^2*sin(d*x + c)^3 - 84*A*a^2*sin(d*x + c)^2 + 39*B*a^2*sin(d*x + c)^2 + 114*A*a^2*sin(d*x + c) - 45*B*a^2*sin(d*x + c) - 60*A*a^2 + 9*B*a^2)/(sin(d*x + c) - 1)^3)/d","A",0
977,1,235,0,0.383620," ","integrate(cos(d*x+c)^6*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""giac"")","\frac{B a^{2} \cos\left(9 \, d x + 9 \, c\right)}{2304 \, d} - \frac{B a^{2} \sin\left(6 \, d x + 6 \, c\right)}{96 \, d} + \frac{5}{128} \, {\left(9 \, A a^{2} + 2 \, B a^{2}\right)} x - \frac{{\left(8 \, A a^{2} + B a^{2}\right)} \cos\left(7 \, d x + 7 \, c\right)}{1792 \, d} - \frac{{\left(2 \, A a^{2} + B a^{2}\right)} \cos\left(5 \, d x + 5 \, c\right)}{64 \, d} - \frac{{\left(18 \, A a^{2} + 11 \, B a^{2}\right)} \cos\left(3 \, d x + 3 \, c\right)}{192 \, d} - \frac{{\left(20 \, A a^{2} + 13 \, B a^{2}\right)} \cos\left(d x + c\right)}{128 \, d} - \frac{{\left(A a^{2} + 2 \, B a^{2}\right)} \sin\left(8 \, d x + 8 \, c\right)}{1024 \, d} + \frac{{\left(5 \, A a^{2} - 2 \, B a^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)}{128 \, d} + \frac{{\left(8 \, A a^{2} + B a^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)}{32 \, d}"," ",0,"1/2304*B*a^2*cos(9*d*x + 9*c)/d - 1/96*B*a^2*sin(6*d*x + 6*c)/d + 5/128*(9*A*a^2 + 2*B*a^2)*x - 1/1792*(8*A*a^2 + B*a^2)*cos(7*d*x + 7*c)/d - 1/64*(2*A*a^2 + B*a^2)*cos(5*d*x + 5*c)/d - 1/192*(18*A*a^2 + 11*B*a^2)*cos(3*d*x + 3*c)/d - 1/128*(20*A*a^2 + 13*B*a^2)*cos(d*x + c)/d - 1/1024*(A*a^2 + 2*B*a^2)*sin(8*d*x + 8*c)/d + 1/128*(5*A*a^2 - 2*B*a^2)*sin(4*d*x + 4*c)/d + 1/32*(8*A*a^2 + B*a^2)*sin(2*d*x + 2*c)/d","A",0
978,1,192,0,0.300591," ","integrate(cos(d*x+c)^4*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""giac"")","\frac{B a^{2} \cos\left(7 \, d x + 7 \, c\right)}{448 \, d} + \frac{1}{16} \, {\left(7 \, A a^{2} + 2 \, B a^{2}\right)} x - \frac{{\left(8 \, A a^{2} + 3 \, B a^{2}\right)} \cos\left(5 \, d x + 5 \, c\right)}{320 \, d} - \frac{{\left(8 \, A a^{2} + 5 \, B a^{2}\right)} \cos\left(3 \, d x + 3 \, c\right)}{64 \, d} - \frac{{\left(16 \, A a^{2} + 11 \, B a^{2}\right)} \cos\left(d x + c\right)}{64 \, d} - \frac{{\left(A a^{2} + 2 \, B a^{2}\right)} \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} + \frac{{\left(A a^{2} - 2 \, B a^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{{\left(17 \, A a^{2} + 2 \, B a^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d}"," ",0,"1/448*B*a^2*cos(7*d*x + 7*c)/d + 1/16*(7*A*a^2 + 2*B*a^2)*x - 1/320*(8*A*a^2 + 3*B*a^2)*cos(5*d*x + 5*c)/d - 1/64*(8*A*a^2 + 5*B*a^2)*cos(3*d*x + 3*c)/d - 1/64*(16*A*a^2 + 11*B*a^2)*cos(d*x + c)/d - 1/192*(A*a^2 + 2*B*a^2)*sin(6*d*x + 6*c)/d + 1/64*(A*a^2 - 2*B*a^2)*sin(4*d*x + 4*c)/d + 1/64*(17*A*a^2 + 2*B*a^2)*sin(2*d*x + 2*c)/d","A",0
979,1,130,0,0.229545," ","integrate(cos(d*x+c)^2*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""giac"")","\frac{B a^{2} \cos\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{A a^{2} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d} + \frac{1}{8} \, {\left(5 \, A a^{2} + 2 \, B a^{2}\right)} x - \frac{{\left(8 \, A a^{2} + 5 \, B a^{2}\right)} \cos\left(3 \, d x + 3 \, c\right)}{48 \, d} - \frac{{\left(4 \, A a^{2} + 3 \, B a^{2}\right)} \cos\left(d x + c\right)}{8 \, d} - \frac{{\left(A a^{2} + 2 \, B a^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d}"," ",0,"1/80*B*a^2*cos(5*d*x + 5*c)/d + 1/4*A*a^2*sin(2*d*x + 2*c)/d + 1/8*(5*A*a^2 + 2*B*a^2)*x - 1/48*(8*A*a^2 + 5*B*a^2)*cos(3*d*x + 3*c)/d - 1/8*(4*A*a^2 + 3*B*a^2)*cos(d*x + c)/d - 1/32*(A*a^2 + 2*B*a^2)*sin(4*d*x + 4*c)/d","A",0
980,1,125,0,0.200686," ","integrate(sec(d*x+c)^2*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""giac"")","-\frac{{\left(A a^{2} + 2 \, B a^{2}\right)} {\left(d x + c\right)} + \frac{2 \, {\left(2 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, A a^{2} + 3 \, B a^{2}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1}}{d}"," ",0,"-((A*a^2 + 2*B*a^2)*(d*x + c) + 2*(2*A*a^2*tan(1/2*d*x + 1/2*c)^2 + 2*B*a^2*tan(1/2*d*x + 1/2*c)^2 - B*a^2*tan(1/2*d*x + 1/2*c) + 2*A*a^2 + 3*B*a^2)/(tan(1/2*d*x + 1/2*c)^3 - tan(1/2*d*x + 1/2*c)^2 + tan(1/2*d*x + 1/2*c) - 1))/d","B",0
981,1,78,0,0.197924," ","integrate(sec(d*x+c)^4*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""giac"")","-\frac{2 \, {\left(3 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, A a^{2} - B a^{2}\right)}}{3 \, d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}}"," ",0,"-2/3*(3*A*a^2*tan(1/2*d*x + 1/2*c)^2 - 3*A*a^2*tan(1/2*d*x + 1/2*c) + 3*B*a^2*tan(1/2*d*x + 1/2*c) + 2*A*a^2 - B*a^2)/(d*(tan(1/2*d*x + 1/2*c) - 1)^3)","A",0
982,1,192,0,0.212663," ","integrate(sec(d*x+c)^6*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{15 \, {\left(A a^{2} - B a^{2}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1} + \frac{105 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 15 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 270 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 360 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 40 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 210 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 50 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 63 \, A a^{2} - 7 \, B a^{2}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{5}}}{60 \, d}"," ",0,"-1/60*(15*(A*a^2 - B*a^2)/(tan(1/2*d*x + 1/2*c) + 1) + (105*A*a^2*tan(1/2*d*x + 1/2*c)^4 + 15*B*a^2*tan(1/2*d*x + 1/2*c)^4 - 270*A*a^2*tan(1/2*d*x + 1/2*c)^3 + 30*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 360*A*a^2*tan(1/2*d*x + 1/2*c)^2 - 40*B*a^2*tan(1/2*d*x + 1/2*c)^2 - 210*A*a^2*tan(1/2*d*x + 1/2*c) + 50*B*a^2*tan(1/2*d*x + 1/2*c) + 63*A*a^2 - 7*B*a^2)/(tan(1/2*d*x + 1/2*c) - 1)^5)/d","A",0
983,1,325,0,0.234903," ","integrate(sec(d*x+c)^8*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{35 \, {\left(9 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 6 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 15 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8 \, A a^{2} - 5 \, B a^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{3}} + \frac{1365 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 210 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 5775 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 105 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12250 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 175 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 14350 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 910 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 10185 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 756 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3955 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 427 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 760 \, A a^{2} - 31 \, B a^{2}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{7}}}{840 \, d}"," ",0,"-1/840*(35*(9*A*a^2*tan(1/2*d*x + 1/2*c)^2 - 6*B*a^2*tan(1/2*d*x + 1/2*c)^2 + 15*A*a^2*tan(1/2*d*x + 1/2*c) - 9*B*a^2*tan(1/2*d*x + 1/2*c) + 8*A*a^2 - 5*B*a^2)/(tan(1/2*d*x + 1/2*c) + 1)^3 + (1365*A*a^2*tan(1/2*d*x + 1/2*c)^6 + 210*B*a^2*tan(1/2*d*x + 1/2*c)^6 - 5775*A*a^2*tan(1/2*d*x + 1/2*c)^5 - 105*B*a^2*tan(1/2*d*x + 1/2*c)^5 + 12250*A*a^2*tan(1/2*d*x + 1/2*c)^4 - 175*B*a^2*tan(1/2*d*x + 1/2*c)^4 - 14350*A*a^2*tan(1/2*d*x + 1/2*c)^3 + 910*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 10185*A*a^2*tan(1/2*d*x + 1/2*c)^2 - 756*B*a^2*tan(1/2*d*x + 1/2*c)^2 - 3955*A*a^2*tan(1/2*d*x + 1/2*c) + 427*B*a^2*tan(1/2*d*x + 1/2*c) + 760*A*a^2 - 31*B*a^2)/(tan(1/2*d*x + 1/2*c) - 1)^7)/d","B",0
984,1,461,0,0.254762," ","integrate(sec(d*x+c)^10*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{21 \, {\left(435 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 225 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 1470 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 690 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2060 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 940 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1330 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 590 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 353 \, A a^{2} - 163 \, B a^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{5}} + \frac{31185 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 4725 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 185220 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 11340 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 546840 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 15120 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 961380 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3780 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1101618 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 24318 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 828492 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 33852 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 404208 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 19368 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 116172 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6732 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 16373 \, A a^{2} - 223 \, B a^{2}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{9}}}{20160 \, d}"," ",0,"-1/20160*(21*(435*A*a^2*tan(1/2*d*x + 1/2*c)^4 - 225*B*a^2*tan(1/2*d*x + 1/2*c)^4 + 1470*A*a^2*tan(1/2*d*x + 1/2*c)^3 - 690*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 2060*A*a^2*tan(1/2*d*x + 1/2*c)^2 - 940*B*a^2*tan(1/2*d*x + 1/2*c)^2 + 1330*A*a^2*tan(1/2*d*x + 1/2*c) - 590*B*a^2*tan(1/2*d*x + 1/2*c) + 353*A*a^2 - 163*B*a^2)/(tan(1/2*d*x + 1/2*c) + 1)^5 + (31185*A*a^2*tan(1/2*d*x + 1/2*c)^8 + 4725*B*a^2*tan(1/2*d*x + 1/2*c)^8 - 185220*A*a^2*tan(1/2*d*x + 1/2*c)^7 - 11340*B*a^2*tan(1/2*d*x + 1/2*c)^7 + 546840*A*a^2*tan(1/2*d*x + 1/2*c)^6 + 15120*B*a^2*tan(1/2*d*x + 1/2*c)^6 - 961380*A*a^2*tan(1/2*d*x + 1/2*c)^5 + 3780*B*a^2*tan(1/2*d*x + 1/2*c)^5 + 1101618*A*a^2*tan(1/2*d*x + 1/2*c)^4 - 24318*B*a^2*tan(1/2*d*x + 1/2*c)^4 - 828492*A*a^2*tan(1/2*d*x + 1/2*c)^3 + 33852*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 404208*A*a^2*tan(1/2*d*x + 1/2*c)^2 - 19368*B*a^2*tan(1/2*d*x + 1/2*c)^2 - 116172*A*a^2*tan(1/2*d*x + 1/2*c) + 6732*B*a^2*tan(1/2*d*x + 1/2*c) + 16373*A*a^2 - 223*B*a^2)/(tan(1/2*d*x + 1/2*c) - 1)^9)/d","B",0
985,1,597,0,0.298411," ","integrate(sec(d*x+c)^12*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{33 \, {\left(6825 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 2940 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 34965 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 13755 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 79800 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 30065 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 100170 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36470 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 73017 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 26166 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 29169 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 10367 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5142 \, A a^{2} - 1901 \, B a^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{7}} + \frac{661815 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 97020 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 5083155 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 405405 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 19355490 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 952875 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 45446940 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1122660 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 72295146 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 557172 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 80611146 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 563178 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 63771840 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1126950 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 35253900 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 955020 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 13119975 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 406120 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2978811 \, A a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 97163 \, B a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 330966 \, A a^{2} - 13 \, B a^{2}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{11}}}{443520 \, d}"," ",0,"-1/443520*(33*(6825*A*a^2*tan(1/2*d*x + 1/2*c)^6 - 2940*B*a^2*tan(1/2*d*x + 1/2*c)^6 + 34965*A*a^2*tan(1/2*d*x + 1/2*c)^5 - 13755*B*a^2*tan(1/2*d*x + 1/2*c)^5 + 79800*A*a^2*tan(1/2*d*x + 1/2*c)^4 - 30065*B*a^2*tan(1/2*d*x + 1/2*c)^4 + 100170*A*a^2*tan(1/2*d*x + 1/2*c)^3 - 36470*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 73017*A*a^2*tan(1/2*d*x + 1/2*c)^2 - 26166*B*a^2*tan(1/2*d*x + 1/2*c)^2 + 29169*A*a^2*tan(1/2*d*x + 1/2*c) - 10367*B*a^2*tan(1/2*d*x + 1/2*c) + 5142*A*a^2 - 1901*B*a^2)/(tan(1/2*d*x + 1/2*c) + 1)^7 + (661815*A*a^2*tan(1/2*d*x + 1/2*c)^10 + 97020*B*a^2*tan(1/2*d*x + 1/2*c)^10 - 5083155*A*a^2*tan(1/2*d*x + 1/2*c)^9 - 405405*B*a^2*tan(1/2*d*x + 1/2*c)^9 + 19355490*A*a^2*tan(1/2*d*x + 1/2*c)^8 + 952875*B*a^2*tan(1/2*d*x + 1/2*c)^8 - 45446940*A*a^2*tan(1/2*d*x + 1/2*c)^7 - 1122660*B*a^2*tan(1/2*d*x + 1/2*c)^7 + 72295146*A*a^2*tan(1/2*d*x + 1/2*c)^6 + 557172*B*a^2*tan(1/2*d*x + 1/2*c)^6 - 80611146*A*a^2*tan(1/2*d*x + 1/2*c)^5 + 563178*B*a^2*tan(1/2*d*x + 1/2*c)^5 + 63771840*A*a^2*tan(1/2*d*x + 1/2*c)^4 - 1126950*B*a^2*tan(1/2*d*x + 1/2*c)^4 - 35253900*A*a^2*tan(1/2*d*x + 1/2*c)^3 + 955020*B*a^2*tan(1/2*d*x + 1/2*c)^3 + 13119975*A*a^2*tan(1/2*d*x + 1/2*c)^2 - 406120*B*a^2*tan(1/2*d*x + 1/2*c)^2 - 2978811*A*a^2*tan(1/2*d*x + 1/2*c) + 97163*B*a^2*tan(1/2*d*x + 1/2*c) + 330966*A*a^2 - 13*B*a^2)/(tan(1/2*d*x + 1/2*c) - 1)^11)/d","B",0
986,1,283,0,0.893616," ","integrate(cos(d*x+c)^7*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""giac"")","\frac{B a^{3} \sin\left(11 \, d x + 11 \, c\right)}{11264 \, d} + \frac{{\left(A a^{3} + 3 \, B a^{3}\right)} \cos\left(10 \, d x + 10 \, c\right)}{5120 \, d} - \frac{{\left(A a^{3} - B a^{3}\right)} \cos\left(8 \, d x + 8 \, c\right)}{512 \, d} - \frac{{\left(23 \, A a^{3} + 5 \, B a^{3}\right)} \cos\left(6 \, d x + 6 \, c\right)}{1024 \, d} - \frac{{\left(11 \, A a^{3} + 5 \, B a^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)}{128 \, d} - \frac{7 \, {\left(13 \, A a^{3} + 7 \, B a^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)}{512 \, d} - \frac{{\left(4 \, A a^{3} + 3 \, B a^{3}\right)} \sin\left(9 \, d x + 9 \, c\right)}{3072 \, d} - \frac{{\left(44 \, A a^{3} + 61 \, B a^{3}\right)} \sin\left(7 \, d x + 7 \, c\right)}{7168 \, d} + \frac{{\left(16 \, A a^{3} - 107 \, B a^{3}\right)} \sin\left(5 \, d x + 5 \, c\right)}{5120 \, d} + \frac{{\left(56 \, A a^{3} - B a^{3}\right)} \sin\left(3 \, d x + 3 \, c\right)}{512 \, d} + \frac{91 \, {\left(4 \, A a^{3} + B a^{3}\right)} \sin\left(d x + c\right)}{512 \, d}"," ",0,"1/11264*B*a^3*sin(11*d*x + 11*c)/d + 1/5120*(A*a^3 + 3*B*a^3)*cos(10*d*x + 10*c)/d - 1/512*(A*a^3 - B*a^3)*cos(8*d*x + 8*c)/d - 1/1024*(23*A*a^3 + 5*B*a^3)*cos(6*d*x + 6*c)/d - 1/128*(11*A*a^3 + 5*B*a^3)*cos(4*d*x + 4*c)/d - 7/512*(13*A*a^3 + 7*B*a^3)*cos(2*d*x + 2*c)/d - 1/3072*(4*A*a^3 + 3*B*a^3)*sin(9*d*x + 9*c)/d - 1/7168*(44*A*a^3 + 61*B*a^3)*sin(7*d*x + 7*c)/d + 1/5120*(16*A*a^3 - 107*B*a^3)*sin(5*d*x + 5*c)/d + 1/512*(56*A*a^3 - B*a^3)*sin(3*d*x + 3*c)/d + 91/512*(4*A*a^3 + B*a^3)*sin(d*x + c)/d","B",0
987,1,230,0,0.597877," ","integrate(cos(d*x+c)^5*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""giac"")","\frac{B a^{3} \sin\left(9 \, d x + 9 \, c\right)}{2304 \, d} + \frac{{\left(A a^{3} + 3 \, B a^{3}\right)} \cos\left(8 \, d x + 8 \, c\right)}{1024 \, d} - \frac{{\left(5 \, A a^{3} - B a^{3}\right)} \cos\left(6 \, d x + 6 \, c\right)}{384 \, d} - \frac{{\left(25 \, A a^{3} + 11 \, B a^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)}{256 \, d} - \frac{{\left(33 \, A a^{3} + 19 \, B a^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)}{128 \, d} - \frac{{\left(12 \, A a^{3} + 11 \, B a^{3}\right)} \sin\left(7 \, d x + 7 \, c\right)}{1792 \, d} - \frac{{\left(A a^{3} + 2 \, B a^{3}\right)} \sin\left(5 \, d x + 5 \, c\right)}{64 \, d} + \frac{{\left(17 \, A a^{3} - 4 \, B a^{3}\right)} \sin\left(3 \, d x + 3 \, c\right)}{192 \, d} + \frac{11 \, {\left(10 \, A a^{3} + 3 \, B a^{3}\right)} \sin\left(d x + c\right)}{128 \, d}"," ",0,"1/2304*B*a^3*sin(9*d*x + 9*c)/d + 1/1024*(A*a^3 + 3*B*a^3)*cos(8*d*x + 8*c)/d - 1/384*(5*A*a^3 - B*a^3)*cos(6*d*x + 6*c)/d - 1/256*(25*A*a^3 + 11*B*a^3)*cos(4*d*x + 4*c)/d - 1/128*(33*A*a^3 + 19*B*a^3)*cos(2*d*x + 2*c)/d - 1/1792*(12*A*a^3 + 11*B*a^3)*sin(7*d*x + 7*c)/d - 1/64*(A*a^3 + 2*B*a^3)*sin(5*d*x + 5*c)/d + 1/192*(17*A*a^3 - 4*B*a^3)*sin(3*d*x + 3*c)/d + 11/128*(10*A*a^3 + 3*B*a^3)*sin(d*x + c)/d","B",0
988,1,172,0,0.345459," ","integrate(cos(d*x+c)^3*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""giac"")","-\frac{30 \, B a^{3} \sin\left(d x + c\right)^{7} + 35 \, A a^{3} \sin\left(d x + c\right)^{6} + 105 \, B a^{3} \sin\left(d x + c\right)^{6} + 126 \, A a^{3} \sin\left(d x + c\right)^{5} + 84 \, B a^{3} \sin\left(d x + c\right)^{5} + 105 \, A a^{3} \sin\left(d x + c\right)^{4} - 105 \, B a^{3} \sin\left(d x + c\right)^{4} - 140 \, A a^{3} \sin\left(d x + c\right)^{3} - 210 \, B a^{3} \sin\left(d x + c\right)^{3} - 315 \, A a^{3} \sin\left(d x + c\right)^{2} - 105 \, B a^{3} \sin\left(d x + c\right)^{2} - 210 \, A a^{3} \sin\left(d x + c\right)}{210 \, d}"," ",0,"-1/210*(30*B*a^3*sin(d*x + c)^7 + 35*A*a^3*sin(d*x + c)^6 + 105*B*a^3*sin(d*x + c)^6 + 126*A*a^3*sin(d*x + c)^5 + 84*B*a^3*sin(d*x + c)^5 + 105*A*a^3*sin(d*x + c)^4 - 105*B*a^3*sin(d*x + c)^4 - 140*A*a^3*sin(d*x + c)^3 - 210*B*a^3*sin(d*x + c)^3 - 315*A*a^3*sin(d*x + c)^2 - 105*B*a^3*sin(d*x + c)^2 - 210*A*a^3*sin(d*x + c))/d","B",0
989,1,116,0,0.227076," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""giac"")","\frac{4 \, B a^{3} \sin\left(d x + c\right)^{5} + 5 \, A a^{3} \sin\left(d x + c\right)^{4} + 15 \, B a^{3} \sin\left(d x + c\right)^{4} + 20 \, A a^{3} \sin\left(d x + c\right)^{3} + 20 \, B a^{3} \sin\left(d x + c\right)^{3} + 30 \, A a^{3} \sin\left(d x + c\right)^{2} + 10 \, B a^{3} \sin\left(d x + c\right)^{2} + 20 \, A a^{3} \sin\left(d x + c\right)}{20 \, d}"," ",0,"1/20*(4*B*a^3*sin(d*x + c)^5 + 5*A*a^3*sin(d*x + c)^4 + 15*B*a^3*sin(d*x + c)^4 + 20*A*a^3*sin(d*x + c)^3 + 20*B*a^3*sin(d*x + c)^3 + 30*A*a^3*sin(d*x + c)^2 + 10*B*a^3*sin(d*x + c)^2 + 20*A*a^3*sin(d*x + c))/d","B",0
990,1,289,0,0.210868," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""giac"")","\frac{2 \, {\left(6 \, {\left(A a^{3} + B a^{3}\right)} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right) - 12 \, {\left(A a^{3} + B a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{11 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 11 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 9 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 42 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 18 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 28 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 42 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 9 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 11 \, A a^{3} + 11 \, B a^{3}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}\right)}}{3 \, d}"," ",0,"2/3*(6*(A*a^3 + B*a^3)*log(tan(1/2*d*x + 1/2*c)^2 + 1) - 12*(A*a^3 + B*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - (11*A*a^3*tan(1/2*d*x + 1/2*c)^6 + 11*B*a^3*tan(1/2*d*x + 1/2*c)^6 + 9*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 12*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 36*A*a^3*tan(1/2*d*x + 1/2*c)^4 + 42*B*a^3*tan(1/2*d*x + 1/2*c)^4 + 18*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 28*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 36*A*a^3*tan(1/2*d*x + 1/2*c)^2 + 42*B*a^3*tan(1/2*d*x + 1/2*c)^2 + 9*A*a^3*tan(1/2*d*x + 1/2*c) + 12*B*a^3*tan(1/2*d*x + 1/2*c) + 11*A*a^3 + 11*B*a^3)/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","B",0
991,1,228,0,0.262731," ","integrate(sec(d*x+c)^3*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""giac"")","-\frac{{\left(A a^{3} + 3 \, B a^{3}\right)} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right) - 2 \, {\left(A a^{3} + 3 \, B a^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A a^{3} + 3 \, B a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + \frac{3 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 9 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 10 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 22 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, A a^{3} + 9 \, B a^{3}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{2}}}{d}"," ",0,"-((A*a^3 + 3*B*a^3)*log(tan(1/2*d*x + 1/2*c)^2 + 1) - 2*(A*a^3 + 3*B*a^3)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - (A*a^3*tan(1/2*d*x + 1/2*c)^2 + 3*B*a^3*tan(1/2*d*x + 1/2*c)^2 + 2*B*a^3*tan(1/2*d*x + 1/2*c) + A*a^3 + 3*B*a^3)/(tan(1/2*d*x + 1/2*c)^2 + 1) + (3*A*a^3*tan(1/2*d*x + 1/2*c)^2 + 9*B*a^3*tan(1/2*d*x + 1/2*c)^2 - 10*A*a^3*tan(1/2*d*x + 1/2*c) - 22*B*a^3*tan(1/2*d*x + 1/2*c) + 3*A*a^3 + 9*B*a^3)/(tan(1/2*d*x + 1/2*c) - 1)^2)/d","B",0
992,1,82,0,0.261819," ","integrate(sec(d*x+c)^5*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""giac"")","\frac{2 \, {\left(A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{4}}"," ",0,"2*(A*a^3*tan(1/2*d*x + 1/2*c)^3 - A*a^3*tan(1/2*d*x + 1/2*c)^2 + B*a^3*tan(1/2*d*x + 1/2*c)^2 + A*a^3*tan(1/2*d*x + 1/2*c))/(d*(tan(1/2*d*x + 1/2*c) - 1)^4)","A",0
993,1,158,0,0.292837," ","integrate(sec(d*x+c)^7*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""giac"")","\frac{6 \, {\left(A a^{3} - B a^{3}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - 6 \, {\left(A a^{3} - B a^{3}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) + \frac{11 \, A a^{3} \sin\left(d x + c\right)^{3} - 11 \, B a^{3} \sin\left(d x + c\right)^{3} - 45 \, A a^{3} \sin\left(d x + c\right)^{2} + 45 \, B a^{3} \sin\left(d x + c\right)^{2} + 69 \, A a^{3} \sin\left(d x + c\right) - 69 \, B a^{3} \sin\left(d x + c\right) - 51 \, A a^{3} + 19 \, B a^{3}}{{\left(\sin\left(d x + c\right) - 1\right)}^{3}}}{96 \, d}"," ",0,"1/96*(6*(A*a^3 - B*a^3)*log(abs(sin(d*x + c) + 1)) - 6*(A*a^3 - B*a^3)*log(abs(sin(d*x + c) - 1)) + (11*A*a^3*sin(d*x + c)^3 - 11*B*a^3*sin(d*x + c)^3 - 45*A*a^3*sin(d*x + c)^2 + 45*B*a^3*sin(d*x + c)^2 + 69*A*a^3*sin(d*x + c) - 69*B*a^3*sin(d*x + c) - 51*A*a^3 + 19*B*a^3)/(sin(d*x + c) - 1)^3)/d","A",0
994,1,237,0,0.315274," ","integrate(sec(d*x+c)^9*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""giac"")","\frac{12 \, {\left(5 \, A a^{3} - 3 \, B a^{3}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - 12 \, {\left(5 \, A a^{3} - 3 \, B a^{3}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - \frac{12 \, {\left(5 \, A a^{3} \sin\left(d x + c\right) - 3 \, B a^{3} \sin\left(d x + c\right) + 7 \, A a^{3} - 5 \, B a^{3}\right)}}{\sin\left(d x + c\right) + 1} + \frac{125 \, A a^{3} \sin\left(d x + c\right)^{4} - 75 \, B a^{3} \sin\left(d x + c\right)^{4} - 596 \, A a^{3} \sin\left(d x + c\right)^{3} + 348 \, B a^{3} \sin\left(d x + c\right)^{3} + 1110 \, A a^{3} \sin\left(d x + c\right)^{2} - 618 \, B a^{3} \sin\left(d x + c\right)^{2} - 996 \, A a^{3} \sin\left(d x + c\right) + 492 \, B a^{3} \sin\left(d x + c\right) + 405 \, A a^{3} - 99 \, B a^{3}}{{\left(\sin\left(d x + c\right) - 1\right)}^{4}}}{768 \, d}"," ",0,"1/768*(12*(5*A*a^3 - 3*B*a^3)*log(abs(sin(d*x + c) + 1)) - 12*(5*A*a^3 - 3*B*a^3)*log(abs(sin(d*x + c) - 1)) - 12*(5*A*a^3*sin(d*x + c) - 3*B*a^3*sin(d*x + c) + 7*A*a^3 - 5*B*a^3)/(sin(d*x + c) + 1) + (125*A*a^3*sin(d*x + c)^4 - 75*B*a^3*sin(d*x + c)^4 - 596*A*a^3*sin(d*x + c)^3 + 348*B*a^3*sin(d*x + c)^3 + 1110*A*a^3*sin(d*x + c)^2 - 618*B*a^3*sin(d*x + c)^2 - 996*A*a^3*sin(d*x + c) + 492*B*a^3*sin(d*x + c) + 405*A*a^3 - 99*B*a^3)/(sin(d*x + c) - 1)^4)/d","A",0
995,1,273,0,0.744629," ","integrate(cos(d*x+c)^6*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""giac"")","\frac{B a^{3} \sin\left(10 \, d x + 10 \, c\right)}{5120 \, d} + \frac{11}{256} \, {\left(10 \, A a^{3} + 3 \, B a^{3}\right)} x + \frac{{\left(A a^{3} + 3 \, B a^{3}\right)} \cos\left(9 \, d x + 9 \, c\right)}{2304 \, d} - \frac{{\left(9 \, A a^{3} - 5 \, B a^{3}\right)} \cos\left(7 \, d x + 7 \, c\right)}{1792 \, d} - \frac{{\left(3 \, A a^{3} + B a^{3}\right)} \cos\left(5 \, d x + 5 \, c\right)}{64 \, d} - \frac{{\left(29 \, A a^{3} + 15 \, B a^{3}\right)} \cos\left(3 \, d x + 3 \, c\right)}{192 \, d} - \frac{{\left(33 \, A a^{3} + 19 \, B a^{3}\right)} \cos\left(d x + c\right)}{128 \, d} - \frac{{\left(6 \, A a^{3} + 5 \, B a^{3}\right)} \sin\left(8 \, d x + 8 \, c\right)}{2048 \, d} - \frac{{\left(32 \, A a^{3} + 51 \, B a^{3}\right)} \sin\left(6 \, d x + 6 \, c\right)}{3072 \, d} + \frac{{\left(6 \, A a^{3} - 7 \, B a^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)}{256 \, d} + \frac{{\left(144 \, A a^{3} + 25 \, B a^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)}{512 \, d}"," ",0,"1/5120*B*a^3*sin(10*d*x + 10*c)/d + 11/256*(10*A*a^3 + 3*B*a^3)*x + 1/2304*(A*a^3 + 3*B*a^3)*cos(9*d*x + 9*c)/d - 1/1792*(9*A*a^3 - 5*B*a^3)*cos(7*d*x + 7*c)/d - 1/64*(3*A*a^3 + B*a^3)*cos(5*d*x + 5*c)/d - 1/192*(29*A*a^3 + 15*B*a^3)*cos(3*d*x + 3*c)/d - 1/128*(33*A*a^3 + 19*B*a^3)*cos(d*x + c)/d - 1/2048*(6*A*a^3 + 5*B*a^3)*sin(8*d*x + 8*c)/d - 1/3072*(32*A*a^3 + 51*B*a^3)*sin(6*d*x + 6*c)/d + 1/256*(6*A*a^3 - 7*B*a^3)*sin(4*d*x + 4*c)/d + 1/512*(144*A*a^3 + 25*B*a^3)*sin(2*d*x + 2*c)/d","A",0
996,1,217,0,0.379480," ","integrate(cos(d*x+c)^4*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""giac"")","\frac{B a^{3} \sin\left(8 \, d x + 8 \, c\right)}{1024 \, d} + \frac{9}{128} \, {\left(8 \, A a^{3} + 3 \, B a^{3}\right)} x + \frac{{\left(A a^{3} + 3 \, B a^{3}\right)} \cos\left(7 \, d x + 7 \, c\right)}{448 \, d} - \frac{{\left(11 \, A a^{3} + B a^{3}\right)} \cos\left(5 \, d x + 5 \, c\right)}{320 \, d} - \frac{{\left(13 \, A a^{3} + 7 \, B a^{3}\right)} \cos\left(3 \, d x + 3 \, c\right)}{64 \, d} - \frac{{\left(27 \, A a^{3} + 17 \, B a^{3}\right)} \cos\left(d x + c\right)}{64 \, d} - \frac{{\left(A a^{3} + B a^{3}\right)} \sin\left(6 \, d x + 6 \, c\right)}{64 \, d} - \frac{{\left(2 \, A a^{3} + 7 \, B a^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)}{128 \, d} + \frac{{\left(19 \, A a^{3} + 3 \, B a^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d}"," ",0,"1/1024*B*a^3*sin(8*d*x + 8*c)/d + 9/128*(8*A*a^3 + 3*B*a^3)*x + 1/448*(A*a^3 + 3*B*a^3)*cos(7*d*x + 7*c)/d - 1/320*(11*A*a^3 + B*a^3)*cos(5*d*x + 5*c)/d - 1/64*(13*A*a^3 + 7*B*a^3)*cos(3*d*x + 3*c)/d - 1/64*(27*A*a^3 + 17*B*a^3)*cos(d*x + c)/d - 1/64*(A*a^3 + B*a^3)*sin(6*d*x + 6*c)/d - 1/128*(2*A*a^3 + 7*B*a^3)*sin(4*d*x + 4*c)/d + 1/64*(19*A*a^3 + 3*B*a^3)*sin(2*d*x + 2*c)/d","A",0
997,1,165,0,0.293760," ","integrate(cos(d*x+c)^2*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""giac"")","\frac{B a^{3} \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} + \frac{7}{16} \, {\left(2 \, A a^{3} + B a^{3}\right)} x + \frac{{\left(A a^{3} + 3 \, B a^{3}\right)} \cos\left(5 \, d x + 5 \, c\right)}{80 \, d} - \frac{{\left(13 \, A a^{3} + 7 \, B a^{3}\right)} \cos\left(3 \, d x + 3 \, c\right)}{48 \, d} - \frac{{\left(7 \, A a^{3} + 5 \, B a^{3}\right)} \cos\left(d x + c\right)}{8 \, d} - \frac{{\left(6 \, A a^{3} + 7 \, B a^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{{\left(16 \, A a^{3} - B a^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d}"," ",0,"1/192*B*a^3*sin(6*d*x + 6*c)/d + 7/16*(2*A*a^3 + B*a^3)*x + 1/80*(A*a^3 + 3*B*a^3)*cos(5*d*x + 5*c)/d - 1/48*(13*A*a^3 + 7*B*a^3)*cos(3*d*x + 3*c)/d - 1/8*(7*A*a^3 + 5*B*a^3)*cos(d*x + c)/d - 1/64*(6*A*a^3 + 7*B*a^3)*sin(4*d*x + 4*c)/d + 1/64*(16*A*a^3 - B*a^3)*sin(2*d*x + 2*c)/d","A",0
998,1,147,0,0.197361," ","integrate(sec(d*x+c)^2*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""giac"")","-\frac{3 \, {\left(2 \, A a^{3} + 3 \, B a^{3}\right)} {\left(d x + c\right)} + \frac{16 \, {\left(A a^{3} + B a^{3}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1} + \frac{2 \, {\left(B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 6 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, A a^{3} - 6 \, B a^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"-1/2*(3*(2*A*a^3 + 3*B*a^3)*(d*x + c) + 16*(A*a^3 + B*a^3)/(tan(1/2*d*x + 1/2*c) - 1) + 2*(B*a^3*tan(1/2*d*x + 1/2*c)^3 - 2*A*a^3*tan(1/2*d*x + 1/2*c)^2 - 6*B*a^3*tan(1/2*d*x + 1/2*c)^2 - B*a^3*tan(1/2*d*x + 1/2*c) - 2*A*a^3 - 6*B*a^3)/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","A",0
999,1,93,0,0.250384," ","integrate(sec(d*x+c)^4*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""giac"")","\frac{3 \, {\left(d x + c\right)} B a^{3} - \frac{2 \, {\left(3 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + A a^{3} - 5 \, B a^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*(d*x + c)*B*a^3 - 2*(3*A*a^3*tan(1/2*d*x + 1/2*c)^2 - 3*B*a^3*tan(1/2*d*x + 1/2*c)^2 + 12*B*a^3*tan(1/2*d*x + 1/2*c) + A*a^3 - 5*B*a^3)/(tan(1/2*d*x + 1/2*c) - 1)^3)/d","A",0
1000,1,146,0,0.249532," ","integrate(sec(d*x+c)^6*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""giac"")","-\frac{2 \, {\left(15 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 30 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 20 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 7 \, A a^{3} - 3 \, B a^{3}\right)}}{15 \, d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{5}}"," ",0,"-2/15*(15*A*a^3*tan(1/2*d*x + 1/2*c)^4 - 30*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 15*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 40*A*a^3*tan(1/2*d*x + 1/2*c)^2 - 15*B*a^3*tan(1/2*d*x + 1/2*c)^2 - 20*A*a^3*tan(1/2*d*x + 1/2*c) + 15*B*a^3*tan(1/2*d*x + 1/2*c) + 7*A*a^3 - 3*B*a^3)/(d*(tan(1/2*d*x + 1/2*c) - 1)^5)","A",0
1001,1,260,0,0.286108," ","integrate(sec(d*x+c)^8*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{35 \, {\left(A a^{3} - B a^{3}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1} + \frac{525 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 35 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 1960 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 280 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4025 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 665 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 4480 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1120 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3143 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 791 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1176 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 392 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 243 \, A a^{3} - 51 \, B a^{3}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{7}}}{280 \, d}"," ",0,"-1/280*(35*(A*a^3 - B*a^3)/(tan(1/2*d*x + 1/2*c) + 1) + (525*A*a^3*tan(1/2*d*x + 1/2*c)^6 + 35*B*a^3*tan(1/2*d*x + 1/2*c)^6 - 1960*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 280*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 4025*A*a^3*tan(1/2*d*x + 1/2*c)^4 - 665*B*a^3*tan(1/2*d*x + 1/2*c)^4 - 4480*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 1120*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 3143*A*a^3*tan(1/2*d*x + 1/2*c)^2 - 791*B*a^3*tan(1/2*d*x + 1/2*c)^2 - 1176*A*a^3*tan(1/2*d*x + 1/2*c) + 392*B*a^3*tan(1/2*d*x + 1/2*c) + 243*A*a^3 - 51*B*a^3)/(tan(1/2*d*x + 1/2*c) - 1)^7)/d","B",0
1002,1,393,0,0.298430," ","integrate(sec(d*x+c)^10*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{21 \, {\left(21 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 36 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 19 \, A a^{3} - 13 \, B a^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}^{3}} + \frac{3591 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 315 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 19656 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 756 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 56196 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 4200 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 95760 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 11340 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 107730 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 14994 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 79464 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 13356 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 38484 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 6768 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 10944 \, A a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2196 \, B a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1615 \, A a^{3} - 209 \, B a^{3}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}^{9}}}{2016 \, d}"," ",0,"-1/2016*(21*(21*A*a^3*tan(1/2*d*x + 1/2*c)^2 - 15*B*a^3*tan(1/2*d*x + 1/2*c)^2 + 36*A*a^3*tan(1/2*d*x + 1/2*c) - 24*B*a^3*tan(1/2*d*x + 1/2*c) + 19*A*a^3 - 13*B*a^3)/(tan(1/2*d*x + 1/2*c) + 1)^3 + (3591*A*a^3*tan(1/2*d*x + 1/2*c)^8 + 315*B*a^3*tan(1/2*d*x + 1/2*c)^8 - 19656*A*a^3*tan(1/2*d*x + 1/2*c)^7 + 756*B*a^3*tan(1/2*d*x + 1/2*c)^7 + 56196*A*a^3*tan(1/2*d*x + 1/2*c)^6 - 4200*B*a^3*tan(1/2*d*x + 1/2*c)^6 - 95760*A*a^3*tan(1/2*d*x + 1/2*c)^5 + 11340*B*a^3*tan(1/2*d*x + 1/2*c)^5 + 107730*A*a^3*tan(1/2*d*x + 1/2*c)^4 - 14994*B*a^3*tan(1/2*d*x + 1/2*c)^4 - 79464*A*a^3*tan(1/2*d*x + 1/2*c)^3 + 13356*B*a^3*tan(1/2*d*x + 1/2*c)^3 + 38484*A*a^3*tan(1/2*d*x + 1/2*c)^2 - 6768*B*a^3*tan(1/2*d*x + 1/2*c)^2 - 10944*A*a^3*tan(1/2*d*x + 1/2*c) + 2196*B*a^3*tan(1/2*d*x + 1/2*c) + 1615*A*a^3 - 209*B*a^3)/(tan(1/2*d*x + 1/2*c) - 1)^9)/d","B",0
1003,1,139,0,0.208072," ","integrate(cos(d*x+c)^7*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{30 \, B \sin\left(d x + c\right)^{7} + 35 \, A \sin\left(d x + c\right)^{6} - 35 \, B \sin\left(d x + c\right)^{6} - 42 \, A \sin\left(d x + c\right)^{5} - 84 \, B \sin\left(d x + c\right)^{5} - 105 \, A \sin\left(d x + c\right)^{4} + 105 \, B \sin\left(d x + c\right)^{4} + 140 \, A \sin\left(d x + c\right)^{3} + 70 \, B \sin\left(d x + c\right)^{3} + 105 \, A \sin\left(d x + c\right)^{2} - 105 \, B \sin\left(d x + c\right)^{2} - 210 \, A \sin\left(d x + c\right)}{210 \, a d}"," ",0,"-1/210*(30*B*sin(d*x + c)^7 + 35*A*sin(d*x + c)^6 - 35*B*sin(d*x + c)^6 - 42*A*sin(d*x + c)^5 - 84*B*sin(d*x + c)^5 - 105*A*sin(d*x + c)^4 + 105*B*sin(d*x + c)^4 + 140*A*sin(d*x + c)^3 + 70*B*sin(d*x + c)^3 + 105*A*sin(d*x + c)^2 - 105*B*sin(d*x + c)^2 - 210*A*sin(d*x + c))/(a*d)","A",0
1004,1,95,0,0.192156," ","integrate(cos(d*x+c)^5*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{12 \, B \sin\left(d x + c\right)^{5} + 15 \, A \sin\left(d x + c\right)^{4} - 15 \, B \sin\left(d x + c\right)^{4} - 20 \, A \sin\left(d x + c\right)^{3} - 20 \, B \sin\left(d x + c\right)^{3} - 30 \, A \sin\left(d x + c\right)^{2} + 30 \, B \sin\left(d x + c\right)^{2} + 60 \, A \sin\left(d x + c\right)}{60 \, a d}"," ",0,"1/60*(12*B*sin(d*x + c)^5 + 15*A*sin(d*x + c)^4 - 15*B*sin(d*x + c)^4 - 20*A*sin(d*x + c)^3 - 20*B*sin(d*x + c)^3 - 30*A*sin(d*x + c)^2 + 30*B*sin(d*x + c)^2 + 60*A*sin(d*x + c))/(a*d)","A",0
1005,1,51,0,0.183965," ","integrate(cos(d*x+c)^3*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x, algorithm=""giac"")","-\frac{2 \, B \sin\left(d x + c\right)^{3} + 3 \, A \sin\left(d x + c\right)^{2} - 3 \, B \sin\left(d x + c\right)^{2} - 6 \, A \sin\left(d x + c\right)}{6 \, a d}"," ",0,"-1/6*(2*B*sin(d*x + c)^3 + 3*A*sin(d*x + c)^2 - 3*B*sin(d*x + c)^2 - 6*A*sin(d*x + c))/(a*d)","A",0
1006,1,35,0,0.168771," ","integrate(cos(d*x+c)*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(A - B\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} + \frac{B \sin\left(d x + c\right)}{a}}{d}"," ",0,"((A - B)*log(abs(sin(d*x + c) + 1))/a + B*sin(d*x + c)/a)/d","A",0
1007,1,79,0,0.194448," ","integrate(sec(d*x+c)*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{{\left(A + B\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} - \frac{{\left(A + B\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a} - \frac{A \sin\left(d x + c\right) + B \sin\left(d x + c\right) + 3 \, A - B}{a {\left(\sin\left(d x + c\right) + 1\right)}}}{4 \, d}"," ",0,"1/4*((A + B)*log(abs(sin(d*x + c) + 1))/a - (A + B)*log(abs(sin(d*x + c) - 1))/a - (A*sin(d*x + c) + B*sin(d*x + c) + 3*A - B)/(a*(sin(d*x + c) + 1)))/d","A",0
1008,1,147,0,0.226454," ","integrate(sec(d*x+c)^3*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{2 \, {\left(3 \, A + B\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} - \frac{2 \, {\left(3 \, A + B\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a} + \frac{2 \, {\left(3 \, A \sin\left(d x + c\right) + B \sin\left(d x + c\right) - 5 \, A - 3 \, B\right)}}{a {\left(\sin\left(d x + c\right) - 1\right)}} - \frac{9 \, A \sin\left(d x + c\right)^{2} + 3 \, B \sin\left(d x + c\right)^{2} + 26 \, A \sin\left(d x + c\right) + 6 \, B \sin\left(d x + c\right) + 21 \, A - B}{a {\left(\sin\left(d x + c\right) + 1\right)}^{2}}}{32 \, d}"," ",0,"1/32*(2*(3*A + B)*log(abs(sin(d*x + c) + 1))/a - 2*(3*A + B)*log(abs(sin(d*x + c) - 1))/a + 2*(3*A*sin(d*x + c) + B*sin(d*x + c) - 5*A - 3*B)/(a*(sin(d*x + c) - 1)) - (9*A*sin(d*x + c)^2 + 3*B*sin(d*x + c)^2 + 26*A*sin(d*x + c) + 6*B*sin(d*x + c) + 21*A - B)/(a*(sin(d*x + c) + 1)^2))/d","A",0
1009,1,192,0,0.264522," ","integrate(sec(d*x+c)^5*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{6 \, {\left(5 \, A + B\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} - \frac{6 \, {\left(5 \, A + B\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a} + \frac{3 \, {\left(15 \, A \sin\left(d x + c\right)^{2} + 3 \, B \sin\left(d x + c\right)^{2} - 38 \, A \sin\left(d x + c\right) - 10 \, B \sin\left(d x + c\right) + 25 \, A + 9 \, B\right)}}{a {\left(\sin\left(d x + c\right) - 1\right)}^{2}} - \frac{55 \, A \sin\left(d x + c\right)^{3} + 11 \, B \sin\left(d x + c\right)^{3} + 201 \, A \sin\left(d x + c\right)^{2} + 33 \, B \sin\left(d x + c\right)^{2} + 255 \, A \sin\left(d x + c\right) + 27 \, B \sin\left(d x + c\right) + 117 \, A - 3 \, B}{a {\left(\sin\left(d x + c\right) + 1\right)}^{3}}}{192 \, d}"," ",0,"1/192*(6*(5*A + B)*log(abs(sin(d*x + c) + 1))/a - 6*(5*A + B)*log(abs(sin(d*x + c) - 1))/a + 3*(15*A*sin(d*x + c)^2 + 3*B*sin(d*x + c)^2 - 38*A*sin(d*x + c) - 10*B*sin(d*x + c) + 25*A + 9*B)/(a*(sin(d*x + c) - 1)^2) - (55*A*sin(d*x + c)^3 + 11*B*sin(d*x + c)^3 + 201*A*sin(d*x + c)^2 + 33*B*sin(d*x + c)^2 + 255*A*sin(d*x + c) + 27*B*sin(d*x + c) + 117*A - 3*B)/(a*(sin(d*x + c) + 1)^3))/d","A",0
1010,1,236,0,0.312861," ","integrate(sec(d*x+c)^7*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{60 \, {\left(7 \, A + B\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a} - \frac{60 \, {\left(7 \, A + B\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a} + \frac{2 \, {\left(385 \, A \sin\left(d x + c\right)^{3} + 55 \, B \sin\left(d x + c\right)^{3} - 1335 \, A \sin\left(d x + c\right)^{2} - 225 \, B \sin\left(d x + c\right)^{2} + 1575 \, A \sin\left(d x + c\right) + 321 \, B \sin\left(d x + c\right) - 641 \, A - 167 \, B\right)}}{a {\left(\sin\left(d x + c\right) - 1\right)}^{3}} - \frac{875 \, A \sin\left(d x + c\right)^{4} + 125 \, B \sin\left(d x + c\right)^{4} + 3980 \, A \sin\left(d x + c\right)^{3} + 500 \, B \sin\left(d x + c\right)^{3} + 6930 \, A \sin\left(d x + c\right)^{2} + 702 \, B \sin\left(d x + c\right)^{2} + 5548 \, A \sin\left(d x + c\right) + 340 \, B \sin\left(d x + c\right) + 1771 \, A - 35 \, B}{a {\left(\sin\left(d x + c\right) + 1\right)}^{4}}}{3072 \, d}"," ",0,"1/3072*(60*(7*A + B)*log(abs(sin(d*x + c) + 1))/a - 60*(7*A + B)*log(abs(sin(d*x + c) - 1))/a + 2*(385*A*sin(d*x + c)^3 + 55*B*sin(d*x + c)^3 - 1335*A*sin(d*x + c)^2 - 225*B*sin(d*x + c)^2 + 1575*A*sin(d*x + c) + 321*B*sin(d*x + c) - 641*A - 167*B)/(a*(sin(d*x + c) - 1)^3) - (875*A*sin(d*x + c)^4 + 125*B*sin(d*x + c)^4 + 3980*A*sin(d*x + c)^3 + 500*B*sin(d*x + c)^3 + 6930*A*sin(d*x + c)^2 + 702*B*sin(d*x + c)^2 + 5548*A*sin(d*x + c) + 340*B*sin(d*x + c) + 1771*A - 35*B)/(a*(sin(d*x + c) + 1)^4))/d","A",0
1011,1,95,0,0.230444," ","integrate(cos(d*x+c)^7*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{5 \, B \sin\left(d x + c\right)^{6} + 6 \, A \sin\left(d x + c\right)^{5} - 12 \, B \sin\left(d x + c\right)^{5} - 15 \, A \sin\left(d x + c\right)^{4} + 20 \, B \sin\left(d x + c\right)^{3} + 30 \, A \sin\left(d x + c\right)^{2} - 15 \, B \sin\left(d x + c\right)^{2} - 30 \, A \sin\left(d x + c\right)}{30 \, a^{2} d}"," ",0,"-1/30*(5*B*sin(d*x + c)^6 + 6*A*sin(d*x + c)^5 - 12*B*sin(d*x + c)^5 - 15*A*sin(d*x + c)^4 + 20*B*sin(d*x + c)^3 + 30*A*sin(d*x + c)^2 - 15*B*sin(d*x + c)^2 - 30*A*sin(d*x + c))/(a^2*d)","A",0
1012,1,73,0,0.224597," ","integrate(cos(d*x+c)^5*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{3 \, B \sin\left(d x + c\right)^{4} + 4 \, A \sin\left(d x + c\right)^{3} - 8 \, B \sin\left(d x + c\right)^{3} - 12 \, A \sin\left(d x + c\right)^{2} + 6 \, B \sin\left(d x + c\right)^{2} + 12 \, A \sin\left(d x + c\right)}{12 \, a^{2} d}"," ",0,"1/12*(3*B*sin(d*x + c)^4 + 4*A*sin(d*x + c)^3 - 8*B*sin(d*x + c)^3 - 12*A*sin(d*x + c)^2 + 6*B*sin(d*x + c)^2 + 12*A*sin(d*x + c))/(a^2*d)","A",0
1013,1,92,0,0.199841," ","integrate(cos(d*x+c)^3*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{4 \, {\left(A - B\right)} \log\left(\frac{{\left| a \sin\left(d x + c\right) + a \right|}}{{\left(a \sin\left(d x + c\right) + a\right)}^{2} {\left| a \right|}}\right)}{a^{2}} + \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{2} {\left(B + \frac{2 \, {\left(A a^{2} - 3 \, B a^{2}\right)}}{{\left(a \sin\left(d x + c\right) + a\right)} a}\right)}}{a^{4}}}{2 \, d}"," ",0,"-1/2*(4*(A - B)*log(abs(a*sin(d*x + c) + a)/((a*sin(d*x + c) + a)^2*abs(a)))/a^2 + (a*sin(d*x + c) + a)^2*(B + 2*(A*a^2 - 3*B*a^2)/((a*sin(d*x + c) + a)*a))/a^4)/d","A",0
1014,1,76,0,0.175381," ","integrate(cos(d*x+c)*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{B {\left(\frac{\log\left(\frac{{\left| a \sin\left(d x + c\right) + a \right|}}{{\left(a \sin\left(d x + c\right) + a\right)}^{2} {\left| a \right|}}\right)}{a} - \frac{1}{a \sin\left(d x + c\right) + a}\right)}}{a} + \frac{A}{{\left(a \sin\left(d x + c\right) + a\right)} a}}{d}"," ",0,"-(B*(log(abs(a*sin(d*x + c) + a)/((a*sin(d*x + c) + a)^2*abs(a)))/a - 1/(a*sin(d*x + c) + a))/a + A/((a*sin(d*x + c) + a)*a))/d","A",0
1015,1,104,0,0.196133," ","integrate(sec(d*x+c)*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(A + B\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{2}} - \frac{2 \, {\left(A + B\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{2}} - \frac{3 \, A \sin\left(d x + c\right)^{2} + 3 \, B \sin\left(d x + c\right)^{2} + 10 \, A \sin\left(d x + c\right) + 10 \, B \sin\left(d x + c\right) + 11 \, A + 3 \, B}{a^{2} {\left(\sin\left(d x + c\right) + 1\right)}^{2}}}{16 \, d}"," ",0,"1/16*(2*(A + B)*log(abs(sin(d*x + c) + 1))/a^2 - 2*(A + B)*log(abs(sin(d*x + c) - 1))/a^2 - (3*A*sin(d*x + c)^2 + 3*B*sin(d*x + c)^2 + 10*A*sin(d*x + c) + 10*B*sin(d*x + c) + 11*A + 3*B)/(a^2*(sin(d*x + c) + 1)^2))/d","A",0
1016,1,169,0,0.321365," ","integrate(sec(d*x+c)^3*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{6 \, {\left(2 \, A + B\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{2}} - \frac{6 \, {\left(2 \, A + B\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{2}} + \frac{6 \, {\left(2 \, A \sin\left(d x + c\right) + B \sin\left(d x + c\right) - 3 \, A - 2 \, B\right)}}{a^{2} {\left(\sin\left(d x + c\right) - 1\right)}} - \frac{22 \, A \sin\left(d x + c\right)^{3} + 11 \, B \sin\left(d x + c\right)^{3} + 84 \, A \sin\left(d x + c\right)^{2} + 39 \, B \sin\left(d x + c\right)^{2} + 114 \, A \sin\left(d x + c\right) + 45 \, B \sin\left(d x + c\right) + 60 \, A + 9 \, B}{a^{2} {\left(\sin\left(d x + c\right) + 1\right)}^{3}}}{96 \, d}"," ",0,"1/96*(6*(2*A + B)*log(abs(sin(d*x + c) + 1))/a^2 - 6*(2*A + B)*log(abs(sin(d*x + c) - 1))/a^2 + 6*(2*A*sin(d*x + c) + B*sin(d*x + c) - 3*A - 2*B)/(a^2*(sin(d*x + c) - 1)) - (22*A*sin(d*x + c)^3 + 11*B*sin(d*x + c)^3 + 84*A*sin(d*x + c)^2 + 39*B*sin(d*x + c)^2 + 114*A*sin(d*x + c) + 45*B*sin(d*x + c) + 60*A + 9*B)/(a^2*(sin(d*x + c) + 1)^3))/d","A",0
1017,1,214,0,0.335661," ","integrate(sec(d*x+c)^5*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{60 \, {\left(3 \, A + B\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{2}} - \frac{60 \, {\left(3 \, A + B\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{2}} + \frac{6 \, {\left(45 \, A \sin\left(d x + c\right)^{2} + 15 \, B \sin\left(d x + c\right)^{2} - 110 \, A \sin\left(d x + c\right) - 42 \, B \sin\left(d x + c\right) + 69 \, A + 31 \, B\right)}}{a^{2} {\left(\sin\left(d x + c\right) - 1\right)}^{2}} - \frac{375 \, A \sin\left(d x + c\right)^{4} + 125 \, B \sin\left(d x + c\right)^{4} + 1740 \, A \sin\left(d x + c\right)^{3} + 548 \, B \sin\left(d x + c\right)^{3} + 3114 \, A \sin\left(d x + c\right)^{2} + 894 \, B \sin\left(d x + c\right)^{2} + 2604 \, A \sin\left(d x + c\right) + 612 \, B \sin\left(d x + c\right) + 903 \, A + 93 \, B}{a^{2} {\left(\sin\left(d x + c\right) + 1\right)}^{4}}}{1536 \, d}"," ",0,"1/1536*(60*(3*A + B)*log(abs(sin(d*x + c) + 1))/a^2 - 60*(3*A + B)*log(abs(sin(d*x + c) - 1))/a^2 + 6*(45*A*sin(d*x + c)^2 + 15*B*sin(d*x + c)^2 - 110*A*sin(d*x + c) - 42*B*sin(d*x + c) + 69*A + 31*B)/(a^2*(sin(d*x + c) - 1)^2) - (375*A*sin(d*x + c)^4 + 125*B*sin(d*x + c)^4 + 1740*A*sin(d*x + c)^3 + 548*B*sin(d*x + c)^3 + 3114*A*sin(d*x + c)^2 + 894*B*sin(d*x + c)^2 + 2604*A*sin(d*x + c) + 612*B*sin(d*x + c) + 903*A + 93*B)/(a^2*(sin(d*x + c) + 1)^4))/d","A",0
1018,1,258,0,0.393258," ","integrate(sec(d*x+c)^7*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{420 \, {\left(4 \, A + B\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{2}} - \frac{420 \, {\left(4 \, A + B\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{2}} + \frac{10 \, {\left(308 \, A \sin\left(d x + c\right)^{3} + 77 \, B \sin\left(d x + c\right)^{3} - 1050 \, A \sin\left(d x + c\right)^{2} - 285 \, B \sin\left(d x + c\right)^{2} + 1212 \, A \sin\left(d x + c\right) + 363 \, B \sin\left(d x + c\right) - 478 \, A - 163 \, B\right)}}{a^{2} {\left(\sin\left(d x + c\right) - 1\right)}^{3}} - \frac{3836 \, A \sin\left(d x + c\right)^{5} + 959 \, B \sin\left(d x + c\right)^{5} + 21280 \, A \sin\left(d x + c\right)^{4} + 5095 \, B \sin\left(d x + c\right)^{4} + 47960 \, A \sin\left(d x + c\right)^{3} + 10790 \, B \sin\left(d x + c\right)^{3} + 55360 \, A \sin\left(d x + c\right)^{2} + 11230 \, B \sin\left(d x + c\right)^{2} + 33260 \, A \sin\left(d x + c\right) + 5435 \, B \sin\left(d x + c\right) + 8608 \, A + 667 \, B}{a^{2} {\left(\sin\left(d x + c\right) + 1\right)}^{5}}}{15360 \, d}"," ",0,"1/15360*(420*(4*A + B)*log(abs(sin(d*x + c) + 1))/a^2 - 420*(4*A + B)*log(abs(sin(d*x + c) - 1))/a^2 + 10*(308*A*sin(d*x + c)^3 + 77*B*sin(d*x + c)^3 - 1050*A*sin(d*x + c)^2 - 285*B*sin(d*x + c)^2 + 1212*A*sin(d*x + c) + 363*B*sin(d*x + c) - 478*A - 163*B)/(a^2*(sin(d*x + c) - 1)^3) - (3836*A*sin(d*x + c)^5 + 959*B*sin(d*x + c)^5 + 21280*A*sin(d*x + c)^4 + 5095*B*sin(d*x + c)^4 + 47960*A*sin(d*x + c)^3 + 10790*B*sin(d*x + c)^3 + 55360*A*sin(d*x + c)^2 + 11230*B*sin(d*x + c)^2 + 33260*A*sin(d*x + c) + 5435*B*sin(d*x + c) + 8608*A + 667*B)/(a^2*(sin(d*x + c) + 1)^5))/d","A",0
1019,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^p*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""giac"")","\int {\left(B \sin\left(f x + e\right) + A\right)} \left(g \cos\left(f x + e\right)\right)^{p} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(g*cos(f*x + e))^p*(a*sin(f*x + e) + a)^m, x)","F",0
1020,1,1402,0,0.285294," ","integrate(cos(f*x+e)^7*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""giac"")","-\frac{\frac{{\left({\left(a \sin\left(f x + e\right) + a\right)}^{7} {\left(a \sin\left(f x + e\right) + a\right)}^{m} m^{3} - 6 \, {\left(a \sin\left(f x + e\right) + a\right)}^{6} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a m^{3} + 12 \, {\left(a \sin\left(f x + e\right) + a\right)}^{5} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{2} m^{3} - 8 \, {\left(a \sin\left(f x + e\right) + a\right)}^{4} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{3} m^{3} + 15 \, {\left(a \sin\left(f x + e\right) + a\right)}^{7} {\left(a \sin\left(f x + e\right) + a\right)}^{m} m^{2} - 96 \, {\left(a \sin\left(f x + e\right) + a\right)}^{6} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a m^{2} + 204 \, {\left(a \sin\left(f x + e\right) + a\right)}^{5} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{2} m^{2} - 144 \, {\left(a \sin\left(f x + e\right) + a\right)}^{4} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{3} m^{2} + 74 \, {\left(a \sin\left(f x + e\right) + a\right)}^{7} {\left(a \sin\left(f x + e\right) + a\right)}^{m} m - 498 \, {\left(a \sin\left(f x + e\right) + a\right)}^{6} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a m + 1128 \, {\left(a \sin\left(f x + e\right) + a\right)}^{5} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{2} m - 856 \, {\left(a \sin\left(f x + e\right) + a\right)}^{4} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{3} m + 120 \, {\left(a \sin\left(f x + e\right) + a\right)}^{7} {\left(a \sin\left(f x + e\right) + a\right)}^{m} - 840 \, {\left(a \sin\left(f x + e\right) + a\right)}^{6} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a + 2016 \, {\left(a \sin\left(f x + e\right) + a\right)}^{5} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{2} - 1680 \, {\left(a \sin\left(f x + e\right) + a\right)}^{4} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{3}\right)} A}{a^{6} m^{4} + 22 \, a^{6} m^{3} + 179 \, a^{6} m^{2} + 638 \, a^{6} m + 840 \, a^{6}} + \frac{{\left({\left(a \sin\left(f x + e\right) + a\right)}^{8} {\left(a \sin\left(f x + e\right) + a\right)}^{m} m^{4} - 7 \, {\left(a \sin\left(f x + e\right) + a\right)}^{7} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a m^{4} + 18 \, {\left(a \sin\left(f x + e\right) + a\right)}^{6} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{2} m^{4} - 20 \, {\left(a \sin\left(f x + e\right) + a\right)}^{5} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{3} m^{4} + 8 \, {\left(a \sin\left(f x + e\right) + a\right)}^{4} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{4} m^{4} + 22 \, {\left(a \sin\left(f x + e\right) + a\right)}^{8} {\left(a \sin\left(f x + e\right) + a\right)}^{m} m^{3} - 161 \, {\left(a \sin\left(f x + e\right) + a\right)}^{7} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a m^{3} + 432 \, {\left(a \sin\left(f x + e\right) + a\right)}^{6} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{2} m^{3} - 500 \, {\left(a \sin\left(f x + e\right) + a\right)}^{5} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{3} m^{3} + 208 \, {\left(a \sin\left(f x + e\right) + a\right)}^{4} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{4} m^{3} + 179 \, {\left(a \sin\left(f x + e\right) + a\right)}^{8} {\left(a \sin\left(f x + e\right) + a\right)}^{m} m^{2} - 1358 \, {\left(a \sin\left(f x + e\right) + a\right)}^{7} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a m^{2} + 3798 \, {\left(a \sin\left(f x + e\right) + a\right)}^{6} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{2} m^{2} - 4600 \, {\left(a \sin\left(f x + e\right) + a\right)}^{5} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{3} m^{2} + 2008 \, {\left(a \sin\left(f x + e\right) + a\right)}^{4} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{4} m^{2} + 638 \, {\left(a \sin\left(f x + e\right) + a\right)}^{8} {\left(a \sin\left(f x + e\right) + a\right)}^{m} m - 4984 \, {\left(a \sin\left(f x + e\right) + a\right)}^{7} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a m + 14472 \, {\left(a \sin\left(f x + e\right) + a\right)}^{6} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{2} m - 18400 \, {\left(a \sin\left(f x + e\right) + a\right)}^{5} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{3} m + 8528 \, {\left(a \sin\left(f x + e\right) + a\right)}^{4} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{4} m + 840 \, {\left(a \sin\left(f x + e\right) + a\right)}^{8} {\left(a \sin\left(f x + e\right) + a\right)}^{m} - 6720 \, {\left(a \sin\left(f x + e\right) + a\right)}^{7} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a + 20160 \, {\left(a \sin\left(f x + e\right) + a\right)}^{6} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{2} - 26880 \, {\left(a \sin\left(f x + e\right) + a\right)}^{5} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{3} + 13440 \, {\left(a \sin\left(f x + e\right) + a\right)}^{4} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{4}\right)} B}{{\left(a^{6} m^{5} + 30 \, a^{6} m^{4} + 355 \, a^{6} m^{3} + 2070 \, a^{6} m^{2} + 5944 \, a^{6} m + 6720 \, a^{6}\right)} a}}{a f}"," ",0,"-(((a*sin(f*x + e) + a)^7*(a*sin(f*x + e) + a)^m*m^3 - 6*(a*sin(f*x + e) + a)^6*(a*sin(f*x + e) + a)^m*a*m^3 + 12*(a*sin(f*x + e) + a)^5*(a*sin(f*x + e) + a)^m*a^2*m^3 - 8*(a*sin(f*x + e) + a)^4*(a*sin(f*x + e) + a)^m*a^3*m^3 + 15*(a*sin(f*x + e) + a)^7*(a*sin(f*x + e) + a)^m*m^2 - 96*(a*sin(f*x + e) + a)^6*(a*sin(f*x + e) + a)^m*a*m^2 + 204*(a*sin(f*x + e) + a)^5*(a*sin(f*x + e) + a)^m*a^2*m^2 - 144*(a*sin(f*x + e) + a)^4*(a*sin(f*x + e) + a)^m*a^3*m^2 + 74*(a*sin(f*x + e) + a)^7*(a*sin(f*x + e) + a)^m*m - 498*(a*sin(f*x + e) + a)^6*(a*sin(f*x + e) + a)^m*a*m + 1128*(a*sin(f*x + e) + a)^5*(a*sin(f*x + e) + a)^m*a^2*m - 856*(a*sin(f*x + e) + a)^4*(a*sin(f*x + e) + a)^m*a^3*m + 120*(a*sin(f*x + e) + a)^7*(a*sin(f*x + e) + a)^m - 840*(a*sin(f*x + e) + a)^6*(a*sin(f*x + e) + a)^m*a + 2016*(a*sin(f*x + e) + a)^5*(a*sin(f*x + e) + a)^m*a^2 - 1680*(a*sin(f*x + e) + a)^4*(a*sin(f*x + e) + a)^m*a^3)*A/(a^6*m^4 + 22*a^6*m^3 + 179*a^6*m^2 + 638*a^6*m + 840*a^6) + ((a*sin(f*x + e) + a)^8*(a*sin(f*x + e) + a)^m*m^4 - 7*(a*sin(f*x + e) + a)^7*(a*sin(f*x + e) + a)^m*a*m^4 + 18*(a*sin(f*x + e) + a)^6*(a*sin(f*x + e) + a)^m*a^2*m^4 - 20*(a*sin(f*x + e) + a)^5*(a*sin(f*x + e) + a)^m*a^3*m^4 + 8*(a*sin(f*x + e) + a)^4*(a*sin(f*x + e) + a)^m*a^4*m^4 + 22*(a*sin(f*x + e) + a)^8*(a*sin(f*x + e) + a)^m*m^3 - 161*(a*sin(f*x + e) + a)^7*(a*sin(f*x + e) + a)^m*a*m^3 + 432*(a*sin(f*x + e) + a)^6*(a*sin(f*x + e) + a)^m*a^2*m^3 - 500*(a*sin(f*x + e) + a)^5*(a*sin(f*x + e) + a)^m*a^3*m^3 + 208*(a*sin(f*x + e) + a)^4*(a*sin(f*x + e) + a)^m*a^4*m^3 + 179*(a*sin(f*x + e) + a)^8*(a*sin(f*x + e) + a)^m*m^2 - 1358*(a*sin(f*x + e) + a)^7*(a*sin(f*x + e) + a)^m*a*m^2 + 3798*(a*sin(f*x + e) + a)^6*(a*sin(f*x + e) + a)^m*a^2*m^2 - 4600*(a*sin(f*x + e) + a)^5*(a*sin(f*x + e) + a)^m*a^3*m^2 + 2008*(a*sin(f*x + e) + a)^4*(a*sin(f*x + e) + a)^m*a^4*m^2 + 638*(a*sin(f*x + e) + a)^8*(a*sin(f*x + e) + a)^m*m - 4984*(a*sin(f*x + e) + a)^7*(a*sin(f*x + e) + a)^m*a*m + 14472*(a*sin(f*x + e) + a)^6*(a*sin(f*x + e) + a)^m*a^2*m - 18400*(a*sin(f*x + e) + a)^5*(a*sin(f*x + e) + a)^m*a^3*m + 8528*(a*sin(f*x + e) + a)^4*(a*sin(f*x + e) + a)^m*a^4*m + 840*(a*sin(f*x + e) + a)^8*(a*sin(f*x + e) + a)^m - 6720*(a*sin(f*x + e) + a)^7*(a*sin(f*x + e) + a)^m*a + 20160*(a*sin(f*x + e) + a)^6*(a*sin(f*x + e) + a)^m*a^2 - 26880*(a*sin(f*x + e) + a)^5*(a*sin(f*x + e) + a)^m*a^3 + 13440*(a*sin(f*x + e) + a)^4*(a*sin(f*x + e) + a)^m*a^4)*B/((a^6*m^5 + 30*a^6*m^4 + 355*a^6*m^3 + 2070*a^6*m^2 + 5944*a^6*m + 6720*a^6)*a))/(a*f)","B",0
1021,1,861,0,0.225289," ","integrate(cos(f*x+e)^5*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""giac"")","\frac{\frac{{\left({\left(a \sin\left(f x + e\right) + a\right)}^{5} {\left(a \sin\left(f x + e\right) + a\right)}^{m} m^{2} - 4 \, {\left(a \sin\left(f x + e\right) + a\right)}^{4} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a m^{2} + 4 \, {\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{2} m^{2} + 7 \, {\left(a \sin\left(f x + e\right) + a\right)}^{5} {\left(a \sin\left(f x + e\right) + a\right)}^{m} m - 32 \, {\left(a \sin\left(f x + e\right) + a\right)}^{4} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a m + 36 \, {\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{2} m + 12 \, {\left(a \sin\left(f x + e\right) + a\right)}^{5} {\left(a \sin\left(f x + e\right) + a\right)}^{m} - 60 \, {\left(a \sin\left(f x + e\right) + a\right)}^{4} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a + 80 \, {\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{2}\right)} A}{a^{4} m^{3} + 12 \, a^{4} m^{2} + 47 \, a^{4} m + 60 \, a^{4}} + \frac{{\left({\left(a \sin\left(f x + e\right) + a\right)}^{6} {\left(a \sin\left(f x + e\right) + a\right)}^{m} m^{3} - 5 \, {\left(a \sin\left(f x + e\right) + a\right)}^{5} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a m^{3} + 8 \, {\left(a \sin\left(f x + e\right) + a\right)}^{4} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{2} m^{3} - 4 \, {\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{3} m^{3} + 12 \, {\left(a \sin\left(f x + e\right) + a\right)}^{6} {\left(a \sin\left(f x + e\right) + a\right)}^{m} m^{2} - 65 \, {\left(a \sin\left(f x + e\right) + a\right)}^{5} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a m^{2} + 112 \, {\left(a \sin\left(f x + e\right) + a\right)}^{4} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{2} m^{2} - 60 \, {\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{3} m^{2} + 47 \, {\left(a \sin\left(f x + e\right) + a\right)}^{6} {\left(a \sin\left(f x + e\right) + a\right)}^{m} m - 270 \, {\left(a \sin\left(f x + e\right) + a\right)}^{5} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a m + 504 \, {\left(a \sin\left(f x + e\right) + a\right)}^{4} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{2} m - 296 \, {\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{3} m + 60 \, {\left(a \sin\left(f x + e\right) + a\right)}^{6} {\left(a \sin\left(f x + e\right) + a\right)}^{m} - 360 \, {\left(a \sin\left(f x + e\right) + a\right)}^{5} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a + 720 \, {\left(a \sin\left(f x + e\right) + a\right)}^{4} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{2} - 480 \, {\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{3}\right)} B}{{\left(a^{4} m^{4} + 18 \, a^{4} m^{3} + 119 \, a^{4} m^{2} + 342 \, a^{4} m + 360 \, a^{4}\right)} a}}{a f}"," ",0,"(((a*sin(f*x + e) + a)^5*(a*sin(f*x + e) + a)^m*m^2 - 4*(a*sin(f*x + e) + a)^4*(a*sin(f*x + e) + a)^m*a*m^2 + 4*(a*sin(f*x + e) + a)^3*(a*sin(f*x + e) + a)^m*a^2*m^2 + 7*(a*sin(f*x + e) + a)^5*(a*sin(f*x + e) + a)^m*m - 32*(a*sin(f*x + e) + a)^4*(a*sin(f*x + e) + a)^m*a*m + 36*(a*sin(f*x + e) + a)^3*(a*sin(f*x + e) + a)^m*a^2*m + 12*(a*sin(f*x + e) + a)^5*(a*sin(f*x + e) + a)^m - 60*(a*sin(f*x + e) + a)^4*(a*sin(f*x + e) + a)^m*a + 80*(a*sin(f*x + e) + a)^3*(a*sin(f*x + e) + a)^m*a^2)*A/(a^4*m^3 + 12*a^4*m^2 + 47*a^4*m + 60*a^4) + ((a*sin(f*x + e) + a)^6*(a*sin(f*x + e) + a)^m*m^3 - 5*(a*sin(f*x + e) + a)^5*(a*sin(f*x + e) + a)^m*a*m^3 + 8*(a*sin(f*x + e) + a)^4*(a*sin(f*x + e) + a)^m*a^2*m^3 - 4*(a*sin(f*x + e) + a)^3*(a*sin(f*x + e) + a)^m*a^3*m^3 + 12*(a*sin(f*x + e) + a)^6*(a*sin(f*x + e) + a)^m*m^2 - 65*(a*sin(f*x + e) + a)^5*(a*sin(f*x + e) + a)^m*a*m^2 + 112*(a*sin(f*x + e) + a)^4*(a*sin(f*x + e) + a)^m*a^2*m^2 - 60*(a*sin(f*x + e) + a)^3*(a*sin(f*x + e) + a)^m*a^3*m^2 + 47*(a*sin(f*x + e) + a)^6*(a*sin(f*x + e) + a)^m*m - 270*(a*sin(f*x + e) + a)^5*(a*sin(f*x + e) + a)^m*a*m + 504*(a*sin(f*x + e) + a)^4*(a*sin(f*x + e) + a)^m*a^2*m - 296*(a*sin(f*x + e) + a)^3*(a*sin(f*x + e) + a)^m*a^3*m + 60*(a*sin(f*x + e) + a)^6*(a*sin(f*x + e) + a)^m - 360*(a*sin(f*x + e) + a)^5*(a*sin(f*x + e) + a)^m*a + 720*(a*sin(f*x + e) + a)^4*(a*sin(f*x + e) + a)^m*a^2 - 480*(a*sin(f*x + e) + a)^3*(a*sin(f*x + e) + a)^m*a^3)*B/((a^4*m^4 + 18*a^4*m^3 + 119*a^4*m^2 + 342*a^4*m + 360*a^4)*a))/(a*f)","B",0
1022,1,458,0,0.185306," ","integrate(cos(f*x+e)^3*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""giac"")","-\frac{\frac{{\left({\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(a \sin\left(f x + e\right) + a\right)}^{m} m - 2 \, {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a m + 2 \, {\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(a \sin\left(f x + e\right) + a\right)}^{m} - 6 \, {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a\right)} A}{a^{2} m^{2} + 5 \, a^{2} m + 6 \, a^{2}} + \frac{{\left({\left(a \sin\left(f x + e\right) + a\right)}^{4} {\left(a \sin\left(f x + e\right) + a\right)}^{m} m^{2} - 3 \, {\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a m^{2} + 2 \, {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{2} m^{2} + 5 \, {\left(a \sin\left(f x + e\right) + a\right)}^{4} {\left(a \sin\left(f x + e\right) + a\right)}^{m} m - 18 \, {\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a m + 14 \, {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{2} m + 6 \, {\left(a \sin\left(f x + e\right) + a\right)}^{4} {\left(a \sin\left(f x + e\right) + a\right)}^{m} - 24 \, {\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a + 24 \, {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a^{2}\right)} B}{{\left(a^{2} m^{3} + 9 \, a^{2} m^{2} + 26 \, a^{2} m + 24 \, a^{2}\right)} a}}{a f}"," ",0,"-(((a*sin(f*x + e) + a)^3*(a*sin(f*x + e) + a)^m*m - 2*(a*sin(f*x + e) + a)^2*(a*sin(f*x + e) + a)^m*a*m + 2*(a*sin(f*x + e) + a)^3*(a*sin(f*x + e) + a)^m - 6*(a*sin(f*x + e) + a)^2*(a*sin(f*x + e) + a)^m*a)*A/(a^2*m^2 + 5*a^2*m + 6*a^2) + ((a*sin(f*x + e) + a)^4*(a*sin(f*x + e) + a)^m*m^2 - 3*(a*sin(f*x + e) + a)^3*(a*sin(f*x + e) + a)^m*a*m^2 + 2*(a*sin(f*x + e) + a)^2*(a*sin(f*x + e) + a)^m*a^2*m^2 + 5*(a*sin(f*x + e) + a)^4*(a*sin(f*x + e) + a)^m*m - 18*(a*sin(f*x + e) + a)^3*(a*sin(f*x + e) + a)^m*a*m + 14*(a*sin(f*x + e) + a)^2*(a*sin(f*x + e) + a)^m*a^2*m + 6*(a*sin(f*x + e) + a)^4*(a*sin(f*x + e) + a)^m - 24*(a*sin(f*x + e) + a)^3*(a*sin(f*x + e) + a)^m*a + 24*(a*sin(f*x + e) + a)^2*(a*sin(f*x + e) + a)^m*a^2)*B/((a^2*m^3 + 9*a^2*m^2 + 26*a^2*m + 24*a^2)*a))/(a*f)","B",0
1023,1,156,0,0.159819," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""giac"")","\frac{\frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m + 1} A}{m + 1} + \frac{{\left({\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m} m - {\left(a \sin\left(f x + e\right) + a\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a m + {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m} - 2 \, {\left(a \sin\left(f x + e\right) + a\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} a\right)} B}{{\left(m^{2} + 3 \, m + 2\right)} a}}{a f}"," ",0,"((a*sin(f*x + e) + a)^(m + 1)*A/(m + 1) + ((a*sin(f*x + e) + a)^2*(a*sin(f*x + e) + a)^m*m - (a*sin(f*x + e) + a)*(a*sin(f*x + e) + a)^m*a*m + (a*sin(f*x + e) + a)^2*(a*sin(f*x + e) + a)^m - 2*(a*sin(f*x + e) + a)*(a*sin(f*x + e) + a)^m*a)*B/((m^2 + 3*m + 2)*a))/(a*f)","B",0
1024,0,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""giac"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m*sec(f*x + e), x)","F",0
1025,0,0,0,0.000000," ","integrate(sec(f*x+e)^3*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""giac"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m*sec(f*x + e)^3, x)","F",0
1026,0,0,0,0.000000," ","integrate(sec(f*x+e)^5*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""giac"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)^{5}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m*sec(f*x + e)^5, x)","F",0
1027,0,0,0,0.000000," ","integrate(cos(f*x+e)^6*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""giac"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)^{6}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m*cos(f*x + e)^6, x)","F",0
1028,0,0,0,0.000000," ","integrate(cos(f*x+e)^4*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""giac"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m*cos(f*x + e)^4, x)","F",0
1029,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""giac"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m*cos(f*x + e)^2, x)","F",0
1030,0,0,0,0.000000," ","integrate(sec(f*x+e)^2*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""giac"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m*sec(f*x + e)^2, x)","F",0
1031,0,0,0,0.000000," ","integrate(sec(f*x+e)^4*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""giac"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m*sec(f*x + e)^4, x)","F",0
1032,0,0,0,0.000000," ","integrate(sec(f*x+e)^6*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""giac"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)^{6}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m*sec(f*x + e)^6, x)","F",0
1033,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^p*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(-4-p),x, algorithm=""giac"")","\int {\left(B \sin\left(f x + e\right) + A\right)} \left(g \cos\left(f x + e\right)\right)^{p} {\left(-c \sin\left(f x + e\right) + c\right)}^{-p - 4}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(g*cos(f*x + e))^p*(-c*sin(f*x + e) + c)^(-p - 4), x)","F",0
1034,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^p*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(-3-p),x, algorithm=""giac"")","\int {\left(B \sin\left(f x + e\right) + A\right)} \left(g \cos\left(f x + e\right)\right)^{p} {\left(-c \sin\left(f x + e\right) + c\right)}^{-p - 3}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(g*cos(f*x + e))^p*(-c*sin(f*x + e) + c)^(-p - 3), x)","F",0
1035,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^p*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(-2-p),x, algorithm=""giac"")","\int {\left(B \sin\left(f x + e\right) + A\right)} \left(g \cos\left(f x + e\right)\right)^{p} {\left(-c \sin\left(f x + e\right) + c\right)}^{-p - 2}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(g*cos(f*x + e))^p*(-c*sin(f*x + e) + c)^(-p - 2), x)","F",0
1036,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^p*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(-1-p),x, algorithm=""giac"")","\int {\left(B \sin\left(f x + e\right) + A\right)} \left(g \cos\left(f x + e\right)\right)^{p} {\left(-c \sin\left(f x + e\right) + c\right)}^{-p - 1}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(g*cos(f*x + e))^p*(-c*sin(f*x + e) + c)^(-p - 1), x)","F",0
1037,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^p*(A+B*sin(f*x+e))/((c-c*sin(f*x+e))^p),x, algorithm=""giac"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} \left(g \cos\left(f x + e\right)\right)^{p}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{p}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(g*cos(f*x + e))^p/(-c*sin(f*x + e) + c)^p, x)","F",0
1038,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^p*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1-p),x, algorithm=""giac"")","\int {\left(B \sin\left(f x + e\right) + A\right)} \left(g \cos\left(f x + e\right)\right)^{p} {\left(-c \sin\left(f x + e\right) + c\right)}^{-p + 1}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(g*cos(f*x + e))^p*(-c*sin(f*x + e) + c)^(-p + 1), x)","F",0
1039,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^p*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(2-p),x, algorithm=""giac"")","\int {\left(B \sin\left(f x + e\right) + A\right)} \left(g \cos\left(f x + e\right)\right)^{p} {\left(-c \sin\left(f x + e\right) + c\right)}^{-p + 2}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(g*cos(f*x + e))^p*(-c*sin(f*x + e) + c)^(-p + 2), x)","F",0
1040,-2,0,0,0.000000," ","integrate((g*cos(f*x+e))^p*(a+a*sin(f*x+e))^m*(A*m-A*(1+m+p)*sin(f*x+e)),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)-(-A*exp(-m*ln(2)+2*m*ln(2*abs(tan((2*f*x-pi+2*exp(1))/8)^2-1)/(tan((2*f*x-pi+2*exp(1))/8)^2+1))+m*ln(abs(a))-p*ln(2)+p*ln(2*abs(tan((2*f*x-pi+2*exp(1))/8)^2-1)/(tan((2*f*x-pi+2*exp(1))/8)^2+1))+p*ln(4*abs(g)*abs(tan((2*f*x-pi+2*exp(1))/8))/(tan((2*f*x-pi+2*exp(1))/8)^2+1)))*tan((4*m*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+3*pi+2*exp(1))*1/4/pi)+4*m*pi*floor((f*x+pi+exp(1))*1/2/pi)+4*m*pi*floor(-(sign(a)-2)/4)+m*pi*sign(a)-2*m*pi*sign(tan((f*x+exp(1))/2)^2-1)-3*m*pi+2*p*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+3*pi+2*exp(1))*1/4/pi)+2*p*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)+4*p*pi*floor((f*x+pi+exp(1))*1/2/pi)+p*pi*sign(g)*sign(g*tan((f*x+exp(1))/2)^2-2*g*tan((f*x+exp(1))/2)+g)*sign(tan((f*x+exp(1))/2)^2-1)+p*pi*sign(g*tan((f*x+exp(1))/2)^2-2*g*tan((f*x+exp(1))/2)+g)-p*pi*sign(tan((f*x+exp(1))/2)^2-1)-p*pi)/4)^2*tan((f*x+exp(1))/2)^2+A*exp(-m*ln(2)+2*m*ln(2*abs(tan((2*f*x-pi+2*exp(1))/8)^2-1)/(tan((2*f*x-pi+2*exp(1))/8)^2+1))+m*ln(abs(a))-p*ln(2)+p*ln(2*abs(tan((2*f*x-pi+2*exp(1))/8)^2-1)/(tan((2*f*x-pi+2*exp(1))/8)^2+1))+p*ln(4*abs(g)*abs(tan((2*f*x-pi+2*exp(1))/8))/(tan((2*f*x-pi+2*exp(1))/8)^2+1)))*tan((4*m*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+3*pi+2*exp(1))*1/4/pi)+4*m*pi*floor((f*x+pi+exp(1))*1/2/pi)+4*m*pi*floor(-(sign(a)-2)/4)+m*pi*sign(a)-2*m*pi*sign(tan((f*x+exp(1))/2)^2-1)-3*m*pi+2*p*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+3*pi+2*exp(1))*1/4/pi)+2*p*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)+4*p*pi*floor((f*x+pi+exp(1))*1/2/pi)+p*pi*sign(g)*sign(g*tan((f*x+exp(1))/2)^2-2*g*tan((f*x+exp(1))/2)+g)*sign(tan((f*x+exp(1))/2)^2-1)+p*pi*sign(g*tan((f*x+exp(1))/2)^2-2*g*tan((f*x+exp(1))/2)+g)-p*pi*sign(tan((f*x+exp(1))/2)^2-1)-p*pi)/4)^2+A*exp(-m*ln(2)+2*m*ln(2*abs(tan((2*f*x-pi+2*exp(1))/8)^2-1)/(tan((2*f*x-pi+2*exp(1))/8)^2+1))+m*ln(abs(a))-p*ln(2)+p*ln(2*abs(tan((2*f*x-pi+2*exp(1))/8)^2-1)/(tan((2*f*x-pi+2*exp(1))/8)^2+1))+p*ln(4*abs(g)*abs(tan((2*f*x-pi+2*exp(1))/8))/(tan((2*f*x-pi+2*exp(1))/8)^2+1)))*tan((f*x+exp(1))/2)^2-A*exp(-m*ln(2)+2*m*ln(2*abs(tan((2*f*x-pi+2*exp(1))/8)^2-1)/(tan((2*f*x-pi+2*exp(1))/8)^2+1))+m*ln(abs(a))-p*ln(2)+p*ln(2*abs(tan((2*f*x-pi+2*exp(1))/8)^2-1)/(tan((2*f*x-pi+2*exp(1))/8)^2+1))+p*ln(4*abs(g)*abs(tan((2*f*x-pi+2*exp(1))/8))/(tan((2*f*x-pi+2*exp(1))/8)^2+1))))/(f*tan((4*m*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+3*pi+2*exp(1))*1/4/pi)+4*m*pi*floor((f*x+pi+exp(1))*1/2/pi)+4*m*pi*floor(-(sign(a)-2)/4)+m*pi*sign(a)-2*m*pi*sign(tan((f*x+exp(1))/2)^2-1)-3*m*pi+2*p*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+3*pi+2*exp(1))*1/4/pi)+2*p*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)+4*p*pi*floor((f*x+pi+exp(1))*1/2/pi)+p*pi*sign(g)*sign(g*tan((f*x+exp(1))/2)^2-2*g*tan((f*x+exp(1))/2)+g)*sign(tan((f*x+exp(1))/2)^2-1)+p*pi*sign(g*tan((f*x+exp(1))/2)^2-2*g*tan((f*x+exp(1))/2)+g)-p*pi*sign(tan((f*x+exp(1))/2)^2-1)-p*pi)/4)^2*tan((f*x+exp(1))/2)^2+f*tan((4*m*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+3*pi+2*exp(1))*1/4/pi)+4*m*pi*floor((f*x+pi+exp(1))*1/2/pi)+4*m*pi*floor(-(sign(a)-2)/4)+m*pi*sign(a)-2*m*pi*sign(tan((f*x+exp(1))/2)^2-1)-3*m*pi+2*p*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+3*pi+2*exp(1))*1/4/pi)+2*p*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)+4*p*pi*floor((f*x+pi+exp(1))*1/2/pi)+p*pi*sign(g)*sign(g*tan((f*x+exp(1))/2)^2-2*g*tan((f*x+exp(1))/2)+g)*sign(tan((f*x+exp(1))/2)^2-1)+p*pi*sign(g*tan((f*x+exp(1))/2)^2-2*g*tan((f*x+exp(1))/2)+g)-p*pi*sign(tan((f*x+exp(1))/2)^2-1)-p*pi)/4)^2+f*tan((f*x+exp(1))/2)^2+f)","F(-2)",0
1041,-2,0,0,0.000000," ","integrate((g*cos(f*x+e))^p*(a-a*sin(f*x+e))^m*(A*m+A*(1+m+p)*sin(f*x+e)),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)(-A*exp(-m*ln(2)+2*m*ln(4*abs(tan((2*f*x-pi+2*exp(1))/8))/(tan((2*f*x-pi+2*exp(1))/8)^2+1))+m*ln(abs(a))-p*ln(2)+p*ln(2*abs(g)*abs(tan((2*f*x-pi+2*exp(1))/8)^2-1)/(tan((2*f*x-pi+2*exp(1))/8)^2+1))+p*ln(4*abs(tan((2*f*x-pi+2*exp(1))/8))/(tan((2*f*x-pi+2*exp(1))/8)^2+1)))*tan((4*m*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)+4*m*pi*floor((f*x+pi+exp(1))*1/2/pi)+4*m*pi*floor(-(sign(a)-4)/4)+m*pi*sign(a)+2*m*pi*sign(tan((f*x+exp(1))/2)^2-1)+m*pi+2*p*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+3*pi+2*exp(1))*1/4/pi)+2*p*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)+4*p*pi*floor((f*x+pi+exp(1))*1/2/pi)-p*pi*sign(g)*sign(g*tan((f*x+exp(1))/2)^2+2*g*tan((f*x+exp(1))/2)+g)*sign(tan((f*x+exp(1))/2)^2-1)-p*pi*sign(g*tan((f*x+exp(1))/2)^2+2*g*tan((f*x+exp(1))/2)+g)+p*pi*sign(tan((f*x+exp(1))/2)^2-1)+p*pi)/4)^2*tan((f*x+exp(1))/2)^2+A*exp(-m*ln(2)+2*m*ln(4*abs(tan((2*f*x-pi+2*exp(1))/8))/(tan((2*f*x-pi+2*exp(1))/8)^2+1))+m*ln(abs(a))-p*ln(2)+p*ln(2*abs(g)*abs(tan((2*f*x-pi+2*exp(1))/8)^2-1)/(tan((2*f*x-pi+2*exp(1))/8)^2+1))+p*ln(4*abs(tan((2*f*x-pi+2*exp(1))/8))/(tan((2*f*x-pi+2*exp(1))/8)^2+1)))*tan((4*m*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)+4*m*pi*floor((f*x+pi+exp(1))*1/2/pi)+4*m*pi*floor(-(sign(a)-4)/4)+m*pi*sign(a)+2*m*pi*sign(tan((f*x+exp(1))/2)^2-1)+m*pi+2*p*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+3*pi+2*exp(1))*1/4/pi)+2*p*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)+4*p*pi*floor((f*x+pi+exp(1))*1/2/pi)-p*pi*sign(g)*sign(g*tan((f*x+exp(1))/2)^2+2*g*tan((f*x+exp(1))/2)+g)*sign(tan((f*x+exp(1))/2)^2-1)-p*pi*sign(g*tan((f*x+exp(1))/2)^2+2*g*tan((f*x+exp(1))/2)+g)+p*pi*sign(tan((f*x+exp(1))/2)^2-1)+p*pi)/4)^2+A*exp(-m*ln(2)+2*m*ln(4*abs(tan((2*f*x-pi+2*exp(1))/8))/(tan((2*f*x-pi+2*exp(1))/8)^2+1))+m*ln(abs(a))-p*ln(2)+p*ln(2*abs(g)*abs(tan((2*f*x-pi+2*exp(1))/8)^2-1)/(tan((2*f*x-pi+2*exp(1))/8)^2+1))+p*ln(4*abs(tan((2*f*x-pi+2*exp(1))/8))/(tan((2*f*x-pi+2*exp(1))/8)^2+1)))*tan((f*x+exp(1))/2)^2-A*exp(-m*ln(2)+2*m*ln(4*abs(tan((2*f*x-pi+2*exp(1))/8))/(tan((2*f*x-pi+2*exp(1))/8)^2+1))+m*ln(abs(a))-p*ln(2)+p*ln(2*abs(g)*abs(tan((2*f*x-pi+2*exp(1))/8)^2-1)/(tan((2*f*x-pi+2*exp(1))/8)^2+1))+p*ln(4*abs(tan((2*f*x-pi+2*exp(1))/8))/(tan((2*f*x-pi+2*exp(1))/8)^2+1))))/(f*tan((4*m*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)+4*m*pi*floor((f*x+pi+exp(1))*1/2/pi)+4*m*pi*floor(-(sign(a)-4)/4)+m*pi*sign(a)+2*m*pi*sign(tan((f*x+exp(1))/2)^2-1)+m*pi+2*p*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+3*pi+2*exp(1))*1/4/pi)+2*p*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)+4*p*pi*floor((f*x+pi+exp(1))*1/2/pi)-p*pi*sign(g)*sign(g*tan((f*x+exp(1))/2)^2+2*g*tan((f*x+exp(1))/2)+g)*sign(tan((f*x+exp(1))/2)^2-1)-p*pi*sign(g*tan((f*x+exp(1))/2)^2+2*g*tan((f*x+exp(1))/2)+g)+p*pi*sign(tan((f*x+exp(1))/2)^2-1)+p*pi)/4)^2*tan((f*x+exp(1))/2)^2+f*tan((4*m*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)+4*m*pi*floor((f*x+pi+exp(1))*1/2/pi)+4*m*pi*floor(-(sign(a)-4)/4)+m*pi*sign(a)+2*m*pi*sign(tan((f*x+exp(1))/2)^2-1)+m*pi+2*p*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+3*pi+2*exp(1))*1/4/pi)+2*p*pi*floor((2*f*x-4*pi*floor((f*x+pi+exp(1))*1/2/pi)+pi+2*exp(1))*1/4/pi)+4*p*pi*floor((f*x+pi+exp(1))*1/2/pi)-p*pi*sign(g)*sign(g*tan((f*x+exp(1))/2)^2+2*g*tan((f*x+exp(1))/2)+g)*sign(tan((f*x+exp(1))/2)^2-1)-p*pi*sign(g*tan((f*x+exp(1))/2)^2+2*g*tan((f*x+exp(1))/2)+g)+p*pi*sign(tan((f*x+exp(1))/2)^2-1)+p*pi)/4)^2+f*tan((f*x+exp(1))/2)^2+f)","F(-2)",0
1042,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^p*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x, algorithm=""giac"")","\int \left(g \cos\left(f x + e\right)\right)^{p} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(d \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^p*(a*sin(f*x + e) + a)^m*(d*sin(f*x + e) + c)^n, x)","F",0
1043,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^p*(a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^n,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{2} \left(g \cos\left(f x + e\right)\right)^{p} {\left(d \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^2*(g*cos(f*x + e))^p*(d*sin(f*x + e) + c)^n, x)","F",0
1044,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^p*(a+a*sin(f*x+e))*(c+d*sin(f*x+e))^n,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)} \left(g \cos\left(f x + e\right)\right)^{p} {\left(d \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)*(g*cos(f*x + e))^p*(d*sin(f*x + e) + c)^n, x)","F",0
1045,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^p*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{p} {\left(d \sin\left(f x + e\right) + c\right)}^{n}}{a \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^p*(d*sin(f*x + e) + c)^n/(a*sin(f*x + e) + a), x)","F",0
1046,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^p*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^2,x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{p} {\left(d \sin\left(f x + e\right) + c\right)}^{n}}{{\left(a \sin\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^p*(d*sin(f*x + e) + c)^n/(a*sin(f*x + e) + a)^2, x)","F",0
1047,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^p*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^3,x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{p} {\left(d \sin\left(f x + e\right) + c\right)}^{n}}{{\left(a \sin\left(f x + e\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^p*(d*sin(f*x + e) + c)^n/(a*sin(f*x + e) + a)^3, x)","F",0
1048,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^p*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^4,x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{p} {\left(d \sin\left(f x + e\right) + c\right)}^{n}}{{\left(a \sin\left(f x + e\right) + a\right)}^{4}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^p*(d*sin(f*x + e) + c)^n/(a*sin(f*x + e) + a)^4, x)","F",0
1049,0,0,0,0.000000," ","integrate((g*sec(f*x+e))^p*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x, algorithm=""giac"")","\int \left(g \sec\left(f x + e\right)\right)^{p} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(d \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((g*sec(f*x + e))^p*(a*sin(f*x + e) + a)^m*(d*sin(f*x + e) + c)^n, x)","F",0
1050,1,92,0,0.203881," ","integrate(cos(d*x+c)^2*sin(d*x+c)^3*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{1}{16} \, b x + \frac{a \cos\left(5 \, d x + 5 \, c\right)}{80 \, d} - \frac{a \cos\left(3 \, d x + 3 \, c\right)}{48 \, d} - \frac{a \cos\left(d x + c\right)}{8 \, d} + \frac{b \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} - \frac{b \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} - \frac{b \sin\left(2 \, d x + 2 \, c\right)}{64 \, d}"," ",0,"1/16*b*x + 1/80*a*cos(5*d*x + 5*c)/d - 1/48*a*cos(3*d*x + 3*c)/d - 1/8*a*cos(d*x + c)/d + 1/192*b*sin(6*d*x + 6*c)/d - 1/64*b*sin(4*d*x + 4*c)/d - 1/64*b*sin(2*d*x + 2*c)/d","A",0
1051,1,62,0,0.183011," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{1}{8} \, a x + \frac{b \cos\left(5 \, d x + 5 \, c\right)}{80 \, d} - \frac{b \cos\left(3 \, d x + 3 \, c\right)}{48 \, d} - \frac{b \cos\left(d x + c\right)}{8 \, d} - \frac{a \sin\left(4 \, d x + 4 \, c\right)}{32 \, d}"," ",0,"1/8*a*x + 1/80*b*cos(5*d*x + 5*c)/d - 1/48*b*cos(3*d*x + 3*c)/d - 1/8*b*cos(d*x + c)/d - 1/32*a*sin(4*d*x + 4*c)/d","A",0
1052,1,47,0,0.145888," ","integrate(cos(d*x+c)^2*sin(d*x+c)*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{1}{8} \, b x - \frac{a \cos\left(3 \, d x + 3 \, c\right)}{12 \, d} - \frac{a \cos\left(d x + c\right)}{4 \, d} - \frac{b \sin\left(4 \, d x + 4 \, c\right)}{32 \, d}"," ",0,"1/8*b*x - 1/12*a*cos(3*d*x + 3*c)/d - 1/4*a*cos(d*x + c)/d - 1/32*b*sin(4*d*x + 4*c)/d","A",0
1053,1,87,0,0.154296," ","integrate(cos(d*x+c)^2*csc(d*x+c)*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{{\left(d x + c\right)} b + 2 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{2 \, {\left(b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, a\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*((d*x + c)*b + 2*a*log(abs(tan(1/2*d*x + 1/2*c))) - 2*(b*tan(1/2*d*x + 1/2*c)^3 - 2*a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c) - 2*a)/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","A",0
1054,1,108,0,0.170951," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2*(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{6 \, {\left(d x + c\right)} a - 6 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 10 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}}{6 \, d}"," ",0,"-1/6*(6*(d*x + c)*a - 6*b*log(abs(tan(1/2*d*x + 1/2*c))) - 3*a*tan(1/2*d*x + 1/2*c) + (2*b*tan(1/2*d*x + 1/2*c)^3 + 3*a*tan(1/2*d*x + 1/2*c)^2 - 10*b*tan(1/2*d*x + 1/2*c) + 3*a)/(tan(1/2*d*x + 1/2*c)^3 + tan(1/2*d*x + 1/2*c)))/d","B",0
1055,1,95,0,0.172366," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, {\left(d x + c\right)} b - 4 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 4 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{6 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}}{8 \, d}"," ",0,"1/8*(a*tan(1/2*d*x + 1/2*c)^2 - 8*(d*x + c)*b - 4*a*log(abs(tan(1/2*d*x + 1/2*c))) + 4*b*tan(1/2*d*x + 1/2*c) + (6*a*tan(1/2*d*x + 1/2*c)^2 - 4*b*tan(1/2*d*x + 1/2*c) - a)/tan(1/2*d*x + 1/2*c)^2)/d","A",0
1056,1,115,0,0.185569," ","integrate(cos(d*x+c)^2*csc(d*x+c)^4*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{22 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{24 \, d}"," ",0,"1/24*(a*tan(1/2*d*x + 1/2*c)^3 + 3*b*tan(1/2*d*x + 1/2*c)^2 - 12*b*log(abs(tan(1/2*d*x + 1/2*c))) - 3*a*tan(1/2*d*x + 1/2*c) + (22*b*tan(1/2*d*x + 1/2*c)^3 + 3*a*tan(1/2*d*x + 1/2*c)^2 - 3*b*tan(1/2*d*x + 1/2*c) - a)/tan(1/2*d*x + 1/2*c)^3)/d","B",0
1057,1,116,0,0.189848," ","integrate(cos(d*x+c)^2*csc(d*x+c)^5*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 8 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 24 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{50 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 24 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 8 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}}}{192 \, d}"," ",0,"1/192*(3*a*tan(1/2*d*x + 1/2*c)^4 + 8*b*tan(1/2*d*x + 1/2*c)^3 - 24*a*log(abs(tan(1/2*d*x + 1/2*c))) - 24*b*tan(1/2*d*x + 1/2*c) + (50*a*tan(1/2*d*x + 1/2*c)^4 + 24*b*tan(1/2*d*x + 1/2*c)^3 - 8*b*tan(1/2*d*x + 1/2*c) - 3*a)/tan(1/2*d*x + 1/2*c)^4)/d","A",0
1058,1,144,0,0.180073," ","integrate(cos(d*x+c)^2*csc(d*x+c)^6*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{6 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 10 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 60 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{274 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 60 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 10 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{960 \, d}"," ",0,"1/960*(6*a*tan(1/2*d*x + 1/2*c)^5 + 15*b*tan(1/2*d*x + 1/2*c)^4 + 10*a*tan(1/2*d*x + 1/2*c)^3 - 120*b*log(abs(tan(1/2*d*x + 1/2*c))) - 60*a*tan(1/2*d*x + 1/2*c) + (274*b*tan(1/2*d*x + 1/2*c)^5 + 60*a*tan(1/2*d*x + 1/2*c)^4 - 10*a*tan(1/2*d*x + 1/2*c)^2 - 15*b*tan(1/2*d*x + 1/2*c) - 6*a)/tan(1/2*d*x + 1/2*c)^5)/d","A",0
1059,1,141,0,0.242950," ","integrate(cos(d*x+c)^2*sin(d*x+c)^3*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{1}{8} \, a b x - \frac{b^{2} \cos\left(7 \, d x + 7 \, c\right)}{448 \, d} + \frac{a b \sin\left(6 \, d x + 6 \, c\right)}{96 \, d} - \frac{a b \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} - \frac{a b \sin\left(2 \, d x + 2 \, c\right)}{32 \, d} + \frac{{\left(4 \, a^{2} + 3 \, b^{2}\right)} \cos\left(5 \, d x + 5 \, c\right)}{320 \, d} - \frac{{\left(4 \, a^{2} + b^{2}\right)} \cos\left(3 \, d x + 3 \, c\right)}{192 \, d} - \frac{{\left(8 \, a^{2} + 5 \, b^{2}\right)} \cos\left(d x + c\right)}{64 \, d}"," ",0,"1/8*a*b*x - 1/448*b^2*cos(7*d*x + 7*c)/d + 1/96*a*b*sin(6*d*x + 6*c)/d - 1/32*a*b*sin(4*d*x + 4*c)/d - 1/32*a*b*sin(2*d*x + 2*c)/d + 1/320*(4*a^2 + 3*b^2)*cos(5*d*x + 5*c)/d - 1/192*(4*a^2 + b^2)*cos(3*d*x + 3*c)/d - 1/64*(8*a^2 + 5*b^2)*cos(d*x + c)/d","A",0
1060,1,115,0,0.235628," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{1}{16} \, {\left(2 \, a^{2} + b^{2}\right)} x + \frac{a b \cos\left(5 \, d x + 5 \, c\right)}{40 \, d} - \frac{a b \cos\left(3 \, d x + 3 \, c\right)}{24 \, d} - \frac{a b \cos\left(d x + c\right)}{4 \, d} + \frac{b^{2} \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} - \frac{b^{2} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d} - \frac{{\left(2 \, a^{2} + b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)}{64 \, d}"," ",0,"1/16*(2*a^2 + b^2)*x + 1/40*a*b*cos(5*d*x + 5*c)/d - 1/24*a*b*cos(3*d*x + 3*c)/d - 1/4*a*b*cos(d*x + c)/d + 1/192*b^2*sin(6*d*x + 6*c)/d - 1/64*b^2*sin(2*d*x + 2*c)/d - 1/64*(2*a^2 + b^2)*sin(4*d*x + 4*c)/d","A",0
1061,1,82,0,0.182210," ","integrate(cos(d*x+c)^2*sin(d*x+c)*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{1}{4} \, a b x + \frac{b^{2} \cos\left(5 \, d x + 5 \, c\right)}{80 \, d} - \frac{a b \sin\left(4 \, d x + 4 \, c\right)}{16 \, d} - \frac{{\left(4 \, a^{2} + b^{2}\right)} \cos\left(3 \, d x + 3 \, c\right)}{48 \, d} - \frac{{\left(2 \, a^{2} + b^{2}\right)} \cos\left(d x + c\right)}{8 \, d}"," ",0,"1/4*a*b*x + 1/80*b^2*cos(5*d*x + 5*c)/d - 1/16*a*b*sin(4*d*x + 4*c)/d - 1/48*(4*a^2 + b^2)*cos(3*d*x + 3*c)/d - 1/8*(2*a^2 + b^2)*cos(d*x + c)/d","A",0
1062,1,133,0,0.200207," ","integrate(cos(d*x+c)^2*csc(d*x+c)*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{3 \, {\left(d x + c\right)} a b + 3 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{2 \, {\left(3 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 3 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 6 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a^{2} + b^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*(d*x + c)*a*b + 3*a^2*log(abs(tan(1/2*d*x + 1/2*c))) - 2*(3*a*b*tan(1/2*d*x + 1/2*c)^5 - 3*a^2*tan(1/2*d*x + 1/2*c)^4 + 3*b^2*tan(1/2*d*x + 1/2*c)^4 - 6*a^2*tan(1/2*d*x + 1/2*c)^2 - 3*a*b*tan(1/2*d*x + 1/2*c) - 3*a^2 + b^2)/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
1063,1,148,0,0.187531," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{4 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - {\left(2 \, a^{2} - b^{2}\right)} {\left(d x + c\right)} - \frac{4 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)} - \frac{2 \, {\left(b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, a b\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(4*a*b*log(abs(tan(1/2*d*x + 1/2*c))) + a^2*tan(1/2*d*x + 1/2*c) - (2*a^2 - b^2)*(d*x + c) - (4*a*b*tan(1/2*d*x + 1/2*c) + a^2)/tan(1/2*d*x + 1/2*c) - 2*(b^2*tan(1/2*d*x + 1/2*c)^3 - 4*a*b*tan(1/2*d*x + 1/2*c)^2 - b^2*tan(1/2*d*x + 1/2*c) - 4*a*b)/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","A",0
1064,1,148,0,0.196597," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 16 \, {\left(d x + c\right)} a b + 8 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, {\left(a^{2} - 2 \, b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + \frac{16 \, b^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + \frac{6 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}}{8 \, d}"," ",0,"1/8*(a^2*tan(1/2*d*x + 1/2*c)^2 - 16*(d*x + c)*a*b + 8*a*b*tan(1/2*d*x + 1/2*c) - 4*(a^2 - 2*b^2)*log(abs(tan(1/2*d*x + 1/2*c))) + 16*b^2/(tan(1/2*d*x + 1/2*c)^2 + 1) + (6*a^2*tan(1/2*d*x + 1/2*c)^2 - 12*b^2*tan(1/2*d*x + 1/2*c)^2 - 8*a*b*tan(1/2*d*x + 1/2*c) - a^2)/tan(1/2*d*x + 1/2*c)^2)/d","A",0
1065,1,167,0,0.214483," ","integrate(cos(d*x+c)^2*csc(d*x+c)^4*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 24 \, {\left(d x + c\right)} b^{2} - 24 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{44 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 6 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{24 \, d}"," ",0,"1/24*(a^2*tan(1/2*d*x + 1/2*c)^3 + 6*a*b*tan(1/2*d*x + 1/2*c)^2 - 24*(d*x + c)*b^2 - 24*a*b*log(abs(tan(1/2*d*x + 1/2*c))) - 3*a^2*tan(1/2*d*x + 1/2*c) + 12*b^2*tan(1/2*d*x + 1/2*c) + (44*a*b*tan(1/2*d*x + 1/2*c)^3 + 3*a^2*tan(1/2*d*x + 1/2*c)^2 - 12*b^2*tan(1/2*d*x + 1/2*c)^2 - 6*a*b*tan(1/2*d*x + 1/2*c) - a^2)/tan(1/2*d*x + 1/2*c)^3)/d","A",0
1066,1,182,0,0.217884," ","integrate(cos(d*x+c)^2*csc(d*x+c)^5*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 16 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 24 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 48 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, {\left(a^{2} + 4 \, b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + \frac{50 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 200 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 48 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 16 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}}}{192 \, d}"," ",0,"1/192*(3*a^2*tan(1/2*d*x + 1/2*c)^4 + 16*a*b*tan(1/2*d*x + 1/2*c)^3 + 24*b^2*tan(1/2*d*x + 1/2*c)^2 - 48*a*b*tan(1/2*d*x + 1/2*c) - 24*(a^2 + 4*b^2)*log(abs(tan(1/2*d*x + 1/2*c))) + (50*a^2*tan(1/2*d*x + 1/2*c)^4 + 200*b^2*tan(1/2*d*x + 1/2*c)^4 + 48*a*b*tan(1/2*d*x + 1/2*c)^3 - 24*b^2*tan(1/2*d*x + 1/2*c)^2 - 16*a*b*tan(1/2*d*x + 1/2*c) - 3*a^2)/tan(1/2*d*x + 1/2*c)^4)/d","A",0
1067,1,222,0,0.216030," ","integrate(cos(d*x+c)^2*csc(d*x+c)^6*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 5 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 20 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 30 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 60 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{274 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 30 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 60 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 5 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 20 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{480 \, d}"," ",0,"1/480*(3*a^2*tan(1/2*d*x + 1/2*c)^5 + 15*a*b*tan(1/2*d*x + 1/2*c)^4 + 5*a^2*tan(1/2*d*x + 1/2*c)^3 + 20*b^2*tan(1/2*d*x + 1/2*c)^3 - 120*a*b*log(abs(tan(1/2*d*x + 1/2*c))) - 30*a^2*tan(1/2*d*x + 1/2*c) - 60*b^2*tan(1/2*d*x + 1/2*c) + (274*a*b*tan(1/2*d*x + 1/2*c)^5 + 30*a^2*tan(1/2*d*x + 1/2*c)^4 + 60*b^2*tan(1/2*d*x + 1/2*c)^4 - 5*a^2*tan(1/2*d*x + 1/2*c)^2 - 20*b^2*tan(1/2*d*x + 1/2*c)^2 - 15*a*b*tan(1/2*d*x + 1/2*c) - 3*a^2)/tan(1/2*d*x + 1/2*c)^5)/d","A",0
1068,1,276,0,0.231529," ","integrate(cos(d*x+c)^2*csc(d*x+c)^7*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{5 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 24 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 30 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 40 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 240 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 120 \, {\left(a^{2} + 2 \, b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + \frac{294 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 588 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 240 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 40 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 30 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 24 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6}}}{1920 \, d}"," ",0,"1/1920*(5*a^2*tan(1/2*d*x + 1/2*c)^6 + 24*a*b*tan(1/2*d*x + 1/2*c)^5 + 15*a^2*tan(1/2*d*x + 1/2*c)^4 + 30*b^2*tan(1/2*d*x + 1/2*c)^4 + 40*a*b*tan(1/2*d*x + 1/2*c)^3 - 15*a^2*tan(1/2*d*x + 1/2*c)^2 - 240*a*b*tan(1/2*d*x + 1/2*c) - 120*(a^2 + 2*b^2)*log(abs(tan(1/2*d*x + 1/2*c))) + (294*a^2*tan(1/2*d*x + 1/2*c)^6 + 588*b^2*tan(1/2*d*x + 1/2*c)^6 + 240*a*b*tan(1/2*d*x + 1/2*c)^5 + 15*a^2*tan(1/2*d*x + 1/2*c)^4 - 40*a*b*tan(1/2*d*x + 1/2*c)^3 - 15*a^2*tan(1/2*d*x + 1/2*c)^2 - 30*b^2*tan(1/2*d*x + 1/2*c)^2 - 24*a*b*tan(1/2*d*x + 1/2*c) - 5*a^2)/tan(1/2*d*x + 1/2*c)^6)/d","A",0
1069,1,166,0,0.277116," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{b^{3} \cos\left(7 \, d x + 7 \, c\right)}{448 \, d} + \frac{a b^{2} \sin\left(6 \, d x + 6 \, c\right)}{64 \, d} - \frac{3 \, a b^{2} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d} + \frac{1}{16} \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} x + \frac{3 \, {\left(4 \, a^{2} b + b^{3}\right)} \cos\left(5 \, d x + 5 \, c\right)}{320 \, d} - \frac{{\left(12 \, a^{2} b + b^{3}\right)} \cos\left(3 \, d x + 3 \, c\right)}{192 \, d} - \frac{{\left(24 \, a^{2} b + 5 \, b^{3}\right)} \cos\left(d x + c\right)}{64 \, d} - \frac{{\left(2 \, a^{3} + 3 \, a b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)}{64 \, d}"," ",0,"-1/448*b^3*cos(7*d*x + 7*c)/d + 1/64*a*b^2*sin(6*d*x + 6*c)/d - 3/64*a*b^2*sin(2*d*x + 2*c)/d + 1/16*(2*a^3 + 3*a*b^2)*x + 3/320*(4*a^2*b + b^3)*cos(5*d*x + 5*c)/d - 1/192*(12*a^2*b + b^3)*cos(3*d*x + 3*c)/d - 1/64*(24*a^2*b + 5*b^3)*cos(d*x + c)/d - 1/64*(2*a^3 + 3*a*b^2)*sin(4*d*x + 4*c)/d","A",0
1070,1,139,0,0.252979," ","integrate(cos(d*x+c)^2*sin(d*x+c)*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{3 \, a b^{2} \cos\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{b^{3} \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} - \frac{b^{3} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d} + \frac{1}{16} \, {\left(6 \, a^{2} b + b^{3}\right)} x - \frac{{\left(4 \, a^{3} + 3 \, a b^{2}\right)} \cos\left(3 \, d x + 3 \, c\right)}{48 \, d} - \frac{{\left(2 \, a^{3} + 3 \, a b^{2}\right)} \cos\left(d x + c\right)}{8 \, d} - \frac{{\left(6 \, a^{2} b + b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)}{64 \, d}"," ",0,"3/80*a*b^2*cos(5*d*x + 5*c)/d + 1/192*b^3*sin(6*d*x + 6*c)/d - 1/64*b^3*sin(2*d*x + 2*c)/d + 1/16*(6*a^2*b + b^3)*x - 1/48*(4*a^3 + 3*a*b^2)*cos(3*d*x + 3*c)/d - 1/8*(2*a^3 + 3*a*b^2)*cos(d*x + c)/d - 1/64*(6*a^2*b + b^3)*sin(4*d*x + 4*c)/d","A",0
1071,1,293,0,0.233105," ","integrate(cos(d*x+c)^2*csc(d*x+c)*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{8 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + {\left(12 \, a^{2} b + b^{3}\right)} {\left(d x + c\right)} - \frac{2 \, {\left(12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 8 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 24 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 7 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 24 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 24 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 7 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 8 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, a^{3} + 8 \, a b^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{8 \, d}"," ",0,"1/8*(8*a^3*log(abs(tan(1/2*d*x + 1/2*c))) + (12*a^2*b + b^3)*(d*x + c) - 2*(12*a^2*b*tan(1/2*d*x + 1/2*c)^7 - b^3*tan(1/2*d*x + 1/2*c)^7 - 8*a^3*tan(1/2*d*x + 1/2*c)^6 + 24*a*b^2*tan(1/2*d*x + 1/2*c)^6 + 12*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 7*b^3*tan(1/2*d*x + 1/2*c)^5 - 24*a^3*tan(1/2*d*x + 1/2*c)^4 + 24*a*b^2*tan(1/2*d*x + 1/2*c)^4 - 12*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 7*b^3*tan(1/2*d*x + 1/2*c)^3 - 24*a^3*tan(1/2*d*x + 1/2*c)^2 + 8*a*b^2*tan(1/2*d*x + 1/2*c)^2 - 12*a^2*b*tan(1/2*d*x + 1/2*c) + b^3*tan(1/2*d*x + 1/2*c) - 8*a^3 + 8*a*b^2)/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","B",0
1072,1,199,0,0.236989," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{18 \, a^{2} b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} {\left(d x + c\right)} - \frac{3 \, {\left(6 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)} - \frac{2 \, {\left(9 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 6 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 36 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 18 \, a^{2} b + 2 \, b^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(18*a^2*b*log(abs(tan(1/2*d*x + 1/2*c))) + 3*a^3*tan(1/2*d*x + 1/2*c) - 3*(2*a^3 - 3*a*b^2)*(d*x + c) - 3*(6*a^2*b*tan(1/2*d*x + 1/2*c) + a^3)/tan(1/2*d*x + 1/2*c) - 2*(9*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 18*a^2*b*tan(1/2*d*x + 1/2*c)^4 + 6*b^3*tan(1/2*d*x + 1/2*c)^4 - 36*a^2*b*tan(1/2*d*x + 1/2*c)^2 - 9*a*b^2*tan(1/2*d*x + 1/2*c) - 18*a^2*b + 2*b^3)/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","B",0
1073,1,272,0,0.299094," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, {\left(6 \, a^{2} b - b^{3}\right)} {\left(d x + c\right)} - 4 \, {\left(a^{3} - 6 \, a b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + \frac{2 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 12 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 8 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 24 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 24 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{3}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}^{2}}}{8 \, d}"," ",0,"1/8*(a^3*tan(1/2*d*x + 1/2*c)^2 + 12*a^2*b*tan(1/2*d*x + 1/2*c) - 4*(6*a^2*b - b^3)*(d*x + c) - 4*(a^3 - 6*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c))) + (2*a^3*tan(1/2*d*x + 1/2*c)^6 - 12*a*b^2*tan(1/2*d*x + 1/2*c)^6 - 12*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 8*b^3*tan(1/2*d*x + 1/2*c)^5 + 3*a^3*tan(1/2*d*x + 1/2*c)^4 + 24*a*b^2*tan(1/2*d*x + 1/2*c)^4 - 24*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 8*b^3*tan(1/2*d*x + 1/2*c)^3 + 36*a*b^2*tan(1/2*d*x + 1/2*c)^2 - 12*a^2*b*tan(1/2*d*x + 1/2*c) - a^3)/(tan(1/2*d*x + 1/2*c)^3 + tan(1/2*d*x + 1/2*c))^2)/d","B",0
1074,1,222,0,0.249043," ","integrate(cos(d*x+c)^2*csc(d*x+c)^4*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 72 \, {\left(d x + c\right)} a b^{2} - 3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{48 \, b^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} - 12 \, {\left(3 \, a^{2} b - 2 \, b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + \frac{66 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 44 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 36 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{24 \, d}"," ",0,"1/24*(a^3*tan(1/2*d*x + 1/2*c)^3 + 9*a^2*b*tan(1/2*d*x + 1/2*c)^2 - 72*(d*x + c)*a*b^2 - 3*a^3*tan(1/2*d*x + 1/2*c) + 36*a*b^2*tan(1/2*d*x + 1/2*c) + 48*b^3/(tan(1/2*d*x + 1/2*c)^2 + 1) - 12*(3*a^2*b - 2*b^3)*log(abs(tan(1/2*d*x + 1/2*c))) + (66*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 44*b^3*tan(1/2*d*x + 1/2*c)^3 + 3*a^3*tan(1/2*d*x + 1/2*c)^2 - 36*a*b^2*tan(1/2*d*x + 1/2*c)^2 - 9*a^2*b*tan(1/2*d*x + 1/2*c) - a^3)/tan(1/2*d*x + 1/2*c)^3)/d","A",0
1075,1,234,0,0.263606," ","integrate(cos(d*x+c)^2*csc(d*x+c)^5*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 24 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 72 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 192 \, {\left(d x + c\right)} b^{3} - 72 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 96 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, {\left(a^{3} + 12 \, a b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + \frac{50 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 600 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 72 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 96 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 72 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 24 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}}}{192 \, d}"," ",0,"1/192*(3*a^3*tan(1/2*d*x + 1/2*c)^4 + 24*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 72*a*b^2*tan(1/2*d*x + 1/2*c)^2 - 192*(d*x + c)*b^3 - 72*a^2*b*tan(1/2*d*x + 1/2*c) + 96*b^3*tan(1/2*d*x + 1/2*c) - 24*(a^3 + 12*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c))) + (50*a^3*tan(1/2*d*x + 1/2*c)^4 + 600*a*b^2*tan(1/2*d*x + 1/2*c)^4 + 72*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 96*b^3*tan(1/2*d*x + 1/2*c)^3 - 72*a*b^2*tan(1/2*d*x + 1/2*c)^2 - 24*a^2*b*tan(1/2*d*x + 1/2*c) - 3*a^3)/tan(1/2*d*x + 1/2*c)^4)/d","A",0
1076,1,290,0,0.266032," ","integrate(cos(d*x+c)^2*csc(d*x+c)^6*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{6 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 45 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 10 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 60 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 360 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 120 \, {\left(3 \, a^{2} b + 4 \, b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + \frac{822 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1096 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 60 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 360 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 120 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 10 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 120 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 45 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{960 \, d}"," ",0,"1/960*(6*a^3*tan(1/2*d*x + 1/2*c)^5 + 45*a^2*b*tan(1/2*d*x + 1/2*c)^4 + 10*a^3*tan(1/2*d*x + 1/2*c)^3 + 120*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 120*b^3*tan(1/2*d*x + 1/2*c)^2 - 60*a^3*tan(1/2*d*x + 1/2*c) - 360*a*b^2*tan(1/2*d*x + 1/2*c) - 120*(3*a^2*b + 4*b^3)*log(abs(tan(1/2*d*x + 1/2*c))) + (822*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 1096*b^3*tan(1/2*d*x + 1/2*c)^5 + 60*a^3*tan(1/2*d*x + 1/2*c)^4 + 360*a*b^2*tan(1/2*d*x + 1/2*c)^4 - 120*b^3*tan(1/2*d*x + 1/2*c)^3 - 10*a^3*tan(1/2*d*x + 1/2*c)^2 - 120*a*b^2*tan(1/2*d*x + 1/2*c)^2 - 45*a^2*b*tan(1/2*d*x + 1/2*c) - 6*a^3)/tan(1/2*d*x + 1/2*c)^5)/d","A",0
1077,1,354,0,0.293829," ","integrate(cos(d*x+c)^2*csc(d*x+c)^7*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{5 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 36 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 90 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 60 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 80 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 360 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 240 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 120 \, {\left(a^{3} + 6 \, a b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + \frac{294 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 1764 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 360 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 240 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 60 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 80 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 90 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 36 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6}}}{1920 \, d}"," ",0,"1/1920*(5*a^3*tan(1/2*d*x + 1/2*c)^6 + 36*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 15*a^3*tan(1/2*d*x + 1/2*c)^4 + 90*a*b^2*tan(1/2*d*x + 1/2*c)^4 + 60*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 80*b^3*tan(1/2*d*x + 1/2*c)^3 - 15*a^3*tan(1/2*d*x + 1/2*c)^2 - 360*a^2*b*tan(1/2*d*x + 1/2*c) - 240*b^3*tan(1/2*d*x + 1/2*c) - 120*(a^3 + 6*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c))) + (294*a^3*tan(1/2*d*x + 1/2*c)^6 + 1764*a*b^2*tan(1/2*d*x + 1/2*c)^6 + 360*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 240*b^3*tan(1/2*d*x + 1/2*c)^5 + 15*a^3*tan(1/2*d*x + 1/2*c)^4 - 60*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 80*b^3*tan(1/2*d*x + 1/2*c)^3 - 15*a^3*tan(1/2*d*x + 1/2*c)^2 - 90*a*b^2*tan(1/2*d*x + 1/2*c)^2 - 36*a^2*b*tan(1/2*d*x + 1/2*c) - 5*a^3)/tan(1/2*d*x + 1/2*c)^6)/d","A",0
1078,1,261,0,0.196483," ","integrate(cos(d*x+c)^2*sin(d*x+c)^3/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(4 \, a^{3} - a b^{2}\right)} {\left(d x + c\right)}}{b^{5}} - \frac{6 \, {\left(4 \, a^{4} - 3 \, a^{2} b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{5}} + \frac{6 \, {\left(a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)} b^{4}} + \frac{2 \, {\left(3 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 3 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 18 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, a^{2} - b^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} b^{4}}}{3 \, d}"," ",0,"1/3*(3*(4*a^3 - a*b^2)*(d*x + c)/b^5 - 6*(4*a^4 - 3*a^2*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^5) + 6*(a^2*b*tan(1/2*d*x + 1/2*c) + a^3)/((a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)*b^4) + 2*(3*a*b*tan(1/2*d*x + 1/2*c)^5 + 9*a^2*tan(1/2*d*x + 1/2*c)^4 - 3*b^2*tan(1/2*d*x + 1/2*c)^4 + 18*a^2*tan(1/2*d*x + 1/2*c)^2 - 3*a*b*tan(1/2*d*x + 1/2*c) + 9*a^2 - b^2)/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*b^4))/d","A",0
1079,1,211,0,0.194736," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{{\left(6 \, a^{2} - b^{2}\right)} {\left(d x + c\right)}}{b^{4}} - \frac{4 \, {\left(3 \, a^{3} - 2 \, a b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{4}} + \frac{4 \, {\left(a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)} b^{3}} + \frac{2 \, {\left(b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, a\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} b^{3}}}{2 \, d}"," ",0,"-1/2*((6*a^2 - b^2)*(d*x + c)/b^4 - 4*(3*a^3 - 2*a*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^4) + 4*(a*b*tan(1/2*d*x + 1/2*c) + a^2)/((a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)*b^3) + 2*(b*tan(1/2*d*x + 1/2*c)^3 + 4*a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c) + 4*a)/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*b^3))/d","A",0
1080,1,191,0,0.192405," ","integrate(cos(d*x+c)^2*sin(d*x+c)/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{{\left(d x + c\right)} a}{b^{3}} - \frac{{\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} {\left(2 \, a^{2} - b^{2}\right)}}{\sqrt{a^{2} - b^{2}} b^{3}} + \frac{b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, a}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)} b^{2}}\right)}}{d}"," ",0,"2*((d*x + c)*a/b^3 - (pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))*(2*a^2 - b^2)/(sqrt(a^2 - b^2)*b^3) + (b*tan(1/2*d*x + 1/2*c)^3 + 2*a*tan(1/2*d*x + 1/2*c)^2 + 3*b*tan(1/2*d*x + 1/2*c) + 2*a)/((a*tan(1/2*d*x + 1/2*c)^4 + 2*b*tan(1/2*d*x + 1/2*c)^3 + 2*a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)*b^2))/d","A",0
1081,1,130,0,0.209943," ","integrate(cos(d*x+c)^2*csc(d*x+c)/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} b}{\sqrt{a^{2} - b^{2}} a^{2}} - \frac{\log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} - \frac{2 \, {\left(b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)} a^{2}}}{d}"," ",0,"-(2*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))*b/(sqrt(a^2 - b^2)*a^2) - log(abs(tan(1/2*d*x + 1/2*c)))/a^2 - 2*(b*tan(1/2*d*x + 1/2*c) + a)/((a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)*a^2))/d","A",0
1082,1,218,0,0.198663," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{12 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} - \frac{3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{2}} + \frac{12 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} {\left(a^{2} - 2 \, b^{2}\right)}}{\sqrt{a^{2} - b^{2}} a^{3}} - \frac{4 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 14 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a^{2}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} a^{3}}}{6 \, d}"," ",0,"-1/6*(12*b*log(abs(tan(1/2*d*x + 1/2*c)))/a^3 - 3*tan(1/2*d*x + 1/2*c)/a^2 + 12*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))*(a^2 - 2*b^2)/(sqrt(a^2 - b^2)*a^3) - (4*a*b*tan(1/2*d*x + 1/2*c)^3 - 3*a^2*tan(1/2*d*x + 1/2*c)^2 - 4*b^2*tan(1/2*d*x + 1/2*c)^2 - 14*a*b*tan(1/2*d*x + 1/2*c) - 3*a^2)/((a*tan(1/2*d*x + 1/2*c)^3 + 2*b*tan(1/2*d*x + 1/2*c)^2 + a*tan(1/2*d*x + 1/2*c))*a^3))/d","A",0
1083,1,257,0,0.214813," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{4 \, {\left(a^{2} - 6 \, b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{4}} - \frac{16 \, {\left(2 \, a^{2} b - 3 \, b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{4}} - \frac{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{4}} - \frac{16 \, {\left(b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a b^{2}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)} a^{4}} - \frac{6 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 36 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 8 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{2}}{a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}}{8 \, d}"," ",0,"-1/8*(4*(a^2 - 6*b^2)*log(abs(tan(1/2*d*x + 1/2*c)))/a^4 - 16*(2*a^2*b - 3*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^4) - (a^2*tan(1/2*d*x + 1/2*c)^2 - 8*a*b*tan(1/2*d*x + 1/2*c))/a^4 - 16*(b^3*tan(1/2*d*x + 1/2*c) + a*b^2)/((a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)*a^4) - (6*a^2*tan(1/2*d*x + 1/2*c)^2 - 36*b^2*tan(1/2*d*x + 1/2*c)^2 + 8*a*b*tan(1/2*d*x + 1/2*c) - a^2)/(a^4*tan(1/2*d*x + 1/2*c)^2))/d","A",0
1084,1,329,0,0.223970," ","integrate(cos(d*x+c)^2*csc(d*x+c)^4/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{24 \, {\left(a^{2} b - 4 \, b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{5}} - \frac{48 \, {\left(3 \, a^{2} b^{2} - 4 \, b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{5}} + \frac{a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}} - \frac{48 \, {\left(b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a b^{3}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)} a^{5}} - \frac{44 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 176 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 36 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 6 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3}}{a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{24 \, d}"," ",0,"1/24*(24*(a^2*b - 4*b^3)*log(abs(tan(1/2*d*x + 1/2*c)))/a^5 - 48*(3*a^2*b^2 - 4*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^5) + (a^4*tan(1/2*d*x + 1/2*c)^3 - 6*a^3*b*tan(1/2*d*x + 1/2*c)^2 - 3*a^4*tan(1/2*d*x + 1/2*c) + 36*a^2*b^2*tan(1/2*d*x + 1/2*c))/a^6 - 48*(b^4*tan(1/2*d*x + 1/2*c) + a*b^3)/((a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)*a^5) - (44*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 176*b^3*tan(1/2*d*x + 1/2*c)^3 - 3*a^3*tan(1/2*d*x + 1/2*c)^2 + 36*a*b^2*tan(1/2*d*x + 1/2*c)^2 - 6*a^2*b*tan(1/2*d*x + 1/2*c) + a^3)/(a^5*tan(1/2*d*x + 1/2*c)^3))/d","A",0
1085,1,535,0,0.242999," ","integrate(cos(d*x+c)^2*sin(d*x+c)^3/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(12 \, a^{5} - 19 \, a^{3} b^{2} + 6 \, a b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{2} b^{5} - b^{7}\right)} \sqrt{a^{2} - b^{2}}} - \frac{2 \, {\left(6 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 5 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 5 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 14 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 54 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 45 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 15 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 44 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 90 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 87 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 30 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 42 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 39 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, a^{5} - 11 \, a^{3} b^{2}\right)}}{{\left(a^{2} b^{4} - b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}^{2}} - \frac{{\left(12 \, a^{2} - b^{2}\right)} {\left(d x + c\right)}}{b^{5}}}{2 \, d}"," ",0,"1/2*(2*(12*a^5 - 19*a^3*b^2 + 6*a*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/((a^2*b^5 - b^7)*sqrt(a^2 - b^2)) - 2*(6*a^4*b*tan(1/2*d*x + 1/2*c)^7 - 5*a^2*b^3*tan(1/2*d*x + 1/2*c)^7 + 12*a^5*tan(1/2*d*x + 1/2*c)^6 + 5*a^3*b^2*tan(1/2*d*x + 1/2*c)^6 - 14*a*b^4*tan(1/2*d*x + 1/2*c)^6 + 54*a^4*b*tan(1/2*d*x + 1/2*c)^5 - 45*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 - 4*b^5*tan(1/2*d*x + 1/2*c)^5 + 36*a^5*tan(1/2*d*x + 1/2*c)^4 + 15*a^3*b^2*tan(1/2*d*x + 1/2*c)^4 - 44*a*b^4*tan(1/2*d*x + 1/2*c)^4 + 90*a^4*b*tan(1/2*d*x + 1/2*c)^3 - 87*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + 4*b^5*tan(1/2*d*x + 1/2*c)^3 + 36*a^5*tan(1/2*d*x + 1/2*c)^2 - a^3*b^2*tan(1/2*d*x + 1/2*c)^2 - 30*a*b^4*tan(1/2*d*x + 1/2*c)^2 + 42*a^4*b*tan(1/2*d*x + 1/2*c) - 39*a^2*b^3*tan(1/2*d*x + 1/2*c) + 12*a^5 - 11*a^3*b^2)/((a^2*b^4 - b^6)*(a*tan(1/2*d*x + 1/2*c)^4 + 2*b*tan(1/2*d*x + 1/2*c)^3 + 2*a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)^2) - (12*a^2 - b^2)*(d*x + c)/b^5)/d","B",0
1086,1,302,0,0.219895," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{{\left(6 \, a^{4} - 9 \, a^{2} b^{2} + 2 \, b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{2} b^{4} - b^{6}\right)} \sqrt{a^{2} - b^{2}}} - \frac{3 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 5 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 6 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 13 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 10 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, a^{4} - 3 \, a^{2} b^{2}}{{\left(a^{2} b^{3} - b^{5}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}^{2}} - \frac{3 \, {\left(d x + c\right)} a}{b^{4}} - \frac{2}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} b^{3}}}{d}"," ",0,"-((6*a^4 - 9*a^2*b^2 + 2*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/((a^2*b^4 - b^6)*sqrt(a^2 - b^2)) - (3*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 2*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 4*a^4*tan(1/2*d*x + 1/2*c)^2 + 5*a^2*b^2*tan(1/2*d*x + 1/2*c)^2 - 6*b^4*tan(1/2*d*x + 1/2*c)^2 + 13*a^3*b*tan(1/2*d*x + 1/2*c) - 10*a*b^3*tan(1/2*d*x + 1/2*c) + 4*a^4 - 3*a^2*b^2)/((a^2*b^3 - b^5)*(a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)^2) - 3*(d*x + c)*a/b^4 - 2/((tan(1/2*d*x + 1/2*c)^2 + 1)*b^3))/d","A",0
1087,1,256,0,0.230590," ","integrate(cos(d*x+c)^2*sin(d*x+c)/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{{\left(2 \, a^{3} - 3 \, a b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{2} b^{3} - b^{5}\right)} \sqrt{a^{2} - b^{2}}} - \frac{a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 7 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, a^{4} - a^{2} b^{2}}{{\left(a^{3} b^{2} - a b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}^{2}} - \frac{d x + c}{b^{3}}}{d}"," ",0,"((2*a^3 - 3*a*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/((a^2*b^3 - b^5)*sqrt(a^2 - b^2)) - (a^3*b*tan(1/2*d*x + 1/2*c)^3 + 2*a^4*tan(1/2*d*x + 1/2*c)^2 + 3*a^2*b^2*tan(1/2*d*x + 1/2*c)^2 - 2*b^4*tan(1/2*d*x + 1/2*c)^2 + 7*a^3*b*tan(1/2*d*x + 1/2*c) - 4*a*b^3*tan(1/2*d*x + 1/2*c) + 2*a^4 - a^2*b^2)/((a^3*b^2 - a*b^4)*(a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)^2) - (d*x + c)/b^3)/d","A",0
1088,1,277,0,0.256539," ","integrate(cos(d*x+c)^2*csc(d*x+c)/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{{\left(3 \, a^{2} b - 2 \, b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{5} - a^{3} b^{2}\right)} \sqrt{a^{2} - b^{2}}} - \frac{3 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 6 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 5 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, a^{4} - 3 \, a^{2} b^{2}}{{\left(a^{5} - a^{3} b^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}^{2}} - \frac{\log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}}}{d}"," ",0,"-((3*a^2*b - 2*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/((a^5 - a^3*b^2)*sqrt(a^2 - b^2)) - (3*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 4*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 2*a^4*tan(1/2*d*x + 1/2*c)^2 + a^2*b^2*tan(1/2*d*x + 1/2*c)^2 - 6*b^4*tan(1/2*d*x + 1/2*c)^2 + 5*a^3*b*tan(1/2*d*x + 1/2*c) - 8*a*b^3*tan(1/2*d*x + 1/2*c) + 2*a^4 - 3*a^2*b^2)/((a^5 - a^3*b^2)*(a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)^2) - log(abs(tan(1/2*d*x + 1/2*c)))/a^3)/d","A",0
1089,1,339,0,0.269828," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(2 \, a^{4} - 9 \, a^{2} b^{2} + 6 \, b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{6} - a^{4} b^{2}\right)} \sqrt{a^{2} - b^{2}}} + \frac{2 \, {\left(5 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 10 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 11 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 14 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, a^{4} b - 5 \, a^{2} b^{3}\right)}}{{\left(a^{6} - a^{4} b^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}^{2}} + \frac{6 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{4}} - \frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3}} - \frac{6 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a}{a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}}{2 \, d}"," ",0,"-1/2*(2*(2*a^4 - 9*a^2*b^2 + 6*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/((a^6 - a^4*b^2)*sqrt(a^2 - b^2)) + 2*(5*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 6*a*b^4*tan(1/2*d*x + 1/2*c)^3 + 4*a^4*b*tan(1/2*d*x + 1/2*c)^2 + 3*a^2*b^3*tan(1/2*d*x + 1/2*c)^2 - 10*b^5*tan(1/2*d*x + 1/2*c)^2 + 11*a^3*b^2*tan(1/2*d*x + 1/2*c) - 14*a*b^4*tan(1/2*d*x + 1/2*c) + 4*a^4*b - 5*a^2*b^3)/((a^6 - a^4*b^2)*(a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)^2) + 6*b*log(abs(tan(1/2*d*x + 1/2*c)))/a^4 - tan(1/2*d*x + 1/2*c)/a^3 - (6*b*tan(1/2*d*x + 1/2*c) - a)/(a^4*tan(1/2*d*x + 1/2*c)))/d","A",0
1090,1,526,0,0.284803," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{8 \, {\left(6 \, a^{4} b - 19 \, a^{2} b^{3} + 12 \, b^{5}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{7} - a^{5} b^{2}\right)} \sqrt{a^{2} - b^{2}}} + \frac{2 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 26 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 24 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 20 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 60 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 32 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 53 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 64 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 16 \, b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 28 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 60 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 112 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 68 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 76 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 8 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{6} + a^{4} b^{2}}{{\left(a^{7} - a^{5} b^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}^{2}} - \frac{4 \, {\left(a^{2} - 12 \, b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{5}} + \frac{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{8 \, d}"," ",0,"1/8*(8*(6*a^4*b - 19*a^2*b^3 + 12*b^5)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/((a^7 - a^5*b^2)*sqrt(a^2 - b^2)) + (2*a^6*tan(1/2*d*x + 1/2*c)^6 - 26*a^4*b^2*tan(1/2*d*x + 1/2*c)^6 + 24*a^2*b^4*tan(1/2*d*x + 1/2*c)^6 + 20*a^5*b*tan(1/2*d*x + 1/2*c)^5 - 60*a^3*b^3*tan(1/2*d*x + 1/2*c)^5 + 32*a*b^5*tan(1/2*d*x + 1/2*c)^5 + 3*a^6*tan(1/2*d*x + 1/2*c)^4 + 53*a^4*b^2*tan(1/2*d*x + 1/2*c)^4 - 64*a^2*b^4*tan(1/2*d*x + 1/2*c)^4 - 16*b^6*tan(1/2*d*x + 1/2*c)^4 + 28*a^5*b*tan(1/2*d*x + 1/2*c)^3 + 60*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 - 112*a*b^5*tan(1/2*d*x + 1/2*c)^3 + 68*a^4*b^2*tan(1/2*d*x + 1/2*c)^2 - 76*a^2*b^4*tan(1/2*d*x + 1/2*c)^2 + 8*a^5*b*tan(1/2*d*x + 1/2*c) - 8*a^3*b^3*tan(1/2*d*x + 1/2*c) - a^6 + a^4*b^2)/((a^7 - a^5*b^2)*(a*tan(1/2*d*x + 1/2*c)^3 + 2*b*tan(1/2*d*x + 1/2*c)^2 + a*tan(1/2*d*x + 1/2*c))^2) - 4*(a^2 - 12*b^2)*log(abs(tan(1/2*d*x + 1/2*c)))/a^5 + (a^3*tan(1/2*d*x + 1/2*c)^2 - 12*a^2*b*tan(1/2*d*x + 1/2*c))/a^6)/d","B",0
1091,0,0,0,0.000000," ","integrate(cos(f*x+e)^2/(a+b*sin(f*x+e))^(5/2)/(d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\cos\left(f x + e\right)^{2}}{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} \sqrt{d \sin\left(f x + e\right)}}\,{d x}"," ",0,"integrate(cos(f*x + e)^2/((b*sin(f*x + e) + a)^(5/2)*sqrt(d*sin(f*x + e))), x)","F",0
1092,1,107,0,0.298620," ","integrate(cos(d*x+c)^4*sin(d*x+c)^4*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{3}{128} \, a x - \frac{b \cos\left(9 \, d x + 9 \, c\right)}{2304 \, d} + \frac{b \cos\left(7 \, d x + 7 \, c\right)}{1792 \, d} + \frac{b \cos\left(5 \, d x + 5 \, c\right)}{320 \, d} - \frac{b \cos\left(3 \, d x + 3 \, c\right)}{192 \, d} - \frac{3 \, b \cos\left(d x + c\right)}{128 \, d} + \frac{a \sin\left(8 \, d x + 8 \, c\right)}{1024 \, d} - \frac{a \sin\left(4 \, d x + 4 \, c\right)}{128 \, d}"," ",0,"3/128*a*x - 1/2304*b*cos(9*d*x + 9*c)/d + 1/1792*b*cos(7*d*x + 7*c)/d + 1/320*b*cos(5*d*x + 5*c)/d - 1/192*b*cos(3*d*x + 3*c)/d - 3/128*b*cos(d*x + c)/d + 1/1024*a*sin(8*d*x + 8*c)/d - 1/128*a*sin(4*d*x + 4*c)/d","A",0
1093,1,92,0,0.224477," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{3}{128} \, b x + \frac{a \cos\left(7 \, d x + 7 \, c\right)}{448 \, d} + \frac{a \cos\left(5 \, d x + 5 \, c\right)}{320 \, d} - \frac{a \cos\left(3 \, d x + 3 \, c\right)}{64 \, d} - \frac{3 \, a \cos\left(d x + c\right)}{64 \, d} + \frac{b \sin\left(8 \, d x + 8 \, c\right)}{1024 \, d} - \frac{b \sin\left(4 \, d x + 4 \, c\right)}{128 \, d}"," ",0,"3/128*b*x + 1/448*a*cos(7*d*x + 7*c)/d + 1/320*a*cos(5*d*x + 5*c)/d - 1/64*a*cos(3*d*x + 3*c)/d - 3/64*a*cos(d*x + c)/d + 1/1024*b*sin(8*d*x + 8*c)/d - 1/128*b*sin(4*d*x + 4*c)/d","A",0
1094,1,107,0,0.200084," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{1}{16} \, a x + \frac{b \cos\left(7 \, d x + 7 \, c\right)}{448 \, d} + \frac{b \cos\left(5 \, d x + 5 \, c\right)}{320 \, d} - \frac{b \cos\left(3 \, d x + 3 \, c\right)}{64 \, d} - \frac{3 \, b \cos\left(d x + c\right)}{64 \, d} - \frac{a \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} - \frac{a \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{a \sin\left(2 \, d x + 2 \, c\right)}{64 \, d}"," ",0,"1/16*a*x + 1/448*b*cos(7*d*x + 7*c)/d + 1/320*b*cos(5*d*x + 5*c)/d - 1/64*b*cos(3*d*x + 3*c)/d - 3/64*b*cos(d*x + c)/d - 1/192*a*sin(6*d*x + 6*c)/d - 1/64*a*sin(4*d*x + 4*c)/d + 1/64*a*sin(2*d*x + 2*c)/d","A",0
1095,1,92,0,0.173539," ","integrate(cos(d*x+c)^4*sin(d*x+c)*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{1}{16} \, b x - \frac{a \cos\left(5 \, d x + 5 \, c\right)}{80 \, d} - \frac{a \cos\left(3 \, d x + 3 \, c\right)}{16 \, d} - \frac{a \cos\left(d x + c\right)}{8 \, d} - \frac{b \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} - \frac{b \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{b \sin\left(2 \, d x + 2 \, c\right)}{64 \, d}"," ",0,"1/16*b*x - 1/80*a*cos(5*d*x + 5*c)/d - 1/16*a*cos(3*d*x + 3*c)/d - 1/8*a*cos(d*x + c)/d - 1/192*b*sin(6*d*x + 6*c)/d - 1/64*b*sin(4*d*x + 4*c)/d + 1/64*b*sin(2*d*x + 2*c)/d","A",0
1096,1,145,0,0.170225," ","integrate(cos(d*x+c)^4*csc(d*x+c)*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{9 \, {\left(d x + c\right)} b + 24 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{2 \, {\left(15 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 48 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 9 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 96 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 9 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 80 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 32 \, a\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(9*(d*x + c)*b + 24*a*log(abs(tan(1/2*d*x + 1/2*c))) - 2*(15*b*tan(1/2*d*x + 1/2*c)^7 - 48*a*tan(1/2*d*x + 1/2*c)^6 - 9*b*tan(1/2*d*x + 1/2*c)^5 - 96*a*tan(1/2*d*x + 1/2*c)^4 + 9*b*tan(1/2*d*x + 1/2*c)^3 - 80*a*tan(1/2*d*x + 1/2*c)^2 - 15*b*tan(1/2*d*x + 1/2*c) - 32*a)/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","A",0
1097,1,142,0,0.209462," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2*(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{9 \, {\left(d x + c\right)} a - 6 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{3 \, {\left(2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)} - \frac{2 \, {\left(3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 12 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8 \, b\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"-1/6*(9*(d*x + c)*a - 6*b*log(abs(tan(1/2*d*x + 1/2*c))) - 3*a*tan(1/2*d*x + 1/2*c) + 3*(2*b*tan(1/2*d*x + 1/2*c) + a)/tan(1/2*d*x + 1/2*c) - 2*(3*a*tan(1/2*d*x + 1/2*c)^5 + 12*b*tan(1/2*d*x + 1/2*c)^4 + 12*b*tan(1/2*d*x + 1/2*c)^2 - 3*a*tan(1/2*d*x + 1/2*c) + 8*b)/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
1098,1,163,0,0.193156," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, {\left(d x + c\right)} b - 12 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 4 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{6 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 4 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 5 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 16 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}^{2}}}{8 \, d}"," ",0,"1/8*(a*tan(1/2*d*x + 1/2*c)^2 - 12*(d*x + c)*b - 12*a*log(abs(tan(1/2*d*x + 1/2*c))) + 4*b*tan(1/2*d*x + 1/2*c) + (6*a*tan(1/2*d*x + 1/2*c)^6 + 4*b*tan(1/2*d*x + 1/2*c)^5 - 5*a*tan(1/2*d*x + 1/2*c)^4 - 16*b*tan(1/2*d*x + 1/2*c)^3 - 12*a*tan(1/2*d*x + 1/2*c)^2 - 4*b*tan(1/2*d*x + 1/2*c) - a)/(tan(1/2*d*x + 1/2*c)^3 + tan(1/2*d*x + 1/2*c))^2)/d","A",0
1099,1,141,0,0.195008," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 \, {\left(d x + c\right)} a - 36 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 15 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{48 \, b}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + \frac{66 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{24 \, d}"," ",0,"1/24*(a*tan(1/2*d*x + 1/2*c)^3 + 3*b*tan(1/2*d*x + 1/2*c)^2 + 24*(d*x + c)*a - 36*b*log(abs(tan(1/2*d*x + 1/2*c))) - 15*a*tan(1/2*d*x + 1/2*c) - 48*b/(tan(1/2*d*x + 1/2*c)^2 + 1) + (66*b*tan(1/2*d*x + 1/2*c)^3 + 15*a*tan(1/2*d*x + 1/2*c)^2 - 3*b*tan(1/2*d*x + 1/2*c) - a)/tan(1/2*d*x + 1/2*c)^3)/d","A",0
1100,1,153,0,0.209252," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 8 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 192 \, {\left(d x + c\right)} b + 72 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 120 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{150 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 120 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 8 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}}}{192 \, d}"," ",0,"1/192*(3*a*tan(1/2*d*x + 1/2*c)^4 + 8*b*tan(1/2*d*x + 1/2*c)^3 - 24*a*tan(1/2*d*x + 1/2*c)^2 + 192*(d*x + c)*b + 72*a*log(abs(tan(1/2*d*x + 1/2*c))) - 120*b*tan(1/2*d*x + 1/2*c) - (150*a*tan(1/2*d*x + 1/2*c)^4 - 120*b*tan(1/2*d*x + 1/2*c)^3 - 24*a*tan(1/2*d*x + 1/2*c)^2 + 8*b*tan(1/2*d*x + 1/2*c) + 3*a)/tan(1/2*d*x + 1/2*c)^4)/d","A",0
1101,1,173,0,0.224975," ","integrate(cos(d*x+c)^4*csc(d*x+c)^6*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 5 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 10 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 120 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 20 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{274 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 20 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 40 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 10 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 5 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{320 \, d}"," ",0,"1/320*(2*a*tan(1/2*d*x + 1/2*c)^5 + 5*b*tan(1/2*d*x + 1/2*c)^4 - 10*a*tan(1/2*d*x + 1/2*c)^3 - 40*b*tan(1/2*d*x + 1/2*c)^2 + 120*b*log(abs(tan(1/2*d*x + 1/2*c))) + 20*a*tan(1/2*d*x + 1/2*c) - (274*b*tan(1/2*d*x + 1/2*c)^5 + 20*a*tan(1/2*d*x + 1/2*c)^4 - 40*b*tan(1/2*d*x + 1/2*c)^3 - 10*a*tan(1/2*d*x + 1/2*c)^2 + 5*b*tan(1/2*d*x + 1/2*c) + 2*a)/tan(1/2*d*x + 1/2*c)^5)/d","B",0
1102,1,201,0,0.242155," ","integrate(cos(d*x+c)^4*csc(d*x+c)^7*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{5 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 12 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 60 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 120 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 120 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{294 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 120 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 60 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6}}}{1920 \, d}"," ",0,"1/1920*(5*a*tan(1/2*d*x + 1/2*c)^6 + 12*b*tan(1/2*d*x + 1/2*c)^5 - 15*a*tan(1/2*d*x + 1/2*c)^4 - 60*b*tan(1/2*d*x + 1/2*c)^3 - 15*a*tan(1/2*d*x + 1/2*c)^2 + 120*a*log(abs(tan(1/2*d*x + 1/2*c))) + 120*b*tan(1/2*d*x + 1/2*c) - (294*a*tan(1/2*d*x + 1/2*c)^6 + 120*b*tan(1/2*d*x + 1/2*c)^5 - 15*a*tan(1/2*d*x + 1/2*c)^4 - 60*b*tan(1/2*d*x + 1/2*c)^3 - 15*a*tan(1/2*d*x + 1/2*c)^2 + 12*b*tan(1/2*d*x + 1/2*c) + 5*a)/tan(1/2*d*x + 1/2*c)^6)/d","B",0
1103,1,229,0,0.229606," ","integrate(cos(d*x+c)^4*csc(d*x+c)^8*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{15 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 35 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 21 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 105 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 105 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 105 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 840 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 315 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{2178 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 315 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 105 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 105 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 105 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 21 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 35 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7}}}{13440 \, d}"," ",0,"1/13440*(15*a*tan(1/2*d*x + 1/2*c)^7 + 35*b*tan(1/2*d*x + 1/2*c)^6 - 21*a*tan(1/2*d*x + 1/2*c)^5 - 105*b*tan(1/2*d*x + 1/2*c)^4 - 105*a*tan(1/2*d*x + 1/2*c)^3 - 105*b*tan(1/2*d*x + 1/2*c)^2 + 840*b*log(abs(tan(1/2*d*x + 1/2*c))) + 315*a*tan(1/2*d*x + 1/2*c) - (2178*b*tan(1/2*d*x + 1/2*c)^7 + 315*a*tan(1/2*d*x + 1/2*c)^6 - 105*b*tan(1/2*d*x + 1/2*c)^5 - 105*a*tan(1/2*d*x + 1/2*c)^4 - 105*b*tan(1/2*d*x + 1/2*c)^3 - 21*a*tan(1/2*d*x + 1/2*c)^2 + 35*b*tan(1/2*d*x + 1/2*c) + 15*a)/tan(1/2*d*x + 1/2*c)^7)/d","B",0
1104,1,201,0,0.256888," ","integrate(cos(d*x+c)^4*csc(d*x+c)^9*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{35 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 80 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 112 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 280 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 560 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1680 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 1680 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{4566 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 1680 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 560 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 280 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 112 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 80 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 35 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8}}}{71680 \, d}"," ",0,"1/71680*(35*a*tan(1/2*d*x + 1/2*c)^8 + 80*b*tan(1/2*d*x + 1/2*c)^7 - 112*b*tan(1/2*d*x + 1/2*c)^5 - 280*a*tan(1/2*d*x + 1/2*c)^4 - 560*b*tan(1/2*d*x + 1/2*c)^3 + 1680*a*log(abs(tan(1/2*d*x + 1/2*c))) + 1680*b*tan(1/2*d*x + 1/2*c) - (4566*a*tan(1/2*d*x + 1/2*c)^8 + 1680*b*tan(1/2*d*x + 1/2*c)^7 - 560*b*tan(1/2*d*x + 1/2*c)^5 - 280*a*tan(1/2*d*x + 1/2*c)^4 - 112*b*tan(1/2*d*x + 1/2*c)^3 + 80*b*tan(1/2*d*x + 1/2*c) + 35*a)/tan(1/2*d*x + 1/2*c)^8)/d","A",0
1105,1,142,0,0.371794," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{3}{64} \, a b x - \frac{b^{2} \cos\left(9 \, d x + 9 \, c\right)}{2304 \, d} + \frac{a b \sin\left(8 \, d x + 8 \, c\right)}{512 \, d} - \frac{a b \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{{\left(4 \, a^{2} + b^{2}\right)} \cos\left(7 \, d x + 7 \, c\right)}{1792 \, d} + \frac{{\left(a^{2} + b^{2}\right)} \cos\left(5 \, d x + 5 \, c\right)}{320 \, d} - \frac{{\left(3 \, a^{2} + b^{2}\right)} \cos\left(3 \, d x + 3 \, c\right)}{192 \, d} - \frac{3 \, {\left(2 \, a^{2} + b^{2}\right)} \cos\left(d x + c\right)}{128 \, d}"," ",0,"3/64*a*b*x - 1/2304*b^2*cos(9*d*x + 9*c)/d + 1/512*a*b*sin(8*d*x + 8*c)/d - 1/64*a*b*sin(4*d*x + 4*c)/d + 1/1792*(4*a^2 + b^2)*cos(7*d*x + 7*c)/d + 1/320*(a^2 + b^2)*cos(5*d*x + 5*c)/d - 1/192*(3*a^2 + b^2)*cos(3*d*x + 3*c)/d - 3/128*(2*a^2 + b^2)*cos(d*x + c)/d","A",0
1106,1,150,0,0.314368," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{1}{128} \, {\left(8 \, a^{2} + 3 \, b^{2}\right)} x + \frac{a b \cos\left(7 \, d x + 7 \, c\right)}{224 \, d} + \frac{a b \cos\left(5 \, d x + 5 \, c\right)}{160 \, d} - \frac{a b \cos\left(3 \, d x + 3 \, c\right)}{32 \, d} - \frac{3 \, a b \cos\left(d x + c\right)}{32 \, d} + \frac{b^{2} \sin\left(8 \, d x + 8 \, c\right)}{1024 \, d} - \frac{a^{2} \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} + \frac{a^{2} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d} - \frac{{\left(2 \, a^{2} + b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)}{128 \, d}"," ",0,"1/128*(8*a^2 + 3*b^2)*x + 1/224*a*b*cos(7*d*x + 7*c)/d + 1/160*a*b*cos(5*d*x + 5*c)/d - 1/32*a*b*cos(3*d*x + 3*c)/d - 3/32*a*b*cos(d*x + c)/d + 1/1024*b^2*sin(8*d*x + 8*c)/d - 1/192*a^2*sin(6*d*x + 6*c)/d + 1/64*a^2*sin(2*d*x + 2*c)/d - 1/128*(2*a^2 + b^2)*sin(4*d*x + 4*c)/d","A",0
1107,1,141,0,0.216284," ","integrate(cos(d*x+c)^4*sin(d*x+c)*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{1}{8} \, a b x + \frac{b^{2} \cos\left(7 \, d x + 7 \, c\right)}{448 \, d} - \frac{a b \sin\left(6 \, d x + 6 \, c\right)}{96 \, d} - \frac{a b \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{a b \sin\left(2 \, d x + 2 \, c\right)}{32 \, d} - \frac{{\left(4 \, a^{2} - b^{2}\right)} \cos\left(5 \, d x + 5 \, c\right)}{320 \, d} - \frac{{\left(4 \, a^{2} + b^{2}\right)} \cos\left(3 \, d x + 3 \, c\right)}{64 \, d} - \frac{{\left(8 \, a^{2} + 3 \, b^{2}\right)} \cos\left(d x + c\right)}{64 \, d}"," ",0,"1/8*a*b*x + 1/448*b^2*cos(7*d*x + 7*c)/d - 1/96*a*b*sin(6*d*x + 6*c)/d - 1/32*a*b*sin(4*d*x + 4*c)/d + 1/32*a*b*sin(2*d*x + 2*c)/d - 1/320*(4*a^2 - b^2)*cos(5*d*x + 5*c)/d - 1/64*(4*a^2 + b^2)*cos(3*d*x + 3*c)/d - 1/64*(8*a^2 + 3*b^2)*cos(d*x + c)/d","A",0
1108,1,213,0,0.212028," ","integrate(cos(d*x+c)^4*csc(d*x+c)*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{45 \, {\left(d x + c\right)} a b + 60 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{2 \, {\left(75 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 120 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 60 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 30 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 360 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 440 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 120 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 30 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 280 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 75 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 80 \, a^{2} + 12 \, b^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5}}}{60 \, d}"," ",0,"1/60*(45*(d*x + c)*a*b + 60*a^2*log(abs(tan(1/2*d*x + 1/2*c))) - 2*(75*a*b*tan(1/2*d*x + 1/2*c)^9 - 120*a^2*tan(1/2*d*x + 1/2*c)^8 + 60*b^2*tan(1/2*d*x + 1/2*c)^8 + 30*a*b*tan(1/2*d*x + 1/2*c)^7 - 360*a^2*tan(1/2*d*x + 1/2*c)^6 - 440*a^2*tan(1/2*d*x + 1/2*c)^4 + 120*b^2*tan(1/2*d*x + 1/2*c)^4 - 30*a*b*tan(1/2*d*x + 1/2*c)^3 - 280*a^2*tan(1/2*d*x + 1/2*c)^2 - 75*a*b*tan(1/2*d*x + 1/2*c) - 80*a^2 + 12*b^2)/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","B",0
1109,1,274,0,0.221702," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{48 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 12 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, {\left(4 \, a^{2} - b^{2}\right)} {\left(d x + c\right)} - \frac{12 \, {\left(4 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)} + \frac{2 \, {\left(12 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 96 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 12 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 192 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 12 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 160 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 64 \, a b\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(48*a*b*log(abs(tan(1/2*d*x + 1/2*c))) + 12*a^2*tan(1/2*d*x + 1/2*c) - 9*(4*a^2 - b^2)*(d*x + c) - 12*(4*a*b*tan(1/2*d*x + 1/2*c) + a^2)/tan(1/2*d*x + 1/2*c) + 2*(12*a^2*tan(1/2*d*x + 1/2*c)^7 - 15*b^2*tan(1/2*d*x + 1/2*c)^7 + 96*a*b*tan(1/2*d*x + 1/2*c)^6 + 12*a^2*tan(1/2*d*x + 1/2*c)^5 + 9*b^2*tan(1/2*d*x + 1/2*c)^5 + 192*a*b*tan(1/2*d*x + 1/2*c)^4 - 12*a^2*tan(1/2*d*x + 1/2*c)^3 - 9*b^2*tan(1/2*d*x + 1/2*c)^3 + 160*a*b*tan(1/2*d*x + 1/2*c)^2 - 12*a^2*tan(1/2*d*x + 1/2*c) + 15*b^2*tan(1/2*d*x + 1/2*c) + 64*a*b)/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","A",0
1110,1,252,0,0.236273," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 72 \, {\left(d x + c\right)} a b + 24 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, {\left(3 \, a^{2} - 2 \, b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + \frac{3 \, {\left(18 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{2}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}} + \frac{16 \, {\left(3 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 6 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 6 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 6 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a^{2} + 4 \, b^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{24 \, d}"," ",0,"1/24*(3*a^2*tan(1/2*d*x + 1/2*c)^2 - 72*(d*x + c)*a*b + 24*a*b*tan(1/2*d*x + 1/2*c) - 12*(3*a^2 - 2*b^2)*log(abs(tan(1/2*d*x + 1/2*c))) + 3*(18*a^2*tan(1/2*d*x + 1/2*c)^2 - 12*b^2*tan(1/2*d*x + 1/2*c)^2 - 8*a*b*tan(1/2*d*x + 1/2*c) - a^2)/tan(1/2*d*x + 1/2*c)^2 + 16*(3*a*b*tan(1/2*d*x + 1/2*c)^5 - 3*a^2*tan(1/2*d*x + 1/2*c)^4 + 6*b^2*tan(1/2*d*x + 1/2*c)^4 - 6*a^2*tan(1/2*d*x + 1/2*c)^2 + 6*b^2*tan(1/2*d*x + 1/2*c)^2 - 3*a*b*tan(1/2*d*x + 1/2*c) - 3*a^2 + 4*b^2)/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
1111,1,241,0,0.259284," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 72 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, {\left(2 \, a^{2} - 3 \, b^{2}\right)} {\left(d x + c\right)} + \frac{24 \, {\left(b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, a b\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}} + \frac{132 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 6 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{24 \, d}"," ",0,"1/24*(a^2*tan(1/2*d*x + 1/2*c)^3 + 6*a*b*tan(1/2*d*x + 1/2*c)^2 - 72*a*b*log(abs(tan(1/2*d*x + 1/2*c))) - 15*a^2*tan(1/2*d*x + 1/2*c) + 12*b^2*tan(1/2*d*x + 1/2*c) + 12*(2*a^2 - 3*b^2)*(d*x + c) + 24*(b^2*tan(1/2*d*x + 1/2*c)^3 - 4*a*b*tan(1/2*d*x + 1/2*c)^2 - b^2*tan(1/2*d*x + 1/2*c) - 4*a*b)/(tan(1/2*d*x + 1/2*c)^2 + 1)^2 + (132*a*b*tan(1/2*d*x + 1/2*c)^3 + 15*a^2*tan(1/2*d*x + 1/2*c)^2 - 12*b^2*tan(1/2*d*x + 1/2*c)^2 - 6*a*b*tan(1/2*d*x + 1/2*c) - a^2)/tan(1/2*d*x + 1/2*c)^3)/d","A",0
1112,1,244,0,0.280814," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 16 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 384 \, {\left(d x + c\right)} a b - 240 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 72 \, {\left(a^{2} - 4 \, b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{384 \, b^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} - \frac{150 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 600 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 240 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 16 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}}}{192 \, d}"," ",0,"1/192*(3*a^2*tan(1/2*d*x + 1/2*c)^4 + 16*a*b*tan(1/2*d*x + 1/2*c)^3 - 24*a^2*tan(1/2*d*x + 1/2*c)^2 + 24*b^2*tan(1/2*d*x + 1/2*c)^2 + 384*(d*x + c)*a*b - 240*a*b*tan(1/2*d*x + 1/2*c) + 72*(a^2 - 4*b^2)*log(abs(tan(1/2*d*x + 1/2*c))) - 384*b^2/(tan(1/2*d*x + 1/2*c)^2 + 1) - (150*a^2*tan(1/2*d*x + 1/2*c)^4 - 600*b^2*tan(1/2*d*x + 1/2*c)^4 - 240*a*b*tan(1/2*d*x + 1/2*c)^3 - 24*a^2*tan(1/2*d*x + 1/2*c)^2 + 24*b^2*tan(1/2*d*x + 1/2*c)^2 + 16*a*b*tan(1/2*d*x + 1/2*c) + 3*a^2)/tan(1/2*d*x + 1/2*c)^4)/d","A",0
1113,1,263,0,0.253869," ","integrate(cos(d*x+c)^4*csc(d*x+c)^6*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 20 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 480 \, {\left(d x + c\right)} b^{2} + 360 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 30 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 300 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{822 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 30 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 300 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 120 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 20 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 15 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{480 \, d}"," ",0,"1/480*(3*a^2*tan(1/2*d*x + 1/2*c)^5 + 15*a*b*tan(1/2*d*x + 1/2*c)^4 - 15*a^2*tan(1/2*d*x + 1/2*c)^3 + 20*b^2*tan(1/2*d*x + 1/2*c)^3 - 120*a*b*tan(1/2*d*x + 1/2*c)^2 + 480*(d*x + c)*b^2 + 360*a*b*log(abs(tan(1/2*d*x + 1/2*c))) + 30*a^2*tan(1/2*d*x + 1/2*c) - 300*b^2*tan(1/2*d*x + 1/2*c) - (822*a*b*tan(1/2*d*x + 1/2*c)^5 + 30*a^2*tan(1/2*d*x + 1/2*c)^4 - 300*b^2*tan(1/2*d*x + 1/2*c)^4 - 120*a*b*tan(1/2*d*x + 1/2*c)^3 - 15*a^2*tan(1/2*d*x + 1/2*c)^2 + 20*b^2*tan(1/2*d*x + 1/2*c)^2 + 15*a*b*tan(1/2*d*x + 1/2*c) + 3*a^2)/tan(1/2*d*x + 1/2*c)^5)/d","A",0
1114,1,309,0,0.274189," ","integrate(cos(d*x+c)^4*csc(d*x+c)^7*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{5 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 24 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 30 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 120 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 240 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 240 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, {\left(a^{2} + 6 \, b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{294 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 1764 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 240 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 240 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 120 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 30 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6}}}{1920 \, d}"," ",0,"1/1920*(5*a^2*tan(1/2*d*x + 1/2*c)^6 + 24*a*b*tan(1/2*d*x + 1/2*c)^5 - 15*a^2*tan(1/2*d*x + 1/2*c)^4 + 30*b^2*tan(1/2*d*x + 1/2*c)^4 - 120*a*b*tan(1/2*d*x + 1/2*c)^3 - 15*a^2*tan(1/2*d*x + 1/2*c)^2 - 240*b^2*tan(1/2*d*x + 1/2*c)^2 + 240*a*b*tan(1/2*d*x + 1/2*c) + 120*(a^2 + 6*b^2)*log(abs(tan(1/2*d*x + 1/2*c))) - (294*a^2*tan(1/2*d*x + 1/2*c)^6 + 1764*b^2*tan(1/2*d*x + 1/2*c)^6 + 240*a*b*tan(1/2*d*x + 1/2*c)^5 - 15*a^2*tan(1/2*d*x + 1/2*c)^4 - 240*b^2*tan(1/2*d*x + 1/2*c)^4 - 120*a*b*tan(1/2*d*x + 1/2*c)^3 - 15*a^2*tan(1/2*d*x + 1/2*c)^2 + 30*b^2*tan(1/2*d*x + 1/2*c)^2 + 24*a*b*tan(1/2*d*x + 1/2*c) + 5*a^2)/tan(1/2*d*x + 1/2*c)^6)/d","A",0
1115,1,347,0,0.290220," ","integrate(cos(d*x+c)^4*csc(d*x+c)^8*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 70 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 21 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 84 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 210 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 105 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 420 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 210 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1680 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 315 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 840 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{4356 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 315 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 840 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 210 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 105 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 420 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 210 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 21 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 84 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 70 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7}}}{13440 \, d}"," ",0,"1/13440*(15*a^2*tan(1/2*d*x + 1/2*c)^7 + 70*a*b*tan(1/2*d*x + 1/2*c)^6 - 21*a^2*tan(1/2*d*x + 1/2*c)^5 + 84*b^2*tan(1/2*d*x + 1/2*c)^5 - 210*a*b*tan(1/2*d*x + 1/2*c)^4 - 105*a^2*tan(1/2*d*x + 1/2*c)^3 - 420*b^2*tan(1/2*d*x + 1/2*c)^3 - 210*a*b*tan(1/2*d*x + 1/2*c)^2 + 1680*a*b*log(abs(tan(1/2*d*x + 1/2*c))) + 315*a^2*tan(1/2*d*x + 1/2*c) + 840*b^2*tan(1/2*d*x + 1/2*c) - (4356*a*b*tan(1/2*d*x + 1/2*c)^7 + 315*a^2*tan(1/2*d*x + 1/2*c)^6 + 840*b^2*tan(1/2*d*x + 1/2*c)^6 - 210*a*b*tan(1/2*d*x + 1/2*c)^5 - 105*a^2*tan(1/2*d*x + 1/2*c)^4 - 420*b^2*tan(1/2*d*x + 1/2*c)^4 - 210*a*b*tan(1/2*d*x + 1/2*c)^3 - 21*a^2*tan(1/2*d*x + 1/2*c)^2 + 84*b^2*tan(1/2*d*x + 1/2*c)^2 + 70*a*b*tan(1/2*d*x + 1/2*c) + 15*a^2)/tan(1/2*d*x + 1/2*c)^7)/d","A",0
1116,1,204,0,0.462224," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{b^{3} \cos\left(9 \, d x + 9 \, c\right)}{2304 \, d} + \frac{3 \, a b^{2} \sin\left(8 \, d x + 8 \, c\right)}{1024 \, d} - \frac{a^{3} \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} + \frac{a^{3} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d} + \frac{1}{128} \, {\left(8 \, a^{3} + 9 \, a b^{2}\right)} x + \frac{{\left(12 \, a^{2} b + b^{3}\right)} \cos\left(7 \, d x + 7 \, c\right)}{1792 \, d} + \frac{{\left(3 \, a^{2} b + b^{3}\right)} \cos\left(5 \, d x + 5 \, c\right)}{320 \, d} - \frac{{\left(9 \, a^{2} b + b^{3}\right)} \cos\left(3 \, d x + 3 \, c\right)}{192 \, d} - \frac{3 \, {\left(6 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)}{128 \, d} - \frac{{\left(2 \, a^{3} + 3 \, a b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)}{128 \, d}"," ",0,"-1/2304*b^3*cos(9*d*x + 9*c)/d + 3/1024*a*b^2*sin(8*d*x + 8*c)/d - 1/192*a^3*sin(6*d*x + 6*c)/d + 1/64*a^3*sin(2*d*x + 2*c)/d + 1/128*(8*a^3 + 9*a*b^2)*x + 1/1792*(12*a^2*b + b^3)*cos(7*d*x + 7*c)/d + 1/320*(3*a^2*b + b^3)*cos(5*d*x + 5*c)/d - 1/192*(9*a^2*b + b^3)*cos(3*d*x + 3*c)/d - 3/128*(6*a^2*b + b^3)*cos(d*x + c)/d - 1/128*(2*a^3 + 3*a*b^2)*sin(4*d*x + 4*c)/d","A",0
1117,1,184,0,0.357530," ","integrate(cos(d*x+c)^4*sin(d*x+c)*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{3 \, a b^{2} \cos\left(7 \, d x + 7 \, c\right)}{448 \, d} + \frac{b^{3} \sin\left(8 \, d x + 8 \, c\right)}{1024 \, d} - \frac{a^{2} b \sin\left(6 \, d x + 6 \, c\right)}{64 \, d} + \frac{3 \, a^{2} b \sin\left(2 \, d x + 2 \, c\right)}{64 \, d} + \frac{3}{128} \, {\left(8 \, a^{2} b + b^{3}\right)} x - \frac{{\left(4 \, a^{3} - 3 \, a b^{2}\right)} \cos\left(5 \, d x + 5 \, c\right)}{320 \, d} - \frac{{\left(4 \, a^{3} + 3 \, a b^{2}\right)} \cos\left(3 \, d x + 3 \, c\right)}{64 \, d} - \frac{{\left(8 \, a^{3} + 9 \, a b^{2}\right)} \cos\left(d x + c\right)}{64 \, d} - \frac{{\left(6 \, a^{2} b + b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)}{128 \, d}"," ",0,"3/448*a*b^2*cos(7*d*x + 7*c)/d + 1/1024*b^3*sin(8*d*x + 8*c)/d - 1/64*a^2*b*sin(6*d*x + 6*c)/d + 3/64*a^2*b*sin(2*d*x + 2*c)/d + 3/128*(8*a^2*b + b^3)*x - 1/320*(4*a^3 - 3*a*b^2)*cos(5*d*x + 5*c)/d - 1/64*(4*a^3 + 3*a*b^2)*cos(3*d*x + 3*c)/d - 1/64*(8*a^3 + 9*a*b^2)*cos(d*x + c)/d - 1/128*(6*a^2*b + b^3)*sin(4*d*x + 4*c)/d","A",0
1118,1,427,0,0.265747," ","integrate(cos(d*x+c)^4*csc(d*x+c)*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{240 \, a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 15 \, {\left(18 \, a^{2} b + b^{3}\right)} {\left(d x + c\right)} - \frac{2 \, {\left(450 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 15 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 480 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 720 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 630 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 235 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1920 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 720 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 180 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 390 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 3200 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 1440 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 180 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 390 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 2880 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 1440 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 630 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 235 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1440 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 144 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 450 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 320 \, a^{3} + 144 \, a b^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(240*a^3*log(abs(tan(1/2*d*x + 1/2*c))) + 15*(18*a^2*b + b^3)*(d*x + c) - 2*(450*a^2*b*tan(1/2*d*x + 1/2*c)^11 - 15*b^3*tan(1/2*d*x + 1/2*c)^11 - 480*a^3*tan(1/2*d*x + 1/2*c)^10 + 720*a*b^2*tan(1/2*d*x + 1/2*c)^10 + 630*a^2*b*tan(1/2*d*x + 1/2*c)^9 + 235*b^3*tan(1/2*d*x + 1/2*c)^9 - 1920*a^3*tan(1/2*d*x + 1/2*c)^8 + 720*a*b^2*tan(1/2*d*x + 1/2*c)^8 + 180*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 390*b^3*tan(1/2*d*x + 1/2*c)^7 - 3200*a^3*tan(1/2*d*x + 1/2*c)^6 + 1440*a*b^2*tan(1/2*d*x + 1/2*c)^6 - 180*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 390*b^3*tan(1/2*d*x + 1/2*c)^5 - 2880*a^3*tan(1/2*d*x + 1/2*c)^4 + 1440*a*b^2*tan(1/2*d*x + 1/2*c)^4 - 630*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 235*b^3*tan(1/2*d*x + 1/2*c)^3 - 1440*a^3*tan(1/2*d*x + 1/2*c)^2 + 144*a*b^2*tan(1/2*d*x + 1/2*c)^2 - 450*a^2*b*tan(1/2*d*x + 1/2*c) + 15*b^3*tan(1/2*d*x + 1/2*c) - 320*a^3 + 144*a*b^2)/(tan(1/2*d*x + 1/2*c)^2 + 1)^6)/d","A",0
1119,1,345,0,0.296717," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{120 \, a^{2} b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 20 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, {\left(4 \, a^{3} - 3 \, a b^{2}\right)} {\left(d x + c\right)} - \frac{20 \, {\left(6 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)} + \frac{2 \, {\left(20 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 75 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 240 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 40 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 40 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 30 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 720 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 880 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 80 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 40 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 560 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 20 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 75 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 160 \, a^{2} b - 8 \, b^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5}}}{40 \, d}"," ",0,"1/40*(120*a^2*b*log(abs(tan(1/2*d*x + 1/2*c))) + 20*a^3*tan(1/2*d*x + 1/2*c) - 15*(4*a^3 - 3*a*b^2)*(d*x + c) - 20*(6*a^2*b*tan(1/2*d*x + 1/2*c) + a^3)/tan(1/2*d*x + 1/2*c) + 2*(20*a^3*tan(1/2*d*x + 1/2*c)^9 - 75*a*b^2*tan(1/2*d*x + 1/2*c)^9 + 240*a^2*b*tan(1/2*d*x + 1/2*c)^8 - 40*b^3*tan(1/2*d*x + 1/2*c)^8 + 40*a^3*tan(1/2*d*x + 1/2*c)^7 - 30*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 720*a^2*b*tan(1/2*d*x + 1/2*c)^6 + 880*a^2*b*tan(1/2*d*x + 1/2*c)^4 - 80*b^3*tan(1/2*d*x + 1/2*c)^4 - 40*a^3*tan(1/2*d*x + 1/2*c)^3 + 30*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 560*a^2*b*tan(1/2*d*x + 1/2*c)^2 - 20*a^3*tan(1/2*d*x + 1/2*c) + 75*a*b^2*tan(1/2*d*x + 1/2*c) + 160*a^2*b - 8*b^3)/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","A",0
1120,1,400,0,0.308136," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, {\left(12 \, a^{2} b - b^{3}\right)} {\left(d x + c\right)} - 12 \, {\left(a^{3} - 2 \, a b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + \frac{18 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 36 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}} + \frac{2 \, {\left(12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 5 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 8 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 48 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 24 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 96 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 80 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, a^{3} + 32 \, a b^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{8 \, d}"," ",0,"1/8*(a^3*tan(1/2*d*x + 1/2*c)^2 + 12*a^2*b*tan(1/2*d*x + 1/2*c) - 3*(12*a^2*b - b^3)*(d*x + c) - 12*(a^3 - 2*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c))) + (18*a^3*tan(1/2*d*x + 1/2*c)^2 - 36*a*b^2*tan(1/2*d*x + 1/2*c)^2 - 12*a^2*b*tan(1/2*d*x + 1/2*c) - a^3)/tan(1/2*d*x + 1/2*c)^2 + 2*(12*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 5*b^3*tan(1/2*d*x + 1/2*c)^7 - 8*a^3*tan(1/2*d*x + 1/2*c)^6 + 48*a*b^2*tan(1/2*d*x + 1/2*c)^6 + 12*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 3*b^3*tan(1/2*d*x + 1/2*c)^5 - 24*a^3*tan(1/2*d*x + 1/2*c)^4 + 96*a*b^2*tan(1/2*d*x + 1/2*c)^4 - 12*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 3*b^3*tan(1/2*d*x + 1/2*c)^3 - 24*a^3*tan(1/2*d*x + 1/2*c)^2 + 80*a*b^2*tan(1/2*d*x + 1/2*c)^2 - 12*a^2*b*tan(1/2*d*x + 1/2*c) + 5*b^3*tan(1/2*d*x + 1/2*c) - 8*a^3 + 32*a*b^2)/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","A",0
1121,1,421,0,0.322970," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 27 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 45 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 108 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, {\left(2 \, a^{3} - 9 \, a b^{2}\right)} {\left(d x + c\right)} - 36 \, {\left(9 \, a^{2} b - 2 \, b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + \frac{198 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 44 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 45 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 108 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 135 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 156 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 132 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 324 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 351 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 156 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 126 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 540 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 315 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 148 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 108 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 27 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a^{3}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}^{3}}}{72 \, d}"," ",0,"1/72*(3*a^3*tan(1/2*d*x + 1/2*c)^3 + 27*a^2*b*tan(1/2*d*x + 1/2*c)^2 - 45*a^3*tan(1/2*d*x + 1/2*c) + 108*a*b^2*tan(1/2*d*x + 1/2*c) + 36*(2*a^3 - 9*a*b^2)*(d*x + c) - 36*(9*a^2*b - 2*b^3)*log(abs(tan(1/2*d*x + 1/2*c))) + (198*a^2*b*tan(1/2*d*x + 1/2*c)^9 - 44*b^3*tan(1/2*d*x + 1/2*c)^9 + 45*a^3*tan(1/2*d*x + 1/2*c)^8 + 108*a*b^2*tan(1/2*d*x + 1/2*c)^8 + 135*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 156*b^3*tan(1/2*d*x + 1/2*c)^7 + 132*a^3*tan(1/2*d*x + 1/2*c)^6 - 324*a*b^2*tan(1/2*d*x + 1/2*c)^6 - 351*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 156*b^3*tan(1/2*d*x + 1/2*c)^5 + 126*a^3*tan(1/2*d*x + 1/2*c)^4 - 540*a*b^2*tan(1/2*d*x + 1/2*c)^4 - 315*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 148*b^3*tan(1/2*d*x + 1/2*c)^3 + 36*a^3*tan(1/2*d*x + 1/2*c)^2 - 108*a*b^2*tan(1/2*d*x + 1/2*c)^2 - 27*a^2*b*tan(1/2*d*x + 1/2*c) - 3*a^3)/(tan(1/2*d*x + 1/2*c)^3 + tan(1/2*d*x + 1/2*c))^3)/d","B",0
1122,1,343,0,0.330586," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 8 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 8 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 120 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 32 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 96 \, {\left(2 \, a^{2} b - b^{3}\right)} {\left(d x + c\right)} + 24 \, {\left(a^{3} - 12 \, a b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + \frac{64 \, {\left(b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, a b^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}} - \frac{50 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 600 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 120 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 32 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 8 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 8 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}}}{64 \, d}"," ",0,"1/64*(a^3*tan(1/2*d*x + 1/2*c)^4 + 8*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 8*a^3*tan(1/2*d*x + 1/2*c)^2 + 24*a*b^2*tan(1/2*d*x + 1/2*c)^2 - 120*a^2*b*tan(1/2*d*x + 1/2*c) + 32*b^3*tan(1/2*d*x + 1/2*c) + 96*(2*a^2*b - b^3)*(d*x + c) + 24*(a^3 - 12*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c))) + 64*(b^3*tan(1/2*d*x + 1/2*c)^3 - 6*a*b^2*tan(1/2*d*x + 1/2*c)^2 - b^3*tan(1/2*d*x + 1/2*c) - 6*a*b^2)/(tan(1/2*d*x + 1/2*c)^2 + 1)^2 - (50*a^3*tan(1/2*d*x + 1/2*c)^4 - 600*a*b^2*tan(1/2*d*x + 1/2*c)^4 - 120*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 32*b^3*tan(1/2*d*x + 1/2*c)^3 - 8*a^3*tan(1/2*d*x + 1/2*c)^2 + 24*a*b^2*tan(1/2*d*x + 1/2*c)^2 + 8*a^2*b*tan(1/2*d*x + 1/2*c) + a^3)/tan(1/2*d*x + 1/2*c)^4)/d","A",0
1123,1,356,0,0.348734," ","integrate(cos(d*x+c)^4*csc(d*x+c)^6*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{2 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 10 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 40 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 960 \, {\left(d x + c\right)} a b^{2} + 20 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 600 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{640 \, b^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + 120 \, {\left(3 \, a^{2} b - 4 \, b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{822 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1096 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 20 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 600 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 120 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 10 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 40 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 15 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{320 \, d}"," ",0,"1/320*(2*a^3*tan(1/2*d*x + 1/2*c)^5 + 15*a^2*b*tan(1/2*d*x + 1/2*c)^4 - 10*a^3*tan(1/2*d*x + 1/2*c)^3 + 40*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 120*a^2*b*tan(1/2*d*x + 1/2*c)^2 + 40*b^3*tan(1/2*d*x + 1/2*c)^2 + 960*(d*x + c)*a*b^2 + 20*a^3*tan(1/2*d*x + 1/2*c) - 600*a*b^2*tan(1/2*d*x + 1/2*c) - 640*b^3/(tan(1/2*d*x + 1/2*c)^2 + 1) + 120*(3*a^2*b - 4*b^3)*log(abs(tan(1/2*d*x + 1/2*c))) - (822*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 1096*b^3*tan(1/2*d*x + 1/2*c)^5 + 20*a^3*tan(1/2*d*x + 1/2*c)^4 - 600*a*b^2*tan(1/2*d*x + 1/2*c)^4 - 120*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 40*b^3*tan(1/2*d*x + 1/2*c)^3 - 10*a^3*tan(1/2*d*x + 1/2*c)^2 + 40*a*b^2*tan(1/2*d*x + 1/2*c)^2 + 15*a^2*b*tan(1/2*d*x + 1/2*c) + 2*a^3)/tan(1/2*d*x + 1/2*c)^5)/d","A",0
1124,1,399,0,0.360227," ","integrate(cos(d*x+c)^4*csc(d*x+c)^7*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{5 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 36 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 90 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 180 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 80 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 720 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1920 \, {\left(d x + c\right)} b^{3} + 360 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1200 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, {\left(a^{3} + 18 \, a b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{294 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 5292 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 360 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1200 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 720 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 180 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 80 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 90 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 36 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6}}}{1920 \, d}"," ",0,"1/1920*(5*a^3*tan(1/2*d*x + 1/2*c)^6 + 36*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 15*a^3*tan(1/2*d*x + 1/2*c)^4 + 90*a*b^2*tan(1/2*d*x + 1/2*c)^4 - 180*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 80*b^3*tan(1/2*d*x + 1/2*c)^3 - 15*a^3*tan(1/2*d*x + 1/2*c)^2 - 720*a*b^2*tan(1/2*d*x + 1/2*c)^2 + 1920*(d*x + c)*b^3 + 360*a^2*b*tan(1/2*d*x + 1/2*c) - 1200*b^3*tan(1/2*d*x + 1/2*c) + 120*(a^3 + 18*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c))) - (294*a^3*tan(1/2*d*x + 1/2*c)^6 + 5292*a*b^2*tan(1/2*d*x + 1/2*c)^6 + 360*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 1200*b^3*tan(1/2*d*x + 1/2*c)^5 - 15*a^3*tan(1/2*d*x + 1/2*c)^4 - 720*a*b^2*tan(1/2*d*x + 1/2*c)^4 - 180*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 80*b^3*tan(1/2*d*x + 1/2*c)^3 - 15*a^3*tan(1/2*d*x + 1/2*c)^2 + 90*a*b^2*tan(1/2*d*x + 1/2*c)^2 + 36*a^2*b*tan(1/2*d*x + 1/2*c) + 5*a^3)/tan(1/2*d*x + 1/2*c)^6)/d","A",0
1125,1,456,0,0.388145," ","integrate(cos(d*x+c)^4*csc(d*x+c)^8*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{5 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 35 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 7 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 84 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 105 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 70 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 35 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 420 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 105 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 560 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 105 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 840 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 840 \, {\left(a^{2} b + 2 \, b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{2178 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 4356 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 105 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 840 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 105 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 560 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 35 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 420 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 105 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 70 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 7 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 84 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 35 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7}}}{4480 \, d}"," ",0,"1/4480*(5*a^3*tan(1/2*d*x + 1/2*c)^7 + 35*a^2*b*tan(1/2*d*x + 1/2*c)^6 - 7*a^3*tan(1/2*d*x + 1/2*c)^5 + 84*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 105*a^2*b*tan(1/2*d*x + 1/2*c)^4 + 70*b^3*tan(1/2*d*x + 1/2*c)^4 - 35*a^3*tan(1/2*d*x + 1/2*c)^3 - 420*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 105*a^2*b*tan(1/2*d*x + 1/2*c)^2 - 560*b^3*tan(1/2*d*x + 1/2*c)^2 + 105*a^3*tan(1/2*d*x + 1/2*c) + 840*a*b^2*tan(1/2*d*x + 1/2*c) + 840*(a^2*b + 2*b^3)*log(abs(tan(1/2*d*x + 1/2*c))) - (2178*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 4356*b^3*tan(1/2*d*x + 1/2*c)^7 + 105*a^3*tan(1/2*d*x + 1/2*c)^6 + 840*a*b^2*tan(1/2*d*x + 1/2*c)^6 - 105*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 560*b^3*tan(1/2*d*x + 1/2*c)^5 - 35*a^3*tan(1/2*d*x + 1/2*c)^4 - 420*a*b^2*tan(1/2*d*x + 1/2*c)^4 - 105*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 70*b^3*tan(1/2*d*x + 1/2*c)^3 - 7*a^3*tan(1/2*d*x + 1/2*c)^2 + 84*a*b^2*tan(1/2*d*x + 1/2*c)^2 + 35*a^2*b*tan(1/2*d*x + 1/2*c) + 5*a^3)/tan(1/2*d*x + 1/2*c)^7)/d","A",0
1126,1,457,0,0.388661," ","integrate(cos(d*x+c)^4*csc(d*x+c)^9*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{35 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 240 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 560 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 336 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 448 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 280 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1680 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1680 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2240 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1680 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 5040 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4480 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1680 \, {\left(a^{3} + 8 \, a b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{4566 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 36528 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 5040 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 4480 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1680 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 1680 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 2240 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 280 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1680 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 336 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 448 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 560 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 240 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 35 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8}}}{71680 \, d}"," ",0,"1/71680*(35*a^3*tan(1/2*d*x + 1/2*c)^8 + 240*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 560*a*b^2*tan(1/2*d*x + 1/2*c)^6 - 336*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 448*b^3*tan(1/2*d*x + 1/2*c)^5 - 280*a^3*tan(1/2*d*x + 1/2*c)^4 - 1680*a*b^2*tan(1/2*d*x + 1/2*c)^4 - 1680*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 2240*b^3*tan(1/2*d*x + 1/2*c)^3 - 1680*a*b^2*tan(1/2*d*x + 1/2*c)^2 + 5040*a^2*b*tan(1/2*d*x + 1/2*c) + 4480*b^3*tan(1/2*d*x + 1/2*c) + 1680*(a^3 + 8*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c))) - (4566*a^3*tan(1/2*d*x + 1/2*c)^8 + 36528*a*b^2*tan(1/2*d*x + 1/2*c)^8 + 5040*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 4480*b^3*tan(1/2*d*x + 1/2*c)^7 - 1680*a*b^2*tan(1/2*d*x + 1/2*c)^6 - 1680*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 2240*b^3*tan(1/2*d*x + 1/2*c)^5 - 280*a^3*tan(1/2*d*x + 1/2*c)^4 - 1680*a*b^2*tan(1/2*d*x + 1/2*c)^4 - 336*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 448*b^3*tan(1/2*d*x + 1/2*c)^3 + 560*a*b^2*tan(1/2*d*x + 1/2*c)^2 + 240*a^2*b*tan(1/2*d*x + 1/2*c) + 35*a^3)/tan(1/2*d*x + 1/2*c)^8)/d","A",0
1127,1,536,0,0.231992," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{15 \, {\left(8 \, a^{5} - 8 \, a^{3} b^{2} + a b^{4}\right)} {\left(d x + c\right)}}{b^{7}} - \frac{120 \, {\left(2 \, a^{6} - 3 \, a^{4} b^{2} + a^{2} b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{7}} + \frac{40 \, {\left(a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{5} - a^{3} b^{2}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)} b^{6}} + \frac{2 \, {\left(40 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 25 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 100 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 120 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 20 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 80 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 10 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 400 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 360 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 600 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 440 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 40 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 80 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 10 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 400 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 280 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 40 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 25 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 100 \, a^{4} - 80 \, a^{2} b^{2} + 4 \, b^{4}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5} b^{6}}}{20 \, d}"," ",0,"-1/20*(15*(8*a^5 - 8*a^3*b^2 + a*b^4)*(d*x + c)/b^7 - 120*(2*a^6 - 3*a^4*b^2 + a^2*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^7) + 40*(a^4*b*tan(1/2*d*x + 1/2*c) - a^2*b^3*tan(1/2*d*x + 1/2*c) + a^5 - a^3*b^2)/((a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)*b^6) + 2*(40*a^3*b*tan(1/2*d*x + 1/2*c)^9 - 25*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 100*a^4*tan(1/2*d*x + 1/2*c)^8 - 120*a^2*b^2*tan(1/2*d*x + 1/2*c)^8 + 20*b^4*tan(1/2*d*x + 1/2*c)^8 + 80*a^3*b*tan(1/2*d*x + 1/2*c)^7 - 10*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 400*a^4*tan(1/2*d*x + 1/2*c)^6 - 360*a^2*b^2*tan(1/2*d*x + 1/2*c)^6 + 600*a^4*tan(1/2*d*x + 1/2*c)^4 - 440*a^2*b^2*tan(1/2*d*x + 1/2*c)^4 + 40*b^4*tan(1/2*d*x + 1/2*c)^4 - 80*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 10*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 400*a^4*tan(1/2*d*x + 1/2*c)^2 - 280*a^2*b^2*tan(1/2*d*x + 1/2*c)^2 - 40*a^3*b*tan(1/2*d*x + 1/2*c) + 25*a*b^3*tan(1/2*d*x + 1/2*c) + 100*a^4 - 80*a^2*b^2 + 4*b^4)/((tan(1/2*d*x + 1/2*c)^2 + 1)^5*b^6))/d","A",0
1128,1,449,0,0.209486," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(40 \, a^{4} - 36 \, a^{2} b^{2} + 3 \, b^{4}\right)} {\left(d x + c\right)}}{b^{6}} - \frac{48 \, {\left(5 \, a^{5} - 7 \, a^{3} b^{2} + 2 \, a b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{6}} + \frac{48 \, {\left(a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{4} - a^{2} b^{2}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)} b^{5}} + \frac{2 \, {\left(36 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 96 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 96 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 36 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 288 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 192 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 36 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 288 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 160 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 36 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 96 \, a^{3} - 64 \, a b^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4} b^{5}}}{24 \, d}"," ",0,"1/24*(3*(40*a^4 - 36*a^2*b^2 + 3*b^4)*(d*x + c)/b^6 - 48*(5*a^5 - 7*a^3*b^2 + 2*a*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^6) + 48*(a^3*b*tan(1/2*d*x + 1/2*c) - a*b^3*tan(1/2*d*x + 1/2*c) + a^4 - a^2*b^2)/((a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)*b^5) + 2*(36*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 15*b^3*tan(1/2*d*x + 1/2*c)^7 + 96*a^3*tan(1/2*d*x + 1/2*c)^6 - 96*a*b^2*tan(1/2*d*x + 1/2*c)^6 + 36*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 9*b^3*tan(1/2*d*x + 1/2*c)^5 + 288*a^3*tan(1/2*d*x + 1/2*c)^4 - 192*a*b^2*tan(1/2*d*x + 1/2*c)^4 - 36*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 9*b^3*tan(1/2*d*x + 1/2*c)^3 + 288*a^3*tan(1/2*d*x + 1/2*c)^2 - 160*a*b^2*tan(1/2*d*x + 1/2*c)^2 - 36*a^2*b*tan(1/2*d*x + 1/2*c) + 15*b^3*tan(1/2*d*x + 1/2*c) + 96*a^3 - 64*a*b^2)/((tan(1/2*d*x + 1/2*c)^2 + 1)^4*b^5))/d","A",0
1129,1,300,0,0.197723," ","integrate(cos(d*x+c)^4*sin(d*x+c)/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(4 \, a^{3} - 3 \, a b^{2}\right)} {\left(d x + c\right)}}{b^{5}} - \frac{6 \, {\left(4 \, a^{4} - 5 \, a^{2} b^{2} + b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{5}} + \frac{6 \, {\left(a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3} - a b^{2}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)} b^{4}} + \frac{2 \, {\left(3 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 6 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 18 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 6 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, a^{2} - 4 \, b^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} b^{4}}}{3 \, d}"," ",0,"-1/3*(3*(4*a^3 - 3*a*b^2)*(d*x + c)/b^5 - 6*(4*a^4 - 5*a^2*b^2 + b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^5) + 6*(a^2*b*tan(1/2*d*x + 1/2*c) - b^3*tan(1/2*d*x + 1/2*c) + a^3 - a*b^2)/((a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)*b^4) + 2*(3*a*b*tan(1/2*d*x + 1/2*c)^5 + 9*a^2*tan(1/2*d*x + 1/2*c)^4 - 6*b^2*tan(1/2*d*x + 1/2*c)^4 + 18*a^2*tan(1/2*d*x + 1/2*c)^2 - 6*b^2*tan(1/2*d*x + 1/2*c)^2 - 3*a*b*tan(1/2*d*x + 1/2*c) + 9*a^2 - 4*b^2)/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*b^4))/d","A",0
1130,1,286,0,0.218785," ","integrate(cos(d*x+c)^4*csc(d*x+c)/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(d x + c\right)} a}{b^{3}} - \frac{\log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} - \frac{2 \, {\left(2 \, a^{4} - a^{2} b^{2} - b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{2} b^{3}} + \frac{2 \, {\left(a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, a^{3} - a b^{2}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)} a^{2} b^{2}}}{d}"," ",0,"-(2*(d*x + c)*a/b^3 - log(abs(tan(1/2*d*x + 1/2*c)))/a^2 - 2*(2*a^4 - a^2*b^2 - b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^2*b^3) + 2*(a^2*b*tan(1/2*d*x + 1/2*c)^3 - b^3*tan(1/2*d*x + 1/2*c)^3 + 2*a^3*tan(1/2*d*x + 1/2*c)^2 - a*b^2*tan(1/2*d*x + 1/2*c)^2 + 3*a^2*b*tan(1/2*d*x + 1/2*c) - b^3*tan(1/2*d*x + 1/2*c) + 2*a^3 - a*b^2)/((a*tan(1/2*d*x + 1/2*c)^4 + 2*b*tan(1/2*d*x + 1/2*c)^3 + 2*a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)*a^2*b^2))/d","B",0
1131,1,260,0,0.235832," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{6 \, {\left(d x + c\right)}}{b^{2}} - \frac{12 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} + \frac{3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{2}} - \frac{12 \, {\left(a^{4} + a^{2} b^{2} - 2 \, b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{3} b^{2}} + \frac{4 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 14 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a^{2} b}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} a^{3} b}}{6 \, d}"," ",0,"1/6*(6*(d*x + c)/b^2 - 12*b*log(abs(tan(1/2*d*x + 1/2*c)))/a^3 + 3*tan(1/2*d*x + 1/2*c)/a^2 - 12*(a^4 + a^2*b^2 - 2*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^3*b^2) + (4*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 9*a^2*b*tan(1/2*d*x + 1/2*c)^2 - 4*b^3*tan(1/2*d*x + 1/2*c)^2 + 12*a^3*tan(1/2*d*x + 1/2*c) - 14*a*b^2*tan(1/2*d*x + 1/2*c) - 3*a^2*b)/((a*tan(1/2*d*x + 1/2*c)^3 + 2*b*tan(1/2*d*x + 1/2*c)^2 + a*tan(1/2*d*x + 1/2*c))*a^3*b))/d","A",0
1132,1,275,0,0.232972," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{12 \, {\left(a^{2} - 2 \, b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{4}} - \frac{48 \, {\left(a^{2} b - b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{4}} - \frac{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{4}} + \frac{16 \, {\left(a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3} - a b^{2}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)} a^{4}} - \frac{18 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 36 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 8 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{2}}{a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}}{8 \, d}"," ",0,"-1/8*(12*(a^2 - 2*b^2)*log(abs(tan(1/2*d*x + 1/2*c)))/a^4 - 48*(a^2*b - b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^4) - (a^2*tan(1/2*d*x + 1/2*c)^2 - 8*a*b*tan(1/2*d*x + 1/2*c))/a^4 + 16*(a^2*b*tan(1/2*d*x + 1/2*c) - b^3*tan(1/2*d*x + 1/2*c) + a^3 - a*b^2)/((a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)*a^4) - (18*a^2*tan(1/2*d*x + 1/2*c)^2 - 36*b^2*tan(1/2*d*x + 1/2*c)^2 + 8*a*b*tan(1/2*d*x + 1/2*c) - a^2)/(a^4*tan(1/2*d*x + 1/2*c)^2))/d","A",0
1133,1,356,0,0.252789," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{24 \, {\left(3 \, a^{2} b - 4 \, b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{5}} + \frac{48 \, {\left(a^{4} - 5 \, a^{2} b^{2} + 4 \, b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{5}} + \frac{a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}} + \frac{48 \, {\left(a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3} b - a b^{3}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)} a^{5}} - \frac{132 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 176 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 36 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 6 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3}}{a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{24 \, d}"," ",0,"1/24*(24*(3*a^2*b - 4*b^3)*log(abs(tan(1/2*d*x + 1/2*c)))/a^5 + 48*(a^4 - 5*a^2*b^2 + 4*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^5) + (a^4*tan(1/2*d*x + 1/2*c)^3 - 6*a^3*b*tan(1/2*d*x + 1/2*c)^2 - 15*a^4*tan(1/2*d*x + 1/2*c) + 36*a^2*b^2*tan(1/2*d*x + 1/2*c))/a^6 + 48*(a^2*b^2*tan(1/2*d*x + 1/2*c) - b^4*tan(1/2*d*x + 1/2*c) + a^3*b - a*b^3)/((a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)*a^5) - (132*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 176*b^3*tan(1/2*d*x + 1/2*c)^3 - 15*a^3*tan(1/2*d*x + 1/2*c)^2 + 36*a*b^2*tan(1/2*d*x + 1/2*c)^2 - 6*a^2*b*tan(1/2*d*x + 1/2*c) + a^3)/(a^5*tan(1/2*d*x + 1/2*c)^3))/d","A",0
1134,1,461,0,0.282105," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{24 \, {\left(3 \, a^{4} - 36 \, a^{2} b^{2} + 40 \, b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{6}} - \frac{384 \, {\left(2 \, a^{4} b - 7 \, a^{2} b^{3} + 5 \, b^{5}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{6}} - \frac{384 \, {\left(a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3} b^{2} - a b^{4}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)} a^{6}} + \frac{3 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 16 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 72 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 240 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 384 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{8}} - \frac{150 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1800 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2000 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 240 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 384 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 72 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 16 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a^{4}}{a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}}}{192 \, d}"," ",0,"1/192*(24*(3*a^4 - 36*a^2*b^2 + 40*b^4)*log(abs(tan(1/2*d*x + 1/2*c)))/a^6 - 384*(2*a^4*b - 7*a^2*b^3 + 5*b^5)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^6) - 384*(a^2*b^3*tan(1/2*d*x + 1/2*c) - b^5*tan(1/2*d*x + 1/2*c) + a^3*b^2 - a*b^4)/((a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)*a^6) + (3*a^6*tan(1/2*d*x + 1/2*c)^4 - 16*a^5*b*tan(1/2*d*x + 1/2*c)^3 - 24*a^6*tan(1/2*d*x + 1/2*c)^2 + 72*a^4*b^2*tan(1/2*d*x + 1/2*c)^2 + 240*a^5*b*tan(1/2*d*x + 1/2*c) - 384*a^3*b^3*tan(1/2*d*x + 1/2*c))/a^8 - (150*a^4*tan(1/2*d*x + 1/2*c)^4 - 1800*a^2*b^2*tan(1/2*d*x + 1/2*c)^4 + 2000*b^4*tan(1/2*d*x + 1/2*c)^4 + 240*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 384*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 24*a^4*tan(1/2*d*x + 1/2*c)^2 + 72*a^2*b^2*tan(1/2*d*x + 1/2*c)^2 - 16*a^3*b*tan(1/2*d*x + 1/2*c) + 3*a^4)/(a^6*tan(1/2*d*x + 1/2*c)^4))/d","A",0
1135,1,540,0,0.300375," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(40 \, a^{4} - 24 \, a^{2} b^{2} + b^{4}\right)} {\left(d x + c\right)}}{b^{7}} - \frac{24 \, {\left(10 \, a^{5} - 11 \, a^{3} b^{2} + 2 \, a b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{7}} + \frac{8 \, {\left(9 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 10 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 15 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 10 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 31 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 16 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 10 \, a^{5} - 5 \, a^{3} b^{2}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}^{2} b^{6}} + \frac{2 \, {\left(24 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 5 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 80 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 48 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 24 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 240 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 96 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 24 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 240 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 80 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 24 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 80 \, a^{3} - 32 \, a b^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4} b^{6}}}{8 \, d}"," ",0,"1/8*(3*(40*a^4 - 24*a^2*b^2 + b^4)*(d*x + c)/b^7 - 24*(10*a^5 - 11*a^3*b^2 + 2*a*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^7) + 8*(9*a^4*b*tan(1/2*d*x + 1/2*c)^3 - 4*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + 10*a^5*tan(1/2*d*x + 1/2*c)^2 + 15*a^3*b^2*tan(1/2*d*x + 1/2*c)^2 - 10*a*b^4*tan(1/2*d*x + 1/2*c)^2 + 31*a^4*b*tan(1/2*d*x + 1/2*c) - 16*a^2*b^3*tan(1/2*d*x + 1/2*c) + 10*a^5 - 5*a^3*b^2)/((a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)^2*b^6) + 2*(24*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 5*b^3*tan(1/2*d*x + 1/2*c)^7 + 80*a^3*tan(1/2*d*x + 1/2*c)^6 - 48*a*b^2*tan(1/2*d*x + 1/2*c)^6 + 24*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 3*b^3*tan(1/2*d*x + 1/2*c)^5 + 240*a^3*tan(1/2*d*x + 1/2*c)^4 - 96*a*b^2*tan(1/2*d*x + 1/2*c)^4 - 24*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 3*b^3*tan(1/2*d*x + 1/2*c)^3 + 240*a^3*tan(1/2*d*x + 1/2*c)^2 - 80*a*b^2*tan(1/2*d*x + 1/2*c)^2 - 24*a^2*b*tan(1/2*d*x + 1/2*c) + 5*b^3*tan(1/2*d*x + 1/2*c) + 80*a^3 - 32*a*b^2)/((tan(1/2*d*x + 1/2*c)^2 + 1)^4*b^6))/d","A",0
1136,1,393,0,0.271989," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(20 \, a^{3} - 9 \, a b^{2}\right)} {\left(d x + c\right)}}{b^{6}} - \frac{6 \, {\left(20 \, a^{4} - 19 \, a^{2} b^{2} + 2 \, b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{6}} + \frac{6 \, {\left(7 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 13 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 6 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 25 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 10 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8 \, a^{4} - 3 \, a^{2} b^{2}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}^{2} b^{5}} + \frac{2 \, {\left(9 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 72 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, a^{2} - 8 \, b^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} b^{5}}}{6 \, d}"," ",0,"-1/6*(3*(20*a^3 - 9*a*b^2)*(d*x + c)/b^6 - 6*(20*a^4 - 19*a^2*b^2 + 2*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^6) + 6*(7*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 2*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 8*a^4*tan(1/2*d*x + 1/2*c)^2 + 13*a^2*b^2*tan(1/2*d*x + 1/2*c)^2 - 6*b^4*tan(1/2*d*x + 1/2*c)^2 + 25*a^3*b*tan(1/2*d*x + 1/2*c) - 10*a*b^3*tan(1/2*d*x + 1/2*c) + 8*a^4 - 3*a^2*b^2)/((a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)^2*b^5) + 2*(9*a*b*tan(1/2*d*x + 1/2*c)^5 + 36*a^2*tan(1/2*d*x + 1/2*c)^4 - 12*b^2*tan(1/2*d*x + 1/2*c)^4 + 72*a^2*tan(1/2*d*x + 1/2*c)^2 - 12*b^2*tan(1/2*d*x + 1/2*c)^2 - 9*a*b*tan(1/2*d*x + 1/2*c) + 36*a^2 - 8*b^2)/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*b^5))/d","A",0
1137,1,429,0,0.241123," ","integrate(cos(d*x+c)^4*sin(d*x+c)/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(4 \, a^{2} - b^{2}\right)} {\left(d x + c\right)}}{b^{5}} - \frac{6 \, {\left(4 \, a^{3} - 3 \, a b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{5}} + \frac{2 \, {\left(6 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 15 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 2 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 54 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 45 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 4 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 90 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 29 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 42 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, a^{4} - a^{2} b^{2}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}^{2} a b^{4}}}{2 \, d}"," ",0,"1/2*(3*(4*a^2 - b^2)*(d*x + c)/b^5 - 6*(4*a^3 - 3*a*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^5) + 2*(6*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 12*a^4*tan(1/2*d*x + 1/2*c)^6 + 15*a^2*b^2*tan(1/2*d*x + 1/2*c)^6 - 2*b^4*tan(1/2*d*x + 1/2*c)^6 + 54*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 36*a^4*tan(1/2*d*x + 1/2*c)^4 + 45*a^2*b^2*tan(1/2*d*x + 1/2*c)^4 - 4*b^4*tan(1/2*d*x + 1/2*c)^4 + 90*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 12*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 36*a^4*tan(1/2*d*x + 1/2*c)^2 + 29*a^2*b^2*tan(1/2*d*x + 1/2*c)^2 - 2*b^4*tan(1/2*d*x + 1/2*c)^2 + 42*a^3*b*tan(1/2*d*x + 1/2*c) - 4*a*b^3*tan(1/2*d*x + 1/2*c) + 12*a^4 - a^2*b^2)/((a*tan(1/2*d*x + 1/2*c)^4 + 2*b*tan(1/2*d*x + 1/2*c)^3 + 2*a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)^2*a*b^4))/d","B",0
1138,1,275,0,0.230329," ","integrate(cos(d*x+c)^4*csc(d*x+c)/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{d x + c}{b^{3}} + \frac{\log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} - \frac{{\left(2 \, a^{4} - a^{2} b^{2} + 2 \, b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{3} b^{3}} + \frac{a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 7 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 6 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 7 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, a^{4} + 3 \, a^{2} b^{2}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}^{2} a^{3} b^{2}}}{d}"," ",0,"((d*x + c)/b^3 + log(abs(tan(1/2*d*x + 1/2*c)))/a^3 - (2*a^4 - a^2*b^2 + 2*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^3*b^3) + (a^3*b*tan(1/2*d*x + 1/2*c)^3 + 4*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 2*a^4*tan(1/2*d*x + 1/2*c)^2 + 7*a^2*b^2*tan(1/2*d*x + 1/2*c)^2 + 6*b^4*tan(1/2*d*x + 1/2*c)^2 + 7*a^3*b*tan(1/2*d*x + 1/2*c) + 8*a*b^3*tan(1/2*d*x + 1/2*c) + 2*a^4 + 3*a^2*b^2)/((a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)^2*a^3*b^2))/d","A",0
1139,1,273,0,0.258054," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{6 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{4}} - \frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3}} + \frac{6 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} {\left(a^{2} - 2 \, b^{2}\right)}}{\sqrt{a^{2} - b^{2}} a^{4}} - \frac{6 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a}{a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)} - \frac{2 \, {\left(a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 10 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 14 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, a^{2} b\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}^{2} a^{4}}}{2 \, d}"," ",0,"-1/2*(6*b*log(abs(tan(1/2*d*x + 1/2*c)))/a^4 - tan(1/2*d*x + 1/2*c)/a^3 + 6*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))*(a^2 - 2*b^2)/(sqrt(a^2 - b^2)*a^4) - (6*b*tan(1/2*d*x + 1/2*c) - a)/(a^4*tan(1/2*d*x + 1/2*c)) - 2*(a^3*tan(1/2*d*x + 1/2*c)^3 - 6*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 5*a^2*b*tan(1/2*d*x + 1/2*c)^2 - 10*b^3*tan(1/2*d*x + 1/2*c)^2 - a^3*tan(1/2*d*x + 1/2*c) - 14*a*b^2*tan(1/2*d*x + 1/2*c) - 5*a^2*b)/((a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)^2*a^4))/d","A",0
1140,1,395,0,0.287094," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{12 \, {\left(a^{2} - 4 \, b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{5}} - \frac{24 \, {\left(3 \, a^{2} b - 4 \, b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{5}} - \frac{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}} - \frac{6 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 24 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 12 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 32 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 5 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 48 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 16 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 4 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 112 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 76 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 8 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{4}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}^{2} a^{5}}}{8 \, d}"," ",0,"-1/8*(12*(a^2 - 4*b^2)*log(abs(tan(1/2*d*x + 1/2*c)))/a^5 - 24*(3*a^2*b - 4*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^5) - (a^3*tan(1/2*d*x + 1/2*c)^2 - 12*a^2*b*tan(1/2*d*x + 1/2*c))/a^6 - (6*a^4*tan(1/2*d*x + 1/2*c)^6 - 24*a^2*b^2*tan(1/2*d*x + 1/2*c)^6 + 12*a^3*b*tan(1/2*d*x + 1/2*c)^5 - 32*a*b^3*tan(1/2*d*x + 1/2*c)^5 - 5*a^4*tan(1/2*d*x + 1/2*c)^4 + 48*a^2*b^2*tan(1/2*d*x + 1/2*c)^4 + 16*b^4*tan(1/2*d*x + 1/2*c)^4 + 4*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 112*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 12*a^4*tan(1/2*d*x + 1/2*c)^2 + 76*a^2*b^2*tan(1/2*d*x + 1/2*c)^2 + 8*a^3*b*tan(1/2*d*x + 1/2*c) - a^4)/((a*tan(1/2*d*x + 1/2*c)^3 + 2*b*tan(1/2*d*x + 1/2*c)^2 + a*tan(1/2*d*x + 1/2*c))^2*a^5))/d","A",0
1141,1,451,0,0.292469," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{12 \, {\left(9 \, a^{2} b - 20 \, b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{6}} + \frac{24 \, {\left(2 \, a^{4} - 19 \, a^{2} b^{2} + 20 \, b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{6}} + \frac{24 \, {\left(5 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 10 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 18 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 11 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 26 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, a^{4} b - 9 \, a^{2} b^{3}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}^{2} a^{6}} + \frac{a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 72 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{9}} - \frac{198 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 440 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 72 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3}}{a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{24 \, d}"," ",0,"1/24*(12*(9*a^2*b - 20*b^3)*log(abs(tan(1/2*d*x + 1/2*c)))/a^6 + 24*(2*a^4 - 19*a^2*b^2 + 20*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^6) + 24*(5*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 10*a*b^4*tan(1/2*d*x + 1/2*c)^3 + 4*a^4*b*tan(1/2*d*x + 1/2*c)^2 - a^2*b^3*tan(1/2*d*x + 1/2*c)^2 - 18*b^5*tan(1/2*d*x + 1/2*c)^2 + 11*a^3*b^2*tan(1/2*d*x + 1/2*c) - 26*a*b^4*tan(1/2*d*x + 1/2*c) + 4*a^4*b - 9*a^2*b^3)/((a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)^2*a^6) + (a^6*tan(1/2*d*x + 1/2*c)^3 - 9*a^5*b*tan(1/2*d*x + 1/2*c)^2 - 15*a^6*tan(1/2*d*x + 1/2*c) + 72*a^4*b^2*tan(1/2*d*x + 1/2*c))/a^9 - (198*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 440*b^3*tan(1/2*d*x + 1/2*c)^3 - 15*a^3*tan(1/2*d*x + 1/2*c)^2 + 72*a*b^2*tan(1/2*d*x + 1/2*c)^2 - 9*a^2*b*tan(1/2*d*x + 1/2*c) + a^3)/(a^6*tan(1/2*d*x + 1/2*c)^3))/d","A",0
1142,1,550,0,0.348042," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{24 \, {\left(a^{4} - 24 \, a^{2} b^{2} + 40 \, b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{7}} - \frac{192 \, {\left(2 \, a^{4} b - 11 \, a^{2} b^{3} + 10 \, b^{5}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{7}} - \frac{64 \, {\left(7 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 22 \, b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 17 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 32 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, a^{4} b^{2} - 11 \, a^{2} b^{4}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}^{2} a^{7}} - \frac{50 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1200 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2000 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 120 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 320 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 8 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 48 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{4}}{a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}} + \frac{a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 8 \, a^{8} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 8 \, a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 48 \, a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 120 \, a^{8} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 320 \, a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{12}}}{64 \, d}"," ",0,"1/64*(24*(a^4 - 24*a^2*b^2 + 40*b^4)*log(abs(tan(1/2*d*x + 1/2*c)))/a^7 - 192*(2*a^4*b - 11*a^2*b^3 + 10*b^5)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^7) - 64*(7*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 - 12*a*b^5*tan(1/2*d*x + 1/2*c)^3 + 6*a^4*b^2*tan(1/2*d*x + 1/2*c)^2 + a^2*b^4*tan(1/2*d*x + 1/2*c)^2 - 22*b^6*tan(1/2*d*x + 1/2*c)^2 + 17*a^3*b^3*tan(1/2*d*x + 1/2*c) - 32*a*b^5*tan(1/2*d*x + 1/2*c) + 6*a^4*b^2 - 11*a^2*b^4)/((a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)^2*a^7) - (50*a^4*tan(1/2*d*x + 1/2*c)^4 - 1200*a^2*b^2*tan(1/2*d*x + 1/2*c)^4 + 2000*b^4*tan(1/2*d*x + 1/2*c)^4 + 120*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 320*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 8*a^4*tan(1/2*d*x + 1/2*c)^2 + 48*a^2*b^2*tan(1/2*d*x + 1/2*c)^2 - 8*a^3*b*tan(1/2*d*x + 1/2*c) + a^4)/(a^7*tan(1/2*d*x + 1/2*c)^4) + (a^9*tan(1/2*d*x + 1/2*c)^4 - 8*a^8*b*tan(1/2*d*x + 1/2*c)^3 - 8*a^9*tan(1/2*d*x + 1/2*c)^2 + 48*a^7*b^2*tan(1/2*d*x + 1/2*c)^2 + 120*a^8*b*tan(1/2*d*x + 1/2*c) - 320*a^6*b^3*tan(1/2*d*x + 1/2*c))/a^12)/d","A",0
1143,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2*(a+b*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{b \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{4} \sin\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*sin(d*x + c) + a)*cos(d*x + c)^4*sin(d*x + c)^2, x)","F",0
1144,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)*(a+b*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{b \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{4} \sin\left(d x + c\right)\,{d x}"," ",0,"integrate(sqrt(b*sin(d*x + c) + a)*cos(d*x + c)^4*sin(d*x + c), x)","F",0
1145,-1,0,0,0.000000," ","integrate(cos(d*x+c)^3*cot(d*x+c)*(a+b*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1146,-1,0,0,0.000000," ","integrate(cos(d*x+c)^2*cot(d*x+c)^2*(a+b*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1147,-1,0,0,0.000000," ","integrate(cos(d*x+c)*cot(d*x+c)^3*(a+b*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1148,-1,0,0,0.000000," ","integrate(cot(d*x+c)^4*(a+b*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1149,-1,0,0,0.000000," ","integrate(cot(d*x+c)^4*csc(d*x+c)*(a+b*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1150,-1,0,0,0.000000," ","integrate(cot(d*x+c)^4*csc(d*x+c)^2*(a+b*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1151,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2*(a+b*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{4} \sin\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(3/2)*cos(d*x + c)^4*sin(d*x + c)^2, x)","F",0
1152,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)*(a+b*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{4} \sin\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(3/2)*cos(d*x + c)^4*sin(d*x + c), x)","F",0
1153,-1,0,0,0.000000," ","integrate(cos(d*x+c)^3*cot(d*x+c)*(a+b*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1154,-1,0,0,0.000000," ","integrate(cos(d*x+c)^2*cot(d*x+c)^2*(a+b*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1155,-1,0,0,0.000000," ","integrate(cos(d*x+c)*cot(d*x+c)^3*(a+b*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1156,-1,0,0,0.000000," ","integrate(cot(d*x+c)^4*(a+b*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1157,-1,0,0,0.000000," ","integrate(cot(d*x+c)^4*csc(d*x+c)*(a+b*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1158,-1,0,0,0.000000," ","integrate(cot(d*x+c)^4*csc(d*x+c)^2*(a+b*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1159,-1,0,0,0.000000," ","integrate(cot(d*x+c)^4*csc(d*x+c)^3*(a+b*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1160,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)*(a+b*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{4} \sin\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(5/2)*cos(d*x + c)^4*sin(d*x + c), x)","F",0
1161,-1,0,0,0.000000," ","integrate(cos(d*x+c)^3*cot(d*x+c)*(a+b*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1162,-1,0,0,0.000000," ","integrate(cos(d*x+c)^2*cot(d*x+c)^2*(a+b*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1163,-1,0,0,0.000000," ","integrate(cos(d*x+c)*cot(d*x+c)^3*(a+b*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1164,-1,0,0,0.000000," ","integrate(cot(d*x+c)^4*(a+b*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1165,-1,0,0,0.000000," ","integrate(cot(d*x+c)^4*csc(d*x+c)*(a+b*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1166,-1,0,0,0.000000," ","integrate(cot(d*x+c)^4*csc(d*x+c)^2*(a+b*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1167,-1,0,0,0.000000," ","integrate(cot(d*x+c)^4*csc(d*x+c)^3*(a+b*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1168,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3/(a+b*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{4} \sin\left(d x + c\right)^{3}}{\sqrt{b \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4*sin(d*x + c)^3/sqrt(b*sin(d*x + c) + a), x)","F",0
1169,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2/(a+b*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{4} \sin\left(d x + c\right)^{2}}{\sqrt{b \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4*sin(d*x + c)^2/sqrt(b*sin(d*x + c) + a), x)","F",0
1170,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)/(a+b*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{4} \sin\left(d x + c\right)}{\sqrt{b \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4*sin(d*x + c)/sqrt(b*sin(d*x + c) + a), x)","F",0
1171,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*cot(d*x+c)/(a+b*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{3} \cot\left(d x + c\right)}{\sqrt{b \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^3*cot(d*x + c)/sqrt(b*sin(d*x + c) + a), x)","F",0
1172,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*cot(d*x+c)^2/(a+b*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{2} \cot\left(d x + c\right)^{2}}{\sqrt{b \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2*cot(d*x + c)^2/sqrt(b*sin(d*x + c) + a), x)","F",0
1173,0,0,0,0.000000," ","integrate(cos(d*x+c)*cot(d*x+c)^3/(a+b*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right) \cot\left(d x + c\right)^{3}}{\sqrt{b \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)*cot(d*x + c)^3/sqrt(b*sin(d*x + c) + a), x)","F",0
1174,0,0,0,0.000000," ","integrate(cot(d*x+c)^4/(a+b*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\cot\left(d x + c\right)^{4}}{\sqrt{b \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cot(d*x + c)^4/sqrt(b*sin(d*x + c) + a), x)","F",0
1175,0,0,0,0.000000," ","integrate(cot(d*x+c)^4*csc(d*x+c)/(a+b*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\cot\left(d x + c\right)^{4} \csc\left(d x + c\right)}{\sqrt{b \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cot(d*x + c)^4*csc(d*x + c)/sqrt(b*sin(d*x + c) + a), x)","F",0
1176,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3/(a+b*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{4} \sin\left(d x + c\right)^{3}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4*sin(d*x + c)^3/(b*sin(d*x + c) + a)^(3/2), x)","F",0
1177,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2/(a+b*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{4} \sin\left(d x + c\right)^{2}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4*sin(d*x + c)^2/(b*sin(d*x + c) + a)^(3/2), x)","F",0
1178,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)/(a+b*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{4} \sin\left(d x + c\right)}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4*sin(d*x + c)/(b*sin(d*x + c) + a)^(3/2), x)","F",0
1179,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*cot(d*x+c)/(a+b*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{3} \cot\left(d x + c\right)}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^3*cot(d*x + c)/(b*sin(d*x + c) + a)^(3/2), x)","F",0
1180,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*cot(d*x+c)^2/(a+b*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{2} \cot\left(d x + c\right)^{2}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2*cot(d*x + c)^2/(b*sin(d*x + c) + a)^(3/2), x)","F",0
1181,0,0,0,0.000000," ","integrate(cos(d*x+c)*cot(d*x+c)^3/(a+b*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right) \cot\left(d x + c\right)^{3}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)*cot(d*x + c)^3/(b*sin(d*x + c) + a)^(3/2), x)","F",0
1182,0,0,0,0.000000," ","integrate(cot(d*x+c)^4/(a+b*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\cot\left(d x + c\right)^{4}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cot(d*x + c)^4/(b*sin(d*x + c) + a)^(3/2), x)","F",0
1183,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3/(a+b*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{4} \sin\left(d x + c\right)^{3}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4*sin(d*x + c)^3/(b*sin(d*x + c) + a)^(5/2), x)","F",0
1184,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2/(a+b*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{4} \sin\left(d x + c\right)^{2}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4*sin(d*x + c)^2/(b*sin(d*x + c) + a)^(5/2), x)","F",0
1185,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)/(a+b*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{4} \sin\left(d x + c\right)}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4*sin(d*x + c)/(b*sin(d*x + c) + a)^(5/2), x)","F",0
1186,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*cot(d*x+c)/(a+b*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{3} \cot\left(d x + c\right)}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^3*cot(d*x + c)/(b*sin(d*x + c) + a)^(5/2), x)","F",0
1187,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*cot(d*x+c)^2/(a+b*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{2} \cot\left(d x + c\right)^{2}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2*cot(d*x + c)^2/(b*sin(d*x + c) + a)^(5/2), x)","F",0
1188,0,0,0,0.000000," ","integrate(cos(d*x+c)*cot(d*x+c)^3/(a+b*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right) \cot\left(d x + c\right)^{3}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)*cot(d*x + c)^3/(b*sin(d*x + c) + a)^(5/2), x)","F",0
1189,0,0,0,0.000000," ","integrate(cot(d*x+c)^4/(a+b*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\cot\left(d x + c\right)^{4}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cot(d*x + c)^4/(b*sin(d*x + c) + a)^(5/2), x)","F",0
1190,0,0,0,0.000000," ","integrate(cos(f*x+e)^4/(a+b*sin(f*x+e))^(9/2)/(d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\cos\left(f x + e\right)^{4}}{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{9}{2}} \sqrt{d \sin\left(f x + e\right)}}\,{d x}"," ",0,"integrate(cos(f*x + e)^4/((b*sin(f*x + e) + a)^(9/2)*sqrt(d*sin(f*x + e))), x)","F",0
1191,-1,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^(1/3)/(a+b*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1192,-1,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^n*(a+b*sin(d*x+c))^p,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1193,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^(-3-p)*(a+b*sin(d*x+c))^p,x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{p} \sin\left(d x + c\right)^{-p - 3} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^p*sin(d*x + c)^(-p - 3)*cos(d*x + c)^4, x)","F",0
1194,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^(-4-p)*(a+b*sin(d*x+c))^p,x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{p} \sin\left(d x + c\right)^{-p - 4} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^p*sin(d*x + c)^(-p - 4)*cos(d*x + c)^4, x)","F",0
1195,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^n*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{3} \sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^3*sin(d*x + c)^n*cos(d*x + c)^4, x)","F",0
1196,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^n*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{2} \sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^2*sin(d*x + c)^n*cos(d*x + c)^4, x)","F",0
1197,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^n*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)} \sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)*sin(d*x + c)^n*cos(d*x + c)^4, x)","F",0
1198,1,133,0,0.318841," ","integrate(cos(d*x+c)^5*sin(d*x+c)^5*(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{a \cos\left(10 \, d x + 10 \, c\right)}{5120 \, d} + \frac{5 \, a \cos\left(6 \, d x + 6 \, c\right)}{3072 \, d} - \frac{5 \, a \cos\left(2 \, d x + 2 \, c\right)}{512 \, d} - \frac{b \sin\left(11 \, d x + 11 \, c\right)}{11264 \, d} + \frac{b \sin\left(9 \, d x + 9 \, c\right)}{9216 \, d} + \frac{5 \, b \sin\left(7 \, d x + 7 \, c\right)}{7168 \, d} - \frac{b \sin\left(5 \, d x + 5 \, c\right)}{1024 \, d} - \frac{5 \, b \sin\left(3 \, d x + 3 \, c\right)}{1536 \, d} + \frac{5 \, b \sin\left(d x + c\right)}{512 \, d}"," ",0,"-1/5120*a*cos(10*d*x + 10*c)/d + 5/3072*a*cos(6*d*x + 6*c)/d - 5/512*a*cos(2*d*x + 2*c)/d - 1/11264*b*sin(11*d*x + 11*c)/d + 1/9216*b*sin(9*d*x + 9*c)/d + 5/7168*b*sin(7*d*x + 7*c)/d - 1/1024*b*sin(5*d*x + 5*c)/d - 5/1536*b*sin(3*d*x + 3*c)/d + 5/512*b*sin(d*x + c)/d","A",0
1199,1,118,0,0.318803," ","integrate(cos(d*x+c)^5*sin(d*x+c)^4*(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{b \cos\left(10 \, d x + 10 \, c\right)}{5120 \, d} + \frac{5 \, b \cos\left(6 \, d x + 6 \, c\right)}{3072 \, d} - \frac{5 \, b \cos\left(2 \, d x + 2 \, c\right)}{512 \, d} + \frac{a \sin\left(9 \, d x + 9 \, c\right)}{2304 \, d} + \frac{a \sin\left(7 \, d x + 7 \, c\right)}{1792 \, d} - \frac{a \sin\left(5 \, d x + 5 \, c\right)}{320 \, d} - \frac{a \sin\left(3 \, d x + 3 \, c\right)}{192 \, d} + \frac{3 \, a \sin\left(d x + c\right)}{128 \, d}"," ",0,"-1/5120*b*cos(10*d*x + 10*c)/d + 5/3072*b*cos(6*d*x + 6*c)/d - 5/512*b*cos(2*d*x + 2*c)/d + 1/2304*a*sin(9*d*x + 9*c)/d + 1/1792*a*sin(7*d*x + 7*c)/d - 1/320*a*sin(5*d*x + 5*c)/d - 1/192*a*sin(3*d*x + 3*c)/d + 3/128*a*sin(d*x + c)/d","A",0
1200,1,133,0,0.252425," ","integrate(cos(d*x+c)^5*sin(d*x+c)^3*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{a \cos\left(8 \, d x + 8 \, c\right)}{1024 \, d} + \frac{a \cos\left(6 \, d x + 6 \, c\right)}{384 \, d} - \frac{a \cos\left(4 \, d x + 4 \, c\right)}{256 \, d} - \frac{3 \, a \cos\left(2 \, d x + 2 \, c\right)}{128 \, d} + \frac{b \sin\left(9 \, d x + 9 \, c\right)}{2304 \, d} + \frac{b \sin\left(7 \, d x + 7 \, c\right)}{1792 \, d} - \frac{b \sin\left(5 \, d x + 5 \, c\right)}{320 \, d} - \frac{b \sin\left(3 \, d x + 3 \, c\right)}{192 \, d} + \frac{3 \, b \sin\left(d x + c\right)}{128 \, d}"," ",0,"1/1024*a*cos(8*d*x + 8*c)/d + 1/384*a*cos(6*d*x + 6*c)/d - 1/256*a*cos(4*d*x + 4*c)/d - 3/128*a*cos(2*d*x + 2*c)/d + 1/2304*b*sin(9*d*x + 9*c)/d + 1/1792*b*sin(7*d*x + 7*c)/d - 1/320*b*sin(5*d*x + 5*c)/d - 1/192*b*sin(3*d*x + 3*c)/d + 3/128*b*sin(d*x + c)/d","A",0
1201,1,118,0,0.243285," ","integrate(cos(d*x+c)^5*sin(d*x+c)^2*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{b \cos\left(8 \, d x + 8 \, c\right)}{1024 \, d} + \frac{b \cos\left(6 \, d x + 6 \, c\right)}{384 \, d} - \frac{b \cos\left(4 \, d x + 4 \, c\right)}{256 \, d} - \frac{3 \, b \cos\left(2 \, d x + 2 \, c\right)}{128 \, d} - \frac{a \sin\left(7 \, d x + 7 \, c\right)}{448 \, d} - \frac{3 \, a \sin\left(5 \, d x + 5 \, c\right)}{320 \, d} - \frac{a \sin\left(3 \, d x + 3 \, c\right)}{192 \, d} + \frac{5 \, a \sin\left(d x + c\right)}{64 \, d}"," ",0,"1/1024*b*cos(8*d*x + 8*c)/d + 1/384*b*cos(6*d*x + 6*c)/d - 1/256*b*cos(4*d*x + 4*c)/d - 3/128*b*cos(2*d*x + 2*c)/d - 1/448*a*sin(7*d*x + 7*c)/d - 3/320*a*sin(5*d*x + 5*c)/d - 1/192*a*sin(3*d*x + 3*c)/d + 5/64*a*sin(d*x + c)/d","A",0
1202,1,103,0,0.212338," ","integrate(cos(d*x+c)^5*sin(d*x+c)*(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{a \cos\left(6 \, d x + 6 \, c\right)}{192 \, d} - \frac{a \cos\left(4 \, d x + 4 \, c\right)}{32 \, d} - \frac{5 \, a \cos\left(2 \, d x + 2 \, c\right)}{64 \, d} - \frac{b \sin\left(7 \, d x + 7 \, c\right)}{448 \, d} - \frac{3 \, b \sin\left(5 \, d x + 5 \, c\right)}{320 \, d} - \frac{b \sin\left(3 \, d x + 3 \, c\right)}{192 \, d} + \frac{5 \, b \sin\left(d x + c\right)}{64 \, d}"," ",0,"-1/192*a*cos(6*d*x + 6*c)/d - 1/32*a*cos(4*d*x + 4*c)/d - 5/64*a*cos(2*d*x + 2*c)/d - 1/448*b*sin(7*d*x + 7*c)/d - 3/320*b*sin(5*d*x + 5*c)/d - 1/192*b*sin(3*d*x + 3*c)/d + 5/64*b*sin(d*x + c)/d","A",0
1203,1,70,0,0.207881," ","integrate(cos(d*x+c)^5*csc(d*x+c)*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{12 \, b \sin\left(d x + c\right)^{5} + 15 \, a \sin\left(d x + c\right)^{4} - 40 \, b \sin\left(d x + c\right)^{3} - 60 \, a \sin\left(d x + c\right)^{2} + 60 \, a \log\left({\left| \sin\left(d x + c\right) \right|}\right) + 60 \, b \sin\left(d x + c\right)}{60 \, d}"," ",0,"1/60*(12*b*sin(d*x + c)^5 + 15*a*sin(d*x + c)^4 - 40*b*sin(d*x + c)^3 - 60*a*sin(d*x + c)^2 + 60*a*log(abs(sin(d*x + c))) + 60*b*sin(d*x + c))/d","A",0
1204,1,79,0,0.187150," ","integrate(cos(d*x+c)^5*csc(d*x+c)^2*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{3 \, b \sin\left(d x + c\right)^{4} + 4 \, a \sin\left(d x + c\right)^{3} - 12 \, b \sin\left(d x + c\right)^{2} + 12 \, b \log\left({\left| \sin\left(d x + c\right) \right|}\right) - 24 \, a \sin\left(d x + c\right) - \frac{12 \, {\left(b \sin\left(d x + c\right) + a\right)}}{\sin\left(d x + c\right)}}{12 \, d}"," ",0,"1/12*(3*b*sin(d*x + c)^4 + 4*a*sin(d*x + c)^3 - 12*b*sin(d*x + c)^2 + 12*b*log(abs(sin(d*x + c))) - 24*a*sin(d*x + c) - 12*(b*sin(d*x + c) + a)/sin(d*x + c))/d","A",0
1205,1,82,0,0.226648," ","integrate(cos(d*x+c)^5*csc(d*x+c)^3*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{2 \, b \sin\left(d x + c\right)^{3} + 3 \, a \sin\left(d x + c\right)^{2} - 12 \, a \log\left({\left| \sin\left(d x + c\right) \right|}\right) - 12 \, b \sin\left(d x + c\right) + \frac{3 \, {\left(6 \, a \sin\left(d x + c\right)^{2} - 2 \, b \sin\left(d x + c\right) - a\right)}}{\sin\left(d x + c\right)^{2}}}{6 \, d}"," ",0,"1/6*(2*b*sin(d*x + c)^3 + 3*a*sin(d*x + c)^2 - 12*a*log(abs(sin(d*x + c))) - 12*b*sin(d*x + c) + 3*(6*a*sin(d*x + c)^2 - 2*b*sin(d*x + c) - a)/sin(d*x + c)^2)/d","A",0
1206,1,81,0,0.205681," ","integrate(cos(d*x+c)^5*csc(d*x+c)^4*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{3 \, b \sin\left(d x + c\right)^{2} - 12 \, b \log\left({\left| \sin\left(d x + c\right) \right|}\right) + 6 \, a \sin\left(d x + c\right) + \frac{22 \, b \sin\left(d x + c\right)^{3} + 12 \, a \sin\left(d x + c\right)^{2} - 3 \, b \sin\left(d x + c\right) - 2 \, a}{\sin\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(3*b*sin(d*x + c)^2 - 12*b*log(abs(sin(d*x + c))) + 6*a*sin(d*x + c) + (22*b*sin(d*x + c)^3 + 12*a*sin(d*x + c)^2 - 3*b*sin(d*x + c) - 2*a)/sin(d*x + c)^3)/d","A",0
1207,1,82,0,0.224867," ","integrate(cos(d*x+c)^5*csc(d*x+c)^5*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{12 \, a \log\left({\left| \sin\left(d x + c\right) \right|}\right) + 12 \, b \sin\left(d x + c\right) - \frac{25 \, a \sin\left(d x + c\right)^{4} - 24 \, b \sin\left(d x + c\right)^{3} - 12 \, a \sin\left(d x + c\right)^{2} + 4 \, b \sin\left(d x + c\right) + 3 \, a}{\sin\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"1/12*(12*a*log(abs(sin(d*x + c))) + 12*b*sin(d*x + c) - (25*a*sin(d*x + c)^4 - 24*b*sin(d*x + c)^3 - 12*a*sin(d*x + c)^2 + 4*b*sin(d*x + c) + 3*a)/sin(d*x + c)^4)/d","A",0
1208,1,84,0,0.220356," ","integrate(cos(d*x+c)^5*csc(d*x+c)^6*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{60 \, b \log\left({\left| \sin\left(d x + c\right) \right|}\right) - \frac{137 \, b \sin\left(d x + c\right)^{5} + 60 \, a \sin\left(d x + c\right)^{4} - 60 \, b \sin\left(d x + c\right)^{3} - 40 \, a \sin\left(d x + c\right)^{2} + 15 \, b \sin\left(d x + c\right) + 12 \, a}{\sin\left(d x + c\right)^{5}}}{60 \, d}"," ",0,"1/60*(60*b*log(abs(sin(d*x + c))) - (137*b*sin(d*x + c)^5 + 60*a*sin(d*x + c)^4 - 60*b*sin(d*x + c)^3 - 40*a*sin(d*x + c)^2 + 15*b*sin(d*x + c) + 12*a)/sin(d*x + c)^5)/d","A",0
1209,1,70,0,0.238362," ","integrate(cos(d*x+c)^5*csc(d*x+c)^7*(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{30 \, b \sin\left(d x + c\right)^{5} + 15 \, a \sin\left(d x + c\right)^{4} - 20 \, b \sin\left(d x + c\right)^{3} - 15 \, a \sin\left(d x + c\right)^{2} + 6 \, b \sin\left(d x + c\right) + 5 \, a}{30 \, d \sin\left(d x + c\right)^{6}}"," ",0,"-1/30*(30*b*sin(d*x + c)^5 + 15*a*sin(d*x + c)^4 - 20*b*sin(d*x + c)^3 - 15*a*sin(d*x + c)^2 + 6*b*sin(d*x + c) + 5*a)/(d*sin(d*x + c)^6)","A",0
1210,1,70,0,0.226038," ","integrate(cos(d*x+c)^5*csc(d*x+c)^8*(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{105 \, b \sin\left(d x + c\right)^{5} + 70 \, a \sin\left(d x + c\right)^{4} - 105 \, b \sin\left(d x + c\right)^{3} - 84 \, a \sin\left(d x + c\right)^{2} + 35 \, b \sin\left(d x + c\right) + 30 \, a}{210 \, d \sin\left(d x + c\right)^{7}}"," ",0,"-1/210*(105*b*sin(d*x + c)^5 + 70*a*sin(d*x + c)^4 - 105*b*sin(d*x + c)^3 - 84*a*sin(d*x + c)^2 + 35*b*sin(d*x + c) + 30*a)/(d*sin(d*x + c)^7)","A",0
1211,1,70,0,0.243659," ","integrate(cos(d*x+c)^5*csc(d*x+c)^9*(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{280 \, b \sin\left(d x + c\right)^{5} + 210 \, a \sin\left(d x + c\right)^{4} - 336 \, b \sin\left(d x + c\right)^{3} - 280 \, a \sin\left(d x + c\right)^{2} + 120 \, b \sin\left(d x + c\right) + 105 \, a}{840 \, d \sin\left(d x + c\right)^{8}}"," ",0,"-1/840*(280*b*sin(d*x + c)^5 + 210*a*sin(d*x + c)^4 - 336*b*sin(d*x + c)^3 - 280*a*sin(d*x + c)^2 + 120*b*sin(d*x + c) + 105*a)/(d*sin(d*x + c)^8)","A",0
1212,1,70,0,0.272539," ","integrate(cos(d*x+c)^5*csc(d*x+c)^10*(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{630 \, b \sin\left(d x + c\right)^{5} + 504 \, a \sin\left(d x + c\right)^{4} - 840 \, b \sin\left(d x + c\right)^{3} - 720 \, a \sin\left(d x + c\right)^{2} + 315 \, b \sin\left(d x + c\right) + 280 \, a}{2520 \, d \sin\left(d x + c\right)^{9}}"," ",0,"-1/2520*(630*b*sin(d*x + c)^5 + 504*a*sin(d*x + c)^4 - 840*b*sin(d*x + c)^3 - 720*a*sin(d*x + c)^2 + 315*b*sin(d*x + c) + 280*a)/(d*sin(d*x + c)^9)","A",0
1213,1,70,0,0.257500," ","integrate(cos(d*x+c)^5*csc(d*x+c)^11*(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{252 \, b \sin\left(d x + c\right)^{5} + 210 \, a \sin\left(d x + c\right)^{4} - 360 \, b \sin\left(d x + c\right)^{3} - 315 \, a \sin\left(d x + c\right)^{2} + 140 \, b \sin\left(d x + c\right) + 126 \, a}{1260 \, d \sin\left(d x + c\right)^{10}}"," ",0,"-1/1260*(252*b*sin(d*x + c)^5 + 210*a*sin(d*x + c)^4 - 360*b*sin(d*x + c)^3 - 315*a*sin(d*x + c)^2 + 140*b*sin(d*x + c) + 126*a)/(d*sin(d*x + c)^10)","A",0
1214,1,70,0,0.244080," ","integrate(cos(d*x+c)^5*csc(d*x+c)^12*(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{2310 \, b \sin\left(d x + c\right)^{5} + 1980 \, a \sin\left(d x + c\right)^{4} - 3465 \, b \sin\left(d x + c\right)^{3} - 3080 \, a \sin\left(d x + c\right)^{2} + 1386 \, b \sin\left(d x + c\right) + 1260 \, a}{13860 \, d \sin\left(d x + c\right)^{11}}"," ",0,"-1/13860*(2310*b*sin(d*x + c)^5 + 1980*a*sin(d*x + c)^4 - 3465*b*sin(d*x + c)^3 - 3080*a*sin(d*x + c)^2 + 1386*b*sin(d*x + c) + 1260*a)/(d*sin(d*x + c)^11)","A",0
1215,1,173,0,0.334008," ","integrate(cos(d*x+c)^5*sin(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{a b \cos\left(8 \, d x + 8 \, c\right)}{512 \, d} + \frac{a b \cos\left(6 \, d x + 6 \, c\right)}{192 \, d} - \frac{a b \cos\left(4 \, d x + 4 \, c\right)}{128 \, d} - \frac{3 \, a b \cos\left(2 \, d x + 2 \, c\right)}{64 \, d} + \frac{b^{2} \sin\left(9 \, d x + 9 \, c\right)}{2304 \, d} - \frac{{\left(4 \, a^{2} - b^{2}\right)} \sin\left(7 \, d x + 7 \, c\right)}{1792 \, d} - \frac{{\left(3 \, a^{2} + b^{2}\right)} \sin\left(5 \, d x + 5 \, c\right)}{320 \, d} - \frac{{\left(a^{2} + b^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)}{192 \, d} + \frac{{\left(10 \, a^{2} + 3 \, b^{2}\right)} \sin\left(d x + c\right)}{128 \, d}"," ",0,"1/512*a*b*cos(8*d*x + 8*c)/d + 1/192*a*b*cos(6*d*x + 6*c)/d - 1/128*a*b*cos(4*d*x + 4*c)/d - 3/64*a*b*cos(2*d*x + 2*c)/d + 1/2304*b^2*sin(9*d*x + 9*c)/d - 1/1792*(4*a^2 - b^2)*sin(7*d*x + 7*c)/d - 1/320*(3*a^2 + b^2)*sin(5*d*x + 5*c)/d - 1/192*(a^2 + b^2)*sin(3*d*x + 3*c)/d + 1/128*(10*a^2 + 3*b^2)*sin(d*x + c)/d","A",0
1216,1,152,0,0.266909," ","integrate(cos(d*x+c)^5*sin(d*x+c)*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{b^{2} \cos\left(8 \, d x + 8 \, c\right)}{1024 \, d} - \frac{a b \sin\left(7 \, d x + 7 \, c\right)}{224 \, d} - \frac{3 \, a b \sin\left(5 \, d x + 5 \, c\right)}{160 \, d} - \frac{a b \sin\left(3 \, d x + 3 \, c\right)}{96 \, d} + \frac{5 \, a b \sin\left(d x + c\right)}{32 \, d} - \frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(6 \, d x + 6 \, c\right)}{384 \, d} - \frac{{\left(8 \, a^{2} + b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)}{256 \, d} - \frac{{\left(10 \, a^{2} + 3 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)}{128 \, d}"," ",0,"1/1024*b^2*cos(8*d*x + 8*c)/d - 1/224*a*b*sin(7*d*x + 7*c)/d - 3/160*a*b*sin(5*d*x + 5*c)/d - 1/96*a*b*sin(3*d*x + 3*c)/d + 5/32*a*b*sin(d*x + c)/d - 1/384*(2*a^2 - b^2)*cos(6*d*x + 6*c)/d - 1/256*(8*a^2 + b^2)*cos(4*d*x + 4*c)/d - 1/128*(10*a^2 + 3*b^2)*cos(2*d*x + 2*c)/d","A",0
1217,1,118,0,0.238425," ","integrate(cos(d*x+c)^5*csc(d*x+c)*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{10 \, b^{2} \sin\left(d x + c\right)^{6} + 24 \, a b \sin\left(d x + c\right)^{5} + 15 \, a^{2} \sin\left(d x + c\right)^{4} - 30 \, b^{2} \sin\left(d x + c\right)^{4} - 80 \, a b \sin\left(d x + c\right)^{3} - 60 \, a^{2} \sin\left(d x + c\right)^{2} + 30 \, b^{2} \sin\left(d x + c\right)^{2} + 60 \, a^{2} \log\left({\left| \sin\left(d x + c\right) \right|}\right) + 120 \, a b \sin\left(d x + c\right)}{60 \, d}"," ",0,"1/60*(10*b^2*sin(d*x + c)^6 + 24*a*b*sin(d*x + c)^5 + 15*a^2*sin(d*x + c)^4 - 30*b^2*sin(d*x + c)^4 - 80*a*b*sin(d*x + c)^3 - 60*a^2*sin(d*x + c)^2 + 30*b^2*sin(d*x + c)^2 + 60*a^2*log(abs(sin(d*x + c))) + 120*a*b*sin(d*x + c))/d","A",0
1218,1,127,0,0.241811," ","integrate(cos(d*x+c)^5*csc(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{6 \, b^{2} \sin\left(d x + c\right)^{5} + 15 \, a b \sin\left(d x + c\right)^{4} + 10 \, a^{2} \sin\left(d x + c\right)^{3} - 20 \, b^{2} \sin\left(d x + c\right)^{3} - 60 \, a b \sin\left(d x + c\right)^{2} + 60 \, a b \log\left({\left| \sin\left(d x + c\right) \right|}\right) - 60 \, a^{2} \sin\left(d x + c\right) + 30 \, b^{2} \sin\left(d x + c\right) - \frac{30 \, {\left(2 \, a b \sin\left(d x + c\right) + a^{2}\right)}}{\sin\left(d x + c\right)}}{30 \, d}"," ",0,"1/30*(6*b^2*sin(d*x + c)^5 + 15*a*b*sin(d*x + c)^4 + 10*a^2*sin(d*x + c)^3 - 20*b^2*sin(d*x + c)^3 - 60*a*b*sin(d*x + c)^2 + 60*a*b*log(abs(sin(d*x + c))) - 60*a^2*sin(d*x + c) + 30*b^2*sin(d*x + c) - 30*(2*a*b*sin(d*x + c) + a^2)/sin(d*x + c))/d","A",0
1219,1,140,0,0.257596," ","integrate(cos(d*x+c)^5*csc(d*x+c)^3*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{3 \, b^{2} \sin\left(d x + c\right)^{4} + 8 \, a b \sin\left(d x + c\right)^{3} + 6 \, a^{2} \sin\left(d x + c\right)^{2} - 12 \, b^{2} \sin\left(d x + c\right)^{2} - 48 \, a b \sin\left(d x + c\right) - 12 \, {\left(2 \, a^{2} - b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) \right|}\right) + \frac{6 \, {\left(6 \, a^{2} \sin\left(d x + c\right)^{2} - 3 \, b^{2} \sin\left(d x + c\right)^{2} - 4 \, a b \sin\left(d x + c\right) - a^{2}\right)}}{\sin\left(d x + c\right)^{2}}}{12 \, d}"," ",0,"1/12*(3*b^2*sin(d*x + c)^4 + 8*a*b*sin(d*x + c)^3 + 6*a^2*sin(d*x + c)^2 - 12*b^2*sin(d*x + c)^2 - 48*a*b*sin(d*x + c) - 12*(2*a^2 - b^2)*log(abs(sin(d*x + c))) + 6*(6*a^2*sin(d*x + c)^2 - 3*b^2*sin(d*x + c)^2 - 4*a*b*sin(d*x + c) - a^2)/sin(d*x + c)^2)/d","A",0
1220,1,127,0,0.279129," ","integrate(cos(d*x+c)^5*csc(d*x+c)^4*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{b^{2} \sin\left(d x + c\right)^{3} + 3 \, a b \sin\left(d x + c\right)^{2} - 12 \, a b \log\left({\left| \sin\left(d x + c\right) \right|}\right) + 3 \, a^{2} \sin\left(d x + c\right) - 6 \, b^{2} \sin\left(d x + c\right) + \frac{22 \, a b \sin\left(d x + c\right)^{3} + 6 \, a^{2} \sin\left(d x + c\right)^{2} - 3 \, b^{2} \sin\left(d x + c\right)^{2} - 3 \, a b \sin\left(d x + c\right) - a^{2}}{\sin\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"1/3*(b^2*sin(d*x + c)^3 + 3*a*b*sin(d*x + c)^2 - 12*a*b*log(abs(sin(d*x + c))) + 3*a^2*sin(d*x + c) - 6*b^2*sin(d*x + c) + (22*a*b*sin(d*x + c)^3 + 6*a^2*sin(d*x + c)^2 - 3*b^2*sin(d*x + c)^2 - 3*a*b*sin(d*x + c) - a^2)/sin(d*x + c)^3)/d","A",0
1221,1,138,0,0.289190," ","integrate(cos(d*x+c)^5*csc(d*x+c)^5*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{6 \, b^{2} \sin\left(d x + c\right)^{2} + 24 \, a b \sin\left(d x + c\right) + 12 \, {\left(a^{2} - 2 \, b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) \right|}\right) - \frac{25 \, a^{2} \sin\left(d x + c\right)^{4} - 50 \, b^{2} \sin\left(d x + c\right)^{4} - 48 \, a b \sin\left(d x + c\right)^{3} - 12 \, a^{2} \sin\left(d x + c\right)^{2} + 6 \, b^{2} \sin\left(d x + c\right)^{2} + 8 \, a b \sin\left(d x + c\right) + 3 \, a^{2}}{\sin\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"1/12*(6*b^2*sin(d*x + c)^2 + 24*a*b*sin(d*x + c) + 12*(a^2 - 2*b^2)*log(abs(sin(d*x + c))) - (25*a^2*sin(d*x + c)^4 - 50*b^2*sin(d*x + c)^4 - 48*a*b*sin(d*x + c)^3 - 12*a^2*sin(d*x + c)^2 + 6*b^2*sin(d*x + c)^2 + 8*a*b*sin(d*x + c) + 3*a^2)/sin(d*x + c)^4)/d","A",0
1222,1,131,0,0.268491," ","integrate(cos(d*x+c)^5*csc(d*x+c)^6*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{60 \, a b \log\left({\left| \sin\left(d x + c\right) \right|}\right) + 30 \, b^{2} \sin\left(d x + c\right) - \frac{137 \, a b \sin\left(d x + c\right)^{5} + 30 \, a^{2} \sin\left(d x + c\right)^{4} - 60 \, b^{2} \sin\left(d x + c\right)^{4} - 60 \, a b \sin\left(d x + c\right)^{3} - 20 \, a^{2} \sin\left(d x + c\right)^{2} + 10 \, b^{2} \sin\left(d x + c\right)^{2} + 15 \, a b \sin\left(d x + c\right) + 6 \, a^{2}}{\sin\left(d x + c\right)^{5}}}{30 \, d}"," ",0,"1/30*(60*a*b*log(abs(sin(d*x + c))) + 30*b^2*sin(d*x + c) - (137*a*b*sin(d*x + c)^5 + 30*a^2*sin(d*x + c)^4 - 60*b^2*sin(d*x + c)^4 - 60*a*b*sin(d*x + c)^3 - 20*a^2*sin(d*x + c)^2 + 10*b^2*sin(d*x + c)^2 + 15*a*b*sin(d*x + c) + 6*a^2)/sin(d*x + c)^5)/d","A",0
1223,1,134,0,0.298534," ","integrate(cos(d*x+c)^5*csc(d*x+c)^7*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{60 \, b^{2} \log\left({\left| \sin\left(d x + c\right) \right|}\right) - \frac{147 \, b^{2} \sin\left(d x + c\right)^{6} + 120 \, a b \sin\left(d x + c\right)^{5} + 30 \, a^{2} \sin\left(d x + c\right)^{4} - 60 \, b^{2} \sin\left(d x + c\right)^{4} - 80 \, a b \sin\left(d x + c\right)^{3} - 30 \, a^{2} \sin\left(d x + c\right)^{2} + 15 \, b^{2} \sin\left(d x + c\right)^{2} + 24 \, a b \sin\left(d x + c\right) + 10 \, a^{2}}{\sin\left(d x + c\right)^{6}}}{60 \, d}"," ",0,"1/60*(60*b^2*log(abs(sin(d*x + c))) - (147*b^2*sin(d*x + c)^6 + 120*a*b*sin(d*x + c)^5 + 30*a^2*sin(d*x + c)^4 - 60*b^2*sin(d*x + c)^4 - 80*a*b*sin(d*x + c)^3 - 30*a^2*sin(d*x + c)^2 + 15*b^2*sin(d*x + c)^2 + 24*a*b*sin(d*x + c) + 10*a^2)/sin(d*x + c)^6)/d","A",0
1224,1,118,0,0.284557," ","integrate(cos(d*x+c)^5*csc(d*x+c)^8*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{105 \, b^{2} \sin\left(d x + c\right)^{6} + 105 \, a b \sin\left(d x + c\right)^{5} + 35 \, a^{2} \sin\left(d x + c\right)^{4} - 70 \, b^{2} \sin\left(d x + c\right)^{4} - 105 \, a b \sin\left(d x + c\right)^{3} - 42 \, a^{2} \sin\left(d x + c\right)^{2} + 21 \, b^{2} \sin\left(d x + c\right)^{2} + 35 \, a b \sin\left(d x + c\right) + 15 \, a^{2}}{105 \, d \sin\left(d x + c\right)^{7}}"," ",0,"-1/105*(105*b^2*sin(d*x + c)^6 + 105*a*b*sin(d*x + c)^5 + 35*a^2*sin(d*x + c)^4 - 70*b^2*sin(d*x + c)^4 - 105*a*b*sin(d*x + c)^3 - 42*a^2*sin(d*x + c)^2 + 21*b^2*sin(d*x + c)^2 + 35*a*b*sin(d*x + c) + 15*a^2)/(d*sin(d*x + c)^7)","A",0
1225,1,118,0,0.326663," ","integrate(cos(d*x+c)^5*csc(d*x+c)^9*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{420 \, b^{2} \sin\left(d x + c\right)^{6} + 560 \, a b \sin\left(d x + c\right)^{5} + 210 \, a^{2} \sin\left(d x + c\right)^{4} - 420 \, b^{2} \sin\left(d x + c\right)^{4} - 672 \, a b \sin\left(d x + c\right)^{3} - 280 \, a^{2} \sin\left(d x + c\right)^{2} + 140 \, b^{2} \sin\left(d x + c\right)^{2} + 240 \, a b \sin\left(d x + c\right) + 105 \, a^{2}}{840 \, d \sin\left(d x + c\right)^{8}}"," ",0,"-1/840*(420*b^2*sin(d*x + c)^6 + 560*a*b*sin(d*x + c)^5 + 210*a^2*sin(d*x + c)^4 - 420*b^2*sin(d*x + c)^4 - 672*a*b*sin(d*x + c)^3 - 280*a^2*sin(d*x + c)^2 + 140*b^2*sin(d*x + c)^2 + 240*a*b*sin(d*x + c) + 105*a^2)/(d*sin(d*x + c)^8)","A",0
1226,1,300,0,0.227369," ","integrate(cos(d*x+c)^5*sin(d*x+c)^3/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{60 \, {\left(7 \, a^{6} - 10 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{b^{8}} - \frac{60 \, {\left(7 \, a^{6} b \sin\left(d x + c\right) - 10 \, a^{4} b^{3} \sin\left(d x + c\right) + 3 \, a^{2} b^{5} \sin\left(d x + c\right) + 6 \, a^{7} - 8 \, a^{5} b^{2} + 2 \, a^{3} b^{4}\right)}}{{\left(b \sin\left(d x + c\right) + a\right)} b^{8}} + \frac{10 \, b^{10} \sin\left(d x + c\right)^{6} - 24 \, a b^{9} \sin\left(d x + c\right)^{5} + 45 \, a^{2} b^{8} \sin\left(d x + c\right)^{4} - 30 \, b^{10} \sin\left(d x + c\right)^{4} - 80 \, a^{3} b^{7} \sin\left(d x + c\right)^{3} + 80 \, a b^{9} \sin\left(d x + c\right)^{3} + 150 \, a^{4} b^{6} \sin\left(d x + c\right)^{2} - 180 \, a^{2} b^{8} \sin\left(d x + c\right)^{2} + 30 \, b^{10} \sin\left(d x + c\right)^{2} - 360 \, a^{5} b^{5} \sin\left(d x + c\right) + 480 \, a^{3} b^{7} \sin\left(d x + c\right) - 120 \, a b^{9} \sin\left(d x + c\right)}{b^{12}}}{60 \, d}"," ",0,"1/60*(60*(7*a^6 - 10*a^4*b^2 + 3*a^2*b^4)*log(abs(b*sin(d*x + c) + a))/b^8 - 60*(7*a^6*b*sin(d*x + c) - 10*a^4*b^3*sin(d*x + c) + 3*a^2*b^5*sin(d*x + c) + 6*a^7 - 8*a^5*b^2 + 2*a^3*b^4)/((b*sin(d*x + c) + a)*b^8) + (10*b^10*sin(d*x + c)^6 - 24*a*b^9*sin(d*x + c)^5 + 45*a^2*b^8*sin(d*x + c)^4 - 30*b^10*sin(d*x + c)^4 - 80*a^3*b^7*sin(d*x + c)^3 + 80*a*b^9*sin(d*x + c)^3 + 150*a^4*b^6*sin(d*x + c)^2 - 180*a^2*b^8*sin(d*x + c)^2 + 30*b^10*sin(d*x + c)^2 - 360*a^5*b^5*sin(d*x + c) + 480*a^3*b^7*sin(d*x + c) - 120*a*b^9*sin(d*x + c))/b^12)/d","A",0
1227,1,249,0,0.204423," ","integrate(cos(d*x+c)^5*sin(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{60 \, {\left(3 \, a^{5} - 4 \, a^{3} b^{2} + a b^{4}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{b^{7}} - \frac{30 \, {\left(6 \, a^{5} b \sin\left(d x + c\right) - 8 \, a^{3} b^{3} \sin\left(d x + c\right) + 2 \, a b^{5} \sin\left(d x + c\right) + 5 \, a^{6} - 6 \, a^{4} b^{2} + a^{2} b^{4}\right)}}{{\left(b \sin\left(d x + c\right) + a\right)} b^{7}} - \frac{6 \, b^{8} \sin\left(d x + c\right)^{5} - 15 \, a b^{7} \sin\left(d x + c\right)^{4} + 30 \, a^{2} b^{6} \sin\left(d x + c\right)^{3} - 20 \, b^{8} \sin\left(d x + c\right)^{3} - 60 \, a^{3} b^{5} \sin\left(d x + c\right)^{2} + 60 \, a b^{7} \sin\left(d x + c\right)^{2} + 150 \, a^{4} b^{4} \sin\left(d x + c\right) - 180 \, a^{2} b^{6} \sin\left(d x + c\right) + 30 \, b^{8} \sin\left(d x + c\right)}{b^{10}}}{30 \, d}"," ",0,"-1/30*(60*(3*a^5 - 4*a^3*b^2 + a*b^4)*log(abs(b*sin(d*x + c) + a))/b^7 - 30*(6*a^5*b*sin(d*x + c) - 8*a^3*b^3*sin(d*x + c) + 2*a*b^5*sin(d*x + c) + 5*a^6 - 6*a^4*b^2 + a^2*b^4)/((b*sin(d*x + c) + a)*b^7) - (6*b^8*sin(d*x + c)^5 - 15*a*b^7*sin(d*x + c)^4 + 30*a^2*b^6*sin(d*x + c)^3 - 20*b^8*sin(d*x + c)^3 - 60*a^3*b^5*sin(d*x + c)^2 + 60*a*b^7*sin(d*x + c)^2 + 150*a^4*b^4*sin(d*x + c) - 180*a^2*b^6*sin(d*x + c) + 30*b^8*sin(d*x + c))/b^10)/d","A",0
1228,1,194,0,0.193083," ","integrate(cos(d*x+c)^5*sin(d*x+c)/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{12 \, {\left(5 \, a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{b^{6}} - \frac{12 \, {\left(5 \, a^{4} b \sin\left(d x + c\right) - 6 \, a^{2} b^{3} \sin\left(d x + c\right) + b^{5} \sin\left(d x + c\right) + 4 \, a^{5} - 4 \, a^{3} b^{2}\right)}}{{\left(b \sin\left(d x + c\right) + a\right)} b^{6}} + \frac{3 \, b^{6} \sin\left(d x + c\right)^{4} - 8 \, a b^{5} \sin\left(d x + c\right)^{3} + 18 \, a^{2} b^{4} \sin\left(d x + c\right)^{2} - 12 \, b^{6} \sin\left(d x + c\right)^{2} - 48 \, a^{3} b^{3} \sin\left(d x + c\right) + 48 \, a b^{5} \sin\left(d x + c\right)}{b^{8}}}{12 \, d}"," ",0,"1/12*(12*(5*a^4 - 6*a^2*b^2 + b^4)*log(abs(b*sin(d*x + c) + a))/b^6 - 12*(5*a^4*b*sin(d*x + c) - 6*a^2*b^3*sin(d*x + c) + b^5*sin(d*x + c) + 4*a^5 - 4*a^3*b^2)/((b*sin(d*x + c) + a)*b^6) + (3*b^6*sin(d*x + c)^4 - 8*a*b^5*sin(d*x + c)^3 + 18*a^2*b^4*sin(d*x + c)^2 - 12*b^6*sin(d*x + c)^2 - 48*a^3*b^3*sin(d*x + c) + 48*a*b^5*sin(d*x + c))/b^8)/d","A",0
1229,1,154,0,0.192815," ","integrate(cos(d*x+c)^5*csc(d*x+c)/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2 \, \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a^{2}} + \frac{b^{2} \sin\left(d x + c\right)^{2} - 4 \, a b \sin\left(d x + c\right)}{b^{4}} + \frac{2 \, {\left(3 \, a^{4} - 2 \, a^{2} b^{2} - b^{4}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{2} b^{4}} - \frac{2 \, {\left(3 \, a^{4} b \sin\left(d x + c\right) - 2 \, a^{2} b^{3} \sin\left(d x + c\right) - b^{5} \sin\left(d x + c\right) + 2 \, a^{5} - 2 \, a b^{4}\right)}}{{\left(b \sin\left(d x + c\right) + a\right)} a^{2} b^{4}}}{2 \, d}"," ",0,"1/2*(2*log(abs(sin(d*x + c)))/a^2 + (b^2*sin(d*x + c)^2 - 4*a*b*sin(d*x + c))/b^4 + 2*(3*a^4 - 2*a^2*b^2 - b^4)*log(abs(b*sin(d*x + c) + a))/(a^2*b^4) - 2*(3*a^4*b*sin(d*x + c) - 2*a^2*b^3*sin(d*x + c) - b^5*sin(d*x + c) + 2*a^5 - 2*a*b^4)/((b*sin(d*x + c) + a)*a^2*b^4))/d","A",0
1230,1,131,0,0.218493," ","integrate(cos(d*x+c)^5*csc(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{2 \, b \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a^{3}} - \frac{\sin\left(d x + c\right)}{b^{2}} - \frac{a^{3} \sin\left(d x + c\right)^{2} + 2 \, a^{2} b \sin\left(d x + c\right) - 2 \, b^{3} \sin\left(d x + c\right) - a b^{2}}{{\left(b \sin\left(d x + c\right)^{2} + a \sin\left(d x + c\right)\right)} a^{2} b^{2}} + \frac{2 \, {\left(a^{4} - b^{4}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{3} b^{3}}}{d}"," ",0,"-(2*b*log(abs(sin(d*x + c)))/a^3 - sin(d*x + c)/b^2 - (a^3*sin(d*x + c)^2 + 2*a^2*b*sin(d*x + c) - 2*b^3*sin(d*x + c) - a*b^2)/((b*sin(d*x + c)^2 + a*sin(d*x + c))*a^2*b^2) + 2*(a^4 - b^4)*log(abs(b*sin(d*x + c) + a))/(a^3*b^3))/d","A",0
1231,1,190,0,0.230853," ","integrate(cos(d*x+c)^5*csc(d*x+c)^3/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(2 \, a^{2} - 3 \, b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a^{4}} - \frac{2 \, {\left(a^{4} + 2 \, a^{2} b^{2} - 3 \, b^{4}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{4} b^{2}} + \frac{2 \, {\left(a^{4} \sin\left(d x + c\right) + 2 \, a^{2} b^{2} \sin\left(d x + c\right) - 3 \, b^{4} \sin\left(d x + c\right) + 4 \, a^{3} b - 4 \, a b^{3}\right)}}{{\left(b \sin\left(d x + c\right) + a\right)} a^{4} b} - \frac{6 \, a^{2} \sin\left(d x + c\right)^{2} - 9 \, b^{2} \sin\left(d x + c\right)^{2} + 4 \, a b \sin\left(d x + c\right) - a^{2}}{a^{4} \sin\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(2*(2*a^2 - 3*b^2)*log(abs(sin(d*x + c)))/a^4 - 2*(a^4 + 2*a^2*b^2 - 3*b^4)*log(abs(b*sin(d*x + c) + a))/(a^4*b^2) + 2*(a^4*sin(d*x + c) + 2*a^2*b^2*sin(d*x + c) - 3*b^4*sin(d*x + c) + 4*a^3*b - 4*a*b^3)/((b*sin(d*x + c) + a)*a^4*b) - (6*a^2*sin(d*x + c)^2 - 9*b^2*sin(d*x + c)^2 + 4*a*b*sin(d*x + c) - a^2)/(a^4*sin(d*x + c)^2))/d","A",0
1232,1,211,0,0.249754," ","integrate(cos(d*x+c)^5*csc(d*x+c)^4/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{12 \, {\left(a^{2} b - b^{3}\right)} \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a^{5}} - \frac{12 \, {\left(a^{2} b^{2} - b^{4}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{5} b} + \frac{3 \, {\left(4 \, a^{2} b^{3} \sin\left(d x + c\right) - 4 \, b^{5} \sin\left(d x + c\right) - a^{5} + 6 \, a^{3} b^{2} - 5 \, a b^{4}\right)}}{{\left(b \sin\left(d x + c\right) + a\right)} a^{5} b} - \frac{22 \, a^{2} b \sin\left(d x + c\right)^{3} - 22 \, b^{3} \sin\left(d x + c\right)^{3} - 6 \, a^{3} \sin\left(d x + c\right)^{2} + 9 \, a b^{2} \sin\left(d x + c\right)^{2} - 3 \, a^{2} b \sin\left(d x + c\right) + a^{3}}{a^{5} \sin\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"1/3*(12*(a^2*b - b^3)*log(abs(sin(d*x + c)))/a^5 - 12*(a^2*b^2 - b^4)*log(abs(b*sin(d*x + c) + a))/(a^5*b) + 3*(4*a^2*b^3*sin(d*x + c) - 4*b^5*sin(d*x + c) - a^5 + 6*a^3*b^2 - 5*a*b^4)/((b*sin(d*x + c) + a)*a^5*b) - (22*a^2*b*sin(d*x + c)^3 - 22*b^3*sin(d*x + c)^3 - 6*a^3*sin(d*x + c)^2 + 9*a*b^2*sin(d*x + c)^2 - 3*a^2*b*sin(d*x + c) + a^3)/(a^5*sin(d*x + c)^3))/d","A",0
1233,1,278,0,0.264614," ","integrate(cos(d*x+c)^5*csc(d*x+c)^5/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{12 \, {\left(a^{4} - 6 \, a^{2} b^{2} + 5 \, b^{4}\right)} \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a^{6}} - \frac{12 \, {\left(a^{4} b - 6 \, a^{2} b^{3} + 5 \, b^{5}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{6} b} + \frac{12 \, {\left(a^{4} b \sin\left(d x + c\right) - 6 \, a^{2} b^{3} \sin\left(d x + c\right) + 5 \, b^{5} \sin\left(d x + c\right) + 2 \, a^{5} - 8 \, a^{3} b^{2} + 6 \, a b^{4}\right)}}{{\left(b \sin\left(d x + c\right) + a\right)} a^{6}} - \frac{25 \, a^{4} \sin\left(d x + c\right)^{4} - 150 \, a^{2} b^{2} \sin\left(d x + c\right)^{4} + 125 \, b^{4} \sin\left(d x + c\right)^{4} + 48 \, a^{3} b \sin\left(d x + c\right)^{3} - 48 \, a b^{3} \sin\left(d x + c\right)^{3} - 12 \, a^{4} \sin\left(d x + c\right)^{2} + 18 \, a^{2} b^{2} \sin\left(d x + c\right)^{2} - 8 \, a^{3} b \sin\left(d x + c\right) + 3 \, a^{4}}{a^{6} \sin\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"1/12*(12*(a^4 - 6*a^2*b^2 + 5*b^4)*log(abs(sin(d*x + c)))/a^6 - 12*(a^4*b - 6*a^2*b^3 + 5*b^5)*log(abs(b*sin(d*x + c) + a))/(a^6*b) + 12*(a^4*b*sin(d*x + c) - 6*a^2*b^3*sin(d*x + c) + 5*b^5*sin(d*x + c) + 2*a^5 - 8*a^3*b^2 + 6*a*b^4)/((b*sin(d*x + c) + a)*a^6) - (25*a^4*sin(d*x + c)^4 - 150*a^2*b^2*sin(d*x + c)^4 + 125*b^4*sin(d*x + c)^4 + 48*a^3*b*sin(d*x + c)^3 - 48*a*b^3*sin(d*x + c)^3 - 12*a^4*sin(d*x + c)^2 + 18*a^2*b^2*sin(d*x + c)^2 - 8*a^3*b*sin(d*x + c) + 3*a^4)/(a^6*sin(d*x + c)^4))/d","A",0
1234,1,332,0,0.242808," ","integrate(cos(d*x+c)^5*csc(d*x+c)^6/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{60 \, {\left(a^{4} b - 4 \, a^{2} b^{3} + 3 \, b^{5}\right)} \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a^{7}} - \frac{60 \, {\left(a^{4} b^{2} - 4 \, a^{2} b^{4} + 3 \, b^{6}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{7} b} + \frac{30 \, {\left(2 \, a^{4} b^{2} \sin\left(d x + c\right) - 8 \, a^{2} b^{4} \sin\left(d x + c\right) + 6 \, b^{6} \sin\left(d x + c\right) + 3 \, a^{5} b - 10 \, a^{3} b^{3} + 7 \, a b^{5}\right)}}{{\left(b \sin\left(d x + c\right) + a\right)} a^{7}} - \frac{137 \, a^{4} b \sin\left(d x + c\right)^{5} - 548 \, a^{2} b^{3} \sin\left(d x + c\right)^{5} + 411 \, b^{5} \sin\left(d x + c\right)^{5} - 30 \, a^{5} \sin\left(d x + c\right)^{4} + 180 \, a^{3} b^{2} \sin\left(d x + c\right)^{4} - 150 \, a b^{4} \sin\left(d x + c\right)^{4} - 60 \, a^{4} b \sin\left(d x + c\right)^{3} + 60 \, a^{2} b^{3} \sin\left(d x + c\right)^{3} + 20 \, a^{5} \sin\left(d x + c\right)^{2} - 30 \, a^{3} b^{2} \sin\left(d x + c\right)^{2} + 15 \, a^{4} b \sin\left(d x + c\right) - 6 \, a^{5}}{a^{7} \sin\left(d x + c\right)^{5}}}{30 \, d}"," ",0,"-1/30*(60*(a^4*b - 4*a^2*b^3 + 3*b^5)*log(abs(sin(d*x + c)))/a^7 - 60*(a^4*b^2 - 4*a^2*b^4 + 3*b^6)*log(abs(b*sin(d*x + c) + a))/(a^7*b) + 30*(2*a^4*b^2*sin(d*x + c) - 8*a^2*b^4*sin(d*x + c) + 6*b^6*sin(d*x + c) + 3*a^5*b - 10*a^3*b^3 + 7*a*b^5)/((b*sin(d*x + c) + a)*a^7) - (137*a^4*b*sin(d*x + c)^5 - 548*a^2*b^3*sin(d*x + c)^5 + 411*b^5*sin(d*x + c)^5 - 30*a^5*sin(d*x + c)^4 + 180*a^3*b^2*sin(d*x + c)^4 - 150*a*b^4*sin(d*x + c)^4 - 60*a^4*b*sin(d*x + c)^3 + 60*a^2*b^3*sin(d*x + c)^3 + 20*a^5*sin(d*x + c)^2 - 30*a^3*b^2*sin(d*x + c)^2 + 15*a^4*b*sin(d*x + c) - 6*a^5)/(a^7*sin(d*x + c)^5))/d","A",0
1235,-1,0,0,0.000000," ","integrate(cos(d*x+c)^5*sin(d*x+c)^n*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1236,-1,0,0,0.000000," ","integrate(cos(d*x+c)^5*sin(d*x+c)^n*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1237,0,0,0,0.000000," ","integrate(cos(d*x+c)^5*sin(d*x+c)^n/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\int \frac{\sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{5}}{b \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sin(d*x + c)^n*cos(d*x + c)^5/(b*sin(d*x + c) + a), x)","F",0
1238,0,0,0,0.000000," ","integrate(cos(d*x+c)^5*sin(d*x+c)^n/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{5}}{{\left(b \sin\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sin(d*x + c)^n*cos(d*x + c)^5/(b*sin(d*x + c) + a)^2, x)","F",0
1239,1,214,0,0.786946," ","integrate(cos(d*x+c)^6*sin(d*x+c)^5*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{5}{512} \, a b x + \frac{b^{2} \cos\left(13 \, d x + 13 \, c\right)}{53248 \, d} - \frac{a b \sin\left(12 \, d x + 12 \, c\right)}{12288 \, d} + \frac{3 \, a b \sin\left(8 \, d x + 8 \, c\right)}{4096 \, d} - \frac{15 \, a b \sin\left(4 \, d x + 4 \, c\right)}{4096 \, d} - \frac{{\left(4 \, a^{2} + b^{2}\right)} \cos\left(11 \, d x + 11 \, c\right)}{45056 \, d} - \frac{{\left(2 \, a^{2} + 3 \, b^{2}\right)} \cos\left(9 \, d x + 9 \, c\right)}{18432 \, d} + \frac{{\left(10 \, a^{2} + 3 \, b^{2}\right)} \cos\left(7 \, d x + 7 \, c\right)}{14336 \, d} + \frac{{\left(4 \, a^{2} + 3 \, b^{2}\right)} \cos\left(5 \, d x + 5 \, c\right)}{4096 \, d} - \frac{5 \, {\left(8 \, a^{2} + 3 \, b^{2}\right)} \cos\left(3 \, d x + 3 \, c\right)}{12288 \, d} - \frac{5 \, {\left(2 \, a^{2} + b^{2}\right)} \cos\left(d x + c\right)}{1024 \, d}"," ",0,"5/512*a*b*x + 1/53248*b^2*cos(13*d*x + 13*c)/d - 1/12288*a*b*sin(12*d*x + 12*c)/d + 3/4096*a*b*sin(8*d*x + 8*c)/d - 15/4096*a*b*sin(4*d*x + 4*c)/d - 1/45056*(4*a^2 + b^2)*cos(11*d*x + 11*c)/d - 1/18432*(2*a^2 + 3*b^2)*cos(9*d*x + 9*c)/d + 1/14336*(10*a^2 + 3*b^2)*cos(7*d*x + 7*c)/d + 1/4096*(4*a^2 + 3*b^2)*cos(5*d*x + 5*c)/d - 5/12288*(8*a^2 + 3*b^2)*cos(3*d*x + 3*c)/d - 5/1024*(2*a^2 + b^2)*cos(d*x + c)/d","A",0
1240,1,226,0,0.768377," ","integrate(cos(d*x+c)^6*sin(d*x+c)^4*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{1}{1024} \, {\left(12 \, a^{2} + 5 \, b^{2}\right)} x - \frac{a b \cos\left(11 \, d x + 11 \, c\right)}{5632 \, d} - \frac{a b \cos\left(9 \, d x + 9 \, c\right)}{4608 \, d} + \frac{5 \, a b \cos\left(7 \, d x + 7 \, c\right)}{3584 \, d} + \frac{a b \cos\left(5 \, d x + 5 \, c\right)}{512 \, d} - \frac{5 \, a b \cos\left(3 \, d x + 3 \, c\right)}{768 \, d} - \frac{5 \, a b \cos\left(d x + c\right)}{256 \, d} - \frac{b^{2} \sin\left(12 \, d x + 12 \, c\right)}{24576 \, d} + \frac{a^{2} \sin\left(10 \, d x + 10 \, c\right)}{5120 \, d} - \frac{a^{2} \sin\left(6 \, d x + 6 \, c\right)}{1024 \, d} + \frac{a^{2} \sin\left(2 \, d x + 2 \, c\right)}{512 \, d} + \frac{{\left(4 \, a^{2} + 3 \, b^{2}\right)} \sin\left(8 \, d x + 8 \, c\right)}{8192 \, d} - \frac{{\left(32 \, a^{2} + 15 \, b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)}{8192 \, d}"," ",0,"1/1024*(12*a^2 + 5*b^2)*x - 1/5632*a*b*cos(11*d*x + 11*c)/d - 1/4608*a*b*cos(9*d*x + 9*c)/d + 5/3584*a*b*cos(7*d*x + 7*c)/d + 1/512*a*b*cos(5*d*x + 5*c)/d - 5/768*a*b*cos(3*d*x + 3*c)/d - 5/256*a*b*cos(d*x + c)/d - 1/24576*b^2*sin(12*d*x + 12*c)/d + 1/5120*a^2*sin(10*d*x + 10*c)/d - 1/1024*a^2*sin(6*d*x + 6*c)/d + 1/512*a^2*sin(2*d*x + 2*c)/d + 1/8192*(4*a^2 + 3*b^2)*sin(8*d*x + 8*c)/d - 1/8192*(32*a^2 + 15*b^2)*sin(4*d*x + 4*c)/d","A",0
1241,1,217,0,0.565685," ","integrate(cos(d*x+c)^6*sin(d*x+c)^3*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{3}{128} \, a b x - \frac{b^{2} \cos\left(11 \, d x + 11 \, c\right)}{11264 \, d} + \frac{b^{2} \cos\left(5 \, d x + 5 \, c\right)}{1024 \, d} + \frac{a b \sin\left(10 \, d x + 10 \, c\right)}{2560 \, d} + \frac{a b \sin\left(8 \, d x + 8 \, c\right)}{1024 \, d} - \frac{a b \sin\left(6 \, d x + 6 \, c\right)}{512 \, d} - \frac{a b \sin\left(4 \, d x + 4 \, c\right)}{128 \, d} + \frac{a b \sin\left(2 \, d x + 2 \, c\right)}{256 \, d} + \frac{{\left(4 \, a^{2} - b^{2}\right)} \cos\left(9 \, d x + 9 \, c\right)}{9216 \, d} + \frac{{\left(12 \, a^{2} + 5 \, b^{2}\right)} \cos\left(7 \, d x + 7 \, c\right)}{7168 \, d} - \frac{{\left(16 \, a^{2} + 5 \, b^{2}\right)} \cos\left(3 \, d x + 3 \, c\right)}{1536 \, d} - \frac{{\left(12 \, a^{2} + 5 \, b^{2}\right)} \cos\left(d x + c\right)}{512 \, d}"," ",0,"3/128*a*b*x - 1/11264*b^2*cos(11*d*x + 11*c)/d + 1/1024*b^2*cos(5*d*x + 5*c)/d + 1/2560*a*b*sin(10*d*x + 10*c)/d + 1/1024*a*b*sin(8*d*x + 8*c)/d - 1/512*a*b*sin(6*d*x + 6*c)/d - 1/128*a*b*sin(4*d*x + 4*c)/d + 1/256*a*b*sin(2*d*x + 2*c)/d + 1/9216*(4*a^2 - b^2)*cos(9*d*x + 9*c)/d + 1/7168*(12*a^2 + 5*b^2)*cos(7*d*x + 7*c)/d - 1/1536*(16*a^2 + 5*b^2)*cos(3*d*x + 3*c)/d - 1/512*(12*a^2 + 5*b^2)*cos(d*x + c)/d","A",0
1242,1,189,0,0.362789," ","integrate(cos(d*x+c)^6*sin(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{1}{256} \, {\left(10 \, a^{2} + 3 \, b^{2}\right)} x + \frac{a b \cos\left(9 \, d x + 9 \, c\right)}{1152 \, d} + \frac{3 \, a b \cos\left(7 \, d x + 7 \, c\right)}{896 \, d} - \frac{a b \cos\left(3 \, d x + 3 \, c\right)}{48 \, d} - \frac{3 \, a b \cos\left(d x + c\right)}{64 \, d} + \frac{b^{2} \sin\left(10 \, d x + 10 \, c\right)}{5120 \, d} - \frac{{\left(2 \, a^{2} - b^{2}\right)} \sin\left(8 \, d x + 8 \, c\right)}{2048 \, d} - \frac{{\left(16 \, a^{2} + 3 \, b^{2}\right)} \sin\left(6 \, d x + 6 \, c\right)}{3072 \, d} - \frac{{\left(2 \, a^{2} + b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)}{256 \, d} + \frac{{\left(8 \, a^{2} + b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)}{512 \, d}"," ",0,"1/256*(10*a^2 + 3*b^2)*x + 1/1152*a*b*cos(9*d*x + 9*c)/d + 3/896*a*b*cos(7*d*x + 7*c)/d - 1/48*a*b*cos(3*d*x + 3*c)/d - 3/64*a*b*cos(d*x + c)/d + 1/5120*b^2*sin(10*d*x + 10*c)/d - 1/2048*(2*a^2 - b^2)*sin(8*d*x + 8*c)/d - 1/3072*(16*a^2 + 3*b^2)*sin(6*d*x + 6*c)/d - 1/256*(2*a^2 + b^2)*sin(4*d*x + 4*c)/d + 1/512*(8*a^2 + b^2)*sin(2*d*x + 2*c)/d","A",0
1243,1,176,0,0.281172," ","integrate(cos(d*x+c)^6*sin(d*x+c)*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{5}{64} \, a b x + \frac{b^{2} \cos\left(9 \, d x + 9 \, c\right)}{2304 \, d} - \frac{a^{2} \cos\left(5 \, d x + 5 \, c\right)}{64 \, d} - \frac{a b \sin\left(8 \, d x + 8 \, c\right)}{512 \, d} - \frac{a b \sin\left(6 \, d x + 6 \, c\right)}{96 \, d} - \frac{a b \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{a b \sin\left(2 \, d x + 2 \, c\right)}{32 \, d} - \frac{{\left(4 \, a^{2} - 3 \, b^{2}\right)} \cos\left(7 \, d x + 7 \, c\right)}{1792 \, d} - \frac{{\left(9 \, a^{2} + 2 \, b^{2}\right)} \cos\left(3 \, d x + 3 \, c\right)}{192 \, d} - \frac{{\left(10 \, a^{2} + 3 \, b^{2}\right)} \cos\left(d x + c\right)}{128 \, d}"," ",0,"5/64*a*b*x + 1/2304*b^2*cos(9*d*x + 9*c)/d - 1/64*a^2*cos(5*d*x + 5*c)/d - 1/512*a*b*sin(8*d*x + 8*c)/d - 1/96*a*b*sin(6*d*x + 6*c)/d - 1/64*a*b*sin(4*d*x + 4*c)/d + 1/32*a*b*sin(2*d*x + 2*c)/d - 1/1792*(4*a^2 - 3*b^2)*cos(7*d*x + 7*c)/d - 1/192*(9*a^2 + 2*b^2)*cos(3*d*x + 3*c)/d - 1/128*(10*a^2 + 3*b^2)*cos(d*x + c)/d","A",0
1244,1,291,0,0.270055," ","integrate(cos(d*x+c)^6*csc(d*x+c)*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{525 \, {\left(d x + c\right)} a b + 840 \, a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{2 \, {\left(1155 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 2520 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 840 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 980 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 10080 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 2975 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 20440 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 4200 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 24640 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 2975 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 16968 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2520 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 980 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6496 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1155 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1288 \, a^{2} + 120 \, b^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{7}}}{840 \, d}"," ",0,"1/840*(525*(d*x + c)*a*b + 840*a^2*log(abs(tan(1/2*d*x + 1/2*c))) - 2*(1155*a*b*tan(1/2*d*x + 1/2*c)^13 - 2520*a^2*tan(1/2*d*x + 1/2*c)^12 + 840*b^2*tan(1/2*d*x + 1/2*c)^12 + 980*a*b*tan(1/2*d*x + 1/2*c)^11 - 10080*a^2*tan(1/2*d*x + 1/2*c)^10 + 2975*a*b*tan(1/2*d*x + 1/2*c)^9 - 20440*a^2*tan(1/2*d*x + 1/2*c)^8 + 4200*b^2*tan(1/2*d*x + 1/2*c)^8 - 24640*a^2*tan(1/2*d*x + 1/2*c)^6 - 2975*a*b*tan(1/2*d*x + 1/2*c)^5 - 16968*a^2*tan(1/2*d*x + 1/2*c)^4 + 2520*b^2*tan(1/2*d*x + 1/2*c)^4 - 980*a*b*tan(1/2*d*x + 1/2*c)^3 - 6496*a^2*tan(1/2*d*x + 1/2*c)^2 - 1155*a*b*tan(1/2*d*x + 1/2*c) - 1288*a^2 + 120*b^2)/(tan(1/2*d*x + 1/2*c)^2 + 1)^7)/d","B",0
1245,1,368,0,0.267247," ","integrate(cos(d*x+c)^6*csc(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{480 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 120 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 75 \, {\left(6 \, a^{2} - b^{2}\right)} {\left(d x + c\right)} - \frac{120 \, {\left(4 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)} + \frac{2 \, {\left(270 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 165 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 1440 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 570 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 25 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 4320 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 300 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 450 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 7360 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 300 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 450 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6720 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 570 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 25 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2976 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 270 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 165 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 736 \, a b\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(480*a*b*log(abs(tan(1/2*d*x + 1/2*c))) + 120*a^2*tan(1/2*d*x + 1/2*c) - 75*(6*a^2 - b^2)*(d*x + c) - 120*(4*a*b*tan(1/2*d*x + 1/2*c) + a^2)/tan(1/2*d*x + 1/2*c) + 2*(270*a^2*tan(1/2*d*x + 1/2*c)^11 - 165*b^2*tan(1/2*d*x + 1/2*c)^11 + 1440*a*b*tan(1/2*d*x + 1/2*c)^10 + 570*a^2*tan(1/2*d*x + 1/2*c)^9 + 25*b^2*tan(1/2*d*x + 1/2*c)^9 + 4320*a*b*tan(1/2*d*x + 1/2*c)^8 + 300*a^2*tan(1/2*d*x + 1/2*c)^7 - 450*b^2*tan(1/2*d*x + 1/2*c)^7 + 7360*a*b*tan(1/2*d*x + 1/2*c)^6 - 300*a^2*tan(1/2*d*x + 1/2*c)^5 + 450*b^2*tan(1/2*d*x + 1/2*c)^5 + 6720*a*b*tan(1/2*d*x + 1/2*c)^4 - 570*a^2*tan(1/2*d*x + 1/2*c)^3 - 25*b^2*tan(1/2*d*x + 1/2*c)^3 + 2976*a*b*tan(1/2*d*x + 1/2*c)^2 - 270*a^2*tan(1/2*d*x + 1/2*c) + 165*b^2*tan(1/2*d*x + 1/2*c) + 736*a*b)/(tan(1/2*d*x + 1/2*c)^2 + 1)^6)/d","B",0
1246,1,346,0,0.328721," ","integrate(cos(d*x+c)^6*csc(d*x+c)^3*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 450 \, {\left(d x + c\right)} a b + 120 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 60 \, {\left(5 \, a^{2} - 2 \, b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + \frac{15 \, {\left(30 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{2}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}} + \frac{4 \, {\left(135 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 180 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 180 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 150 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 600 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 360 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 800 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 560 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 150 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 520 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 280 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 135 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 140 \, a^{2} + 92 \, b^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*a^2*tan(1/2*d*x + 1/2*c)^2 - 450*(d*x + c)*a*b + 120*a*b*tan(1/2*d*x + 1/2*c) - 60*(5*a^2 - 2*b^2)*log(abs(tan(1/2*d*x + 1/2*c))) + 15*(30*a^2*tan(1/2*d*x + 1/2*c)^2 - 12*b^2*tan(1/2*d*x + 1/2*c)^2 - 8*a*b*tan(1/2*d*x + 1/2*c) - a^2)/tan(1/2*d*x + 1/2*c)^2 + 4*(135*a*b*tan(1/2*d*x + 1/2*c)^9 - 180*a^2*tan(1/2*d*x + 1/2*c)^8 + 180*b^2*tan(1/2*d*x + 1/2*c)^8 + 150*a*b*tan(1/2*d*x + 1/2*c)^7 - 600*a^2*tan(1/2*d*x + 1/2*c)^6 + 360*b^2*tan(1/2*d*x + 1/2*c)^6 - 800*a^2*tan(1/2*d*x + 1/2*c)^4 + 560*b^2*tan(1/2*d*x + 1/2*c)^4 - 150*a*b*tan(1/2*d*x + 1/2*c)^3 - 520*a^2*tan(1/2*d*x + 1/2*c)^2 + 280*b^2*tan(1/2*d*x + 1/2*c)^2 - 135*a*b*tan(1/2*d*x + 1/2*c) - 140*a^2 + 92*b^2)/(tan(1/2*d*x + 1/2*c)^2 + 1)^5)/d","B",0
1247,1,366,0,0.307761," ","integrate(cos(d*x+c)^6*csc(d*x+c)^4*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 120 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 27 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, {\left(4 \, a^{2} - 3 \, b^{2}\right)} {\left(d x + c\right)} + \frac{220 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 27 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 6 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}} - \frac{2 \, {\left(12 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 27 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 144 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 12 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 336 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 12 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 304 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 112 \, a b\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(a^2*tan(1/2*d*x + 1/2*c)^3 + 6*a*b*tan(1/2*d*x + 1/2*c)^2 - 120*a*b*log(abs(tan(1/2*d*x + 1/2*c))) - 27*a^2*tan(1/2*d*x + 1/2*c) + 12*b^2*tan(1/2*d*x + 1/2*c) + 15*(4*a^2 - 3*b^2)*(d*x + c) + (220*a*b*tan(1/2*d*x + 1/2*c)^3 + 27*a^2*tan(1/2*d*x + 1/2*c)^2 - 12*b^2*tan(1/2*d*x + 1/2*c)^2 - 6*a*b*tan(1/2*d*x + 1/2*c) - a^2)/tan(1/2*d*x + 1/2*c)^3 - 2*(12*a^2*tan(1/2*d*x + 1/2*c)^7 - 27*b^2*tan(1/2*d*x + 1/2*c)^7 + 144*a*b*tan(1/2*d*x + 1/2*c)^6 + 12*a^2*tan(1/2*d*x + 1/2*c)^5 - 3*b^2*tan(1/2*d*x + 1/2*c)^5 + 336*a*b*tan(1/2*d*x + 1/2*c)^4 - 12*a^2*tan(1/2*d*x + 1/2*c)^3 + 3*b^2*tan(1/2*d*x + 1/2*c)^3 + 304*a*b*tan(1/2*d*x + 1/2*c)^2 - 12*a^2*tan(1/2*d*x + 1/2*c) + 27*b^2*tan(1/2*d*x + 1/2*c) + 112*a*b)/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","B",0
1248,1,346,0,0.326539," ","integrate(cos(d*x+c)^6*csc(d*x+c)^5*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 16 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 48 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 960 \, {\left(d x + c\right)} a b - 432 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, {\left(3 \, a^{2} - 4 \, b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{128 \, {\left(3 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 9 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 6 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a^{2} + 7 \, b^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}} - \frac{750 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1000 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 432 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 48 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 16 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}}}{192 \, d}"," ",0,"1/192*(3*a^2*tan(1/2*d*x + 1/2*c)^4 + 16*a*b*tan(1/2*d*x + 1/2*c)^3 - 48*a^2*tan(1/2*d*x + 1/2*c)^2 + 24*b^2*tan(1/2*d*x + 1/2*c)^2 + 960*(d*x + c)*a*b - 432*a*b*tan(1/2*d*x + 1/2*c) + 120*(3*a^2 - 4*b^2)*log(abs(tan(1/2*d*x + 1/2*c))) - 128*(3*a*b*tan(1/2*d*x + 1/2*c)^5 - 3*a^2*tan(1/2*d*x + 1/2*c)^4 + 9*b^2*tan(1/2*d*x + 1/2*c)^4 - 6*a^2*tan(1/2*d*x + 1/2*c)^2 + 12*b^2*tan(1/2*d*x + 1/2*c)^2 - 3*a*b*tan(1/2*d*x + 1/2*c) - 3*a^2 + 7*b^2)/(tan(1/2*d*x + 1/2*c)^2 + 1)^3 - (750*a^2*tan(1/2*d*x + 1/2*c)^4 - 1000*b^2*tan(1/2*d*x + 1/2*c)^4 - 432*a*b*tan(1/2*d*x + 1/2*c)^3 - 48*a^2*tan(1/2*d*x + 1/2*c)^2 + 24*b^2*tan(1/2*d*x + 1/2*c)^2 + 16*a*b*tan(1/2*d*x + 1/2*c) + 3*a^2)/tan(1/2*d*x + 1/2*c)^4)/d","B",0
1249,1,337,0,0.308398," ","integrate(cos(d*x+c)^6*csc(d*x+c)^6*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 35 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 20 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 240 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1800 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 330 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 540 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 240 \, {\left(2 \, a^{2} - 5 \, b^{2}\right)} {\left(d x + c\right)} - \frac{480 \, {\left(b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, a b\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}} - \frac{4110 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 330 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 540 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 240 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 35 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 20 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 15 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{480 \, d}"," ",0,"1/480*(3*a^2*tan(1/2*d*x + 1/2*c)^5 + 15*a*b*tan(1/2*d*x + 1/2*c)^4 - 35*a^2*tan(1/2*d*x + 1/2*c)^3 + 20*b^2*tan(1/2*d*x + 1/2*c)^3 - 240*a*b*tan(1/2*d*x + 1/2*c)^2 + 1800*a*b*log(abs(tan(1/2*d*x + 1/2*c))) + 330*a^2*tan(1/2*d*x + 1/2*c) - 540*b^2*tan(1/2*d*x + 1/2*c) - 240*(2*a^2 - 5*b^2)*(d*x + c) - 480*(b^2*tan(1/2*d*x + 1/2*c)^3 - 4*a*b*tan(1/2*d*x + 1/2*c)^2 - b^2*tan(1/2*d*x + 1/2*c) - 4*a*b)/(tan(1/2*d*x + 1/2*c)^2 + 1)^2 - (4110*a*b*tan(1/2*d*x + 1/2*c)^5 + 330*a^2*tan(1/2*d*x + 1/2*c)^4 - 540*b^2*tan(1/2*d*x + 1/2*c)^4 - 240*a*b*tan(1/2*d*x + 1/2*c)^3 - 35*a^2*tan(1/2*d*x + 1/2*c)^2 + 20*b^2*tan(1/2*d*x + 1/2*c)^2 + 15*a*b*tan(1/2*d*x + 1/2*c) + 3*a^2)/tan(1/2*d*x + 1/2*c)^5)/d","A",0
1250,1,337,0,0.348845," ","integrate(cos(d*x+c)^6*csc(d*x+c)^7*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{5 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 24 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 45 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 30 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 280 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 225 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 480 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3840 \, {\left(d x + c\right)} a b + 2640 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 600 \, {\left(a^{2} - 6 \, b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + \frac{3840 \, b^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} + \frac{1470 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 8820 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 2640 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 225 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 480 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 280 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 45 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 30 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 24 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6}}}{1920 \, d}"," ",0,"1/1920*(5*a^2*tan(1/2*d*x + 1/2*c)^6 + 24*a*b*tan(1/2*d*x + 1/2*c)^5 - 45*a^2*tan(1/2*d*x + 1/2*c)^4 + 30*b^2*tan(1/2*d*x + 1/2*c)^4 - 280*a*b*tan(1/2*d*x + 1/2*c)^3 + 225*a^2*tan(1/2*d*x + 1/2*c)^2 - 480*b^2*tan(1/2*d*x + 1/2*c)^2 - 3840*(d*x + c)*a*b + 2640*a*b*tan(1/2*d*x + 1/2*c) - 600*(a^2 - 6*b^2)*log(abs(tan(1/2*d*x + 1/2*c))) + 3840*b^2/(tan(1/2*d*x + 1/2*c)^2 + 1) + (1470*a^2*tan(1/2*d*x + 1/2*c)^6 - 8820*b^2*tan(1/2*d*x + 1/2*c)^6 - 2640*a*b*tan(1/2*d*x + 1/2*c)^5 - 225*a^2*tan(1/2*d*x + 1/2*c)^4 + 480*b^2*tan(1/2*d*x + 1/2*c)^4 + 280*a*b*tan(1/2*d*x + 1/2*c)^3 + 45*a^2*tan(1/2*d*x + 1/2*c)^2 - 30*b^2*tan(1/2*d*x + 1/2*c)^2 - 24*a*b*tan(1/2*d*x + 1/2*c) - 5*a^2)/tan(1/2*d*x + 1/2*c)^6)/d","B",0
1251,1,356,0,0.335471," ","integrate(cos(d*x+c)^6*csc(d*x+c)^8*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 70 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 105 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 84 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 630 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 315 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 980 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3150 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 13440 \, {\left(d x + c\right)} b^{2} - 8400 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 525 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9240 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{21780 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 525 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 9240 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 3150 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 315 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 980 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 630 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 105 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 84 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 70 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7}}}{13440 \, d}"," ",0,"1/13440*(15*a^2*tan(1/2*d*x + 1/2*c)^7 + 70*a*b*tan(1/2*d*x + 1/2*c)^6 - 105*a^2*tan(1/2*d*x + 1/2*c)^5 + 84*b^2*tan(1/2*d*x + 1/2*c)^5 - 630*a*b*tan(1/2*d*x + 1/2*c)^4 + 315*a^2*tan(1/2*d*x + 1/2*c)^3 - 980*b^2*tan(1/2*d*x + 1/2*c)^3 + 3150*a*b*tan(1/2*d*x + 1/2*c)^2 - 13440*(d*x + c)*b^2 - 8400*a*b*log(abs(tan(1/2*d*x + 1/2*c))) - 525*a^2*tan(1/2*d*x + 1/2*c) + 9240*b^2*tan(1/2*d*x + 1/2*c) + (21780*a*b*tan(1/2*d*x + 1/2*c)^7 + 525*a^2*tan(1/2*d*x + 1/2*c)^6 - 9240*b^2*tan(1/2*d*x + 1/2*c)^6 - 3150*a*b*tan(1/2*d*x + 1/2*c)^5 - 315*a^2*tan(1/2*d*x + 1/2*c)^4 + 980*b^2*tan(1/2*d*x + 1/2*c)^4 + 630*a*b*tan(1/2*d*x + 1/2*c)^3 + 105*a^2*tan(1/2*d*x + 1/2*c)^2 - 84*b^2*tan(1/2*d*x + 1/2*c)^2 - 70*a*b*tan(1/2*d*x + 1/2*c) - 15*a^2)/tan(1/2*d*x + 1/2*c)^7)/d","B",0
1252,1,402,0,0.369867," ","integrate(cos(d*x+c)^6*csc(d*x+c)^9*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{21 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 96 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 112 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 112 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 672 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 168 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1008 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2016 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 336 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 5040 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3360 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1680 \, {\left(a^{2} + 8 \, b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + \frac{4566 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 36528 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 3360 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 336 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 5040 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 2016 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 168 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 1008 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 672 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 112 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 112 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 96 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 21 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8}}}{43008 \, d}"," ",0,"1/43008*(21*a^2*tan(1/2*d*x + 1/2*c)^8 + 96*a*b*tan(1/2*d*x + 1/2*c)^7 - 112*a^2*tan(1/2*d*x + 1/2*c)^6 + 112*b^2*tan(1/2*d*x + 1/2*c)^6 - 672*a*b*tan(1/2*d*x + 1/2*c)^5 + 168*a^2*tan(1/2*d*x + 1/2*c)^4 - 1008*b^2*tan(1/2*d*x + 1/2*c)^4 + 2016*a*b*tan(1/2*d*x + 1/2*c)^3 + 336*a^2*tan(1/2*d*x + 1/2*c)^2 + 5040*b^2*tan(1/2*d*x + 1/2*c)^2 - 3360*a*b*tan(1/2*d*x + 1/2*c) - 1680*(a^2 + 8*b^2)*log(abs(tan(1/2*d*x + 1/2*c))) + (4566*a^2*tan(1/2*d*x + 1/2*c)^8 + 36528*b^2*tan(1/2*d*x + 1/2*c)^8 + 3360*a*b*tan(1/2*d*x + 1/2*c)^7 - 336*a^2*tan(1/2*d*x + 1/2*c)^6 - 5040*b^2*tan(1/2*d*x + 1/2*c)^6 - 2016*a*b*tan(1/2*d*x + 1/2*c)^5 - 168*a^2*tan(1/2*d*x + 1/2*c)^4 + 1008*b^2*tan(1/2*d*x + 1/2*c)^4 + 672*a*b*tan(1/2*d*x + 1/2*c)^3 + 112*a^2*tan(1/2*d*x + 1/2*c)^2 - 112*b^2*tan(1/2*d*x + 1/2*c)^2 - 96*a*b*tan(1/2*d*x + 1/2*c) - 21*a^2)/tan(1/2*d*x + 1/2*c)^8)/d","B",0
1253,1,408,0,0.338880," ","integrate(cos(d*x+c)^6*csc(d*x+c)^10*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{14 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 63 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 54 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 72 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 336 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 504 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 504 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 336 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1512 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1008 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 5040 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 756 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2520 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{14258 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 756 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 2520 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 1008 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 336 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 1512 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 504 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 504 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 336 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 54 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 72 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 63 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 14 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9}}}{64512 \, d}"," ",0,"1/64512*(14*a^2*tan(1/2*d*x + 1/2*c)^9 + 63*a*b*tan(1/2*d*x + 1/2*c)^8 - 54*a^2*tan(1/2*d*x + 1/2*c)^7 + 72*b^2*tan(1/2*d*x + 1/2*c)^7 - 336*a*b*tan(1/2*d*x + 1/2*c)^6 - 504*b^2*tan(1/2*d*x + 1/2*c)^5 + 504*a*b*tan(1/2*d*x + 1/2*c)^4 + 336*a^2*tan(1/2*d*x + 1/2*c)^3 + 1512*b^2*tan(1/2*d*x + 1/2*c)^3 + 1008*a*b*tan(1/2*d*x + 1/2*c)^2 - 5040*a*b*log(abs(tan(1/2*d*x + 1/2*c))) - 756*a^2*tan(1/2*d*x + 1/2*c) - 2520*b^2*tan(1/2*d*x + 1/2*c) + (14258*a*b*tan(1/2*d*x + 1/2*c)^9 + 756*a^2*tan(1/2*d*x + 1/2*c)^8 + 2520*b^2*tan(1/2*d*x + 1/2*c)^8 - 1008*a*b*tan(1/2*d*x + 1/2*c)^7 - 336*a^2*tan(1/2*d*x + 1/2*c)^6 - 1512*b^2*tan(1/2*d*x + 1/2*c)^6 - 504*a*b*tan(1/2*d*x + 1/2*c)^5 + 504*b^2*tan(1/2*d*x + 1/2*c)^4 + 336*a*b*tan(1/2*d*x + 1/2*c)^3 + 54*a^2*tan(1/2*d*x + 1/2*c)^2 - 72*b^2*tan(1/2*d*x + 1/2*c)^2 - 63*a*b*tan(1/2*d*x + 1/2*c) - 14*a^2)/tan(1/2*d*x + 1/2*c)^9)/d","B",0
1254,1,468,0,0.401627," ","integrate(cos(d*x+c)^6*csc(d*x+c)^11*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{126 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 560 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 315 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 630 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 2160 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 630 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 3360 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 2520 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 5040 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 13440 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1260 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 10080 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 30240 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5040 \, {\left(3 \, a^{2} + 10 \, b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + \frac{44286 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 147620 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 30240 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1260 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 10080 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 13440 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 2520 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 5040 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 630 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 3360 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2160 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 315 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 630 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 560 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 126 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10}}}{1290240 \, d}"," ",0,"1/1290240*(126*a^2*tan(1/2*d*x + 1/2*c)^10 + 560*a*b*tan(1/2*d*x + 1/2*c)^9 - 315*a^2*tan(1/2*d*x + 1/2*c)^8 + 630*b^2*tan(1/2*d*x + 1/2*c)^8 - 2160*a*b*tan(1/2*d*x + 1/2*c)^7 - 630*a^2*tan(1/2*d*x + 1/2*c)^6 - 3360*b^2*tan(1/2*d*x + 1/2*c)^6 + 2520*a^2*tan(1/2*d*x + 1/2*c)^4 + 5040*b^2*tan(1/2*d*x + 1/2*c)^4 + 13440*a*b*tan(1/2*d*x + 1/2*c)^3 + 1260*a^2*tan(1/2*d*x + 1/2*c)^2 + 10080*b^2*tan(1/2*d*x + 1/2*c)^2 - 30240*a*b*tan(1/2*d*x + 1/2*c) - 5040*(3*a^2 + 10*b^2)*log(abs(tan(1/2*d*x + 1/2*c))) + (44286*a^2*tan(1/2*d*x + 1/2*c)^10 + 147620*b^2*tan(1/2*d*x + 1/2*c)^10 + 30240*a*b*tan(1/2*d*x + 1/2*c)^9 - 1260*a^2*tan(1/2*d*x + 1/2*c)^8 - 10080*b^2*tan(1/2*d*x + 1/2*c)^8 - 13440*a*b*tan(1/2*d*x + 1/2*c)^7 - 2520*a^2*tan(1/2*d*x + 1/2*c)^6 - 5040*b^2*tan(1/2*d*x + 1/2*c)^6 + 630*a^2*tan(1/2*d*x + 1/2*c)^4 + 3360*b^2*tan(1/2*d*x + 1/2*c)^4 + 2160*a*b*tan(1/2*d*x + 1/2*c)^3 + 315*a^2*tan(1/2*d*x + 1/2*c)^2 - 630*b^2*tan(1/2*d*x + 1/2*c)^2 - 560*a*b*tan(1/2*d*x + 1/2*c) - 126*a^2)/tan(1/2*d*x + 1/2*c)^10)/d","B",0
1255,1,502,0,0.360095," ","integrate(cos(d*x+c)^6*csc(d*x+c)^12*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{315 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 1386 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 385 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1540 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 3465 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 2475 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 5940 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 6930 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 3465 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 27720 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 11550 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36960 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 13860 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 166320 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 34650 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 83160 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{502266 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 34650 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 83160 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 13860 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 11550 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 36960 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 27720 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 3465 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 6930 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2475 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 5940 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 3465 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 385 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1540 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1386 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 315 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11}}}{7096320 \, d}"," ",0,"1/7096320*(315*a^2*tan(1/2*d*x + 1/2*c)^11 + 1386*a*b*tan(1/2*d*x + 1/2*c)^10 - 385*a^2*tan(1/2*d*x + 1/2*c)^9 + 1540*b^2*tan(1/2*d*x + 1/2*c)^9 - 3465*a*b*tan(1/2*d*x + 1/2*c)^8 - 2475*a^2*tan(1/2*d*x + 1/2*c)^7 - 5940*b^2*tan(1/2*d*x + 1/2*c)^7 - 6930*a*b*tan(1/2*d*x + 1/2*c)^6 + 3465*a^2*tan(1/2*d*x + 1/2*c)^5 + 27720*a*b*tan(1/2*d*x + 1/2*c)^4 + 11550*a^2*tan(1/2*d*x + 1/2*c)^3 + 36960*b^2*tan(1/2*d*x + 1/2*c)^3 + 13860*a*b*tan(1/2*d*x + 1/2*c)^2 - 166320*a*b*log(abs(tan(1/2*d*x + 1/2*c))) - 34650*a^2*tan(1/2*d*x + 1/2*c) - 83160*b^2*tan(1/2*d*x + 1/2*c) + (502266*a*b*tan(1/2*d*x + 1/2*c)^11 + 34650*a^2*tan(1/2*d*x + 1/2*c)^10 + 83160*b^2*tan(1/2*d*x + 1/2*c)^10 - 13860*a*b*tan(1/2*d*x + 1/2*c)^9 - 11550*a^2*tan(1/2*d*x + 1/2*c)^8 - 36960*b^2*tan(1/2*d*x + 1/2*c)^8 - 27720*a*b*tan(1/2*d*x + 1/2*c)^7 - 3465*a^2*tan(1/2*d*x + 1/2*c)^6 + 6930*a*b*tan(1/2*d*x + 1/2*c)^5 + 2475*a^2*tan(1/2*d*x + 1/2*c)^4 + 5940*b^2*tan(1/2*d*x + 1/2*c)^4 + 3465*a*b*tan(1/2*d*x + 1/2*c)^3 + 385*a^2*tan(1/2*d*x + 1/2*c)^2 - 1540*b^2*tan(1/2*d*x + 1/2*c)^2 - 1386*a*b*tan(1/2*d*x + 1/2*c) - 315*a^2)/tan(1/2*d*x + 1/2*c)^11)/d","B",0
1256,1,965,0,0.267823," ","integrate(cos(d*x+c)^6*sin(d*x+c)^3/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{105 \, {\left(64 \, a^{7} - 120 \, a^{5} b^{2} + 60 \, a^{3} b^{4} - 5 \, a b^{6}\right)} {\left(d x + c\right)}}{b^{9}} - \frac{1680 \, {\left(8 \, a^{8} - 19 \, a^{6} b^{2} + 14 \, a^{4} b^{4} - 3 \, a^{2} b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{9}} + \frac{1680 \, {\left(a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)} b^{8}} + \frac{2 \, {\left(2520 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 3780 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 1155 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 5880 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 12600 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 7560 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 840 \, b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 10080 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 11760 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 980 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 35280 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 67200 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 30240 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 12600 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 12180 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 2975 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 88200 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 152600 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 61320 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 4200 \, b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 117600 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 190400 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 73920 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 12600 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12180 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 2975 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 88200 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 138600 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 50904 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 2520 \, b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 10080 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 11760 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 980 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 35280 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 56000 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 19488 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2520 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3780 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1155 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5880 \, a^{6} - 9800 \, a^{4} b^{2} + 3864 \, a^{2} b^{4} - 120 \, b^{6}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{7} b^{8}}}{840 \, d}"," ",0,"1/840*(105*(64*a^7 - 120*a^5*b^2 + 60*a^3*b^4 - 5*a*b^6)*(d*x + c)/b^9 - 1680*(8*a^8 - 19*a^6*b^2 + 14*a^4*b^4 - 3*a^2*b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^9) + 1680*(a^6*b*tan(1/2*d*x + 1/2*c) - 2*a^4*b^3*tan(1/2*d*x + 1/2*c) + a^2*b^5*tan(1/2*d*x + 1/2*c) + a^7 - 2*a^5*b^2 + a^3*b^4)/((a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)*b^8) + 2*(2520*a^5*b*tan(1/2*d*x + 1/2*c)^13 - 3780*a^3*b^3*tan(1/2*d*x + 1/2*c)^13 + 1155*a*b^5*tan(1/2*d*x + 1/2*c)^13 + 5880*a^6*tan(1/2*d*x + 1/2*c)^12 - 12600*a^4*b^2*tan(1/2*d*x + 1/2*c)^12 + 7560*a^2*b^4*tan(1/2*d*x + 1/2*c)^12 - 840*b^6*tan(1/2*d*x + 1/2*c)^12 + 10080*a^5*b*tan(1/2*d*x + 1/2*c)^11 - 11760*a^3*b^3*tan(1/2*d*x + 1/2*c)^11 + 980*a*b^5*tan(1/2*d*x + 1/2*c)^11 + 35280*a^6*tan(1/2*d*x + 1/2*c)^10 - 67200*a^4*b^2*tan(1/2*d*x + 1/2*c)^10 + 30240*a^2*b^4*tan(1/2*d*x + 1/2*c)^10 + 12600*a^5*b*tan(1/2*d*x + 1/2*c)^9 - 12180*a^3*b^3*tan(1/2*d*x + 1/2*c)^9 + 2975*a*b^5*tan(1/2*d*x + 1/2*c)^9 + 88200*a^6*tan(1/2*d*x + 1/2*c)^8 - 152600*a^4*b^2*tan(1/2*d*x + 1/2*c)^8 + 61320*a^2*b^4*tan(1/2*d*x + 1/2*c)^8 - 4200*b^6*tan(1/2*d*x + 1/2*c)^8 + 117600*a^6*tan(1/2*d*x + 1/2*c)^6 - 190400*a^4*b^2*tan(1/2*d*x + 1/2*c)^6 + 73920*a^2*b^4*tan(1/2*d*x + 1/2*c)^6 - 12600*a^5*b*tan(1/2*d*x + 1/2*c)^5 + 12180*a^3*b^3*tan(1/2*d*x + 1/2*c)^5 - 2975*a*b^5*tan(1/2*d*x + 1/2*c)^5 + 88200*a^6*tan(1/2*d*x + 1/2*c)^4 - 138600*a^4*b^2*tan(1/2*d*x + 1/2*c)^4 + 50904*a^2*b^4*tan(1/2*d*x + 1/2*c)^4 - 2520*b^6*tan(1/2*d*x + 1/2*c)^4 - 10080*a^5*b*tan(1/2*d*x + 1/2*c)^3 + 11760*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 - 980*a*b^5*tan(1/2*d*x + 1/2*c)^3 + 35280*a^6*tan(1/2*d*x + 1/2*c)^2 - 56000*a^4*b^2*tan(1/2*d*x + 1/2*c)^2 + 19488*a^2*b^4*tan(1/2*d*x + 1/2*c)^2 - 2520*a^5*b*tan(1/2*d*x + 1/2*c) + 3780*a^3*b^3*tan(1/2*d*x + 1/2*c) - 1155*a*b^5*tan(1/2*d*x + 1/2*c) + 5880*a^6 - 9800*a^4*b^2 + 3864*a^2*b^4 - 120*b^6)/((tan(1/2*d*x + 1/2*c)^2 + 1)^7*b^8))/d","A",0
1257,1,835,0,0.241526," ","integrate(cos(d*x+c)^6*sin(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{15 \, {\left(112 \, a^{6} - 200 \, a^{4} b^{2} + 90 \, a^{2} b^{4} - 5 \, b^{6}\right)} {\left(d x + c\right)}}{b^{8}} - \frac{480 \, {\left(7 \, a^{7} - 16 \, a^{5} b^{2} + 11 \, a^{3} b^{4} - 2 \, a b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{8}} + \frac{480 \, {\left(a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)} b^{7}} + \frac{2 \, {\left(600 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 810 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 165 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 1440 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 2880 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 1440 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 1800 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1710 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 25 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 7200 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 12480 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 4320 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 1200 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 900 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 450 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 14400 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 22400 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 7360 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 1200 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 900 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 450 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 14400 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 21120 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 6720 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1800 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1710 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 25 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 7200 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 10560 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2976 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 600 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 810 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 165 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1440 \, a^{5} - 2240 \, a^{3} b^{2} + 736 \, a b^{4}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6} b^{7}}}{240 \, d}"," ",0,"-1/240*(15*(112*a^6 - 200*a^4*b^2 + 90*a^2*b^4 - 5*b^6)*(d*x + c)/b^8 - 480*(7*a^7 - 16*a^5*b^2 + 11*a^3*b^4 - 2*a*b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^8) + 480*(a^5*b*tan(1/2*d*x + 1/2*c) - 2*a^3*b^3*tan(1/2*d*x + 1/2*c) + a*b^5*tan(1/2*d*x + 1/2*c) + a^6 - 2*a^4*b^2 + a^2*b^4)/((a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)*b^7) + 2*(600*a^4*b*tan(1/2*d*x + 1/2*c)^11 - 810*a^2*b^3*tan(1/2*d*x + 1/2*c)^11 + 165*b^5*tan(1/2*d*x + 1/2*c)^11 + 1440*a^5*tan(1/2*d*x + 1/2*c)^10 - 2880*a^3*b^2*tan(1/2*d*x + 1/2*c)^10 + 1440*a*b^4*tan(1/2*d*x + 1/2*c)^10 + 1800*a^4*b*tan(1/2*d*x + 1/2*c)^9 - 1710*a^2*b^3*tan(1/2*d*x + 1/2*c)^9 - 25*b^5*tan(1/2*d*x + 1/2*c)^9 + 7200*a^5*tan(1/2*d*x + 1/2*c)^8 - 12480*a^3*b^2*tan(1/2*d*x + 1/2*c)^8 + 4320*a*b^4*tan(1/2*d*x + 1/2*c)^8 + 1200*a^4*b*tan(1/2*d*x + 1/2*c)^7 - 900*a^2*b^3*tan(1/2*d*x + 1/2*c)^7 + 450*b^5*tan(1/2*d*x + 1/2*c)^7 + 14400*a^5*tan(1/2*d*x + 1/2*c)^6 - 22400*a^3*b^2*tan(1/2*d*x + 1/2*c)^6 + 7360*a*b^4*tan(1/2*d*x + 1/2*c)^6 - 1200*a^4*b*tan(1/2*d*x + 1/2*c)^5 + 900*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 - 450*b^5*tan(1/2*d*x + 1/2*c)^5 + 14400*a^5*tan(1/2*d*x + 1/2*c)^4 - 21120*a^3*b^2*tan(1/2*d*x + 1/2*c)^4 + 6720*a*b^4*tan(1/2*d*x + 1/2*c)^4 - 1800*a^4*b*tan(1/2*d*x + 1/2*c)^3 + 1710*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + 25*b^5*tan(1/2*d*x + 1/2*c)^3 + 7200*a^5*tan(1/2*d*x + 1/2*c)^2 - 10560*a^3*b^2*tan(1/2*d*x + 1/2*c)^2 + 2976*a*b^4*tan(1/2*d*x + 1/2*c)^2 - 600*a^4*b*tan(1/2*d*x + 1/2*c) + 810*a^2*b^3*tan(1/2*d*x + 1/2*c) - 165*b^5*tan(1/2*d*x + 1/2*c) + 1440*a^5 - 2240*a^3*b^2 + 736*a*b^4)/((tan(1/2*d*x + 1/2*c)^2 + 1)^6*b^7))/d","A",0
1258,1,593,0,0.226169," ","integrate(cos(d*x+c)^6*sin(d*x+c)/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{15 \, {\left(24 \, a^{5} - 40 \, a^{3} b^{2} + 15 \, a b^{4}\right)} {\left(d x + c\right)}}{b^{7}} - \frac{120 \, {\left(6 \, a^{6} - 13 \, a^{4} b^{2} + 8 \, a^{2} b^{4} - b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{7}} + \frac{120 \, {\left(a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)} b^{6}} + \frac{2 \, {\left(120 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 135 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 300 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 540 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 180 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 240 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 150 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1200 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 1800 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 360 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 1800 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 2400 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 560 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 240 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 150 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1200 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1560 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 280 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 120 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 135 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 300 \, a^{4} - 420 \, a^{2} b^{2} + 92 \, b^{4}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5} b^{6}}}{60 \, d}"," ",0,"1/60*(15*(24*a^5 - 40*a^3*b^2 + 15*a*b^4)*(d*x + c)/b^7 - 120*(6*a^6 - 13*a^4*b^2 + 8*a^2*b^4 - b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^7) + 120*(a^4*b*tan(1/2*d*x + 1/2*c) - 2*a^2*b^3*tan(1/2*d*x + 1/2*c) + b^5*tan(1/2*d*x + 1/2*c) + a^5 - 2*a^3*b^2 + a*b^4)/((a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)*b^6) + 2*(120*a^3*b*tan(1/2*d*x + 1/2*c)^9 - 135*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 300*a^4*tan(1/2*d*x + 1/2*c)^8 - 540*a^2*b^2*tan(1/2*d*x + 1/2*c)^8 + 180*b^4*tan(1/2*d*x + 1/2*c)^8 + 240*a^3*b*tan(1/2*d*x + 1/2*c)^7 - 150*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 1200*a^4*tan(1/2*d*x + 1/2*c)^6 - 1800*a^2*b^2*tan(1/2*d*x + 1/2*c)^6 + 360*b^4*tan(1/2*d*x + 1/2*c)^6 + 1800*a^4*tan(1/2*d*x + 1/2*c)^4 - 2400*a^2*b^2*tan(1/2*d*x + 1/2*c)^4 + 560*b^4*tan(1/2*d*x + 1/2*c)^4 - 240*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 150*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 1200*a^4*tan(1/2*d*x + 1/2*c)^2 - 1560*a^2*b^2*tan(1/2*d*x + 1/2*c)^2 + 280*b^4*tan(1/2*d*x + 1/2*c)^2 - 120*a^3*b*tan(1/2*d*x + 1/2*c) + 135*a*b^3*tan(1/2*d*x + 1/2*c) + 300*a^4 - 420*a^2*b^2 + 92*b^4)/((tan(1/2*d*x + 1/2*c)^2 + 1)^5*b^6))/d","B",0
1259,1,353,0,0.258527," ","integrate(cos(d*x+c)^6*csc(d*x+c)/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{3 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} + \frac{3 \, {\left(4 \, a^{3} - 5 \, a b^{2}\right)} {\left(d x + c\right)}}{b^{5}} - \frac{6 \, {\left(4 \, a^{6} - 7 \, a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{2} b^{5}} + \frac{2 \, {\left(3 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 9 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 18 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, a^{2} - 7 \, b^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} b^{4}} + \frac{6 \, {\left(a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)} a^{2} b^{4}}}{3 \, d}"," ",0,"1/3*(3*log(abs(tan(1/2*d*x + 1/2*c)))/a^2 + 3*(4*a^3 - 5*a*b^2)*(d*x + c)/b^5 - 6*(4*a^6 - 7*a^4*b^2 + 2*a^2*b^4 + b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^2*b^5) + 2*(3*a*b*tan(1/2*d*x + 1/2*c)^5 + 9*a^2*tan(1/2*d*x + 1/2*c)^4 - 9*b^2*tan(1/2*d*x + 1/2*c)^4 + 18*a^2*tan(1/2*d*x + 1/2*c)^2 - 12*b^2*tan(1/2*d*x + 1/2*c)^2 - 3*a*b*tan(1/2*d*x + 1/2*c) + 9*a^2 - 7*b^2)/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*b^4) + 6*(a^4*b*tan(1/2*d*x + 1/2*c) - 2*a^2*b^3*tan(1/2*d*x + 1/2*c) + b^5*tan(1/2*d*x + 1/2*c) + a^5 - 2*a^3*b^2 + a*b^4)/((a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)*a^2*b^4))/d","A",0
1260,1,384,0,0.223623," ","integrate(cos(d*x+c)^6*csc(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{12 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} - \frac{3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{2}} + \frac{3 \, {\left(6 \, a^{2} - 5 \, b^{2}\right)} {\left(d x + c\right)}}{b^{4}} + \frac{6 \, {\left(b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, a\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} b^{3}} - \frac{12 \, {\left(3 \, a^{6} - 4 \, a^{4} b^{2} - a^{2} b^{4} + 2 \, b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{3} b^{4}} - \frac{4 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 21 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 14 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a^{2} b^{3}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} a^{3} b^{3}}}{6 \, d}"," ",0,"-1/6*(12*b*log(abs(tan(1/2*d*x + 1/2*c)))/a^3 - 3*tan(1/2*d*x + 1/2*c)/a^2 + 3*(6*a^2 - 5*b^2)*(d*x + c)/b^4 + 6*(b*tan(1/2*d*x + 1/2*c)^3 + 4*a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c) + 4*a)/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*b^3) - 12*(3*a^6 - 4*a^4*b^2 - a^2*b^4 + 2*b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^3*b^4) - (4*a*b^4*tan(1/2*d*x + 1/2*c)^3 - 12*a^4*b*tan(1/2*d*x + 1/2*c)^2 + 21*a^2*b^3*tan(1/2*d*x + 1/2*c)^2 - 4*b^5*tan(1/2*d*x + 1/2*c)^2 - 12*a^5*tan(1/2*d*x + 1/2*c) + 24*a^3*b^2*tan(1/2*d*x + 1/2*c) - 14*a*b^4*tan(1/2*d*x + 1/2*c) - 3*a^2*b^3)/((a*tan(1/2*d*x + 1/2*c)^3 + 2*b*tan(1/2*d*x + 1/2*c)^2 + a*tan(1/2*d*x + 1/2*c))*a^3*b^3))/d","A",0
1261,1,463,0,0.278246," ","integrate(cos(d*x+c)^6*csc(d*x+c)^3/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{16 \, {\left(d x + c\right)} a}{b^{3}} - \frac{4 \, {\left(5 \, a^{2} - 6 \, b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{4}} + \frac{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{4}} + \frac{30 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 36 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 8 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{2}}{a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}} - \frac{16 \, {\left(2 \, a^{6} - a^{4} b^{2} - 4 \, a^{2} b^{4} + 3 \, b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{4} b^{3}} + \frac{16 \, {\left(a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)} a^{4} b^{2}}}{8 \, d}"," ",0,"1/8*(16*(d*x + c)*a/b^3 - 4*(5*a^2 - 6*b^2)*log(abs(tan(1/2*d*x + 1/2*c)))/a^4 + (a^2*tan(1/2*d*x + 1/2*c)^2 - 8*a*b*tan(1/2*d*x + 1/2*c))/a^4 + (30*a^2*tan(1/2*d*x + 1/2*c)^2 - 36*b^2*tan(1/2*d*x + 1/2*c)^2 + 8*a*b*tan(1/2*d*x + 1/2*c) - a^2)/(a^4*tan(1/2*d*x + 1/2*c)^2) - 16*(2*a^6 - a^4*b^2 - 4*a^2*b^4 + 3*b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^4*b^3) + 16*(a^4*b*tan(1/2*d*x + 1/2*c)^3 - 2*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + b^5*tan(1/2*d*x + 1/2*c)^3 + 2*a^5*tan(1/2*d*x + 1/2*c)^2 - 2*a^3*b^2*tan(1/2*d*x + 1/2*c)^2 + a*b^4*tan(1/2*d*x + 1/2*c)^2 + 3*a^4*b*tan(1/2*d*x + 1/2*c) - 2*a^2*b^3*tan(1/2*d*x + 1/2*c) + b^5*tan(1/2*d*x + 1/2*c) + 2*a^5 - 2*a^3*b^2 + a*b^4)/((a*tan(1/2*d*x + 1/2*c)^4 + 2*b*tan(1/2*d*x + 1/2*c)^3 + 2*a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)*a^4*b^2))/d","A",0
1262,1,399,0,0.275990," ","integrate(cos(d*x+c)^6*csc(d*x+c)^4/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{24 \, {\left(d x + c\right)}}{b^{2}} - \frac{24 \, {\left(5 \, a^{2} b - 4 \, b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{5}} - \frac{a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 27 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}} - \frac{48 \, {\left(a^{6} + 2 \, a^{4} b^{2} - 7 \, a^{2} b^{4} + 4 \, b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{5} b^{2}} + \frac{48 \, {\left(a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)} a^{5} b} + \frac{220 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 176 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 27 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 36 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 6 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3}}{a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{24 \, d}"," ",0,"-1/24*(24*(d*x + c)/b^2 - 24*(5*a^2*b - 4*b^3)*log(abs(tan(1/2*d*x + 1/2*c)))/a^5 - (a^4*tan(1/2*d*x + 1/2*c)^3 - 6*a^3*b*tan(1/2*d*x + 1/2*c)^2 - 27*a^4*tan(1/2*d*x + 1/2*c) + 36*a^2*b^2*tan(1/2*d*x + 1/2*c))/a^6 - 48*(a^6 + 2*a^4*b^2 - 7*a^2*b^4 + 4*b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^5*b^2) + 48*(a^4*b*tan(1/2*d*x + 1/2*c) - 2*a^2*b^3*tan(1/2*d*x + 1/2*c) + b^5*tan(1/2*d*x + 1/2*c) + a^5 - 2*a^3*b^2 + a*b^4)/((a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)*a^5*b) + (220*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 176*b^3*tan(1/2*d*x + 1/2*c)^3 - 27*a^3*tan(1/2*d*x + 1/2*c)^2 + 36*a*b^2*tan(1/2*d*x + 1/2*c)^2 - 6*a^2*b*tan(1/2*d*x + 1/2*c) + a^3)/(a^5*tan(1/2*d*x + 1/2*c)^3))/d","A",0
1263,1,475,0,0.287985," ","integrate(cos(d*x+c)^6*csc(d*x+c)^5/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{120 \, {\left(3 \, a^{4} - 12 \, a^{2} b^{2} + 8 \, b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{6}} - \frac{1920 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{6}} + \frac{384 \, {\left(a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)} a^{6}} + \frac{3 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 16 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 48 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 72 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 432 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 384 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{8}} - \frac{750 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 3000 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2000 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 432 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 384 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 48 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 72 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 16 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a^{4}}{a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}}}{192 \, d}"," ",0,"1/192*(120*(3*a^4 - 12*a^2*b^2 + 8*b^4)*log(abs(tan(1/2*d*x + 1/2*c)))/a^6 - 1920*(a^4*b - 2*a^2*b^3 + b^5)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^6) + 384*(a^4*b*tan(1/2*d*x + 1/2*c) - 2*a^2*b^3*tan(1/2*d*x + 1/2*c) + b^5*tan(1/2*d*x + 1/2*c) + a^5 - 2*a^3*b^2 + a*b^4)/((a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)*a^6) + (3*a^6*tan(1/2*d*x + 1/2*c)^4 - 16*a^5*b*tan(1/2*d*x + 1/2*c)^3 - 48*a^6*tan(1/2*d*x + 1/2*c)^2 + 72*a^4*b^2*tan(1/2*d*x + 1/2*c)^2 + 432*a^5*b*tan(1/2*d*x + 1/2*c) - 384*a^3*b^3*tan(1/2*d*x + 1/2*c))/a^8 - (750*a^4*tan(1/2*d*x + 1/2*c)^4 - 3000*a^2*b^2*tan(1/2*d*x + 1/2*c)^4 + 2000*b^4*tan(1/2*d*x + 1/2*c)^4 + 432*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 384*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 48*a^4*tan(1/2*d*x + 1/2*c)^2 + 72*a^2*b^2*tan(1/2*d*x + 1/2*c)^2 - 16*a^3*b*tan(1/2*d*x + 1/2*c) + 3*a^4)/(a^6*tan(1/2*d*x + 1/2*c)^4))/d","A",0
1264,1,596,0,0.289456," ","integrate(cos(d*x+c)^6*csc(d*x+c)^6/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{120 \, {\left(15 \, a^{4} b - 40 \, a^{2} b^{3} + 24 \, b^{5}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{7}} + \frac{960 \, {\left(a^{6} - 8 \, a^{4} b^{2} + 13 \, a^{2} b^{4} - 6 \, b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{7}} + \frac{960 \, {\left(a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)} a^{7}} - \frac{3 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 35 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 60 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 240 \, a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 240 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 330 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1620 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1200 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{10}} - \frac{4110 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 10960 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6576 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 330 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 1620 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1200 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 240 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 240 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 35 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 60 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 15 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a^{5}}{a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{480 \, d}"," ",0,"-1/480*(120*(15*a^4*b - 40*a^2*b^3 + 24*b^5)*log(abs(tan(1/2*d*x + 1/2*c)))/a^7 + 960*(a^6 - 8*a^4*b^2 + 13*a^2*b^4 - 6*b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^7) + 960*(a^4*b^2*tan(1/2*d*x + 1/2*c) - 2*a^2*b^4*tan(1/2*d*x + 1/2*c) + b^6*tan(1/2*d*x + 1/2*c) + a^5*b - 2*a^3*b^3 + a*b^5)/((a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)*a^7) - (3*a^8*tan(1/2*d*x + 1/2*c)^5 - 15*a^7*b*tan(1/2*d*x + 1/2*c)^4 - 35*a^8*tan(1/2*d*x + 1/2*c)^3 + 60*a^6*b^2*tan(1/2*d*x + 1/2*c)^3 + 240*a^7*b*tan(1/2*d*x + 1/2*c)^2 - 240*a^5*b^3*tan(1/2*d*x + 1/2*c)^2 + 330*a^8*tan(1/2*d*x + 1/2*c) - 1620*a^6*b^2*tan(1/2*d*x + 1/2*c) + 1200*a^4*b^4*tan(1/2*d*x + 1/2*c))/a^10 - (4110*a^4*b*tan(1/2*d*x + 1/2*c)^5 - 10960*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 + 6576*b^5*tan(1/2*d*x + 1/2*c)^5 - 330*a^5*tan(1/2*d*x + 1/2*c)^4 + 1620*a^3*b^2*tan(1/2*d*x + 1/2*c)^4 - 1200*a*b^4*tan(1/2*d*x + 1/2*c)^4 - 240*a^4*b*tan(1/2*d*x + 1/2*c)^3 + 240*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + 35*a^5*tan(1/2*d*x + 1/2*c)^2 - 60*a^3*b^2*tan(1/2*d*x + 1/2*c)^2 + 15*a^4*b*tan(1/2*d*x + 1/2*c) - 3*a^5)/(a^7*tan(1/2*d*x + 1/2*c)^5))/d","A",0
1265,1,736,0,0.297225," ","integrate(cos(d*x+c)^6*csc(d*x+c)^7/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{120 \, {\left(5 \, a^{6} - 90 \, a^{4} b^{2} + 200 \, a^{2} b^{4} - 112 \, b^{6}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{8}} - \frac{3840 \, {\left(2 \, a^{6} b - 11 \, a^{4} b^{3} + 16 \, a^{2} b^{5} - 7 \, b^{7}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{8}} - \frac{3840 \, {\left(a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)} a^{8}} - \frac{5 \, a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 24 \, a^{9} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 45 \, a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 90 \, a^{8} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 280 \, a^{9} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 320 \, a^{7} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 225 \, a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1440 \, a^{8} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1200 \, a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2640 \, a^{9} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8640 \, a^{7} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5760 \, a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{12}} - \frac{1470 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 26460 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 58800 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 32928 \, b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 2640 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 8640 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 5760 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 225 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 1440 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1200 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 280 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 320 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 45 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 90 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, a^{6}}{a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6}}}{1920 \, d}"," ",0,"-1/1920*(120*(5*a^6 - 90*a^4*b^2 + 200*a^2*b^4 - 112*b^6)*log(abs(tan(1/2*d*x + 1/2*c)))/a^8 - 3840*(2*a^6*b - 11*a^4*b^3 + 16*a^2*b^5 - 7*b^7)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^8) - 3840*(a^4*b^3*tan(1/2*d*x + 1/2*c) - 2*a^2*b^5*tan(1/2*d*x + 1/2*c) + b^7*tan(1/2*d*x + 1/2*c) + a^5*b^2 - 2*a^3*b^4 + a*b^6)/((a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)*a^8) - (5*a^10*tan(1/2*d*x + 1/2*c)^6 - 24*a^9*b*tan(1/2*d*x + 1/2*c)^5 - 45*a^10*tan(1/2*d*x + 1/2*c)^4 + 90*a^8*b^2*tan(1/2*d*x + 1/2*c)^4 + 280*a^9*b*tan(1/2*d*x + 1/2*c)^3 - 320*a^7*b^3*tan(1/2*d*x + 1/2*c)^3 + 225*a^10*tan(1/2*d*x + 1/2*c)^2 - 1440*a^8*b^2*tan(1/2*d*x + 1/2*c)^2 + 1200*a^6*b^4*tan(1/2*d*x + 1/2*c)^2 - 2640*a^9*b*tan(1/2*d*x + 1/2*c) + 8640*a^7*b^3*tan(1/2*d*x + 1/2*c) - 5760*a^5*b^5*tan(1/2*d*x + 1/2*c))/a^12 - (1470*a^6*tan(1/2*d*x + 1/2*c)^6 - 26460*a^4*b^2*tan(1/2*d*x + 1/2*c)^6 + 58800*a^2*b^4*tan(1/2*d*x + 1/2*c)^6 - 32928*b^6*tan(1/2*d*x + 1/2*c)^6 + 2640*a^5*b*tan(1/2*d*x + 1/2*c)^5 - 8640*a^3*b^3*tan(1/2*d*x + 1/2*c)^5 + 5760*a*b^5*tan(1/2*d*x + 1/2*c)^5 - 225*a^6*tan(1/2*d*x + 1/2*c)^4 + 1440*a^4*b^2*tan(1/2*d*x + 1/2*c)^4 - 1200*a^2*b^4*tan(1/2*d*x + 1/2*c)^4 - 280*a^5*b*tan(1/2*d*x + 1/2*c)^3 + 320*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 + 45*a^6*tan(1/2*d*x + 1/2*c)^2 - 90*a^4*b^2*tan(1/2*d*x + 1/2*c)^2 + 24*a^5*b*tan(1/2*d*x + 1/2*c) - 5*a^6)/(a^8*tan(1/2*d*x + 1/2*c)^6))/d","A",0
1266,1,968,0,0.335629," ","integrate(cos(d*x+c)^6*sin(d*x+c)^3/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{15 \, {\left(448 \, a^{6} - 600 \, a^{4} b^{2} + 180 \, a^{2} b^{4} - 5 \, b^{6}\right)} {\left(d x + c\right)}}{b^{9}} - \frac{240 \, {\left(56 \, a^{7} - 103 \, a^{5} b^{2} + 53 \, a^{3} b^{4} - 6 \, a b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{9}} + \frac{240 \, {\left(13 \, a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 17 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 14 \, a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 9 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 33 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 10 \, a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 43 \, a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 59 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 16 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 14 \, a^{7} - 19 \, a^{5} b^{2} + 5 \, a^{3} b^{4}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}^{2} b^{8}} + \frac{2 \, {\left(1800 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 1620 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 165 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 5040 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 7200 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 2160 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 5400 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 3420 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 25 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 25200 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 31200 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 6480 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 3600 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1800 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 450 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 50400 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 56000 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 11040 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 3600 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1800 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 450 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 50400 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 52800 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 10080 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 5400 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3420 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 25 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 25200 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 26400 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 4464 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1800 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1620 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 165 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5040 \, a^{5} - 5600 \, a^{3} b^{2} + 1104 \, a b^{4}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6} b^{8}}}{240 \, d}"," ",0,"-1/240*(15*(448*a^6 - 600*a^4*b^2 + 180*a^2*b^4 - 5*b^6)*(d*x + c)/b^9 - 240*(56*a^7 - 103*a^5*b^2 + 53*a^3*b^4 - 6*a*b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^9) + 240*(13*a^6*b*tan(1/2*d*x + 1/2*c)^3 - 17*a^4*b^3*tan(1/2*d*x + 1/2*c)^3 + 4*a^2*b^5*tan(1/2*d*x + 1/2*c)^3 + 14*a^7*tan(1/2*d*x + 1/2*c)^2 + 9*a^5*b^2*tan(1/2*d*x + 1/2*c)^2 - 33*a^3*b^4*tan(1/2*d*x + 1/2*c)^2 + 10*a*b^6*tan(1/2*d*x + 1/2*c)^2 + 43*a^6*b*tan(1/2*d*x + 1/2*c) - 59*a^4*b^3*tan(1/2*d*x + 1/2*c) + 16*a^2*b^5*tan(1/2*d*x + 1/2*c) + 14*a^7 - 19*a^5*b^2 + 5*a^3*b^4)/((a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)^2*b^8) + 2*(1800*a^4*b*tan(1/2*d*x + 1/2*c)^11 - 1620*a^2*b^3*tan(1/2*d*x + 1/2*c)^11 + 165*b^5*tan(1/2*d*x + 1/2*c)^11 + 5040*a^5*tan(1/2*d*x + 1/2*c)^10 - 7200*a^3*b^2*tan(1/2*d*x + 1/2*c)^10 + 2160*a*b^4*tan(1/2*d*x + 1/2*c)^10 + 5400*a^4*b*tan(1/2*d*x + 1/2*c)^9 - 3420*a^2*b^3*tan(1/2*d*x + 1/2*c)^9 - 25*b^5*tan(1/2*d*x + 1/2*c)^9 + 25200*a^5*tan(1/2*d*x + 1/2*c)^8 - 31200*a^3*b^2*tan(1/2*d*x + 1/2*c)^8 + 6480*a*b^4*tan(1/2*d*x + 1/2*c)^8 + 3600*a^4*b*tan(1/2*d*x + 1/2*c)^7 - 1800*a^2*b^3*tan(1/2*d*x + 1/2*c)^7 + 450*b^5*tan(1/2*d*x + 1/2*c)^7 + 50400*a^5*tan(1/2*d*x + 1/2*c)^6 - 56000*a^3*b^2*tan(1/2*d*x + 1/2*c)^6 + 11040*a*b^4*tan(1/2*d*x + 1/2*c)^6 - 3600*a^4*b*tan(1/2*d*x + 1/2*c)^5 + 1800*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 - 450*b^5*tan(1/2*d*x + 1/2*c)^5 + 50400*a^5*tan(1/2*d*x + 1/2*c)^4 - 52800*a^3*b^2*tan(1/2*d*x + 1/2*c)^4 + 10080*a*b^4*tan(1/2*d*x + 1/2*c)^4 - 5400*a^4*b*tan(1/2*d*x + 1/2*c)^3 + 3420*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + 25*b^5*tan(1/2*d*x + 1/2*c)^3 + 25200*a^5*tan(1/2*d*x + 1/2*c)^2 - 26400*a^3*b^2*tan(1/2*d*x + 1/2*c)^2 + 4464*a*b^4*tan(1/2*d*x + 1/2*c)^2 - 1800*a^4*b*tan(1/2*d*x + 1/2*c) + 1620*a^2*b^3*tan(1/2*d*x + 1/2*c) - 165*b^5*tan(1/2*d*x + 1/2*c) + 5040*a^5 - 5600*a^3*b^2 + 1104*a*b^4)/((tan(1/2*d*x + 1/2*c)^2 + 1)^6*b^8))/d","A",0
1267,1,724,0,0.283020," ","integrate(cos(d*x+c)^6*sin(d*x+c)^2/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{15 \, {\left(168 \, a^{5} - 200 \, a^{3} b^{2} + 45 \, a b^{4}\right)} {\left(d x + c\right)}}{b^{8}} - \frac{120 \, {\left(42 \, a^{6} - 71 \, a^{4} b^{2} + 31 \, a^{2} b^{4} - 2 \, b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{8}} + \frac{120 \, {\left(11 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 13 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 9 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 27 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 6 \, b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 37 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 47 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 10 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, a^{6} - 15 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}^{2} b^{7}} + \frac{2 \, {\left(600 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 405 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1800 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 2160 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 360 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 1200 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 450 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 7200 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 7200 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 720 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 10800 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 9600 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 1120 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1200 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 450 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 7200 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 6240 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 560 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 600 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 405 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1800 \, a^{4} - 1680 \, a^{2} b^{2} + 184 \, b^{4}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5} b^{7}}}{120 \, d}"," ",0,"1/120*(15*(168*a^5 - 200*a^3*b^2 + 45*a*b^4)*(d*x + c)/b^8 - 120*(42*a^6 - 71*a^4*b^2 + 31*a^2*b^4 - 2*b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^8) + 120*(11*a^5*b*tan(1/2*d*x + 1/2*c)^3 - 13*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 + 2*a*b^5*tan(1/2*d*x + 1/2*c)^3 + 12*a^6*tan(1/2*d*x + 1/2*c)^2 + 9*a^4*b^2*tan(1/2*d*x + 1/2*c)^2 - 27*a^2*b^4*tan(1/2*d*x + 1/2*c)^2 + 6*b^6*tan(1/2*d*x + 1/2*c)^2 + 37*a^5*b*tan(1/2*d*x + 1/2*c) - 47*a^3*b^3*tan(1/2*d*x + 1/2*c) + 10*a*b^5*tan(1/2*d*x + 1/2*c) + 12*a^6 - 15*a^4*b^2 + 3*a^2*b^4)/((a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)^2*b^7) + 2*(600*a^3*b*tan(1/2*d*x + 1/2*c)^9 - 405*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 1800*a^4*tan(1/2*d*x + 1/2*c)^8 - 2160*a^2*b^2*tan(1/2*d*x + 1/2*c)^8 + 360*b^4*tan(1/2*d*x + 1/2*c)^8 + 1200*a^3*b*tan(1/2*d*x + 1/2*c)^7 - 450*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 7200*a^4*tan(1/2*d*x + 1/2*c)^6 - 7200*a^2*b^2*tan(1/2*d*x + 1/2*c)^6 + 720*b^4*tan(1/2*d*x + 1/2*c)^6 + 10800*a^4*tan(1/2*d*x + 1/2*c)^4 - 9600*a^2*b^2*tan(1/2*d*x + 1/2*c)^4 + 1120*b^4*tan(1/2*d*x + 1/2*c)^4 - 1200*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 450*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 7200*a^4*tan(1/2*d*x + 1/2*c)^2 - 6240*a^2*b^2*tan(1/2*d*x + 1/2*c)^2 + 560*b^4*tan(1/2*d*x + 1/2*c)^2 - 600*a^3*b*tan(1/2*d*x + 1/2*c) + 405*a*b^3*tan(1/2*d*x + 1/2*c) + 1800*a^4 - 1680*a^2*b^2 + 184*b^4)/((tan(1/2*d*x + 1/2*c)^2 + 1)^5*b^7))/d","A",0
1268,1,581,0,0.247089," ","integrate(cos(d*x+c)^6*sin(d*x+c)/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{15 \, {\left(8 \, a^{4} - 8 \, a^{2} b^{2} + b^{4}\right)} {\left(d x + c\right)}}{b^{7}} - \frac{120 \, {\left(2 \, a^{5} - 3 \, a^{3} b^{2} + a b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{7}} + \frac{8 \, {\left(9 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 10 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 9 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 21 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 31 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 35 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 10 \, a^{6} - 11 \, a^{4} b^{2} + a^{2} b^{4}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}^{2} a b^{6}} + \frac{2 \, {\left(24 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 9 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 80 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 72 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 24 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 240 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 168 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 24 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 240 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 152 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 24 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 80 \, a^{3} - 56 \, a b^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4} b^{6}}}{8 \, d}"," ",0,"-1/8*(15*(8*a^4 - 8*a^2*b^2 + b^4)*(d*x + c)/b^7 - 120*(2*a^5 - 3*a^3*b^2 + a*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^7) + 8*(9*a^5*b*tan(1/2*d*x + 1/2*c)^3 - 9*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 + 10*a^6*tan(1/2*d*x + 1/2*c)^2 + 9*a^4*b^2*tan(1/2*d*x + 1/2*c)^2 - 21*a^2*b^4*tan(1/2*d*x + 1/2*c)^2 + 2*b^6*tan(1/2*d*x + 1/2*c)^2 + 31*a^5*b*tan(1/2*d*x + 1/2*c) - 35*a^3*b^3*tan(1/2*d*x + 1/2*c) + 4*a*b^5*tan(1/2*d*x + 1/2*c) + 10*a^6 - 11*a^4*b^2 + a^2*b^4)/((a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)^2*a*b^6) + 2*(24*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 9*b^3*tan(1/2*d*x + 1/2*c)^7 + 80*a^3*tan(1/2*d*x + 1/2*c)^6 - 72*a*b^2*tan(1/2*d*x + 1/2*c)^6 + 24*a^2*b*tan(1/2*d*x + 1/2*c)^5 - b^3*tan(1/2*d*x + 1/2*c)^5 + 240*a^3*tan(1/2*d*x + 1/2*c)^4 - 168*a*b^2*tan(1/2*d*x + 1/2*c)^4 - 24*a^2*b*tan(1/2*d*x + 1/2*c)^3 + b^3*tan(1/2*d*x + 1/2*c)^3 + 240*a^3*tan(1/2*d*x + 1/2*c)^2 - 152*a*b^2*tan(1/2*d*x + 1/2*c)^2 - 24*a^2*b*tan(1/2*d*x + 1/2*c) + 9*b^3*tan(1/2*d*x + 1/2*c) + 80*a^3 - 56*a*b^2)/((tan(1/2*d*x + 1/2*c)^2 + 1)^4*b^6))/d","B",0
1269,1,635,0,0.255339," ","integrate(cos(d*x+c)^6*csc(d*x+c)/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{2 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} - \frac{{\left(12 \, a^{2} - 5 \, b^{2}\right)} {\left(d x + c\right)}}{b^{5}} + \frac{2 \, {\left(12 \, a^{6} - 11 \, a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{3} b^{5}} - \frac{2 \, {\left(6 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 4 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 13 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 9 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 6 \, b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 54 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 16 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 39 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 21 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 12 \, b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 90 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 27 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 20 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 23 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 6 \, b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 42 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 11 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, a^{6} - 3 \, a^{4} b^{2} - 3 \, a^{2} b^{4}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}^{2} a^{3} b^{4}}}{2 \, d}"," ",0,"1/2*(2*log(abs(tan(1/2*d*x + 1/2*c)))/a^3 - (12*a^2 - 5*b^2)*(d*x + c)/b^5 + 2*(12*a^6 - 11*a^4*b^2 + a^2*b^4 - 2*b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^3*b^5) - 2*(6*a^5*b*tan(1/2*d*x + 1/2*c)^7 - a^3*b^3*tan(1/2*d*x + 1/2*c)^7 - 4*a*b^5*tan(1/2*d*x + 1/2*c)^7 + 12*a^6*tan(1/2*d*x + 1/2*c)^6 + 13*a^4*b^2*tan(1/2*d*x + 1/2*c)^6 - 9*a^2*b^4*tan(1/2*d*x + 1/2*c)^6 - 6*b^6*tan(1/2*d*x + 1/2*c)^6 + 54*a^5*b*tan(1/2*d*x + 1/2*c)^5 - 9*a^3*b^3*tan(1/2*d*x + 1/2*c)^5 - 16*a*b^5*tan(1/2*d*x + 1/2*c)^5 + 36*a^6*tan(1/2*d*x + 1/2*c)^4 + 39*a^4*b^2*tan(1/2*d*x + 1/2*c)^4 - 21*a^2*b^4*tan(1/2*d*x + 1/2*c)^4 - 12*b^6*tan(1/2*d*x + 1/2*c)^4 + 90*a^5*b*tan(1/2*d*x + 1/2*c)^3 - 27*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 - 20*a*b^5*tan(1/2*d*x + 1/2*c)^3 + 36*a^6*tan(1/2*d*x + 1/2*c)^2 + 23*a^4*b^2*tan(1/2*d*x + 1/2*c)^2 - 15*a^2*b^4*tan(1/2*d*x + 1/2*c)^2 - 6*b^6*tan(1/2*d*x + 1/2*c)^2 + 42*a^5*b*tan(1/2*d*x + 1/2*c) - 11*a^3*b^3*tan(1/2*d*x + 1/2*c) - 8*a*b^5*tan(1/2*d*x + 1/2*c) + 12*a^6 - 3*a^4*b^2 - 3*a^2*b^4)/((a*tan(1/2*d*x + 1/2*c)^4 + 2*b*tan(1/2*d*x + 1/2*c)^3 + 2*a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)^2*a^3*b^4))/d","A",0
1270,1,461,0,0.275469," ","integrate(cos(d*x+c)^6*csc(d*x+c)^2/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{6 \, {\left(d x + c\right)} a}{b^{4}} - \frac{6 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{4}} + \frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3}} - \frac{6 \, {\left(2 \, a^{6} - a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{4} b^{4}} + \frac{2 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 4 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a b^{3}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} a^{4} b^{3}} + \frac{2 \, {\left(3 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 9 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 10 \, b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 13 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 14 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, a^{6} + a^{4} b^{2} - 5 \, a^{2} b^{4}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}^{2} a^{4} b^{3}}}{2 \, d}"," ",0,"1/2*(6*(d*x + c)*a/b^4 - 6*b*log(abs(tan(1/2*d*x + 1/2*c)))/a^4 + tan(1/2*d*x + 1/2*c)/a^3 - 6*(2*a^6 - a^4*b^2 + a^2*b^4 - 2*b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^4*b^4) + (2*b^4*tan(1/2*d*x + 1/2*c)^3 - a*b^3*tan(1/2*d*x + 1/2*c)^2 + 4*a^4*tan(1/2*d*x + 1/2*c) + 2*b^4*tan(1/2*d*x + 1/2*c) - a*b^3)/((tan(1/2*d*x + 1/2*c)^3 + tan(1/2*d*x + 1/2*c))*a^4*b^3) + 2*(3*a^5*b*tan(1/2*d*x + 1/2*c)^3 + 3*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 - 6*a*b^5*tan(1/2*d*x + 1/2*c)^3 + 4*a^6*tan(1/2*d*x + 1/2*c)^2 + 9*a^4*b^2*tan(1/2*d*x + 1/2*c)^2 - 3*a^2*b^4*tan(1/2*d*x + 1/2*c)^2 - 10*b^6*tan(1/2*d*x + 1/2*c)^2 + 13*a^5*b*tan(1/2*d*x + 1/2*c) + a^3*b^3*tan(1/2*d*x + 1/2*c) - 14*a*b^5*tan(1/2*d*x + 1/2*c) + 4*a^6 + a^4*b^2 - 5*a^2*b^4)/((a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)^2*a^4*b^3))/d","A",0
1271,1,512,0,0.292195," ","integrate(cos(d*x+c)^6*csc(d*x+c)^3/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{8 \, {\left(d x + c\right)}}{b^{3}} + \frac{4 \, {\left(5 \, a^{2} - 12 \, b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{5}} - \frac{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}} - \frac{8 \, {\left(2 \, a^{6} - a^{4} b^{2} + 11 \, a^{2} b^{4} - 12 \, b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{5} b^{3}} - \frac{10 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 24 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 8 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 32 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 16 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 53 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 16 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 16 \, b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 56 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 44 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 112 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 16 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 32 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 76 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 8 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{4} b^{2}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}^{2} a^{5} b^{2}}}{8 \, d}"," ",0,"-1/8*(8*(d*x + c)/b^3 + 4*(5*a^2 - 12*b^2)*log(abs(tan(1/2*d*x + 1/2*c)))/a^5 - (a^3*tan(1/2*d*x + 1/2*c)^2 - 12*a^2*b*tan(1/2*d*x + 1/2*c))/a^6 - 8*(2*a^6 - a^4*b^2 + 11*a^2*b^4 - 12*b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^5*b^3) - (10*a^4*b^2*tan(1/2*d*x + 1/2*c)^6 - 24*a^2*b^4*tan(1/2*d*x + 1/2*c)^6 - 8*a^5*b*tan(1/2*d*x + 1/2*c)^5 - 4*a^3*b^3*tan(1/2*d*x + 1/2*c)^5 - 32*a*b^5*tan(1/2*d*x + 1/2*c)^5 - 16*a^6*tan(1/2*d*x + 1/2*c)^4 - 53*a^4*b^2*tan(1/2*d*x + 1/2*c)^4 + 16*a^2*b^4*tan(1/2*d*x + 1/2*c)^4 + 16*b^6*tan(1/2*d*x + 1/2*c)^4 - 56*a^5*b*tan(1/2*d*x + 1/2*c)^3 - 44*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 + 112*a*b^5*tan(1/2*d*x + 1/2*c)^3 - 16*a^6*tan(1/2*d*x + 1/2*c)^2 - 32*a^4*b^2*tan(1/2*d*x + 1/2*c)^2 + 76*a^2*b^4*tan(1/2*d*x + 1/2*c)^2 + 8*a^3*b^3*tan(1/2*d*x + 1/2*c) - a^4*b^2)/((a*tan(1/2*d*x + 1/2*c)^3 + 2*b*tan(1/2*d*x + 1/2*c)^2 + a*tan(1/2*d*x + 1/2*c))^2*a^5*b^2))/d","A",0
1272,1,478,0,0.292894," ","integrate(cos(d*x+c)^6*csc(d*x+c)^4/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{60 \, {\left(3 \, a^{2} b - 4 \, b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{6}} + \frac{120 \, {\left(a^{4} - 5 \, a^{2} b^{2} + 4 \, b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{6}} - \frac{24 \, {\left(a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 11 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 10 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 18 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 25 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 26 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, a^{4} b + 9 \, a^{2} b^{3}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}^{2} a^{6}} + \frac{a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 27 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 72 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{9}} - \frac{330 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 440 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 27 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 72 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3}}{a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{24 \, d}"," ",0,"1/24*(60*(3*a^2*b - 4*b^3)*log(abs(tan(1/2*d*x + 1/2*c)))/a^6 + 120*(a^4 - 5*a^2*b^2 + 4*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^6) - 24*(a^5*tan(1/2*d*x + 1/2*c)^3 - 11*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 + 10*a*b^4*tan(1/2*d*x + 1/2*c)^3 - 9*a^4*b*tan(1/2*d*x + 1/2*c)^2 - 9*a^2*b^3*tan(1/2*d*x + 1/2*c)^2 + 18*b^5*tan(1/2*d*x + 1/2*c)^2 - a^5*tan(1/2*d*x + 1/2*c) - 25*a^3*b^2*tan(1/2*d*x + 1/2*c) + 26*a*b^4*tan(1/2*d*x + 1/2*c) - 9*a^4*b + 9*a^2*b^3)/((a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)^2*a^6) + (a^6*tan(1/2*d*x + 1/2*c)^3 - 9*a^5*b*tan(1/2*d*x + 1/2*c)^2 - 27*a^6*tan(1/2*d*x + 1/2*c) + 72*a^4*b^2*tan(1/2*d*x + 1/2*c))/a^9 - (330*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 440*b^3*tan(1/2*d*x + 1/2*c)^3 - 27*a^3*tan(1/2*d*x + 1/2*c)^2 + 72*a*b^2*tan(1/2*d*x + 1/2*c)^2 - 9*a^2*b*tan(1/2*d*x + 1/2*c) + a^3)/(a^6*tan(1/2*d*x + 1/2*c)^3))/d","A",0
1273,1,603,0,0.344482," ","integrate(cos(d*x+c)^6*csc(d*x+c)^5/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{120 \, {\left(a^{4} - 8 \, a^{2} b^{2} + 8 \, b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{7}} - \frac{960 \, {\left(a^{4} b - 3 \, a^{2} b^{3} + 2 \, b^{5}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{7}} + \frac{64 \, {\left(3 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 22 \, b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 5 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 37 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 32 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, a^{6} - 13 \, a^{4} b^{2} + 11 \, a^{2} b^{4}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}^{2} a^{7}} - \frac{250 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 2000 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2000 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 216 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 320 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 16 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 48 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{4}}{a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}} + \frac{a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 8 \, a^{8} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 16 \, a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 48 \, a^{7} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 216 \, a^{8} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 320 \, a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{12}}}{64 \, d}"," ",0,"1/64*(120*(a^4 - 8*a^2*b^2 + 8*b^4)*log(abs(tan(1/2*d*x + 1/2*c)))/a^7 - 960*(a^4*b - 3*a^2*b^3 + 2*b^5)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^7) + 64*(3*a^5*b*tan(1/2*d*x + 1/2*c)^3 - 15*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 + 12*a*b^5*tan(1/2*d*x + 1/2*c)^3 + 2*a^6*tan(1/2*d*x + 1/2*c)^2 - 9*a^4*b^2*tan(1/2*d*x + 1/2*c)^2 - 15*a^2*b^4*tan(1/2*d*x + 1/2*c)^2 + 22*b^6*tan(1/2*d*x + 1/2*c)^2 + 5*a^5*b*tan(1/2*d*x + 1/2*c) - 37*a^3*b^3*tan(1/2*d*x + 1/2*c) + 32*a*b^5*tan(1/2*d*x + 1/2*c) + 2*a^6 - 13*a^4*b^2 + 11*a^2*b^4)/((a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)^2*a^7) - (250*a^4*tan(1/2*d*x + 1/2*c)^4 - 2000*a^2*b^2*tan(1/2*d*x + 1/2*c)^4 + 2000*b^4*tan(1/2*d*x + 1/2*c)^4 + 216*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 320*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 16*a^4*tan(1/2*d*x + 1/2*c)^2 + 48*a^2*b^2*tan(1/2*d*x + 1/2*c)^2 - 8*a^3*b*tan(1/2*d*x + 1/2*c) + a^4)/(a^7*tan(1/2*d*x + 1/2*c)^4) + (a^9*tan(1/2*d*x + 1/2*c)^4 - 8*a^8*b*tan(1/2*d*x + 1/2*c)^3 - 16*a^9*tan(1/2*d*x + 1/2*c)^2 + 48*a^7*b^2*tan(1/2*d*x + 1/2*c)^2 + 216*a^8*b*tan(1/2*d*x + 1/2*c) - 320*a^6*b^3*tan(1/2*d*x + 1/2*c))/a^12)/d","A",0
1274,1,731,0,0.335105," ","integrate(cos(d*x+c)^6*csc(d*x+c)^6/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{120 \, {\left(45 \, a^{4} b - 200 \, a^{2} b^{3} + 168 \, b^{5}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{8}} + \frac{960 \, {\left(2 \, a^{6} - 31 \, a^{4} b^{2} + 71 \, a^{2} b^{4} - 42 \, b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{8}} + \frac{960 \, {\left(5 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 19 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 14 \, a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 21 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 26 \, b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 11 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 49 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 38 \, a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, a^{6} b - 17 \, a^{4} b^{3} + 13 \, a^{2} b^{5}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}^{2} a^{8}} - \frac{12330 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 54800 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 46032 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 660 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 6480 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 7200 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 720 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1200 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 70 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 240 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 45 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, a^{5}}{a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}} - \frac{6 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 45 \, a^{11} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 70 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 240 \, a^{10} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 720 \, a^{11} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1200 \, a^{9} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 660 \, a^{12} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6480 \, a^{10} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 7200 \, a^{8} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{15}}}{960 \, d}"," ",0,"-1/960*(120*(45*a^4*b - 200*a^2*b^3 + 168*b^5)*log(abs(tan(1/2*d*x + 1/2*c)))/a^8 + 960*(2*a^6 - 31*a^4*b^2 + 71*a^2*b^4 - 42*b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^8) + 960*(5*a^5*b^2*tan(1/2*d*x + 1/2*c)^3 - 19*a^3*b^4*tan(1/2*d*x + 1/2*c)^3 + 14*a*b^6*tan(1/2*d*x + 1/2*c)^3 + 4*a^6*b*tan(1/2*d*x + 1/2*c)^2 - 9*a^4*b^3*tan(1/2*d*x + 1/2*c)^2 - 21*a^2*b^5*tan(1/2*d*x + 1/2*c)^2 + 26*b^7*tan(1/2*d*x + 1/2*c)^2 + 11*a^5*b^2*tan(1/2*d*x + 1/2*c) - 49*a^3*b^4*tan(1/2*d*x + 1/2*c) + 38*a*b^6*tan(1/2*d*x + 1/2*c) + 4*a^6*b - 17*a^4*b^3 + 13*a^2*b^5)/((a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)^2*a^8) - (12330*a^4*b*tan(1/2*d*x + 1/2*c)^5 - 54800*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 + 46032*b^5*tan(1/2*d*x + 1/2*c)^5 - 660*a^5*tan(1/2*d*x + 1/2*c)^4 + 6480*a^3*b^2*tan(1/2*d*x + 1/2*c)^4 - 7200*a*b^4*tan(1/2*d*x + 1/2*c)^4 - 720*a^4*b*tan(1/2*d*x + 1/2*c)^3 + 1200*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + 70*a^5*tan(1/2*d*x + 1/2*c)^2 - 240*a^3*b^2*tan(1/2*d*x + 1/2*c)^2 + 45*a^4*b*tan(1/2*d*x + 1/2*c) - 6*a^5)/(a^8*tan(1/2*d*x + 1/2*c)^5) - (6*a^12*tan(1/2*d*x + 1/2*c)^5 - 45*a^11*b*tan(1/2*d*x + 1/2*c)^4 - 70*a^12*tan(1/2*d*x + 1/2*c)^3 + 240*a^10*b^2*tan(1/2*d*x + 1/2*c)^3 + 720*a^11*b*tan(1/2*d*x + 1/2*c)^2 - 1200*a^9*b^3*tan(1/2*d*x + 1/2*c)^2 + 660*a^12*tan(1/2*d*x + 1/2*c) - 6480*a^10*b^2*tan(1/2*d*x + 1/2*c) + 7200*a^8*b^4*tan(1/2*d*x + 1/2*c))/a^15)/d","A",0
1275,1,1018,0,0.390963," ","integrate(cos(d*x+c)^6*csc(d*x+c)^8/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{840 \, {\left(5 \, a^{6} b - 100 \, a^{4} b^{3} + 280 \, a^{2} b^{5} - 192 \, b^{7}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{10}} - \frac{13440 \, {\left(4 \, a^{6} b^{2} - 27 \, a^{4} b^{4} + 47 \, a^{2} b^{6} - 24 \, b^{8}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{10}} - \frac{4480 \, {\left(9 \, a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 27 \, a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, a^{6} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 33 \, a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 34 \, b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 23 \, a^{5} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 73 \, a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 50 \, a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8 \, a^{6} b^{3} - 25 \, a^{4} b^{5} + 17 \, a^{2} b^{7}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}^{2} a^{10}} - \frac{10890 \, a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 217800 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 609840 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 418176 \, b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 175 \, a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 18480 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 75600 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 62720 \, a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 1575 \, a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 11200 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 11760 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 105 \, a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1960 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2800 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 315 \, a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 700 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 35 \, a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 168 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 35 \, a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, a^{7}}{a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7}} + \frac{5 \, a^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 35 \, a^{17} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 35 \, a^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 168 \, a^{16} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 315 \, a^{17} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 700 \, a^{15} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 105 \, a^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1960 \, a^{16} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2800 \, a^{14} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1575 \, a^{17} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 11200 \, a^{15} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 11760 \, a^{13} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 175 \, a^{18} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18480 \, a^{16} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 75600 \, a^{14} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 62720 \, a^{12} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{21}}}{4480 \, d}"," ",0,"1/4480*(840*(5*a^6*b - 100*a^4*b^3 + 280*a^2*b^5 - 192*b^7)*log(abs(tan(1/2*d*x + 1/2*c)))/a^10 - 13440*(4*a^6*b^2 - 27*a^4*b^4 + 47*a^2*b^6 - 24*b^8)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^10) - 4480*(9*a^5*b^4*tan(1/2*d*x + 1/2*c)^3 - 27*a^3*b^6*tan(1/2*d*x + 1/2*c)^3 + 18*a*b^8*tan(1/2*d*x + 1/2*c)^3 + 8*a^6*b^3*tan(1/2*d*x + 1/2*c)^2 - 9*a^4*b^5*tan(1/2*d*x + 1/2*c)^2 - 33*a^2*b^7*tan(1/2*d*x + 1/2*c)^2 + 34*b^9*tan(1/2*d*x + 1/2*c)^2 + 23*a^5*b^4*tan(1/2*d*x + 1/2*c) - 73*a^3*b^6*tan(1/2*d*x + 1/2*c) + 50*a*b^8*tan(1/2*d*x + 1/2*c) + 8*a^6*b^3 - 25*a^4*b^5 + 17*a^2*b^7)/((a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)^2*a^10) - (10890*a^6*b*tan(1/2*d*x + 1/2*c)^7 - 217800*a^4*b^3*tan(1/2*d*x + 1/2*c)^7 + 609840*a^2*b^5*tan(1/2*d*x + 1/2*c)^7 - 418176*b^7*tan(1/2*d*x + 1/2*c)^7 - 175*a^7*tan(1/2*d*x + 1/2*c)^6 + 18480*a^5*b^2*tan(1/2*d*x + 1/2*c)^6 - 75600*a^3*b^4*tan(1/2*d*x + 1/2*c)^6 + 62720*a*b^6*tan(1/2*d*x + 1/2*c)^6 - 1575*a^6*b*tan(1/2*d*x + 1/2*c)^5 + 11200*a^4*b^3*tan(1/2*d*x + 1/2*c)^5 - 11760*a^2*b^5*tan(1/2*d*x + 1/2*c)^5 + 105*a^7*tan(1/2*d*x + 1/2*c)^4 - 1960*a^5*b^2*tan(1/2*d*x + 1/2*c)^4 + 2800*a^3*b^4*tan(1/2*d*x + 1/2*c)^4 + 315*a^6*b*tan(1/2*d*x + 1/2*c)^3 - 700*a^4*b^3*tan(1/2*d*x + 1/2*c)^3 - 35*a^7*tan(1/2*d*x + 1/2*c)^2 + 168*a^5*b^2*tan(1/2*d*x + 1/2*c)^2 - 35*a^6*b*tan(1/2*d*x + 1/2*c) + 5*a^7)/(a^10*tan(1/2*d*x + 1/2*c)^7) + (5*a^18*tan(1/2*d*x + 1/2*c)^7 - 35*a^17*b*tan(1/2*d*x + 1/2*c)^6 - 35*a^18*tan(1/2*d*x + 1/2*c)^5 + 168*a^16*b^2*tan(1/2*d*x + 1/2*c)^5 + 315*a^17*b*tan(1/2*d*x + 1/2*c)^4 - 700*a^15*b^3*tan(1/2*d*x + 1/2*c)^4 + 105*a^18*tan(1/2*d*x + 1/2*c)^3 - 1960*a^16*b^2*tan(1/2*d*x + 1/2*c)^3 + 2800*a^14*b^4*tan(1/2*d*x + 1/2*c)^3 - 1575*a^17*b*tan(1/2*d*x + 1/2*c)^2 + 11200*a^15*b^3*tan(1/2*d*x + 1/2*c)^2 - 11760*a^13*b^5*tan(1/2*d*x + 1/2*c)^2 - 175*a^18*tan(1/2*d*x + 1/2*c) + 18480*a^16*b^2*tan(1/2*d*x + 1/2*c) - 75600*a^14*b^4*tan(1/2*d*x + 1/2*c) + 62720*a^12*b^6*tan(1/2*d*x + 1/2*c))/a^21)/d","A",0
1276,0,0,0,0.000000," ","integrate(cos(f*x+e)^6/(a+b*sin(f*x+e))^(13/2)/(d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\cos\left(f x + e\right)^{6}}{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{13}{2}} \sqrt{d \sin\left(f x + e\right)}}\,{d x}"," ",0,"integrate(cos(f*x + e)^6/((b*sin(f*x + e) + a)^(13/2)*sqrt(d*sin(f*x + e))), x)","F",0
1277,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^2/(g*cos(f*x+e))^(5/2)/(d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{2}}{\left(g \cos\left(f x + e\right)\right)^{\frac{5}{2}} \sqrt{d \sin\left(f x + e\right)}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^2/((g*cos(f*x + e))^(5/2)*sqrt(d*sin(f*x + e))), x)","F",0
1278,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^2/(g*cos(f*x+e))^(7/2)/(d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{2}}{\left(g \cos\left(f x + e\right)\right)^{\frac{7}{2}} \sqrt{d \sin\left(f x + e\right)}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^2/((g*cos(f*x + e))^(7/2)*sqrt(d*sin(f*x + e))), x)","F",0
1279,1,68,0,0.159859," ","integrate(cos(d*x+c)*sin(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{6 \, a^{3} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{b^{4}} - \frac{2 \, b^{2} \sin\left(d x + c\right)^{3} - 3 \, a b \sin\left(d x + c\right)^{2} + 6 \, a^{2} \sin\left(d x + c\right)}{b^{3}}}{6 \, d}"," ",0,"-1/6*(6*a^3*log(abs(b*sin(d*x + c) + a))/b^4 - (2*b^2*sin(d*x + c)^3 - 3*a*b*sin(d*x + c)^2 + 6*a^2*sin(d*x + c))/b^3)/d","A",0
1280,1,50,0,0.159802," ","integrate(cos(d*x+c)*sin(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{2 \, a^{2} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{b^{3}} + \frac{b \sin\left(d x + c\right)^{2} - 2 \, a \sin\left(d x + c\right)}{b^{2}}}{2 \, d}"," ",0,"1/2*(2*a^2*log(abs(b*sin(d*x + c) + a))/b^3 + (b*sin(d*x + c)^2 - 2*a*sin(d*x + c))/b^2)/d","A",0
1281,1,34,0,0.163476," ","integrate(cos(d*x+c)*sin(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{a \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{b^{2}} - \frac{\sin\left(d x + c\right)}{b}}{d}"," ",0,"-(a*log(abs(b*sin(d*x + c) + a))/b^2 - sin(d*x + c)/b)/d","A",0
1282,1,35,0,0.146616," ","integrate(cos(d*x+c)*csc(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{\log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a} - \frac{\log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a}}{d}"," ",0,"-(log(abs(b*sin(d*x + c) + a))/a - log(abs(sin(d*x + c)))/a)/d","A",0
1283,1,49,0,0.154952," ","integrate(cos(d*x+c)*csc(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{b \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{2}} - \frac{b \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a^{2}} - \frac{1}{a \sin\left(d x + c\right)}}{d}"," ",0,"(b*log(abs(b*sin(d*x + c) + a))/a^2 - b*log(abs(sin(d*x + c)))/a^2 - 1/(a*sin(d*x + c)))/d","A",0
1284,1,71,0,0.156773," ","integrate(cos(d*x+c)*csc(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{2 \, b^{2} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{3}} - \frac{2 \, b^{2} \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a^{3}} - \frac{2 \, a b \sin\left(d x + c\right) - a^{2}}{a^{3} \sin\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(2*b^2*log(abs(b*sin(d*x + c) + a))/a^3 - 2*b^2*log(abs(sin(d*x + c)))/a^3 - (2*a*b*sin(d*x + c) - a^2)/(a^3*sin(d*x + c)^2))/d","A",0
1285,1,467,0,0.169794," ","integrate(cos(d*x+c)^2*sin(d*x+c)^4/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{15 \, {\left(8 \, a^{5} - 4 \, a^{3} b^{2} - a b^{4}\right)} {\left(d x + c\right)}}{b^{6}} - \frac{240 \, {\left(a^{6} - a^{4} b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{6}} + \frac{2 \, {\left(60 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 15 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 120 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 120 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 90 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 480 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 240 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 240 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 720 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 160 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 80 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 120 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 90 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 480 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 80 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 80 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 60 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, a^{4} - 40 \, a^{2} b^{2} - 16 \, b^{4}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5} b^{5}}}{120 \, d}"," ",0,"1/120*(15*(8*a^5 - 4*a^3*b^2 - a*b^4)*(d*x + c)/b^6 - 240*(a^6 - a^4*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^6) + 2*(60*a^3*b*tan(1/2*d*x + 1/2*c)^9 - 15*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 120*a^4*tan(1/2*d*x + 1/2*c)^8 - 120*a^2*b^2*tan(1/2*d*x + 1/2*c)^8 + 120*a^3*b*tan(1/2*d*x + 1/2*c)^7 + 90*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 480*a^4*tan(1/2*d*x + 1/2*c)^6 - 240*a^2*b^2*tan(1/2*d*x + 1/2*c)^6 - 240*b^4*tan(1/2*d*x + 1/2*c)^6 + 720*a^4*tan(1/2*d*x + 1/2*c)^4 - 160*a^2*b^2*tan(1/2*d*x + 1/2*c)^4 + 80*b^4*tan(1/2*d*x + 1/2*c)^4 - 120*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 90*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 480*a^4*tan(1/2*d*x + 1/2*c)^2 - 80*a^2*b^2*tan(1/2*d*x + 1/2*c)^2 - 80*b^4*tan(1/2*d*x + 1/2*c)^2 - 60*a^3*b*tan(1/2*d*x + 1/2*c) + 15*a*b^3*tan(1/2*d*x + 1/2*c) + 120*a^4 - 40*a^2*b^2 - 16*b^4)/((tan(1/2*d*x + 1/2*c)^2 + 1)^5*b^5))/d","B",0
1286,1,366,0,0.181589," ","integrate(cos(d*x+c)^2*sin(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(8 \, a^{4} - 4 \, a^{2} b^{2} - b^{4}\right)} {\left(d x + c\right)}}{b^{5}} - \frac{48 \, {\left(a^{5} - a^{3} b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{5}} + \frac{2 \, {\left(12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 3 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 24 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 21 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 24 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 21 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 72 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, a^{3} - 8 \, a b^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4} b^{4}}}{24 \, d}"," ",0,"-1/24*(3*(8*a^4 - 4*a^2*b^2 - b^4)*(d*x + c)/b^5 - 48*(a^5 - a^3*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^5) + 2*(12*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 3*b^3*tan(1/2*d*x + 1/2*c)^7 + 24*a^3*tan(1/2*d*x + 1/2*c)^6 - 24*a*b^2*tan(1/2*d*x + 1/2*c)^6 + 12*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 21*b^3*tan(1/2*d*x + 1/2*c)^5 + 72*a^3*tan(1/2*d*x + 1/2*c)^4 - 24*a*b^2*tan(1/2*d*x + 1/2*c)^4 - 12*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 21*b^3*tan(1/2*d*x + 1/2*c)^3 + 72*a^3*tan(1/2*d*x + 1/2*c)^2 - 8*a*b^2*tan(1/2*d*x + 1/2*c)^2 - 12*a^2*b*tan(1/2*d*x + 1/2*c) + 3*b^3*tan(1/2*d*x + 1/2*c) + 24*a^3 - 8*a*b^2)/((tan(1/2*d*x + 1/2*c)^2 + 1)^4*b^4))/d","B",0
1287,1,207,0,0.158288," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{3 \, {\left(2 \, a^{3} - a b^{2}\right)} {\left(d x + c\right)}}{b^{4}} - \frac{12 \, {\left(a^{4} - a^{2} b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{4}} + \frac{2 \, {\left(3 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 6 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 12 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, a^{2} - 2 \, b^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} b^{3}}}{6 \, d}"," ",0,"1/6*(3*(2*a^3 - a*b^2)*(d*x + c)/b^4 - 12*(a^4 - a^2*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^4) + 2*(3*a*b*tan(1/2*d*x + 1/2*c)^5 + 6*a^2*tan(1/2*d*x + 1/2*c)^4 - 6*b^2*tan(1/2*d*x + 1/2*c)^4 + 12*a^2*tan(1/2*d*x + 1/2*c)^2 - 3*a*b*tan(1/2*d*x + 1/2*c) + 6*a^2 - 2*b^2)/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*b^3))/d","A",0
1288,1,159,0,0.157382," ","integrate(cos(d*x+c)^2*sin(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{{\left(2 \, a^{2} - b^{2}\right)} {\left(d x + c\right)}}{b^{3}} - \frac{4 \, {\left(a^{3} - a b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{3}} + \frac{2 \, {\left(b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, a\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} b^{2}}}{2 \, d}"," ",0,"-1/2*((2*a^2 - b^2)*(d*x + c)/b^3 - 4*(a^3 - a*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^3) + 2*(b*tan(1/2*d*x + 1/2*c)^3 + 2*a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c) + 2*a)/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*b^2))/d","A",0
1289,1,94,0,0.166487," ","integrate(cos(d*x+c)^2*csc(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{d x + c}{b} - \frac{\log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a} - \frac{2 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} \sqrt{a^{2} - b^{2}}}{a b}}{d}"," ",0,"-((d*x + c)/b - log(abs(tan(1/2*d*x + 1/2*c)))/a - 2*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))*sqrt(a^2 - b^2)/(a*b))/d","A",0
1290,1,129,0,0.196466," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{2 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} - \frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a} + \frac{4 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} \sqrt{a^{2} - b^{2}}}{a^{2}} - \frac{2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a}{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}}{2 \, d}"," ",0,"-1/2*(2*b*log(abs(tan(1/2*d*x + 1/2*c)))/a^2 - tan(1/2*d*x + 1/2*c)/a + 4*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))*sqrt(a^2 - b^2)/a^2 - (2*b*tan(1/2*d*x + 1/2*c) - a)/(a^2*tan(1/2*d*x + 1/2*c)))/d","A",0
1291,1,198,0,0.190835," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{2}} - \frac{4 \, {\left(a^{2} - 2 \, b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} + \frac{16 \, {\left(a^{2} b - b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{3}} + \frac{6 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 4 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{2}}{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}}{8 \, d}"," ",0,"1/8*((a*tan(1/2*d*x + 1/2*c)^2 - 4*b*tan(1/2*d*x + 1/2*c))/a^2 - 4*(a^2 - 2*b^2)*log(abs(tan(1/2*d*x + 1/2*c)))/a^3 + 16*(a^2*b - b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^3) + (6*a^2*tan(1/2*d*x + 1/2*c)^2 - 12*b^2*tan(1/2*d*x + 1/2*c)^2 + 4*a*b*tan(1/2*d*x + 1/2*c) - a^2)/(a^3*tan(1/2*d*x + 1/2*c)^2))/d","A",0
1292,1,270,0,0.188473," ","integrate(cos(d*x+c)^2*csc(d*x+c)^4/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3}} + \frac{12 \, {\left(a^{2} b - 2 \, b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{4}} - \frac{48 \, {\left(a^{2} b^{2} - b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{4}} - \frac{22 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 44 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3}}{a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{24 \, d}"," ",0,"1/24*((a^2*tan(1/2*d*x + 1/2*c)^3 - 3*a*b*tan(1/2*d*x + 1/2*c)^2 - 3*a^2*tan(1/2*d*x + 1/2*c) + 12*b^2*tan(1/2*d*x + 1/2*c))/a^3 + 12*(a^2*b - 2*b^3)*log(abs(tan(1/2*d*x + 1/2*c)))/a^4 - 48*(a^2*b^2 - b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^4) - (22*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 44*b^3*tan(1/2*d*x + 1/2*c)^3 - 3*a^3*tan(1/2*d*x + 1/2*c)^2 + 12*a*b^2*tan(1/2*d*x + 1/2*c)^2 - 3*a^2*b*tan(1/2*d*x + 1/2*c) + a^3)/(a^4*tan(1/2*d*x + 1/2*c)^3))/d","A",0
1293,1,336,0,0.202924," ","integrate(cos(d*x+c)^2*csc(d*x+c)^5/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 8 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 24 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 96 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{4}} - \frac{24 \, {\left(a^{4} + 4 \, a^{2} b^{2} - 8 \, b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{5}} + \frac{384 \, {\left(a^{2} b^{3} - b^{5}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{5}} + \frac{50 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 200 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 400 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 24 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 96 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 8 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a^{4}}{a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}}}{192 \, d}"," ",0,"1/192*((3*a^3*tan(1/2*d*x + 1/2*c)^4 - 8*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 24*a*b^2*tan(1/2*d*x + 1/2*c)^2 + 24*a^2*b*tan(1/2*d*x + 1/2*c) - 96*b^3*tan(1/2*d*x + 1/2*c))/a^4 - 24*(a^4 + 4*a^2*b^2 - 8*b^4)*log(abs(tan(1/2*d*x + 1/2*c)))/a^5 + 384*(a^2*b^3 - b^5)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^5) + (50*a^4*tan(1/2*d*x + 1/2*c)^4 + 200*a^2*b^2*tan(1/2*d*x + 1/2*c)^4 - 400*b^4*tan(1/2*d*x + 1/2*c)^4 - 24*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 96*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 24*a^2*b^2*tan(1/2*d*x + 1/2*c)^2 + 8*a^3*b*tan(1/2*d*x + 1/2*c) - 3*a^4)/(a^5*tan(1/2*d*x + 1/2*c)^4))/d","A",0
1294,1,444,0,0.198735," ","integrate(cos(d*x+c)^2*csc(d*x+c)^6/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{6 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 10 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 60 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 120 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 480 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{5}} + \frac{120 \, {\left(a^{4} b + 4 \, a^{2} b^{3} - 8 \, b^{5}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{6}} - \frac{1920 \, {\left(a^{2} b^{4} - b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{6}} - \frac{274 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1096 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 2192 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 60 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 120 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 480 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 120 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 10 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 40 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, a^{5}}{a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{960 \, d}"," ",0,"1/960*((6*a^4*tan(1/2*d*x + 1/2*c)^5 - 15*a^3*b*tan(1/2*d*x + 1/2*c)^4 + 10*a^4*tan(1/2*d*x + 1/2*c)^3 + 40*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 120*a*b^3*tan(1/2*d*x + 1/2*c)^2 - 60*a^4*tan(1/2*d*x + 1/2*c) - 120*a^2*b^2*tan(1/2*d*x + 1/2*c) + 480*b^4*tan(1/2*d*x + 1/2*c))/a^5 + 120*(a^4*b + 4*a^2*b^3 - 8*b^5)*log(abs(tan(1/2*d*x + 1/2*c)))/a^6 - 1920*(a^2*b^4 - b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^6) - (274*a^4*b*tan(1/2*d*x + 1/2*c)^5 + 1096*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 - 2192*b^5*tan(1/2*d*x + 1/2*c)^5 - 60*a^5*tan(1/2*d*x + 1/2*c)^4 - 120*a^3*b^2*tan(1/2*d*x + 1/2*c)^4 + 480*a*b^4*tan(1/2*d*x + 1/2*c)^4 - 120*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + 10*a^5*tan(1/2*d*x + 1/2*c)^2 + 40*a^3*b^2*tan(1/2*d*x + 1/2*c)^2 - 15*a^4*b*tan(1/2*d*x + 1/2*c) + 6*a^5)/(a^6*tan(1/2*d*x + 1/2*c)^5))/d","B",0
1295,1,149,0,0.173145," ","integrate(cos(d*x+c)^3*sin(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{12 \, b^{4} \sin\left(d x + c\right)^{5} - 15 \, a b^{3} \sin\left(d x + c\right)^{4} + 20 \, a^{2} b^{2} \sin\left(d x + c\right)^{3} - 20 \, b^{4} \sin\left(d x + c\right)^{3} - 30 \, a^{3} b \sin\left(d x + c\right)^{2} + 30 \, a b^{3} \sin\left(d x + c\right)^{2} + 60 \, a^{4} \sin\left(d x + c\right) - 60 \, a^{2} b^{2} \sin\left(d x + c\right)}{b^{5}} - \frac{60 \, {\left(a^{5} - a^{3} b^{2}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{b^{6}}}{60 \, d}"," ",0,"-1/60*((12*b^4*sin(d*x + c)^5 - 15*a*b^3*sin(d*x + c)^4 + 20*a^2*b^2*sin(d*x + c)^3 - 20*b^4*sin(d*x + c)^3 - 30*a^3*b*sin(d*x + c)^2 + 30*a*b^3*sin(d*x + c)^2 + 60*a^4*sin(d*x + c) - 60*a^2*b^2*sin(d*x + c))/b^5 - 60*(a^5 - a^3*b^2)*log(abs(b*sin(d*x + c) + a))/b^6)/d","A",0
1296,1,117,0,0.154954," ","integrate(cos(d*x+c)^3*sin(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{3 \, b^{3} \sin\left(d x + c\right)^{4} - 4 \, a b^{2} \sin\left(d x + c\right)^{3} + 6 \, a^{2} b \sin\left(d x + c\right)^{2} - 6 \, b^{3} \sin\left(d x + c\right)^{2} - 12 \, a^{3} \sin\left(d x + c\right) + 12 \, a b^{2} \sin\left(d x + c\right)}{b^{4}} + \frac{12 \, {\left(a^{4} - a^{2} b^{2}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{b^{5}}}{12 \, d}"," ",0,"-1/12*((3*b^3*sin(d*x + c)^4 - 4*a*b^2*sin(d*x + c)^3 + 6*a^2*b*sin(d*x + c)^2 - 6*b^3*sin(d*x + c)^2 - 12*a^3*sin(d*x + c) + 12*a*b^2*sin(d*x + c))/b^4 + 12*(a^4 - a^2*b^2)*log(abs(b*sin(d*x + c) + a))/b^5)/d","A",0
1297,1,85,0,0.163830," ","integrate(cos(d*x+c)^3*sin(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{2 \, b^{2} \sin\left(d x + c\right)^{3} - 3 \, a b \sin\left(d x + c\right)^{2} + 6 \, a^{2} \sin\left(d x + c\right) - 6 \, b^{2} \sin\left(d x + c\right)}{b^{3}} - \frac{6 \, {\left(a^{3} - a b^{2}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{b^{4}}}{6 \, d}"," ",0,"-1/6*((2*b^2*sin(d*x + c)^3 - 3*a*b*sin(d*x + c)^2 + 6*a^2*sin(d*x + c) - 6*b^2*sin(d*x + c))/b^3 - 6*(a^3 - a*b^2)*log(abs(b*sin(d*x + c) + a))/b^4)/d","A",0
1298,1,56,0,0.178516," ","integrate(cos(d*x+c)^3*csc(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{\log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a} - \frac{\sin\left(d x + c\right)}{b} + \frac{{\left(a^{2} - b^{2}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a b^{2}}}{d}"," ",0,"(log(abs(sin(d*x + c)))/a - sin(d*x + c)/b + (a^2 - b^2)*log(abs(b*sin(d*x + c) + a))/(a*b^2))/d","A",0
1299,1,59,0,0.166678," ","integrate(cos(d*x+c)^3*csc(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{b \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a^{2}} + \frac{{\left(a^{2} - b^{2}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{2} b} + \frac{1}{a \sin\left(d x + c\right)}}{d}"," ",0,"-(b*log(abs(sin(d*x + c)))/a^2 + (a^2 - b^2)*log(abs(b*sin(d*x + c) + a))/(a^2*b) + 1/(a*sin(d*x + c)))/d","A",0
1300,1,88,0,0.175699," ","integrate(cos(d*x+c)^3*csc(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(a^{2} - b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a^{3}} - \frac{2 \, {\left(a^{2} b - b^{3}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{3} b} - \frac{2 \, a b \sin\left(d x + c\right) - a^{2}}{a^{3} \sin\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(2*(a^2 - b^2)*log(abs(sin(d*x + c)))/a^3 - 2*(a^2*b - b^3)*log(abs(b*sin(d*x + c) + a))/(a^3*b) - (2*a*b*sin(d*x + c) - a^2)/(a^3*sin(d*x + c)^2))/d","A",0
1301,1,726,0,0.212585," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{15 \, {\left(16 \, a^{6} - 24 \, a^{4} b^{2} + 6 \, a^{2} b^{4} + b^{6}\right)} {\left(d x + c\right)}}{b^{7}} - \frac{480 \, {\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{7}} + \frac{2 \, {\left(120 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 150 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 15 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 240 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 480 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 240 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 360 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 210 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 235 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1200 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 1920 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 240 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 240 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 60 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 390 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 2400 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 3200 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 480 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 240 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 60 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 390 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2400 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 2880 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 480 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 360 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 210 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 235 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1200 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1440 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 48 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 120 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 150 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 240 \, a^{5} - 320 \, a^{3} b^{2} + 48 \, a b^{4}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6} b^{6}}}{240 \, d}"," ",0,"1/240*(15*(16*a^6 - 24*a^4*b^2 + 6*a^2*b^4 + b^6)*(d*x + c)/b^7 - 480*(a^7 - 2*a^5*b^2 + a^3*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^7) + 2*(120*a^4*b*tan(1/2*d*x + 1/2*c)^11 - 150*a^2*b^3*tan(1/2*d*x + 1/2*c)^11 + 15*b^5*tan(1/2*d*x + 1/2*c)^11 + 240*a^5*tan(1/2*d*x + 1/2*c)^10 - 480*a^3*b^2*tan(1/2*d*x + 1/2*c)^10 + 240*a*b^4*tan(1/2*d*x + 1/2*c)^10 + 360*a^4*b*tan(1/2*d*x + 1/2*c)^9 - 210*a^2*b^3*tan(1/2*d*x + 1/2*c)^9 - 235*b^5*tan(1/2*d*x + 1/2*c)^9 + 1200*a^5*tan(1/2*d*x + 1/2*c)^8 - 1920*a^3*b^2*tan(1/2*d*x + 1/2*c)^8 + 240*a*b^4*tan(1/2*d*x + 1/2*c)^8 + 240*a^4*b*tan(1/2*d*x + 1/2*c)^7 - 60*a^2*b^3*tan(1/2*d*x + 1/2*c)^7 + 390*b^5*tan(1/2*d*x + 1/2*c)^7 + 2400*a^5*tan(1/2*d*x + 1/2*c)^6 - 3200*a^3*b^2*tan(1/2*d*x + 1/2*c)^6 + 480*a*b^4*tan(1/2*d*x + 1/2*c)^6 - 240*a^4*b*tan(1/2*d*x + 1/2*c)^5 + 60*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 - 390*b^5*tan(1/2*d*x + 1/2*c)^5 + 2400*a^5*tan(1/2*d*x + 1/2*c)^4 - 2880*a^3*b^2*tan(1/2*d*x + 1/2*c)^4 + 480*a*b^4*tan(1/2*d*x + 1/2*c)^4 - 360*a^4*b*tan(1/2*d*x + 1/2*c)^3 + 210*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + 235*b^5*tan(1/2*d*x + 1/2*c)^3 + 1200*a^5*tan(1/2*d*x + 1/2*c)^2 - 1440*a^3*b^2*tan(1/2*d*x + 1/2*c)^2 + 48*a*b^4*tan(1/2*d*x + 1/2*c)^2 - 120*a^4*b*tan(1/2*d*x + 1/2*c) + 150*a^2*b^3*tan(1/2*d*x + 1/2*c) - 15*b^5*tan(1/2*d*x + 1/2*c) + 240*a^5 - 320*a^3*b^2 + 48*a*b^4)/((tan(1/2*d*x + 1/2*c)^2 + 1)^6*b^6))/d","B",0
1302,1,458,0,0.171679," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{15 \, {\left(8 \, a^{5} - 12 \, a^{3} b^{2} + 3 \, a b^{4}\right)} {\left(d x + c\right)}}{b^{6}} - \frac{240 \, {\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{6}} + \frac{2 \, {\left(60 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 75 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 120 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 240 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 120 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 120 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 30 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 480 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 720 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 720 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 880 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 240 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 120 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 480 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 560 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 60 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 75 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 120 \, a^{4} - 160 \, a^{2} b^{2} + 24 \, b^{4}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{5} b^{5}}}{120 \, d}"," ",0,"-1/120*(15*(8*a^5 - 12*a^3*b^2 + 3*a*b^4)*(d*x + c)/b^6 - 240*(a^6 - 2*a^4*b^2 + a^2*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^6) + 2*(60*a^3*b*tan(1/2*d*x + 1/2*c)^9 - 75*a*b^3*tan(1/2*d*x + 1/2*c)^9 + 120*a^4*tan(1/2*d*x + 1/2*c)^8 - 240*a^2*b^2*tan(1/2*d*x + 1/2*c)^8 + 120*b^4*tan(1/2*d*x + 1/2*c)^8 + 120*a^3*b*tan(1/2*d*x + 1/2*c)^7 - 30*a*b^3*tan(1/2*d*x + 1/2*c)^7 + 480*a^4*tan(1/2*d*x + 1/2*c)^6 - 720*a^2*b^2*tan(1/2*d*x + 1/2*c)^6 + 720*a^4*tan(1/2*d*x + 1/2*c)^4 - 880*a^2*b^2*tan(1/2*d*x + 1/2*c)^4 + 240*b^4*tan(1/2*d*x + 1/2*c)^4 - 120*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 30*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 480*a^4*tan(1/2*d*x + 1/2*c)^2 - 560*a^2*b^2*tan(1/2*d*x + 1/2*c)^2 - 60*a^3*b*tan(1/2*d*x + 1/2*c) + 75*a*b^3*tan(1/2*d*x + 1/2*c) + 120*a^4 - 160*a^2*b^2 + 24*b^4)/((tan(1/2*d*x + 1/2*c)^2 + 1)^5*b^5))/d","B",0
1303,1,371,0,0.167901," ","integrate(cos(d*x+c)^4*sin(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{3 \, {\left(8 \, a^{4} - 12 \, a^{2} b^{2} + 3 \, b^{4}\right)} {\left(d x + c\right)}}{b^{5}} - \frac{48 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{5}} + \frac{2 \, {\left(12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 15 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 48 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 96 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 72 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 80 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, a^{3} - 32 \, a b^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4} b^{4}}}{24 \, d}"," ",0,"1/24*(3*(8*a^4 - 12*a^2*b^2 + 3*b^4)*(d*x + c)/b^5 - 48*(a^5 - 2*a^3*b^2 + a*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^5) + 2*(12*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 15*b^3*tan(1/2*d*x + 1/2*c)^7 + 24*a^3*tan(1/2*d*x + 1/2*c)^6 - 48*a*b^2*tan(1/2*d*x + 1/2*c)^6 + 12*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 9*b^3*tan(1/2*d*x + 1/2*c)^5 + 72*a^3*tan(1/2*d*x + 1/2*c)^4 - 96*a*b^2*tan(1/2*d*x + 1/2*c)^4 - 12*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 9*b^3*tan(1/2*d*x + 1/2*c)^3 + 72*a^3*tan(1/2*d*x + 1/2*c)^2 - 80*a*b^2*tan(1/2*d*x + 1/2*c)^2 - 12*a^2*b*tan(1/2*d*x + 1/2*c) + 15*b^3*tan(1/2*d*x + 1/2*c) + 24*a^3 - 32*a*b^2)/((tan(1/2*d*x + 1/2*c)^2 + 1)^4*b^4))/d","B",0
1304,1,183,0,0.190901," ","integrate(cos(d*x+c)^4*csc(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{2 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a} + \frac{{\left(2 \, a^{2} - 3 \, b^{2}\right)} {\left(d x + c\right)}}{b^{3}} - \frac{4 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a b^{3}} + \frac{2 \, {\left(b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, a\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} b^{2}}}{2 \, d}"," ",0,"1/2*(2*log(abs(tan(1/2*d*x + 1/2*c)))/a + (2*a^2 - 3*b^2)*(d*x + c)/b^3 - 4*(a^4 - 2*a^2*b^2 + b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a*b^3) + 2*(b*tan(1/2*d*x + 1/2*c)^3 + 2*a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c) + 2*a)/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*b^2))/d","A",0
1305,1,221,0,0.201162," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{6 \, {\left(d x + c\right)} a}{b^{2}} + \frac{6 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} - \frac{3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a} - \frac{12 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{2} b^{2}} - \frac{2 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a b}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} a^{2} b}}{6 \, d}"," ",0,"-1/6*(6*(d*x + c)*a/b^2 + 6*b*log(abs(tan(1/2*d*x + 1/2*c)))/a^2 - 3*tan(1/2*d*x + 1/2*c)/a - 12*(a^4 - 2*a^2*b^2 + b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^2*b^2) - (2*b^2*tan(1/2*d*x + 1/2*c)^3 - 3*a*b*tan(1/2*d*x + 1/2*c)^2 - 12*a^2*tan(1/2*d*x + 1/2*c) + 2*b^2*tan(1/2*d*x + 1/2*c) - 3*a*b)/((tan(1/2*d*x + 1/2*c)^3 + tan(1/2*d*x + 1/2*c))*a^2*b))/d","B",0
1306,1,217,0,0.204344," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{8 \, {\left(d x + c\right)}}{b} + \frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{2}} - \frac{4 \, {\left(3 \, a^{2} - 2 \, b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} - \frac{16 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{3} b} + \frac{18 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 4 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{2}}{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}}{8 \, d}"," ",0,"1/8*(8*(d*x + c)/b + (a*tan(1/2*d*x + 1/2*c)^2 - 4*b*tan(1/2*d*x + 1/2*c))/a^2 - 4*(3*a^2 - 2*b^2)*log(abs(tan(1/2*d*x + 1/2*c)))/a^3 - 16*(a^4 - 2*a^2*b^2 + b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^3*b) + (18*a^2*tan(1/2*d*x + 1/2*c)^2 - 12*b^2*tan(1/2*d*x + 1/2*c)^2 + 4*a*b*tan(1/2*d*x + 1/2*c) - a^2)/(a^3*tan(1/2*d*x + 1/2*c)^2))/d","A",0
1307,1,273,0,0.204756," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3}} + \frac{12 \, {\left(3 \, a^{2} b - 2 \, b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{4}} + \frac{48 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{4}} - \frac{66 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 44 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3}}{a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{24 \, d}"," ",0,"1/24*((a^2*tan(1/2*d*x + 1/2*c)^3 - 3*a*b*tan(1/2*d*x + 1/2*c)^2 - 15*a^2*tan(1/2*d*x + 1/2*c) + 12*b^2*tan(1/2*d*x + 1/2*c))/a^3 + 12*(3*a^2*b - 2*b^3)*log(abs(tan(1/2*d*x + 1/2*c)))/a^4 + 48*(a^4 - 2*a^2*b^2 + b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^4) - (66*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 44*b^3*tan(1/2*d*x + 1/2*c)^3 - 15*a^3*tan(1/2*d*x + 1/2*c)^2 + 12*a*b^2*tan(1/2*d*x + 1/2*c)^2 - 3*a^2*b*tan(1/2*d*x + 1/2*c) + a^3)/(a^4*tan(1/2*d*x + 1/2*c)^3))/d","A",0
1308,1,375,0,0.214405," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 8 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 120 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 96 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{4}} + \frac{24 \, {\left(3 \, a^{4} - 12 \, a^{2} b^{2} + 8 \, b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{5}} - \frac{384 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{5}} - \frac{150 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 600 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 400 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 120 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 96 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a^{4}}{a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}}}{192 \, d}"," ",0,"1/192*((3*a^3*tan(1/2*d*x + 1/2*c)^4 - 8*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 24*a^3*tan(1/2*d*x + 1/2*c)^2 + 24*a*b^2*tan(1/2*d*x + 1/2*c)^2 + 120*a^2*b*tan(1/2*d*x + 1/2*c) - 96*b^3*tan(1/2*d*x + 1/2*c))/a^4 + 24*(3*a^4 - 12*a^2*b^2 + 8*b^4)*log(abs(tan(1/2*d*x + 1/2*c)))/a^5 - 384*(a^4*b - 2*a^2*b^3 + b^5)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^5) - (150*a^4*tan(1/2*d*x + 1/2*c)^4 - 600*a^2*b^2*tan(1/2*d*x + 1/2*c)^4 + 400*b^4*tan(1/2*d*x + 1/2*c)^4 + 120*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 96*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 24*a^4*tan(1/2*d*x + 1/2*c)^2 + 24*a^2*b^2*tan(1/2*d*x + 1/2*c)^2 - 8*a^3*b*tan(1/2*d*x + 1/2*c) + 3*a^4)/(a^5*tan(1/2*d*x + 1/2*c)^4))/d","B",0
1309,1,484,0,0.219240," ","integrate(cos(d*x+c)^4*csc(d*x+c)^6/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{6 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 30 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 120 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 60 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 600 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 480 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{5}} - \frac{120 \, {\left(3 \, a^{4} b - 12 \, a^{2} b^{3} + 8 \, b^{5}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{6}} + \frac{1920 \, {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{6}} + \frac{822 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3288 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2192 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 60 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 600 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 480 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 120 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 40 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 15 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, a^{5}}{a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{960 \, d}"," ",0,"1/960*((6*a^4*tan(1/2*d*x + 1/2*c)^5 - 15*a^3*b*tan(1/2*d*x + 1/2*c)^4 - 30*a^4*tan(1/2*d*x + 1/2*c)^3 + 40*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 120*a^3*b*tan(1/2*d*x + 1/2*c)^2 - 120*a*b^3*tan(1/2*d*x + 1/2*c)^2 + 60*a^4*tan(1/2*d*x + 1/2*c) - 600*a^2*b^2*tan(1/2*d*x + 1/2*c) + 480*b^4*tan(1/2*d*x + 1/2*c))/a^5 - 120*(3*a^4*b - 12*a^2*b^3 + 8*b^5)*log(abs(tan(1/2*d*x + 1/2*c)))/a^6 + 1920*(a^4*b^2 - 2*a^2*b^4 + b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^6) + (822*a^4*b*tan(1/2*d*x + 1/2*c)^5 - 3288*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 + 2192*b^5*tan(1/2*d*x + 1/2*c)^5 - 60*a^5*tan(1/2*d*x + 1/2*c)^4 + 600*a^3*b^2*tan(1/2*d*x + 1/2*c)^4 - 480*a*b^4*tan(1/2*d*x + 1/2*c)^4 - 120*a^4*b*tan(1/2*d*x + 1/2*c)^3 + 120*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + 30*a^5*tan(1/2*d*x + 1/2*c)^2 - 40*a^3*b^2*tan(1/2*d*x + 1/2*c)^2 + 15*a^4*b*tan(1/2*d*x + 1/2*c) - 6*a^5)/(a^6*tan(1/2*d*x + 1/2*c)^5))/d","B",0
1310,1,261,0,0.201845," ","integrate(cos(d*x+c)^5*sin(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{60 \, b^{6} \sin\left(d x + c\right)^{7} - 70 \, a b^{5} \sin\left(d x + c\right)^{6} + 84 \, a^{2} b^{4} \sin\left(d x + c\right)^{5} - 168 \, b^{6} \sin\left(d x + c\right)^{5} - 105 \, a^{3} b^{3} \sin\left(d x + c\right)^{4} + 210 \, a b^{5} \sin\left(d x + c\right)^{4} + 140 \, a^{4} b^{2} \sin\left(d x + c\right)^{3} - 280 \, a^{2} b^{4} \sin\left(d x + c\right)^{3} + 140 \, b^{6} \sin\left(d x + c\right)^{3} - 210 \, a^{5} b \sin\left(d x + c\right)^{2} + 420 \, a^{3} b^{3} \sin\left(d x + c\right)^{2} - 210 \, a b^{5} \sin\left(d x + c\right)^{2} + 420 \, a^{6} \sin\left(d x + c\right) - 840 \, a^{4} b^{2} \sin\left(d x + c\right) + 420 \, a^{2} b^{4} \sin\left(d x + c\right)}{b^{7}} - \frac{420 \, {\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{b^{8}}}{420 \, d}"," ",0,"1/420*((60*b^6*sin(d*x + c)^7 - 70*a*b^5*sin(d*x + c)^6 + 84*a^2*b^4*sin(d*x + c)^5 - 168*b^6*sin(d*x + c)^5 - 105*a^3*b^3*sin(d*x + c)^4 + 210*a*b^5*sin(d*x + c)^4 + 140*a^4*b^2*sin(d*x + c)^3 - 280*a^2*b^4*sin(d*x + c)^3 + 140*b^6*sin(d*x + c)^3 - 210*a^5*b*sin(d*x + c)^2 + 420*a^3*b^3*sin(d*x + c)^2 - 210*a*b^5*sin(d*x + c)^2 + 420*a^6*sin(d*x + c) - 840*a^4*b^2*sin(d*x + c) + 420*a^2*b^4*sin(d*x + c))/b^7 - 420*(a^7 - 2*a^5*b^2 + a^3*b^4)*log(abs(b*sin(d*x + c) + a))/b^8)/d","A",0
1311,1,213,0,0.184581," ","integrate(cos(d*x+c)^5*sin(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{10 \, b^{5} \sin\left(d x + c\right)^{6} - 12 \, a b^{4} \sin\left(d x + c\right)^{5} + 15 \, a^{2} b^{3} \sin\left(d x + c\right)^{4} - 30 \, b^{5} \sin\left(d x + c\right)^{4} - 20 \, a^{3} b^{2} \sin\left(d x + c\right)^{3} + 40 \, a b^{4} \sin\left(d x + c\right)^{3} + 30 \, a^{4} b \sin\left(d x + c\right)^{2} - 60 \, a^{2} b^{3} \sin\left(d x + c\right)^{2} + 30 \, b^{5} \sin\left(d x + c\right)^{2} - 60 \, a^{5} \sin\left(d x + c\right) + 120 \, a^{3} b^{2} \sin\left(d x + c\right) - 60 \, a b^{4} \sin\left(d x + c\right)}{b^{6}} + \frac{60 \, {\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{b^{7}}}{60 \, d}"," ",0,"1/60*((10*b^5*sin(d*x + c)^6 - 12*a*b^4*sin(d*x + c)^5 + 15*a^2*b^3*sin(d*x + c)^4 - 30*b^5*sin(d*x + c)^4 - 20*a^3*b^2*sin(d*x + c)^3 + 40*a*b^4*sin(d*x + c)^3 + 30*a^4*b*sin(d*x + c)^2 - 60*a^2*b^3*sin(d*x + c)^2 + 30*b^5*sin(d*x + c)^2 - 60*a^5*sin(d*x + c) + 120*a^3*b^2*sin(d*x + c) - 60*a*b^4*sin(d*x + c))/b^6 + 60*(a^6 - 2*a^4*b^2 + a^2*b^4)*log(abs(b*sin(d*x + c) + a))/b^7)/d","A",0
1312,1,165,0,0.176668," ","integrate(cos(d*x+c)^5*sin(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{12 \, b^{4} \sin\left(d x + c\right)^{5} - 15 \, a b^{3} \sin\left(d x + c\right)^{4} + 20 \, a^{2} b^{2} \sin\left(d x + c\right)^{3} - 40 \, b^{4} \sin\left(d x + c\right)^{3} - 30 \, a^{3} b \sin\left(d x + c\right)^{2} + 60 \, a b^{3} \sin\left(d x + c\right)^{2} + 60 \, a^{4} \sin\left(d x + c\right) - 120 \, a^{2} b^{2} \sin\left(d x + c\right) + 60 \, b^{4} \sin\left(d x + c\right)}{b^{5}} - \frac{60 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{b^{6}}}{60 \, d}"," ",0,"1/60*((12*b^4*sin(d*x + c)^5 - 15*a*b^3*sin(d*x + c)^4 + 20*a^2*b^2*sin(d*x + c)^3 - 40*b^4*sin(d*x + c)^3 - 30*a^3*b*sin(d*x + c)^2 + 60*a*b^3*sin(d*x + c)^2 + 60*a^4*sin(d*x + c) - 120*a^2*b^2*sin(d*x + c) + 60*b^4*sin(d*x + c))/b^5 - 60*(a^5 - 2*a^3*b^2 + a*b^4)*log(abs(b*sin(d*x + c) + a))/b^6)/d","A",0
1313,1,106,0,0.169112," ","integrate(cos(d*x+c)^5*csc(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{6 \, \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a} + \frac{2 \, b^{2} \sin\left(d x + c\right)^{3} - 3 \, a b \sin\left(d x + c\right)^{2} + 6 \, a^{2} \sin\left(d x + c\right) - 12 \, b^{2} \sin\left(d x + c\right)}{b^{3}} - \frac{6 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a b^{4}}}{6 \, d}"," ",0,"1/6*(6*log(abs(sin(d*x + c)))/a + (2*b^2*sin(d*x + c)^3 - 3*a*b*sin(d*x + c)^2 + 6*a^2*sin(d*x + c) - 12*b^2*sin(d*x + c))/b^3 - 6*(a^4 - 2*a^2*b^2 + b^4)*log(abs(b*sin(d*x + c) + a))/(a*b^4))/d","A",0
1314,1,105,0,0.202096," ","integrate(cos(d*x+c)^5*csc(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{2 \, b \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a^{2}} - \frac{b \sin\left(d x + c\right)^{2} - 2 \, a \sin\left(d x + c\right)}{b^{2}} - \frac{2 \, {\left(b \sin\left(d x + c\right) - a\right)}}{a^{2} \sin\left(d x + c\right)} - \frac{2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{2} b^{3}}}{2 \, d}"," ",0,"-1/2*(2*b*log(abs(sin(d*x + c)))/a^2 - (b*sin(d*x + c)^2 - 2*a*sin(d*x + c))/b^2 - 2*(b*sin(d*x + c) - a)/(a^2*sin(d*x + c)) - 2*(a^4 - 2*a^2*b^2 + b^4)*log(abs(b*sin(d*x + c) + a))/(a^2*b^3))/d","A",0
1315,1,130,0,0.204261," ","integrate(cos(d*x+c)^5*csc(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{2 \, \sin\left(d x + c\right)}{b} - \frac{2 \, {\left(2 \, a^{2} - b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a^{3}} - \frac{2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{3} b^{2}} + \frac{6 \, a^{2} \sin\left(d x + c\right)^{2} - 3 \, b^{2} \sin\left(d x + c\right)^{2} + 2 \, a b \sin\left(d x + c\right) - a^{2}}{a^{3} \sin\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"1/2*(2*sin(d*x + c)/b - 2*(2*a^2 - b^2)*log(abs(sin(d*x + c)))/a^3 - 2*(a^4 - 2*a^2*b^2 + b^4)*log(abs(b*sin(d*x + c) + a))/(a^3*b^2) + (6*a^2*sin(d*x + c)^2 - 3*b^2*sin(d*x + c)^2 + 2*a*b*sin(d*x + c) - a^2)/(a^3*sin(d*x + c)^2))/d","A",0
1316,1,151,0,0.217514," ","integrate(cos(d*x+c)^5*csc(d*x+c)^4/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{6 \, {\left(2 \, a^{2} b - b^{3}\right)} \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a^{4}} + \frac{6 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{4} b} - \frac{22 \, a^{2} b \sin\left(d x + c\right)^{3} - 11 \, b^{3} \sin\left(d x + c\right)^{3} - 12 \, a^{3} \sin\left(d x + c\right)^{2} + 6 \, a b^{2} \sin\left(d x + c\right)^{2} - 3 \, a^{2} b \sin\left(d x + c\right) + 2 \, a^{3}}{a^{4} \sin\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(6*(2*a^2*b - b^3)*log(abs(sin(d*x + c)))/a^4 + 6*(a^4 - 2*a^2*b^2 + b^4)*log(abs(b*sin(d*x + c) + a))/(a^4*b) - (22*a^2*b*sin(d*x + c)^3 - 11*b^3*sin(d*x + c)^3 - 12*a^3*sin(d*x + c)^2 + 6*a*b^2*sin(d*x + c)^2 - 3*a^2*b*sin(d*x + c) + 2*a^3)/(a^4*sin(d*x + c)^3))/d","A",0
1317,1,201,0,0.239016," ","integrate(cos(d*x+c)^5*csc(d*x+c)^5/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{12 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a^{5}} - \frac{12 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{5} b} - \frac{25 \, a^{4} \sin\left(d x + c\right)^{4} - 50 \, a^{2} b^{2} \sin\left(d x + c\right)^{4} + 25 \, b^{4} \sin\left(d x + c\right)^{4} + 24 \, a^{3} b \sin\left(d x + c\right)^{3} - 12 \, a b^{3} \sin\left(d x + c\right)^{3} - 12 \, a^{4} \sin\left(d x + c\right)^{2} + 6 \, a^{2} b^{2} \sin\left(d x + c\right)^{2} - 4 \, a^{3} b \sin\left(d x + c\right) + 3 \, a^{4}}{a^{5} \sin\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"1/12*(12*(a^4 - 2*a^2*b^2 + b^4)*log(abs(sin(d*x + c)))/a^5 - 12*(a^4*b - 2*a^2*b^3 + b^5)*log(abs(b*sin(d*x + c) + a))/(a^5*b) - (25*a^4*sin(d*x + c)^4 - 50*a^2*b^2*sin(d*x + c)^4 + 25*b^4*sin(d*x + c)^4 + 24*a^3*b*sin(d*x + c)^3 - 12*a*b^3*sin(d*x + c)^3 - 12*a^4*sin(d*x + c)^2 + 6*a^2*b^2*sin(d*x + c)^2 - 4*a^3*b*sin(d*x + c) + 3*a^4)/(a^5*sin(d*x + c)^4))/d","A",0
1318,1,251,0,0.209997," ","integrate(cos(d*x+c)^5*csc(d*x+c)^6/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{60 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a^{6}} - \frac{60 \, {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{6} b} - \frac{137 \, a^{4} b \sin\left(d x + c\right)^{5} - 274 \, a^{2} b^{3} \sin\left(d x + c\right)^{5} + 137 \, b^{5} \sin\left(d x + c\right)^{5} - 60 \, a^{5} \sin\left(d x + c\right)^{4} + 120 \, a^{3} b^{2} \sin\left(d x + c\right)^{4} - 60 \, a b^{4} \sin\left(d x + c\right)^{4} - 60 \, a^{4} b \sin\left(d x + c\right)^{3} + 30 \, a^{2} b^{3} \sin\left(d x + c\right)^{3} + 40 \, a^{5} \sin\left(d x + c\right)^{2} - 20 \, a^{3} b^{2} \sin\left(d x + c\right)^{2} + 15 \, a^{4} b \sin\left(d x + c\right) - 12 \, a^{5}}{a^{6} \sin\left(d x + c\right)^{5}}}{60 \, d}"," ",0,"-1/60*(60*(a^4*b - 2*a^2*b^3 + b^5)*log(abs(sin(d*x + c)))/a^6 - 60*(a^4*b^2 - 2*a^2*b^4 + b^6)*log(abs(b*sin(d*x + c) + a))/(a^6*b) - (137*a^4*b*sin(d*x + c)^5 - 274*a^2*b^3*sin(d*x + c)^5 + 137*b^5*sin(d*x + c)^5 - 60*a^5*sin(d*x + c)^4 + 120*a^3*b^2*sin(d*x + c)^4 - 60*a*b^4*sin(d*x + c)^4 - 60*a^4*b*sin(d*x + c)^3 + 30*a^2*b^3*sin(d*x + c)^3 + 40*a^5*sin(d*x + c)^2 - 20*a^3*b^2*sin(d*x + c)^2 + 15*a^4*b*sin(d*x + c) - 12*a^5)/(a^6*sin(d*x + c)^5))/d","A",0
1319,1,301,0,0.229269," ","integrate(cos(d*x+c)^5*csc(d*x+c)^7/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{60 \, {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a^{7}} - \frac{60 \, {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{7} b} - \frac{147 \, a^{4} b^{2} \sin\left(d x + c\right)^{6} - 294 \, a^{2} b^{4} \sin\left(d x + c\right)^{6} + 147 \, b^{6} \sin\left(d x + c\right)^{6} - 60 \, a^{5} b \sin\left(d x + c\right)^{5} + 120 \, a^{3} b^{3} \sin\left(d x + c\right)^{5} - 60 \, a b^{5} \sin\left(d x + c\right)^{5} + 30 \, a^{6} \sin\left(d x + c\right)^{4} - 60 \, a^{4} b^{2} \sin\left(d x + c\right)^{4} + 30 \, a^{2} b^{4} \sin\left(d x + c\right)^{4} + 40 \, a^{5} b \sin\left(d x + c\right)^{3} - 20 \, a^{3} b^{3} \sin\left(d x + c\right)^{3} - 30 \, a^{6} \sin\left(d x + c\right)^{2} + 15 \, a^{4} b^{2} \sin\left(d x + c\right)^{2} - 12 \, a^{5} b \sin\left(d x + c\right) + 10 \, a^{6}}{a^{7} \sin\left(d x + c\right)^{6}}}{60 \, d}"," ",0,"1/60*(60*(a^4*b^2 - 2*a^2*b^4 + b^6)*log(abs(sin(d*x + c)))/a^7 - 60*(a^4*b^3 - 2*a^2*b^5 + b^7)*log(abs(b*sin(d*x + c) + a))/(a^7*b) - (147*a^4*b^2*sin(d*x + c)^6 - 294*a^2*b^4*sin(d*x + c)^6 + 147*b^6*sin(d*x + c)^6 - 60*a^5*b*sin(d*x + c)^5 + 120*a^3*b^3*sin(d*x + c)^5 - 60*a*b^5*sin(d*x + c)^5 + 30*a^6*sin(d*x + c)^4 - 60*a^4*b^2*sin(d*x + c)^4 + 30*a^2*b^4*sin(d*x + c)^4 + 40*a^5*b*sin(d*x + c)^3 - 20*a^3*b^3*sin(d*x + c)^3 - 30*a^6*sin(d*x + c)^2 + 15*a^4*b^2*sin(d*x + c)^2 - 12*a^5*b*sin(d*x + c) + 10*a^6)/(a^7*sin(d*x + c)^6))/d","A",0
1320,1,1244,0,0.208166," ","integrate(cos(d*x+c)^6*sin(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{105 \, {\left(128 \, a^{8} - 320 \, a^{6} b^{2} + 240 \, a^{4} b^{4} - 40 \, a^{2} b^{6} - 5 \, b^{8}\right)} {\left(d x + c\right)}}{b^{9}} - \frac{26880 \, {\left(a^{9} - 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} - a^{3} b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{9}} + \frac{2 \, {\left(6720 \, a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} - 15120 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} + 9240 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} - 525 \, b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} + 13440 \, a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{14} - 40320 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{14} + 40320 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{14} - 13440 \, a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{14} + 33600 \, a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 62160 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 17080 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 13895 \, b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 94080 \, a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 255360 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 201600 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 13440 \, a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 60480 \, a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 95760 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 31640 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 31325 \, b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 282240 \, a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 703360 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 488320 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 67200 \, a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 33600 \, a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 48720 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 23800 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 61775 \, b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 470400 \, a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 1097600 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 721280 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 67200 \, a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 33600 \, a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 48720 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 23800 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 61775 \, b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 470400 \, a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 1052800 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 665728 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 40320 \, a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 60480 \, a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 95760 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 31640 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 31325 \, b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 282240 \, a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 622720 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 375424 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 40320 \, a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 33600 \, a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 62160 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 17080 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 13895 \, b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 94080 \, a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 210560 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 124544 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1920 \, a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 6720 \, a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15120 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9240 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 525 \, b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 13440 \, a^{7} - 31360 \, a^{5} b^{2} + 20608 \, a^{3} b^{4} - 1920 \, a b^{6}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{8} b^{8}}}{13440 \, d}"," ",0,"-1/13440*(105*(128*a^8 - 320*a^6*b^2 + 240*a^4*b^4 - 40*a^2*b^6 - 5*b^8)*(d*x + c)/b^9 - 26880*(a^9 - 3*a^7*b^2 + 3*a^5*b^4 - a^3*b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^9) + 2*(6720*a^6*b*tan(1/2*d*x + 1/2*c)^15 - 15120*a^4*b^3*tan(1/2*d*x + 1/2*c)^15 + 9240*a^2*b^5*tan(1/2*d*x + 1/2*c)^15 - 525*b^7*tan(1/2*d*x + 1/2*c)^15 + 13440*a^7*tan(1/2*d*x + 1/2*c)^14 - 40320*a^5*b^2*tan(1/2*d*x + 1/2*c)^14 + 40320*a^3*b^4*tan(1/2*d*x + 1/2*c)^14 - 13440*a*b^6*tan(1/2*d*x + 1/2*c)^14 + 33600*a^6*b*tan(1/2*d*x + 1/2*c)^13 - 62160*a^4*b^3*tan(1/2*d*x + 1/2*c)^13 + 17080*a^2*b^5*tan(1/2*d*x + 1/2*c)^13 + 13895*b^7*tan(1/2*d*x + 1/2*c)^13 + 94080*a^7*tan(1/2*d*x + 1/2*c)^12 - 255360*a^5*b^2*tan(1/2*d*x + 1/2*c)^12 + 201600*a^3*b^4*tan(1/2*d*x + 1/2*c)^12 - 13440*a*b^6*tan(1/2*d*x + 1/2*c)^12 + 60480*a^6*b*tan(1/2*d*x + 1/2*c)^11 - 95760*a^4*b^3*tan(1/2*d*x + 1/2*c)^11 + 31640*a^2*b^5*tan(1/2*d*x + 1/2*c)^11 - 31325*b^7*tan(1/2*d*x + 1/2*c)^11 + 282240*a^7*tan(1/2*d*x + 1/2*c)^10 - 703360*a^5*b^2*tan(1/2*d*x + 1/2*c)^10 + 488320*a^3*b^4*tan(1/2*d*x + 1/2*c)^10 - 67200*a*b^6*tan(1/2*d*x + 1/2*c)^10 + 33600*a^6*b*tan(1/2*d*x + 1/2*c)^9 - 48720*a^4*b^3*tan(1/2*d*x + 1/2*c)^9 + 23800*a^2*b^5*tan(1/2*d*x + 1/2*c)^9 + 61775*b^7*tan(1/2*d*x + 1/2*c)^9 + 470400*a^7*tan(1/2*d*x + 1/2*c)^8 - 1097600*a^5*b^2*tan(1/2*d*x + 1/2*c)^8 + 721280*a^3*b^4*tan(1/2*d*x + 1/2*c)^8 - 67200*a*b^6*tan(1/2*d*x + 1/2*c)^8 - 33600*a^6*b*tan(1/2*d*x + 1/2*c)^7 + 48720*a^4*b^3*tan(1/2*d*x + 1/2*c)^7 - 23800*a^2*b^5*tan(1/2*d*x + 1/2*c)^7 - 61775*b^7*tan(1/2*d*x + 1/2*c)^7 + 470400*a^7*tan(1/2*d*x + 1/2*c)^6 - 1052800*a^5*b^2*tan(1/2*d*x + 1/2*c)^6 + 665728*a^3*b^4*tan(1/2*d*x + 1/2*c)^6 - 40320*a*b^6*tan(1/2*d*x + 1/2*c)^6 - 60480*a^6*b*tan(1/2*d*x + 1/2*c)^5 + 95760*a^4*b^3*tan(1/2*d*x + 1/2*c)^5 - 31640*a^2*b^5*tan(1/2*d*x + 1/2*c)^5 + 31325*b^7*tan(1/2*d*x + 1/2*c)^5 + 282240*a^7*tan(1/2*d*x + 1/2*c)^4 - 622720*a^5*b^2*tan(1/2*d*x + 1/2*c)^4 + 375424*a^3*b^4*tan(1/2*d*x + 1/2*c)^4 - 40320*a*b^6*tan(1/2*d*x + 1/2*c)^4 - 33600*a^6*b*tan(1/2*d*x + 1/2*c)^3 + 62160*a^4*b^3*tan(1/2*d*x + 1/2*c)^3 - 17080*a^2*b^5*tan(1/2*d*x + 1/2*c)^3 - 13895*b^7*tan(1/2*d*x + 1/2*c)^3 + 94080*a^7*tan(1/2*d*x + 1/2*c)^2 - 210560*a^5*b^2*tan(1/2*d*x + 1/2*c)^2 + 124544*a^3*b^4*tan(1/2*d*x + 1/2*c)^2 - 1920*a*b^6*tan(1/2*d*x + 1/2*c)^2 - 6720*a^6*b*tan(1/2*d*x + 1/2*c) + 15120*a^4*b^3*tan(1/2*d*x + 1/2*c) - 9240*a^2*b^5*tan(1/2*d*x + 1/2*c) + 525*b^7*tan(1/2*d*x + 1/2*c) + 13440*a^7 - 31360*a^5*b^2 + 20608*a^3*b^4 - 1920*a*b^6)/((tan(1/2*d*x + 1/2*c)^2 + 1)^8*b^8))/d","B",0
1321,1,863,0,0.189942," ","integrate(cos(d*x+c)^6*sin(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{105 \, {\left(16 \, a^{7} - 40 \, a^{5} b^{2} + 30 \, a^{3} b^{4} - 5 \, a b^{6}\right)} {\left(d x + c\right)}}{b^{8}} - \frac{3360 \, {\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{8}} + \frac{2 \, {\left(840 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 1890 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 1155 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 1680 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 5040 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 5040 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 1680 \, b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 3360 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 5880 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 980 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 10080 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 26880 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 20160 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 4200 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 6090 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 2975 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 25200 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 61040 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 40880 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 8400 \, b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 33600 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 76160 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 49280 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 4200 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6090 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 2975 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 25200 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 55440 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 33936 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 5040 \, b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 3360 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5880 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 980 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 10080 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 22400 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12992 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 840 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1890 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1155 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1680 \, a^{6} - 3920 \, a^{4} b^{2} + 2576 \, a^{2} b^{4} - 240 \, b^{6}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{7} b^{7}}}{1680 \, d}"," ",0,"1/1680*(105*(16*a^7 - 40*a^5*b^2 + 30*a^3*b^4 - 5*a*b^6)*(d*x + c)/b^8 - 3360*(a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^8) + 2*(840*a^5*b*tan(1/2*d*x + 1/2*c)^13 - 1890*a^3*b^3*tan(1/2*d*x + 1/2*c)^13 + 1155*a*b^5*tan(1/2*d*x + 1/2*c)^13 + 1680*a^6*tan(1/2*d*x + 1/2*c)^12 - 5040*a^4*b^2*tan(1/2*d*x + 1/2*c)^12 + 5040*a^2*b^4*tan(1/2*d*x + 1/2*c)^12 - 1680*b^6*tan(1/2*d*x + 1/2*c)^12 + 3360*a^5*b*tan(1/2*d*x + 1/2*c)^11 - 5880*a^3*b^3*tan(1/2*d*x + 1/2*c)^11 + 980*a*b^5*tan(1/2*d*x + 1/2*c)^11 + 10080*a^6*tan(1/2*d*x + 1/2*c)^10 - 26880*a^4*b^2*tan(1/2*d*x + 1/2*c)^10 + 20160*a^2*b^4*tan(1/2*d*x + 1/2*c)^10 + 4200*a^5*b*tan(1/2*d*x + 1/2*c)^9 - 6090*a^3*b^3*tan(1/2*d*x + 1/2*c)^9 + 2975*a*b^5*tan(1/2*d*x + 1/2*c)^9 + 25200*a^6*tan(1/2*d*x + 1/2*c)^8 - 61040*a^4*b^2*tan(1/2*d*x + 1/2*c)^8 + 40880*a^2*b^4*tan(1/2*d*x + 1/2*c)^8 - 8400*b^6*tan(1/2*d*x + 1/2*c)^8 + 33600*a^6*tan(1/2*d*x + 1/2*c)^6 - 76160*a^4*b^2*tan(1/2*d*x + 1/2*c)^6 + 49280*a^2*b^4*tan(1/2*d*x + 1/2*c)^6 - 4200*a^5*b*tan(1/2*d*x + 1/2*c)^5 + 6090*a^3*b^3*tan(1/2*d*x + 1/2*c)^5 - 2975*a*b^5*tan(1/2*d*x + 1/2*c)^5 + 25200*a^6*tan(1/2*d*x + 1/2*c)^4 - 55440*a^4*b^2*tan(1/2*d*x + 1/2*c)^4 + 33936*a^2*b^4*tan(1/2*d*x + 1/2*c)^4 - 5040*b^6*tan(1/2*d*x + 1/2*c)^4 - 3360*a^5*b*tan(1/2*d*x + 1/2*c)^3 + 5880*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 - 980*a*b^5*tan(1/2*d*x + 1/2*c)^3 + 10080*a^6*tan(1/2*d*x + 1/2*c)^2 - 22400*a^4*b^2*tan(1/2*d*x + 1/2*c)^2 + 12992*a^2*b^4*tan(1/2*d*x + 1/2*c)^2 - 840*a^5*b*tan(1/2*d*x + 1/2*c) + 1890*a^3*b^3*tan(1/2*d*x + 1/2*c) - 1155*a*b^5*tan(1/2*d*x + 1/2*c) + 1680*a^6 - 3920*a^4*b^2 + 2576*a^2*b^4 - 240*b^6)/((tan(1/2*d*x + 1/2*c)^2 + 1)^7*b^7))/d","B",0
1322,1,735,0,0.175344," ","integrate(cos(d*x+c)^6*sin(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{15 \, {\left(16 \, a^{6} - 40 \, a^{4} b^{2} + 30 \, a^{2} b^{4} - 5 \, b^{6}\right)} {\left(d x + c\right)}}{b^{7}} - \frac{480 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{7}} + \frac{2 \, {\left(120 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 270 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 165 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 240 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 720 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 720 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 360 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 570 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 25 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1200 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 3120 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 2160 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 240 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 300 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 450 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 2400 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 5600 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 3680 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 240 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 300 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 450 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2400 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 5280 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 3360 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 360 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 570 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 25 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1200 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2640 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1488 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 120 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 270 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 165 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 240 \, a^{5} - 560 \, a^{3} b^{2} + 368 \, a b^{4}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{6} b^{6}}}{240 \, d}"," ",0,"-1/240*(15*(16*a^6 - 40*a^4*b^2 + 30*a^2*b^4 - 5*b^6)*(d*x + c)/b^7 - 480*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^7) + 2*(120*a^4*b*tan(1/2*d*x + 1/2*c)^11 - 270*a^2*b^3*tan(1/2*d*x + 1/2*c)^11 + 165*b^5*tan(1/2*d*x + 1/2*c)^11 + 240*a^5*tan(1/2*d*x + 1/2*c)^10 - 720*a^3*b^2*tan(1/2*d*x + 1/2*c)^10 + 720*a*b^4*tan(1/2*d*x + 1/2*c)^10 + 360*a^4*b*tan(1/2*d*x + 1/2*c)^9 - 570*a^2*b^3*tan(1/2*d*x + 1/2*c)^9 - 25*b^5*tan(1/2*d*x + 1/2*c)^9 + 1200*a^5*tan(1/2*d*x + 1/2*c)^8 - 3120*a^3*b^2*tan(1/2*d*x + 1/2*c)^8 + 2160*a*b^4*tan(1/2*d*x + 1/2*c)^8 + 240*a^4*b*tan(1/2*d*x + 1/2*c)^7 - 300*a^2*b^3*tan(1/2*d*x + 1/2*c)^7 + 450*b^5*tan(1/2*d*x + 1/2*c)^7 + 2400*a^5*tan(1/2*d*x + 1/2*c)^6 - 5600*a^3*b^2*tan(1/2*d*x + 1/2*c)^6 + 3680*a*b^4*tan(1/2*d*x + 1/2*c)^6 - 240*a^4*b*tan(1/2*d*x + 1/2*c)^5 + 300*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 - 450*b^5*tan(1/2*d*x + 1/2*c)^5 + 2400*a^5*tan(1/2*d*x + 1/2*c)^4 - 5280*a^3*b^2*tan(1/2*d*x + 1/2*c)^4 + 3360*a*b^4*tan(1/2*d*x + 1/2*c)^4 - 360*a^4*b*tan(1/2*d*x + 1/2*c)^3 + 570*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + 25*b^5*tan(1/2*d*x + 1/2*c)^3 + 1200*a^5*tan(1/2*d*x + 1/2*c)^2 - 2640*a^3*b^2*tan(1/2*d*x + 1/2*c)^2 + 1488*a*b^4*tan(1/2*d*x + 1/2*c)^2 - 120*a^4*b*tan(1/2*d*x + 1/2*c) + 270*a^2*b^3*tan(1/2*d*x + 1/2*c) - 165*b^5*tan(1/2*d*x + 1/2*c) + 240*a^5 - 560*a^3*b^2 + 368*a*b^4)/((tan(1/2*d*x + 1/2*c)^2 + 1)^6*b^6))/d","B",0
1323,1,398,0,0.228598," ","integrate(cos(d*x+c)^6*csc(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{24 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a} - \frac{3 \, {\left(8 \, a^{4} - 20 \, a^{2} b^{2} + 15 \, b^{4}\right)} {\left(d x + c\right)}}{b^{5}} + \frac{48 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a b^{5}} - \frac{2 \, {\left(12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 27 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 24 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 72 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 72 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 168 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 72 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 152 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, a^{3} - 56 \, a b^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4} b^{4}}}{24 \, d}"," ",0,"1/24*(24*log(abs(tan(1/2*d*x + 1/2*c)))/a - 3*(8*a^4 - 20*a^2*b^2 + 15*b^4)*(d*x + c)/b^5 + 48*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a*b^5) - 2*(12*a^2*b*tan(1/2*d*x + 1/2*c)^7 - 27*b^3*tan(1/2*d*x + 1/2*c)^7 + 24*a^3*tan(1/2*d*x + 1/2*c)^6 - 72*a*b^2*tan(1/2*d*x + 1/2*c)^6 + 12*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 3*b^3*tan(1/2*d*x + 1/2*c)^5 + 72*a^3*tan(1/2*d*x + 1/2*c)^4 - 168*a*b^2*tan(1/2*d*x + 1/2*c)^4 - 12*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 3*b^3*tan(1/2*d*x + 1/2*c)^3 + 72*a^3*tan(1/2*d*x + 1/2*c)^2 - 152*a*b^2*tan(1/2*d*x + 1/2*c)^2 - 12*a^2*b*tan(1/2*d*x + 1/2*c) + 27*b^3*tan(1/2*d*x + 1/2*c) + 24*a^3 - 56*a*b^2)/((tan(1/2*d*x + 1/2*c)^2 + 1)^4*b^4))/d","A",0
1324,1,302,0,0.194792," ","integrate(cos(d*x+c)^6*csc(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{6 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} - \frac{3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a} - \frac{3 \, {\left(2 \, a^{3} - 5 \, a b^{2}\right)} {\left(d x + c\right)}}{b^{4}} - \frac{3 \, {\left(2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a\right)}}{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)} + \frac{12 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{2} b^{4}} - \frac{2 \, {\left(3 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 18 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 12 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 24 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, a^{2} - 14 \, b^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3} b^{3}}}{6 \, d}"," ",0,"-1/6*(6*b*log(abs(tan(1/2*d*x + 1/2*c)))/a^2 - 3*tan(1/2*d*x + 1/2*c)/a - 3*(2*a^3 - 5*a*b^2)*(d*x + c)/b^4 - 3*(2*b*tan(1/2*d*x + 1/2*c) - a)/(a^2*tan(1/2*d*x + 1/2*c)) + 12*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^2*b^4) - 2*(3*a*b*tan(1/2*d*x + 1/2*c)^5 + 6*a^2*tan(1/2*d*x + 1/2*c)^4 - 18*b^2*tan(1/2*d*x + 1/2*c)^4 + 12*a^2*tan(1/2*d*x + 1/2*c)^2 - 24*b^2*tan(1/2*d*x + 1/2*c)^2 - 3*a*b*tan(1/2*d*x + 1/2*c) + 6*a^2 - 14*b^2)/((tan(1/2*d*x + 1/2*c)^2 + 1)^3*b^3))/d","A",0
1325,1,431,0,0.211493," ","integrate(cos(d*x+c)^6*csc(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{2}} - \frac{4 \, {\left(2 \, a^{2} - 5 \, b^{2}\right)} {\left(d x + c\right)}}{b^{3}} - \frac{4 \, {\left(5 \, a^{2} - 2 \, b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} + \frac{16 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{3} b^{3}} + \frac{10 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 4 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 8 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 16 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 19 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 8 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 8 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 16 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 8 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 4 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{2} b^{2}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}^{2} a^{3} b^{2}}}{8 \, d}"," ",0,"1/8*((a*tan(1/2*d*x + 1/2*c)^2 - 4*b*tan(1/2*d*x + 1/2*c))/a^2 - 4*(2*a^2 - 5*b^2)*(d*x + c)/b^3 - 4*(5*a^2 - 2*b^2)*log(abs(tan(1/2*d*x + 1/2*c)))/a^3 + 16*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^3*b^3) + (10*a^2*b^2*tan(1/2*d*x + 1/2*c)^6 - 4*b^4*tan(1/2*d*x + 1/2*c)^6 - 8*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 4*a*b^3*tan(1/2*d*x + 1/2*c)^5 - 16*a^4*tan(1/2*d*x + 1/2*c)^4 + 19*a^2*b^2*tan(1/2*d*x + 1/2*c)^4 - 8*b^4*tan(1/2*d*x + 1/2*c)^4 + 8*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 8*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 16*a^4*tan(1/2*d*x + 1/2*c)^2 + 8*a^2*b^2*tan(1/2*d*x + 1/2*c)^2 - 4*b^4*tan(1/2*d*x + 1/2*c)^2 + 4*a*b^3*tan(1/2*d*x + 1/2*c) - a^2*b^2)/((tan(1/2*d*x + 1/2*c)^3 + tan(1/2*d*x + 1/2*c))^2*a^3*b^2))/d","B",0
1326,1,317,0,0.215867," ","integrate(cos(d*x+c)^6*csc(d*x+c)^4/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{24 \, {\left(d x + c\right)} a}{b^{2}} + \frac{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 27 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3}} + \frac{48}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} b} + \frac{12 \, {\left(5 \, a^{2} b - 2 \, b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{4}} - \frac{48 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{4} b^{2}} - \frac{110 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 44 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 27 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3}}{a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{24 \, d}"," ",0,"1/24*(24*(d*x + c)*a/b^2 + (a^2*tan(1/2*d*x + 1/2*c)^3 - 3*a*b*tan(1/2*d*x + 1/2*c)^2 - 27*a^2*tan(1/2*d*x + 1/2*c) + 12*b^2*tan(1/2*d*x + 1/2*c))/a^3 + 48/((tan(1/2*d*x + 1/2*c)^2 + 1)*b) + 12*(5*a^2*b - 2*b^3)*log(abs(tan(1/2*d*x + 1/2*c)))/a^4 - 48*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^4*b^2) - (110*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 44*b^3*tan(1/2*d*x + 1/2*c)^3 - 27*a^3*tan(1/2*d*x + 1/2*c)^2 + 12*a*b^2*tan(1/2*d*x + 1/2*c)^2 - 3*a^2*b*tan(1/2*d*x + 1/2*c) + a^3)/(a^4*tan(1/2*d*x + 1/2*c)^3))/d","A",0
1327,1,396,0,0.239527," ","integrate(cos(d*x+c)^6*csc(d*x+c)^5/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{192 \, {\left(d x + c\right)}}{b} - \frac{3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 8 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 48 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 216 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 96 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{4}} - \frac{24 \, {\left(15 \, a^{4} - 20 \, a^{2} b^{2} + 8 \, b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{5}} - \frac{384 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{5} b} + \frac{750 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1000 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 400 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 216 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 96 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 48 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a^{4}}{a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}}}{192 \, d}"," ",0,"-1/192*(192*(d*x + c)/b - (3*a^3*tan(1/2*d*x + 1/2*c)^4 - 8*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 48*a^3*tan(1/2*d*x + 1/2*c)^2 + 24*a*b^2*tan(1/2*d*x + 1/2*c)^2 + 216*a^2*b*tan(1/2*d*x + 1/2*c) - 96*b^3*tan(1/2*d*x + 1/2*c))/a^4 - 24*(15*a^4 - 20*a^2*b^2 + 8*b^4)*log(abs(tan(1/2*d*x + 1/2*c)))/a^5 - 384*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^5*b) + (750*a^4*tan(1/2*d*x + 1/2*c)^4 - 1000*a^2*b^2*tan(1/2*d*x + 1/2*c)^4 + 400*b^4*tan(1/2*d*x + 1/2*c)^4 + 216*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 96*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 48*a^4*tan(1/2*d*x + 1/2*c)^2 + 24*a^2*b^2*tan(1/2*d*x + 1/2*c)^2 - 8*a^3*b*tan(1/2*d*x + 1/2*c) + 3*a^4)/(a^5*tan(1/2*d*x + 1/2*c)^4))/d","B",0
1328,1,490,0,0.226826," ","integrate(cos(d*x+c)^6*csc(d*x+c)^6/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{6 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 70 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 40 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 240 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 120 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 660 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1080 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 480 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{5}} - \frac{120 \, {\left(15 \, a^{4} b - 20 \, a^{2} b^{3} + 8 \, b^{5}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{6}} - \frac{1920 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{6}} + \frac{4110 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 5480 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2192 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 660 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 1080 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 480 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 240 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 70 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 40 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 15 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, a^{5}}{a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{960 \, d}"," ",0,"1/960*((6*a^4*tan(1/2*d*x + 1/2*c)^5 - 15*a^3*b*tan(1/2*d*x + 1/2*c)^4 - 70*a^4*tan(1/2*d*x + 1/2*c)^3 + 40*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 240*a^3*b*tan(1/2*d*x + 1/2*c)^2 - 120*a*b^3*tan(1/2*d*x + 1/2*c)^2 + 660*a^4*tan(1/2*d*x + 1/2*c) - 1080*a^2*b^2*tan(1/2*d*x + 1/2*c) + 480*b^4*tan(1/2*d*x + 1/2*c))/a^5 - 120*(15*a^4*b - 20*a^2*b^3 + 8*b^5)*log(abs(tan(1/2*d*x + 1/2*c)))/a^6 - 1920*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^6) + (4110*a^4*b*tan(1/2*d*x + 1/2*c)^5 - 5480*a^2*b^3*tan(1/2*d*x + 1/2*c)^5 + 2192*b^5*tan(1/2*d*x + 1/2*c)^5 - 660*a^5*tan(1/2*d*x + 1/2*c)^4 + 1080*a^3*b^2*tan(1/2*d*x + 1/2*c)^4 - 480*a*b^4*tan(1/2*d*x + 1/2*c)^4 - 240*a^4*b*tan(1/2*d*x + 1/2*c)^3 + 120*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + 70*a^5*tan(1/2*d*x + 1/2*c)^2 - 40*a^3*b^2*tan(1/2*d*x + 1/2*c)^2 + 15*a^4*b*tan(1/2*d*x + 1/2*c) - 6*a^5)/(a^6*tan(1/2*d*x + 1/2*c)^5))/d","B",0
1329,1,627,0,0.256563," ","integrate(cos(d*x+c)^6*csc(d*x+c)^7/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{5 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 12 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 45 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 30 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 140 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 80 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 225 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 480 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 240 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1320 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2160 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 960 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}} - \frac{120 \, {\left(5 \, a^{6} - 30 \, a^{4} b^{2} + 40 \, a^{2} b^{4} - 16 \, b^{6}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{7}} + \frac{3840 \, {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{7}} + \frac{1470 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 8820 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 11760 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 4704 \, b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 1320 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 2160 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 960 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 225 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 480 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 240 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 140 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 80 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 45 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 30 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, a^{6}}{a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6}}}{1920 \, d}"," ",0,"1/1920*((5*a^5*tan(1/2*d*x + 1/2*c)^6 - 12*a^4*b*tan(1/2*d*x + 1/2*c)^5 - 45*a^5*tan(1/2*d*x + 1/2*c)^4 + 30*a^3*b^2*tan(1/2*d*x + 1/2*c)^4 + 140*a^4*b*tan(1/2*d*x + 1/2*c)^3 - 80*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + 225*a^5*tan(1/2*d*x + 1/2*c)^2 - 480*a^3*b^2*tan(1/2*d*x + 1/2*c)^2 + 240*a*b^4*tan(1/2*d*x + 1/2*c)^2 - 1320*a^4*b*tan(1/2*d*x + 1/2*c) + 2160*a^2*b^3*tan(1/2*d*x + 1/2*c) - 960*b^5*tan(1/2*d*x + 1/2*c))/a^6 - 120*(5*a^6 - 30*a^4*b^2 + 40*a^2*b^4 - 16*b^6)*log(abs(tan(1/2*d*x + 1/2*c)))/a^7 + 3840*(a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^7) + (1470*a^6*tan(1/2*d*x + 1/2*c)^6 - 8820*a^4*b^2*tan(1/2*d*x + 1/2*c)^6 + 11760*a^2*b^4*tan(1/2*d*x + 1/2*c)^6 - 4704*b^6*tan(1/2*d*x + 1/2*c)^6 + 1320*a^5*b*tan(1/2*d*x + 1/2*c)^5 - 2160*a^3*b^3*tan(1/2*d*x + 1/2*c)^5 + 960*a*b^5*tan(1/2*d*x + 1/2*c)^5 - 225*a^6*tan(1/2*d*x + 1/2*c)^4 + 480*a^4*b^2*tan(1/2*d*x + 1/2*c)^4 - 240*a^2*b^4*tan(1/2*d*x + 1/2*c)^4 - 140*a^5*b*tan(1/2*d*x + 1/2*c)^3 + 80*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 + 45*a^6*tan(1/2*d*x + 1/2*c)^2 - 30*a^4*b^2*tan(1/2*d*x + 1/2*c)^2 + 12*a^5*b*tan(1/2*d*x + 1/2*c) - 5*a^6)/(a^7*tan(1/2*d*x + 1/2*c)^6))/d","A",0
1330,1,776,0,0.242065," ","integrate(cos(d*x+c)^6*csc(d*x+c)^8/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{15 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 35 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 105 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 84 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 315 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 210 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 315 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 980 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 560 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1575 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3360 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1680 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 525 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9240 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15120 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6720 \, b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{7}} + \frac{840 \, {\left(5 \, a^{6} b - 30 \, a^{4} b^{3} + 40 \, a^{2} b^{5} - 16 \, b^{7}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{8}} - \frac{26880 \, {\left(a^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{8}} - \frac{10890 \, a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 65340 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 87120 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 34848 \, b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 525 \, a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 9240 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 15120 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 6720 \, a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 1575 \, a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3360 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1680 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 315 \, a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 980 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 560 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 315 \, a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 210 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 105 \, a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 84 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 35 \, a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, a^{7}}{a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7}}}{13440 \, d}"," ",0,"1/13440*((15*a^6*tan(1/2*d*x + 1/2*c)^7 - 35*a^5*b*tan(1/2*d*x + 1/2*c)^6 - 105*a^6*tan(1/2*d*x + 1/2*c)^5 + 84*a^4*b^2*tan(1/2*d*x + 1/2*c)^5 + 315*a^5*b*tan(1/2*d*x + 1/2*c)^4 - 210*a^3*b^3*tan(1/2*d*x + 1/2*c)^4 + 315*a^6*tan(1/2*d*x + 1/2*c)^3 - 980*a^4*b^2*tan(1/2*d*x + 1/2*c)^3 + 560*a^2*b^4*tan(1/2*d*x + 1/2*c)^3 - 1575*a^5*b*tan(1/2*d*x + 1/2*c)^2 + 3360*a^3*b^3*tan(1/2*d*x + 1/2*c)^2 - 1680*a*b^5*tan(1/2*d*x + 1/2*c)^2 - 525*a^6*tan(1/2*d*x + 1/2*c) + 9240*a^4*b^2*tan(1/2*d*x + 1/2*c) - 15120*a^2*b^4*tan(1/2*d*x + 1/2*c) + 6720*b^6*tan(1/2*d*x + 1/2*c))/a^7 + 840*(5*a^6*b - 30*a^4*b^3 + 40*a^2*b^5 - 16*b^7)*log(abs(tan(1/2*d*x + 1/2*c)))/a^8 - 26880*(a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^8) - (10890*a^6*b*tan(1/2*d*x + 1/2*c)^7 - 65340*a^4*b^3*tan(1/2*d*x + 1/2*c)^7 + 87120*a^2*b^5*tan(1/2*d*x + 1/2*c)^7 - 34848*b^7*tan(1/2*d*x + 1/2*c)^7 - 525*a^7*tan(1/2*d*x + 1/2*c)^6 + 9240*a^5*b^2*tan(1/2*d*x + 1/2*c)^6 - 15120*a^3*b^4*tan(1/2*d*x + 1/2*c)^6 + 6720*a*b^6*tan(1/2*d*x + 1/2*c)^6 - 1575*a^6*b*tan(1/2*d*x + 1/2*c)^5 + 3360*a^4*b^3*tan(1/2*d*x + 1/2*c)^5 - 1680*a^2*b^5*tan(1/2*d*x + 1/2*c)^5 + 315*a^7*tan(1/2*d*x + 1/2*c)^4 - 980*a^5*b^2*tan(1/2*d*x + 1/2*c)^4 + 560*a^3*b^4*tan(1/2*d*x + 1/2*c)^4 + 315*a^6*b*tan(1/2*d*x + 1/2*c)^3 - 210*a^4*b^3*tan(1/2*d*x + 1/2*c)^3 - 105*a^7*tan(1/2*d*x + 1/2*c)^2 + 84*a^5*b^2*tan(1/2*d*x + 1/2*c)^2 - 35*a^6*b*tan(1/2*d*x + 1/2*c) + 15*a^7)/(a^8*tan(1/2*d*x + 1/2*c)^7))/d","A",0
1331,1,948,0,0.262194," ","integrate(cos(d*x+c)^6*csc(d*x+c)^9/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{105 \, a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 240 \, a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 560 \, a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 560 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 1680 \, a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1344 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 840 \, a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 5040 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 3360 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 5040 \, a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15680 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 8960 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1680 \, a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 25200 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 53760 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 26880 \, a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 8400 \, a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 147840 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 241920 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 107520 \, b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{8}} - \frac{1680 \, {\left(5 \, a^{8} + 40 \, a^{6} b^{2} - 240 \, a^{4} b^{4} + 320 \, a^{2} b^{6} - 128 \, b^{8}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{9}} + \frac{430080 \, {\left(a^{6} b^{3} - 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} - b^{9}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a^{9}} + \frac{22830 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 182640 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 1095840 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 1461120 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 584448 \, b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 8400 \, a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 147840 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 241920 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 107520 \, a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1680 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 25200 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 53760 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 26880 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 5040 \, a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15680 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 8960 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 840 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 5040 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 3360 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1680 \, a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1344 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 560 \, a^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 560 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 240 \, a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 105 \, a^{8}}{a^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8}}}{215040 \, d}"," ",0,"1/215040*((105*a^7*tan(1/2*d*x + 1/2*c)^8 - 240*a^6*b*tan(1/2*d*x + 1/2*c)^7 - 560*a^7*tan(1/2*d*x + 1/2*c)^6 + 560*a^5*b^2*tan(1/2*d*x + 1/2*c)^6 + 1680*a^6*b*tan(1/2*d*x + 1/2*c)^5 - 1344*a^4*b^3*tan(1/2*d*x + 1/2*c)^5 + 840*a^7*tan(1/2*d*x + 1/2*c)^4 - 5040*a^5*b^2*tan(1/2*d*x + 1/2*c)^4 + 3360*a^3*b^4*tan(1/2*d*x + 1/2*c)^4 - 5040*a^6*b*tan(1/2*d*x + 1/2*c)^3 + 15680*a^4*b^3*tan(1/2*d*x + 1/2*c)^3 - 8960*a^2*b^5*tan(1/2*d*x + 1/2*c)^3 + 1680*a^7*tan(1/2*d*x + 1/2*c)^2 + 25200*a^5*b^2*tan(1/2*d*x + 1/2*c)^2 - 53760*a^3*b^4*tan(1/2*d*x + 1/2*c)^2 + 26880*a*b^6*tan(1/2*d*x + 1/2*c)^2 + 8400*a^6*b*tan(1/2*d*x + 1/2*c) - 147840*a^4*b^3*tan(1/2*d*x + 1/2*c) + 241920*a^2*b^5*tan(1/2*d*x + 1/2*c) - 107520*b^7*tan(1/2*d*x + 1/2*c))/a^8 - 1680*(5*a^8 + 40*a^6*b^2 - 240*a^4*b^4 + 320*a^2*b^6 - 128*b^8)*log(abs(tan(1/2*d*x + 1/2*c)))/a^9 + 430080*(a^6*b^3 - 3*a^4*b^5 + 3*a^2*b^7 - b^9)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a^9) + (22830*a^8*tan(1/2*d*x + 1/2*c)^8 + 182640*a^6*b^2*tan(1/2*d*x + 1/2*c)^8 - 1095840*a^4*b^4*tan(1/2*d*x + 1/2*c)^8 + 1461120*a^2*b^6*tan(1/2*d*x + 1/2*c)^8 - 584448*b^8*tan(1/2*d*x + 1/2*c)^8 - 8400*a^7*b*tan(1/2*d*x + 1/2*c)^7 + 147840*a^5*b^3*tan(1/2*d*x + 1/2*c)^7 - 241920*a^3*b^5*tan(1/2*d*x + 1/2*c)^7 + 107520*a*b^7*tan(1/2*d*x + 1/2*c)^7 - 1680*a^8*tan(1/2*d*x + 1/2*c)^6 - 25200*a^6*b^2*tan(1/2*d*x + 1/2*c)^6 + 53760*a^4*b^4*tan(1/2*d*x + 1/2*c)^6 - 26880*a^2*b^6*tan(1/2*d*x + 1/2*c)^6 + 5040*a^7*b*tan(1/2*d*x + 1/2*c)^5 - 15680*a^5*b^3*tan(1/2*d*x + 1/2*c)^5 + 8960*a^3*b^5*tan(1/2*d*x + 1/2*c)^5 - 840*a^8*tan(1/2*d*x + 1/2*c)^4 + 5040*a^6*b^2*tan(1/2*d*x + 1/2*c)^4 - 3360*a^4*b^4*tan(1/2*d*x + 1/2*c)^4 - 1680*a^7*b*tan(1/2*d*x + 1/2*c)^3 + 1344*a^5*b^3*tan(1/2*d*x + 1/2*c)^3 + 560*a^8*tan(1/2*d*x + 1/2*c)^2 - 560*a^6*b^2*tan(1/2*d*x + 1/2*c)^2 + 240*a^7*b*tan(1/2*d*x + 1/2*c) - 105*a^8)/(a^9*tan(1/2*d*x + 1/2*c)^8))/d","B",0
1332,1,85,0,0.211092," ","integrate(sec(d*x+c)*sin(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{2 \, a^{3} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{2} b^{2} - b^{4}} - \frac{\log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a - b} - \frac{\log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a + b} - \frac{2 \, \sin\left(d x + c\right)}{b}}{2 \, d}"," ",0,"1/2*(2*a^3*log(abs(b*sin(d*x + c) + a))/(a^2*b^2 - b^4) - log(abs(sin(d*x + c) + 1))/(a - b) - log(abs(sin(d*x + c) - 1))/(a + b) - 2*sin(d*x + c)/b)/d","A",0
1333,1,71,0,0.209740," ","integrate(sec(d*x+c)*sin(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{2 \, a^{2} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{2} b - b^{3}} - \frac{\log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a - b} + \frac{\log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a + b}}{2 \, d}"," ",0,"-1/2*(2*a^2*log(abs(b*sin(d*x + c) + a))/(a^2*b - b^3) - log(abs(sin(d*x + c) + 1))/(a - b) + log(abs(sin(d*x + c) - 1))/(a + b))/d","A",0
1334,1,71,0,0.204732," ","integrate(sec(d*x+c)*sin(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{2 \, a b \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{2} b - b^{3}} - \frac{\log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a - b} - \frac{\log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a + b}}{2 \, d}"," ",0,"1/2*(2*a*b*log(abs(b*sin(d*x + c) + a))/(a^2*b - b^3) - log(abs(sin(d*x + c) + 1))/(a - b) - log(abs(sin(d*x + c) - 1))/(a + b))/d","A",0
1335,1,86,0,0.211954," ","integrate(csc(d*x+c)*sec(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{2 \, b^{3} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{3} b - a b^{3}} - \frac{\log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a - b} - \frac{\log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a + b} + \frac{2 \, \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a}}{2 \, d}"," ",0,"1/2*(2*b^3*log(abs(b*sin(d*x + c) + a))/(a^3*b - a*b^3) - log(abs(sin(d*x + c) + 1))/(a - b) - log(abs(sin(d*x + c) - 1))/(a + b) + 2*log(abs(sin(d*x + c)))/a)/d","A",0
1336,1,113,0,0.205442," ","integrate(csc(d*x+c)^2*sec(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{2 \, b^{4} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{4} b - a^{2} b^{3}} - \frac{\log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a - b} + \frac{\log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a + b} + \frac{2 \, b \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a^{2}} - \frac{2 \, {\left(b \sin\left(d x + c\right) - a\right)}}{a^{2} \sin\left(d x + c\right)}}{2 \, d}"," ",0,"-1/2*(2*b^4*log(abs(b*sin(d*x + c) + a))/(a^4*b - a^2*b^3) - log(abs(sin(d*x + c) + 1))/(a - b) + log(abs(sin(d*x + c) - 1))/(a + b) + 2*b*log(abs(sin(d*x + c)))/a^2 - 2*(b*sin(d*x + c) - a)/(a^2*sin(d*x + c)))/d","A",0
1337,1,148,0,0.232234," ","integrate(csc(d*x+c)^3*sec(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{2 \, b^{5} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{5} b - a^{3} b^{3}} - \frac{\log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a - b} - \frac{\log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a + b} + \frac{2 \, {\left(a^{2} + b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a^{3}} - \frac{3 \, a^{2} \sin\left(d x + c\right)^{2} + 3 \, b^{2} \sin\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) + a^{2}}{a^{3} \sin\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"1/2*(2*b^5*log(abs(b*sin(d*x + c) + a))/(a^5*b - a^3*b^3) - log(abs(sin(d*x + c) + 1))/(a - b) - log(abs(sin(d*x + c) - 1))/(a + b) + 2*(a^2 + b^2)*log(abs(sin(d*x + c)))/a^3 - (3*a^2*sin(d*x + c)^2 + 3*b^2*sin(d*x + c)^2 - 2*a*b*sin(d*x + c) + a^2)/(a^3*sin(d*x + c)^2))/d","A",0
1338,1,208,0,0.219382," ","integrate(sec(d*x+c)^2*sin(d*x+c)^5/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{4 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} a^{5}}{{\left(a^{2} b^{3} - b^{5}\right)} \sqrt{a^{2} - b^{2}}} + \frac{4 \, {\left(b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a\right)}}{{\left(a^{2} - b^{2}\right)} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}} - \frac{{\left(2 \, a^{2} + 3 \, b^{2}\right)} {\left(d x + c\right)}}{b^{3}} - \frac{2 \, {\left(b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, a\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2} b^{2}}}{2 \, d}"," ",0,"1/2*(4*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))*a^5/((a^2*b^3 - b^5)*sqrt(a^2 - b^2)) + 4*(b*tan(1/2*d*x + 1/2*c) - a)/((a^2 - b^2)*(tan(1/2*d*x + 1/2*c)^2 - 1)) - (2*a^2 + 3*b^2)*(d*x + c)/b^3 - 2*(b*tan(1/2*d*x + 1/2*c)^3 + 2*a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c) + 2*a)/((tan(1/2*d*x + 1/2*c)^2 + 1)^2*b^2))/d","A",0
1339,1,173,0,0.208059," ","integrate(sec(d*x+c)^2*sin(d*x+c)^4/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} a^{4}}{{\left(a^{2} b^{2} - b^{4}\right)} \sqrt{a^{2} - b^{2}}} - \frac{{\left(d x + c\right)} a}{b^{2}} + \frac{2 \, {\left(a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} - 2 \, b^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1\right)} {\left(a^{2} b - b^{3}\right)}}}{d}"," ",0,"-(2*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))*a^4/((a^2*b^2 - b^4)*sqrt(a^2 - b^2)) - (d*x + c)*a/b^2 + 2*(a*b*tan(1/2*d*x + 1/2*c)^3 - a^2*tan(1/2*d*x + 1/2*c)^2 + a*b*tan(1/2*d*x + 1/2*c) + a^2 - 2*b^2)/((tan(1/2*d*x + 1/2*c)^4 - 1)*(a^2*b - b^3)))/d","A",0
1340,1,131,0,0.287316," ","integrate(sec(d*x+c)^2*sin(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{2 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} a^{3}}{{\left(a^{2} b - b^{3}\right)} \sqrt{a^{2} - b^{2}}} - \frac{d x + c}{b} + \frac{2 \, {\left(b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a\right)}}{{\left(a^{2} - b^{2}\right)} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}}{d}"," ",0,"(2*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))*a^3/((a^2*b - b^3)*sqrt(a^2 - b^2)) - (d*x + c)/b + 2*(b*tan(1/2*d*x + 1/2*c) - a)/((a^2 - b^2)*(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
1341,1,107,0,0.253258," ","integrate(sec(d*x+c)^2*sin(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{{\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} a^{2}}{{\left(a^{2} - b^{2}\right)}^{\frac{3}{2}}} + \frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b}{{\left(a^{2} - b^{2}\right)} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}\right)}}{d}"," ",0,"-2*((pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))*a^2/(a^2 - b^2)^(3/2) + (a*tan(1/2*d*x + 1/2*c) - b)/((a^2 - b^2)*(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
1342,1,106,0,0.216415," ","integrate(sec(d*x+c)^2*sin(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{{\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} a b}{{\left(a^{2} - b^{2}\right)}^{\frac{3}{2}}} + \frac{b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a}{{\left(a^{2} - b^{2}\right)} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}\right)}}{d}"," ",0,"2*((pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))*a*b/(a^2 - b^2)^(3/2) + (b*tan(1/2*d*x + 1/2*c) - a)/((a^2 - b^2)*(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
1343,1,135,0,0.207121," ","integrate(csc(d*x+c)*sec(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{2 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} b^{3}}{{\left(a^{3} - a b^{2}\right)} \sqrt{a^{2} - b^{2}}} + \frac{\log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a} + \frac{2 \, {\left(b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a\right)}}{{\left(a^{2} - b^{2}\right)} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}}{d}"," ",0,"(2*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))*b^3/((a^3 - a*b^2)*sqrt(a^2 - b^2)) + log(abs(tan(1/2*d*x + 1/2*c)))/a + 2*(b*tan(1/2*d*x + 1/2*c) - a)/((a^2 - b^2)*(tan(1/2*d*x + 1/2*c)^2 - 1)))/d","A",0
1344,1,259,0,0.208978," ","integrate(csc(d*x+c)^2*sec(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{12 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} b^{4}}{{\left(a^{4} - a^{2} b^{2}\right)} \sqrt{a^{2} - b^{2}}} + \frac{6 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} - \frac{3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a} - \frac{2 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 10 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a^{3} - 3 \, a b^{2}}{{\left(a^{4} - a^{2} b^{2}\right)} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}}{6 \, d}"," ",0,"-1/6*(12*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))*b^4/((a^4 - a^2*b^2)*sqrt(a^2 - b^2)) + 6*b*log(abs(tan(1/2*d*x + 1/2*c)))/a^2 - 3*tan(1/2*d*x + 1/2*c)/a - (2*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 2*b^3*tan(1/2*d*x + 1/2*c)^3 - 15*a^3*tan(1/2*d*x + 1/2*c)^2 + 3*a*b^2*tan(1/2*d*x + 1/2*c)^2 + 10*a^2*b*tan(1/2*d*x + 1/2*c) + 2*b^3*tan(1/2*d*x + 1/2*c) + 3*a^3 - 3*a*b^2)/((a^4 - a^2*b^2)*(tan(1/2*d*x + 1/2*c)^3 - tan(1/2*d*x + 1/2*c))))/d","B",0
1345,1,245,0,0.242823," ","integrate(csc(d*x+c)^3*sec(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{16 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} b^{5}}{{\left(a^{5} - a^{3} b^{2}\right)} \sqrt{a^{2} - b^{2}}} + \frac{16 \, {\left(b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a\right)}}{{\left(a^{2} - b^{2}\right)} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}} + \frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{2}} + \frac{4 \, {\left(3 \, a^{2} + 2 \, b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} - \frac{18 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2}}{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}}{8 \, d}"," ",0,"1/8*(16*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))*b^5/((a^5 - a^3*b^2)*sqrt(a^2 - b^2)) + 16*(b*tan(1/2*d*x + 1/2*c) - a)/((a^2 - b^2)*(tan(1/2*d*x + 1/2*c)^2 - 1)) + (a*tan(1/2*d*x + 1/2*c)^2 - 4*b*tan(1/2*d*x + 1/2*c))/a^2 + 4*(3*a^2 + 2*b^2)*log(abs(tan(1/2*d*x + 1/2*c)))/a^3 - (18*a^2*tan(1/2*d*x + 1/2*c)^2 + 12*b^2*tan(1/2*d*x + 1/2*c)^2 - 4*a*b*tan(1/2*d*x + 1/2*c) + a^2)/(a^3*tan(1/2*d*x + 1/2*c)^2))/d","A",0
1346,1,177,0,0.240922," ","integrate(sec(d*x+c)^3*sin(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{4 \, a^{3} b \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{4} b - 2 \, a^{2} b^{3} + b^{5}} - \frac{{\left(2 \, a - b\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{2} - 2 \, a b + b^{2}} - \frac{{\left(2 \, a + b\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{2} + 2 \, a b + b^{2}} + \frac{2 \, {\left(a^{3} \sin\left(d x + c\right)^{2} - a^{2} b \sin\left(d x + c\right) + b^{3} \sin\left(d x + c\right) - a b^{2}\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(\sin\left(d x + c\right)^{2} - 1\right)}}}{4 \, d}"," ",0,"-1/4*(4*a^3*b*log(abs(b*sin(d*x + c) + a))/(a^4*b - 2*a^2*b^3 + b^5) - (2*a - b)*log(abs(sin(d*x + c) + 1))/(a^2 - 2*a*b + b^2) - (2*a + b)*log(abs(sin(d*x + c) - 1))/(a^2 + 2*a*b + b^2) + 2*(a^3*sin(d*x + c)^2 - a^2*b*sin(d*x + c) + b^3*sin(d*x + c) - a*b^2)/((a^4 - 2*a^2*b^2 + b^4)*(sin(d*x + c)^2 - 1)))/d","A",0
1347,1,168,0,0.230745," ","integrate(sec(d*x+c)^3*sin(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{4 \, a^{2} b^{2} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{4} b - 2 \, a^{2} b^{3} + b^{5}} - \frac{a \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{2} - 2 \, a b + b^{2}} + \frac{a \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{2} + 2 \, a b + b^{2}} + \frac{2 \, {\left(a^{2} b \sin\left(d x + c\right)^{2} - a^{3} \sin\left(d x + c\right) + a b^{2} \sin\left(d x + c\right) - b^{3}\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(\sin\left(d x + c\right)^{2} - 1\right)}}}{4 \, d}"," ",0,"1/4*(4*a^2*b^2*log(abs(b*sin(d*x + c) + a))/(a^4*b - 2*a^2*b^3 + b^5) - a*log(abs(sin(d*x + c) + 1))/(a^2 - 2*a*b + b^2) + a*log(abs(sin(d*x + c) - 1))/(a^2 + 2*a*b + b^2) + 2*(a^2*b*sin(d*x + c)^2 - a^3*sin(d*x + c) + a*b^2*sin(d*x + c) - b^3)/((a^4 - 2*a^2*b^2 + b^4)*(sin(d*x + c)^2 - 1)))/d","A",0
1348,1,170,0,0.233686," ","integrate(sec(d*x+c)^3*sin(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{4 \, a b^{3} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{4} b - 2 \, a^{2} b^{3} + b^{5}} - \frac{b \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{2} - 2 \, a b + b^{2}} + \frac{b \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{2} + 2 \, a b + b^{2}} + \frac{2 \, {\left(a b^{2} \sin\left(d x + c\right)^{2} - a^{2} b \sin\left(d x + c\right) + b^{3} \sin\left(d x + c\right) + a^{3} - 2 \, a b^{2}\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(\sin\left(d x + c\right)^{2} - 1\right)}}}{4 \, d}"," ",0,"-1/4*(4*a*b^3*log(abs(b*sin(d*x + c) + a))/(a^4*b - 2*a^2*b^3 + b^5) - b*log(abs(sin(d*x + c) + 1))/(a^2 - 2*a*b + b^2) + b*log(abs(sin(d*x + c) - 1))/(a^2 + 2*a*b + b^2) + 2*(a*b^2*sin(d*x + c)^2 - a^2*b*sin(d*x + c) + b^3*sin(d*x + c) + a^3 - 2*a*b^2)/((a^4 - 2*a^2*b^2 + b^4)*(sin(d*x + c)^2 - 1)))/d","A",0
1349,1,210,0,0.232436," ","integrate(csc(d*x+c)*sec(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{4 \, b^{5} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{5} b - 2 \, a^{3} b^{3} + a b^{5}} + \frac{{\left(2 \, a - 3 \, b\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{2} - 2 \, a b + b^{2}} + \frac{{\left(2 \, a + 3 \, b\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{2} + 2 \, a b + b^{2}} - \frac{4 \, \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a} - \frac{2 \, {\left(a^{3} \sin\left(d x + c\right)^{2} - 2 \, a b^{2} \sin\left(d x + c\right)^{2} + a^{2} b \sin\left(d x + c\right) - b^{3} \sin\left(d x + c\right) - 2 \, a^{3} + 3 \, a b^{2}\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(\sin\left(d x + c\right)^{2} - 1\right)}}}{4 \, d}"," ",0,"-1/4*(4*b^5*log(abs(b*sin(d*x + c) + a))/(a^5*b - 2*a^3*b^3 + a*b^5) + (2*a - 3*b)*log(abs(sin(d*x + c) + 1))/(a^2 - 2*a*b + b^2) + (2*a + 3*b)*log(abs(sin(d*x + c) - 1))/(a^2 + 2*a*b + b^2) - 4*log(abs(sin(d*x + c)))/a - 2*(a^3*sin(d*x + c)^2 - 2*a*b^2*sin(d*x + c)^2 + a^2*b*sin(d*x + c) - b^3*sin(d*x + c) - 2*a^3 + 3*a*b^2)/((a^4 - 2*a^2*b^2 + b^4)*(sin(d*x + c)^2 - 1)))/d","A",0
1350,1,279,0,0.236639," ","integrate(csc(d*x+c)^2*sec(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{12 \, b^{6} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}} + \frac{3 \, {\left(3 \, a - 4 \, b\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{2} - 2 \, a b + b^{2}} - \frac{3 \, {\left(3 \, a + 4 \, b\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{2} + 2 \, a b + b^{2}} - \frac{12 \, b \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a^{2}} + \frac{2 \, {\left(2 \, b^{5} \sin\left(d x + c\right)^{3} - 9 \, a^{5} \sin\left(d x + c\right)^{2} + 15 \, a^{3} b^{2} \sin\left(d x + c\right)^{2} - 6 \, a b^{4} \sin\left(d x + c\right)^{2} + 3 \, a^{4} b \sin\left(d x + c\right) - 3 \, a^{2} b^{3} \sin\left(d x + c\right) - 2 \, b^{5} \sin\left(d x + c\right) + 6 \, a^{5} - 12 \, a^{3} b^{2} + 6 \, a b^{4}\right)}}{{\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} {\left(\sin\left(d x + c\right)^{3} - \sin\left(d x + c\right)\right)}}}{12 \, d}"," ",0,"1/12*(12*b^6*log(abs(b*sin(d*x + c) + a))/(a^6*b - 2*a^4*b^3 + a^2*b^5) + 3*(3*a - 4*b)*log(abs(sin(d*x + c) + 1))/(a^2 - 2*a*b + b^2) - 3*(3*a + 4*b)*log(abs(sin(d*x + c) - 1))/(a^2 + 2*a*b + b^2) - 12*b*log(abs(sin(d*x + c)))/a^2 + 2*(2*b^5*sin(d*x + c)^3 - 9*a^5*sin(d*x + c)^2 + 15*a^3*b^2*sin(d*x + c)^2 - 6*a*b^4*sin(d*x + c)^2 + 3*a^4*b*sin(d*x + c) - 3*a^2*b^3*sin(d*x + c) - 2*b^5*sin(d*x + c) + 6*a^5 - 12*a^3*b^2 + 6*a*b^4)/((a^6 - 2*a^4*b^2 + a^2*b^4)*(sin(d*x + c)^3 - sin(d*x + c))))/d","A",0
1351,1,275,0,0.267462," ","integrate(csc(d*x+c)^3*sec(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{4 \, b^{7} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{7} b - 2 \, a^{5} b^{3} + a^{3} b^{5}} + \frac{{\left(4 \, a - 5 \, b\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{2} - 2 \, a b + b^{2}} + \frac{{\left(4 \, a + 5 \, b\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{2} + 2 \, a b + b^{2}} - \frac{2 \, {\left(2 \, a^{3} \sin\left(d x + c\right)^{2} - 3 \, a b^{2} \sin\left(d x + c\right)^{2} + a^{2} b \sin\left(d x + c\right) - b^{3} \sin\left(d x + c\right) - 3 \, a^{3} + 4 \, a b^{2}\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(\sin\left(d x + c\right)^{2} - 1\right)}} - \frac{4 \, {\left(2 \, a^{2} + b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a^{3}} + \frac{2 \, {\left(6 \, a^{2} \sin\left(d x + c\right)^{2} + 3 \, b^{2} \sin\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) + a^{2}\right)}}{a^{3} \sin\left(d x + c\right)^{2}}}{4 \, d}"," ",0,"-1/4*(4*b^7*log(abs(b*sin(d*x + c) + a))/(a^7*b - 2*a^5*b^3 + a^3*b^5) + (4*a - 5*b)*log(abs(sin(d*x + c) + 1))/(a^2 - 2*a*b + b^2) + (4*a + 5*b)*log(abs(sin(d*x + c) - 1))/(a^2 + 2*a*b + b^2) - 2*(2*a^3*sin(d*x + c)^2 - 3*a*b^2*sin(d*x + c)^2 + a^2*b*sin(d*x + c) - b^3*sin(d*x + c) - 3*a^3 + 4*a*b^2)/((a^4 - 2*a^2*b^2 + b^4)*(sin(d*x + c)^2 - 1)) - 4*(2*a^2 + b^2)*log(abs(sin(d*x + c)))/a^3 + 2*(6*a^2*sin(d*x + c)^2 + 3*b^2*sin(d*x + c)^2 - 2*a*b*sin(d*x + c) + a^2)/(a^3*sin(d*x + c)^2))/d","A",0
1352,1,241,0,0.271853," ","integrate(sec(d*x+c)^4*sin(d*x+c)^4/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{3 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} a^{4}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} - b^{2}}} + \frac{3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 10 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 6 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, a^{2} b + 2 \, b^{3}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}\right)}}{3 \, d}"," ",0,"2/3*(3*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))*a^4/((a^4 - 2*a^2*b^2 + b^4)*sqrt(a^2 - b^2)) + (3*a^3*tan(1/2*d*x + 1/2*c)^5 - 3*a^2*b*tan(1/2*d*x + 1/2*c)^4 - 10*a^3*tan(1/2*d*x + 1/2*c)^3 + 4*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 12*a^2*b*tan(1/2*d*x + 1/2*c)^2 - 6*b^3*tan(1/2*d*x + 1/2*c)^2 + 3*a^3*tan(1/2*d*x + 1/2*c) - 5*a^2*b + 2*b^3)/((a^4 - 2*a^2*b^2 + b^4)*(tan(1/2*d*x + 1/2*c)^2 - 1)^3))/d","A",0
1353,1,227,0,0.329633," ","integrate(sec(d*x+c)^4*sin(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{3 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} a^{3} b}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} - b^{2}}} + \frac{3 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 10 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, a^{3} - a b^{2}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}\right)}}{3 \, d}"," ",0,"-2/3*(3*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))*a^3*b/((a^4 - 2*a^2*b^2 + b^4)*sqrt(a^2 - b^2)) + (3*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 3*a*b^2*tan(1/2*d*x + 1/2*c)^4 - 10*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 4*b^3*tan(1/2*d*x + 1/2*c)^3 + 6*a^3*tan(1/2*d*x + 1/2*c)^2 + 3*a^2*b*tan(1/2*d*x + 1/2*c) - 2*a^3 - a*b^2)/((a^4 - 2*a^2*b^2 + b^4)*(tan(1/2*d*x + 1/2*c)^2 - 1)^3))/d","A",0
1354,1,229,0,0.318309," ","integrate(sec(d*x+c)^4*sin(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{3 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} a^{2} b^{2}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} - b^{2}}} + \frac{3 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 4 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, a^{2} b - b^{3}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}\right)}}{3 \, d}"," ",0,"2/3*(3*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))*a^2*b^2/((a^4 - 2*a^2*b^2 + b^4)*sqrt(a^2 - b^2)) + (3*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 3*b^3*tan(1/2*d*x + 1/2*c)^4 - 4*a^3*tan(1/2*d*x + 1/2*c)^3 - 2*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*a^2*b*tan(1/2*d*x + 1/2*c)^2 + 3*a*b^2*tan(1/2*d*x + 1/2*c) - 2*a^2*b - b^3)/((a^4 - 2*a^2*b^2 + b^4)*(tan(1/2*d*x + 1/2*c)^2 - 1)^3))/d","A",0
1355,1,240,0,0.232024," ","integrate(sec(d*x+c)^4*sin(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{3 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} a b^{3}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} - b^{2}}} + \frac{3 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 6 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 4 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3} - 4 \, a b^{2}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}\right)}}{3 \, d}"," ",0,"-2/3*(3*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))*a*b^3/((a^4 - 2*a^2*b^2 + b^4)*sqrt(a^2 - b^2)) + (3*b^3*tan(1/2*d*x + 1/2*c)^5 + 3*a^3*tan(1/2*d*x + 1/2*c)^4 - 6*a*b^2*tan(1/2*d*x + 1/2*c)^4 - 4*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 2*b^3*tan(1/2*d*x + 1/2*c)^3 + 6*a*b^2*tan(1/2*d*x + 1/2*c)^2 + 3*b^3*tan(1/2*d*x + 1/2*c) + a^3 - 4*a*b^2)/((a^4 - 2*a^2*b^2 + b^4)*(tan(1/2*d*x + 1/2*c)^2 - 1)^3))/d","A",0
1356,1,308,0,0.238987," ","integrate(csc(d*x+c)*sec(d*x+c)^4/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{6 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} b^{5}}{{\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \sqrt{a^{2} - b^{2}}} - \frac{3 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a} - \frac{2 \, {\left(3 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 9 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 2 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, a^{3} + 7 \, a b^{2}\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{3 \, d}"," ",0,"-1/3*(6*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))*b^5/((a^5 - 2*a^3*b^2 + a*b^4)*sqrt(a^2 - b^2)) - 3*log(abs(tan(1/2*d*x + 1/2*c)))/a - 2*(3*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 6*b^3*tan(1/2*d*x + 1/2*c)^5 - 6*a^3*tan(1/2*d*x + 1/2*c)^4 + 9*a*b^2*tan(1/2*d*x + 1/2*c)^4 - 2*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 8*b^3*tan(1/2*d*x + 1/2*c)^3 + 6*a^3*tan(1/2*d*x + 1/2*c)^2 - 12*a*b^2*tan(1/2*d*x + 1/2*c)^2 + 3*a^2*b*tan(1/2*d*x + 1/2*c) - 6*b^3*tan(1/2*d*x + 1/2*c) - 4*a^3 + 7*a*b^2)/((a^4 - 2*a^2*b^2 + b^4)*(tan(1/2*d*x + 1/2*c)^2 - 1)^3))/d","A",0
1357,1,357,0,0.227281," ","integrate(csc(d*x+c)^2*sec(d*x+c)^4/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{12 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} b^{6}}{{\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} \sqrt{a^{2} - b^{2}}} - \frac{6 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}} + \frac{3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a} + \frac{3 \, {\left(2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a\right)}}{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)} - \frac{4 \, {\left(6 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 9 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 8 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 14 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 6 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, a^{2} b + 7 \, b^{3}\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(12*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))*b^6/((a^6 - 2*a^4*b^2 + a^2*b^4)*sqrt(a^2 - b^2)) - 6*b*log(abs(tan(1/2*d*x + 1/2*c)))/a^2 + 3*tan(1/2*d*x + 1/2*c)/a + 3*(2*b*tan(1/2*d*x + 1/2*c) - a)/(a^2*tan(1/2*d*x + 1/2*c)) - 4*(6*a^3*tan(1/2*d*x + 1/2*c)^5 - 9*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 6*a^2*b*tan(1/2*d*x + 1/2*c)^4 + 9*b^3*tan(1/2*d*x + 1/2*c)^4 - 8*a^3*tan(1/2*d*x + 1/2*c)^3 + 14*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*a^2*b*tan(1/2*d*x + 1/2*c)^2 - 12*b^3*tan(1/2*d*x + 1/2*c)^2 + 6*a^3*tan(1/2*d*x + 1/2*c) - 9*a*b^2*tan(1/2*d*x + 1/2*c) - 4*a^2*b + 7*b^3)/((a^4 - 2*a^2*b^2 + b^4)*(tan(1/2*d*x + 1/2*c)^2 - 1)^3))/d","A",0
1358,1,417,0,0.239614," ","integrate(csc(d*x+c)^3*sec(d*x+c)^4/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{48 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} b^{7}}{{\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} \sqrt{a^{2} - b^{2}}} - \frac{3 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a^{2}} - \frac{12 \, {\left(5 \, a^{2} + 2 \, b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} - \frac{16 \, {\left(6 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 9 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 12 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 8 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 14 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 18 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 6 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 7 \, a^{3} + 10 \, a b^{2}\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}} + \frac{3 \, {\left(30 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2}\right)}}{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}}{24 \, d}"," ",0,"-1/24*(48*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))*b^7/((a^7 - 2*a^5*b^2 + a^3*b^4)*sqrt(a^2 - b^2)) - 3*(a*tan(1/2*d*x + 1/2*c)^2 - 4*b*tan(1/2*d*x + 1/2*c))/a^2 - 12*(5*a^2 + 2*b^2)*log(abs(tan(1/2*d*x + 1/2*c)))/a^3 - 16*(6*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 9*b^3*tan(1/2*d*x + 1/2*c)^5 - 9*a^3*tan(1/2*d*x + 1/2*c)^4 + 12*a*b^2*tan(1/2*d*x + 1/2*c)^4 - 8*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 14*b^3*tan(1/2*d*x + 1/2*c)^3 + 12*a^3*tan(1/2*d*x + 1/2*c)^2 - 18*a*b^2*tan(1/2*d*x + 1/2*c)^2 + 6*a^2*b*tan(1/2*d*x + 1/2*c) - 9*b^3*tan(1/2*d*x + 1/2*c) - 7*a^3 + 10*a*b^2)/((a^4 - 2*a^2*b^2 + b^4)*(tan(1/2*d*x + 1/2*c)^2 - 1)^3) + 3*(30*a^2*tan(1/2*d*x + 1/2*c)^2 + 12*b^2*tan(1/2*d*x + 1/2*c)^2 - 4*a*b*tan(1/2*d*x + 1/2*c) + a^2)/(a^3*tan(1/2*d*x + 1/2*c)^2))/d","A",0
1359,1,403,0,0.302698," ","integrate(sec(d*x+c)^5*sin(d*x+c)^8/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{16 \, a^{8} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{6} b^{3} - 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} - b^{9}} - \frac{{\left(35 \, a^{2} - 57 \, a b + 24 \, b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} + \frac{{\left(35 \, a^{2} + 57 \, a b + 24 \, b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} + \frac{8 \, {\left(b \sin\left(d x + c\right)^{2} - 2 \, a \sin\left(d x + c\right)\right)}}{b^{2}} + \frac{2 \, {\left(36 \, a^{4} b \sin\left(d x + c\right)^{4} - 48 \, a^{2} b^{3} \sin\left(d x + c\right)^{4} + 18 \, b^{5} \sin\left(d x + c\right)^{4} - 13 \, a^{5} \sin\left(d x + c\right)^{3} + 22 \, a^{3} b^{2} \sin\left(d x + c\right)^{3} - 9 \, a b^{4} \sin\left(d x + c\right)^{3} - 56 \, a^{4} b \sin\left(d x + c\right)^{2} + 68 \, a^{2} b^{3} \sin\left(d x + c\right)^{2} - 24 \, b^{5} \sin\left(d x + c\right)^{2} + 11 \, a^{5} \sin\left(d x + c\right) - 18 \, a^{3} b^{2} \sin\left(d x + c\right) + 7 \, a b^{4} \sin\left(d x + c\right) + 22 \, a^{4} b - 24 \, a^{2} b^{3} + 8 \, b^{5}\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{16 \, d}"," ",0,"-1/16*(16*a^8*log(abs(b*sin(d*x + c) + a))/(a^6*b^3 - 3*a^4*b^5 + 3*a^2*b^7 - b^9) - (35*a^2 - 57*a*b + 24*b^2)*log(abs(sin(d*x + c) + 1))/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) + (35*a^2 + 57*a*b + 24*b^2)*log(abs(sin(d*x + c) - 1))/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) + 8*(b*sin(d*x + c)^2 - 2*a*sin(d*x + c))/b^2 + 2*(36*a^4*b*sin(d*x + c)^4 - 48*a^2*b^3*sin(d*x + c)^4 + 18*b^5*sin(d*x + c)^4 - 13*a^5*sin(d*x + c)^3 + 22*a^3*b^2*sin(d*x + c)^3 - 9*a*b^4*sin(d*x + c)^3 - 56*a^4*b*sin(d*x + c)^2 + 68*a^2*b^3*sin(d*x + c)^2 - 24*b^5*sin(d*x + c)^2 + 11*a^5*sin(d*x + c) - 18*a^3*b^2*sin(d*x + c) + 7*a*b^4*sin(d*x + c) + 22*a^4*b - 24*a^2*b^3 + 8*b^5)/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(sin(d*x + c)^2 - 1)^2))/d","A",0
1360,1,384,0,0.313164," ","integrate(sec(d*x+c)^5*sin(d*x+c)^7/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{16 \, a^{7} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}} - \frac{{\left(24 \, a^{2} - 37 \, a b + 15 \, b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} - \frac{{\left(24 \, a^{2} + 37 \, a b + 15 \, b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} - \frac{16 \, \sin\left(d x + c\right)}{b} + \frac{2 \, {\left(18 \, a^{5} \sin\left(d x + c\right)^{4} - 18 \, a^{3} b^{2} \sin\left(d x + c\right)^{4} + 6 \, a b^{4} \sin\left(d x + c\right)^{4} - 13 \, a^{4} b \sin\left(d x + c\right)^{3} + 22 \, a^{2} b^{3} \sin\left(d x + c\right)^{3} - 9 \, b^{5} \sin\left(d x + c\right)^{3} - 24 \, a^{5} \sin\left(d x + c\right)^{2} + 16 \, a^{3} b^{2} \sin\left(d x + c\right)^{2} - 4 \, a b^{4} \sin\left(d x + c\right)^{2} + 11 \, a^{4} b \sin\left(d x + c\right) - 18 \, a^{2} b^{3} \sin\left(d x + c\right) + 7 \, b^{5} \sin\left(d x + c\right) + 8 \, a^{5} - 2 \, a^{3} b^{2}\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{16 \, d}"," ",0,"1/16*(16*a^7*log(abs(b*sin(d*x + c) + a))/(a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8) - (24*a^2 - 37*a*b + 15*b^2)*log(abs(sin(d*x + c) + 1))/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) - (24*a^2 + 37*a*b + 15*b^2)*log(abs(sin(d*x + c) - 1))/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) - 16*sin(d*x + c)/b + 2*(18*a^5*sin(d*x + c)^4 - 18*a^3*b^2*sin(d*x + c)^4 + 6*a*b^4*sin(d*x + c)^4 - 13*a^4*b*sin(d*x + c)^3 + 22*a^2*b^3*sin(d*x + c)^3 - 9*b^5*sin(d*x + c)^3 - 24*a^5*sin(d*x + c)^2 + 16*a^3*b^2*sin(d*x + c)^2 - 4*a*b^4*sin(d*x + c)^2 + 11*a^4*b*sin(d*x + c) - 18*a^2*b^3*sin(d*x + c) + 7*b^5*sin(d*x + c) + 8*a^5 - 2*a^3*b^2)/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(sin(d*x + c)^2 - 1)^2))/d","A",0
1361,1,371,0,0.293546," ","integrate(sec(d*x+c)^5*sin(d*x+c)^6/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{16 \, a^{6} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}} - \frac{{\left(15 \, a^{2} - 21 \, a b + 8 \, b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} + \frac{{\left(15 \, a^{2} + 21 \, a b + 8 \, b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} + \frac{2 \, {\left(18 \, a^{4} b \sin\left(d x + c\right)^{4} - 18 \, a^{2} b^{3} \sin\left(d x + c\right)^{4} + 6 \, b^{5} \sin\left(d x + c\right)^{4} - 9 \, a^{5} \sin\left(d x + c\right)^{3} + 14 \, a^{3} b^{2} \sin\left(d x + c\right)^{3} - 5 \, a b^{4} \sin\left(d x + c\right)^{3} - 24 \, a^{4} b \sin\left(d x + c\right)^{2} + 16 \, a^{2} b^{3} \sin\left(d x + c\right)^{2} - 4 \, b^{5} \sin\left(d x + c\right)^{2} + 7 \, a^{5} \sin\left(d x + c\right) - 10 \, a^{3} b^{2} \sin\left(d x + c\right) + 3 \, a b^{4} \sin\left(d x + c\right) + 8 \, a^{4} b - 2 \, a^{2} b^{3}\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{16 \, d}"," ",0,"-1/16*(16*a^6*log(abs(b*sin(d*x + c) + a))/(a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7) - (15*a^2 - 21*a*b + 8*b^2)*log(abs(sin(d*x + c) + 1))/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) + (15*a^2 + 21*a*b + 8*b^2)*log(abs(sin(d*x + c) - 1))/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) + 2*(18*a^4*b*sin(d*x + c)^4 - 18*a^2*b^3*sin(d*x + c)^4 + 6*b^5*sin(d*x + c)^4 - 9*a^5*sin(d*x + c)^3 + 14*a^3*b^2*sin(d*x + c)^3 - 5*a*b^4*sin(d*x + c)^3 - 24*a^4*b*sin(d*x + c)^2 + 16*a^2*b^3*sin(d*x + c)^2 - 4*b^5*sin(d*x + c)^2 + 7*a^5*sin(d*x + c) - 10*a^3*b^2*sin(d*x + c) + 3*a*b^4*sin(d*x + c) + 8*a^4*b - 2*a^2*b^3)/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(sin(d*x + c)^2 - 1)^2))/d","A",0
1362,1,343,0,0.308770," ","integrate(sec(d*x+c)^5*sin(d*x+c)^5/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{16 \, a^{5} b \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}} - \frac{{\left(8 \, a^{2} - 9 \, a b + 3 \, b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} - \frac{{\left(8 \, a^{2} + 9 \, a b + 3 \, b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} + \frac{2 \, {\left(6 \, a^{5} \sin\left(d x + c\right)^{4} - 9 \, a^{4} b \sin\left(d x + c\right)^{3} + 14 \, a^{2} b^{3} \sin\left(d x + c\right)^{3} - 5 \, b^{5} \sin\left(d x + c\right)^{3} - 4 \, a^{5} \sin\left(d x + c\right)^{2} - 12 \, a^{3} b^{2} \sin\left(d x + c\right)^{2} + 4 \, a b^{4} \sin\left(d x + c\right)^{2} + 7 \, a^{4} b \sin\left(d x + c\right) - 10 \, a^{2} b^{3} \sin\left(d x + c\right) + 3 \, b^{5} \sin\left(d x + c\right) + 8 \, a^{3} b^{2} - 2 \, a b^{4}\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{16 \, d}"," ",0,"1/16*(16*a^5*b*log(abs(b*sin(d*x + c) + a))/(a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7) - (8*a^2 - 9*a*b + 3*b^2)*log(abs(sin(d*x + c) + 1))/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) - (8*a^2 + 9*a*b + 3*b^2)*log(abs(sin(d*x + c) - 1))/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) + 2*(6*a^5*sin(d*x + c)^4 - 9*a^4*b*sin(d*x + c)^3 + 14*a^2*b^3*sin(d*x + c)^3 - 5*b^5*sin(d*x + c)^3 - 4*a^5*sin(d*x + c)^2 - 12*a^3*b^2*sin(d*x + c)^2 + 4*a*b^4*sin(d*x + c)^2 + 7*a^4*b*sin(d*x + c) - 10*a^2*b^3*sin(d*x + c) + 3*b^5*sin(d*x + c) + 8*a^3*b^2 - 2*a*b^4)/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(sin(d*x + c)^2 - 1)^2))/d","A",0
1363,1,333,0,0.307440," ","integrate(sec(d*x+c)^5*sin(d*x+c)^4/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{16 \, a^{4} b^{2} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}} - \frac{{\left(3 \, a^{2} - a b\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} + \frac{{\left(3 \, a^{2} + a b\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} + \frac{2 \, {\left(6 \, a^{4} b \sin\left(d x + c\right)^{4} - 5 \, a^{5} \sin\left(d x + c\right)^{3} + 6 \, a^{3} b^{2} \sin\left(d x + c\right)^{3} - a b^{4} \sin\left(d x + c\right)^{3} - 4 \, a^{4} b \sin\left(d x + c\right)^{2} - 12 \, a^{2} b^{3} \sin\left(d x + c\right)^{2} + 4 \, b^{5} \sin\left(d x + c\right)^{2} + 3 \, a^{5} \sin\left(d x + c\right) - 2 \, a^{3} b^{2} \sin\left(d x + c\right) - a b^{4} \sin\left(d x + c\right) + 8 \, a^{2} b^{3} - 2 \, b^{5}\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{16 \, d}"," ",0,"-1/16*(16*a^4*b^2*log(abs(b*sin(d*x + c) + a))/(a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7) - (3*a^2 - a*b)*log(abs(sin(d*x + c) + 1))/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) + (3*a^2 + a*b)*log(abs(sin(d*x + c) - 1))/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) + 2*(6*a^4*b*sin(d*x + c)^4 - 5*a^5*sin(d*x + c)^3 + 6*a^3*b^2*sin(d*x + c)^3 - a*b^4*sin(d*x + c)^3 - 4*a^4*b*sin(d*x + c)^2 - 12*a^2*b^3*sin(d*x + c)^2 + 4*b^5*sin(d*x + c)^2 + 3*a^5*sin(d*x + c) - 2*a^3*b^2*sin(d*x + c) - a*b^4*sin(d*x + c) + 8*a^2*b^3 - 2*b^5)/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(sin(d*x + c)^2 - 1)^2))/d","A",0
1364,1,326,0,0.291336," ","integrate(sec(d*x+c)^5*sin(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{16 \, a^{3} b^{3} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}} - \frac{{\left(3 \, a b - b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} + \frac{{\left(3 \, a b + b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} + \frac{2 \, {\left(6 \, a^{3} b^{2} \sin\left(d x + c\right)^{4} - 5 \, a^{4} b \sin\left(d x + c\right)^{3} + 6 \, a^{2} b^{3} \sin\left(d x + c\right)^{3} - b^{5} \sin\left(d x + c\right)^{3} + 4 \, a^{5} \sin\left(d x + c\right)^{2} - 16 \, a^{3} b^{2} \sin\left(d x + c\right)^{2} + 3 \, a^{4} b \sin\left(d x + c\right) - 2 \, a^{2} b^{3} \sin\left(d x + c\right) - b^{5} \sin\left(d x + c\right) - 2 \, a^{5} + 6 \, a^{3} b^{2} + 2 \, a b^{4}\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{16 \, d}"," ",0,"1/16*(16*a^3*b^3*log(abs(b*sin(d*x + c) + a))/(a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7) - (3*a*b - b^2)*log(abs(sin(d*x + c) + 1))/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) + (3*a*b + b^2)*log(abs(sin(d*x + c) - 1))/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) + 2*(6*a^3*b^2*sin(d*x + c)^4 - 5*a^4*b*sin(d*x + c)^3 + 6*a^2*b^3*sin(d*x + c)^3 - b^5*sin(d*x + c)^3 + 4*a^5*sin(d*x + c)^2 - 16*a^3*b^2*sin(d*x + c)^2 + 3*a^4*b*sin(d*x + c) - 2*a^2*b^3*sin(d*x + c) - b^5*sin(d*x + c) - 2*a^5 + 6*a^3*b^2 + 2*a*b^4)/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(sin(d*x + c)^2 - 1)^2))/d","A",0
1365,1,325,0,0.280411," ","integrate(sec(d*x+c)^5*sin(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{16 \, a^{2} b^{4} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}} + \frac{{\left(a^{2} - 3 \, a b\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} - \frac{{\left(a^{2} + 3 \, a b\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} + \frac{2 \, {\left(6 \, a^{2} b^{3} \sin\left(d x + c\right)^{4} - a^{5} \sin\left(d x + c\right)^{3} - 2 \, a^{3} b^{2} \sin\left(d x + c\right)^{3} + 3 \, a b^{4} \sin\left(d x + c\right)^{3} + 4 \, a^{4} b \sin\left(d x + c\right)^{2} - 16 \, a^{2} b^{3} \sin\left(d x + c\right)^{2} - a^{5} \sin\left(d x + c\right) + 6 \, a^{3} b^{2} \sin\left(d x + c\right) - 5 \, a b^{4} \sin\left(d x + c\right) - 2 \, a^{4} b + 6 \, a^{2} b^{3} + 2 \, b^{5}\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{16 \, d}"," ",0,"-1/16*(16*a^2*b^4*log(abs(b*sin(d*x + c) + a))/(a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7) + (a^2 - 3*a*b)*log(abs(sin(d*x + c) + 1))/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) - (a^2 + 3*a*b)*log(abs(sin(d*x + c) - 1))/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) + 2*(6*a^2*b^3*sin(d*x + c)^4 - a^5*sin(d*x + c)^3 - 2*a^3*b^2*sin(d*x + c)^3 + 3*a*b^4*sin(d*x + c)^3 + 4*a^4*b*sin(d*x + c)^2 - 16*a^2*b^3*sin(d*x + c)^2 - a^5*sin(d*x + c) + 6*a^3*b^2*sin(d*x + c) - 5*a*b^4*sin(d*x + c) - 2*a^4*b + 6*a^2*b^3 + 2*b^5)/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(sin(d*x + c)^2 - 1)^2))/d","A",0
1366,1,323,0,0.266382," ","integrate(sec(d*x+c)^5*sin(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{16 \, a b^{5} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}} + \frac{{\left(a b - 3 \, b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} - \frac{{\left(a b + 3 \, b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} + \frac{2 \, {\left(6 \, a b^{4} \sin\left(d x + c\right)^{4} - a^{4} b \sin\left(d x + c\right)^{3} - 2 \, a^{2} b^{3} \sin\left(d x + c\right)^{3} + 3 \, b^{5} \sin\left(d x + c\right)^{3} + 4 \, a^{3} b^{2} \sin\left(d x + c\right)^{2} - 16 \, a b^{4} \sin\left(d x + c\right)^{2} - a^{4} b \sin\left(d x + c\right) + 6 \, a^{2} b^{3} \sin\left(d x + c\right) - 5 \, b^{5} \sin\left(d x + c\right) + 2 \, a^{5} - 8 \, a^{3} b^{2} + 12 \, a b^{4}\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{16 \, d}"," ",0,"1/16*(16*a*b^5*log(abs(b*sin(d*x + c) + a))/(a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7) + (a*b - 3*b^2)*log(abs(sin(d*x + c) + 1))/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) - (a*b + 3*b^2)*log(abs(sin(d*x + c) - 1))/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) + 2*(6*a*b^4*sin(d*x + c)^4 - a^4*b*sin(d*x + c)^3 - 2*a^2*b^3*sin(d*x + c)^3 + 3*b^5*sin(d*x + c)^3 + 4*a^3*b^2*sin(d*x + c)^2 - 16*a*b^4*sin(d*x + c)^2 - a^4*b*sin(d*x + c) + 6*a^2*b^3*sin(d*x + c) - 5*b^5*sin(d*x + c) + 2*a^5 - 8*a^3*b^2 + 12*a*b^4)/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(sin(d*x + c)^2 - 1)^2))/d","A",0
1367,1,391,0,0.234435," ","integrate(csc(d*x+c)*sec(d*x+c)^5/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{16 \, b^{7} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{7} b - 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} - a b^{7}} - \frac{{\left(8 \, a^{2} - 21 \, a b + 15 \, b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} - \frac{{\left(8 \, a^{2} + 21 \, a b + 15 \, b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} + \frac{16 \, \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a} + \frac{2 \, {\left(6 \, a^{5} \sin\left(d x + c\right)^{4} - 18 \, a^{3} b^{2} \sin\left(d x + c\right)^{4} + 18 \, a b^{4} \sin\left(d x + c\right)^{4} + 3 \, a^{4} b \sin\left(d x + c\right)^{3} - 10 \, a^{2} b^{3} \sin\left(d x + c\right)^{3} + 7 \, b^{5} \sin\left(d x + c\right)^{3} - 16 \, a^{5} \sin\left(d x + c\right)^{2} + 48 \, a^{3} b^{2} \sin\left(d x + c\right)^{2} - 44 \, a b^{4} \sin\left(d x + c\right)^{2} - 5 \, a^{4} b \sin\left(d x + c\right) + 14 \, a^{2} b^{3} \sin\left(d x + c\right) - 9 \, b^{5} \sin\left(d x + c\right) + 12 \, a^{5} - 34 \, a^{3} b^{2} + 28 \, a b^{4}\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{16 \, d}"," ",0,"1/16*(16*b^7*log(abs(b*sin(d*x + c) + a))/(a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7) - (8*a^2 - 21*a*b + 15*b^2)*log(abs(sin(d*x + c) + 1))/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) - (8*a^2 + 21*a*b + 15*b^2)*log(abs(sin(d*x + c) - 1))/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) + 16*log(abs(sin(d*x + c)))/a + 2*(6*a^5*sin(d*x + c)^4 - 18*a^3*b^2*sin(d*x + c)^4 + 18*a*b^4*sin(d*x + c)^4 + 3*a^4*b*sin(d*x + c)^3 - 10*a^2*b^3*sin(d*x + c)^3 + 7*b^5*sin(d*x + c)^3 - 16*a^5*sin(d*x + c)^2 + 48*a^3*b^2*sin(d*x + c)^2 - 44*a*b^4*sin(d*x + c)^2 - 5*a^4*b*sin(d*x + c) + 14*a^2*b^3*sin(d*x + c) - 9*b^5*sin(d*x + c) + 12*a^5 - 34*a^3*b^2 + 28*a*b^4)/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(sin(d*x + c)^2 - 1)^2))/d","A",0
1368,1,418,0,0.245969," ","integrate(csc(d*x+c)^2*sec(d*x+c)^5/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{16 \, b^{8} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{8} b - 3 \, a^{6} b^{3} + 3 \, a^{4} b^{5} - a^{2} b^{7}} - \frac{{\left(15 \, a^{2} - 37 \, a b + 24 \, b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} + \frac{{\left(15 \, a^{2} + 37 \, a b + 24 \, b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} + \frac{16 \, b \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a^{2}} + \frac{2 \, {\left(6 \, a^{4} b \sin\left(d x + c\right)^{4} - 18 \, a^{2} b^{3} \sin\left(d x + c\right)^{4} + 18 \, b^{5} \sin\left(d x + c\right)^{4} + 7 \, a^{5} \sin\left(d x + c\right)^{3} - 18 \, a^{3} b^{2} \sin\left(d x + c\right)^{3} + 11 \, a b^{4} \sin\left(d x + c\right)^{3} - 16 \, a^{4} b \sin\left(d x + c\right)^{2} + 48 \, a^{2} b^{3} \sin\left(d x + c\right)^{2} - 44 \, b^{5} \sin\left(d x + c\right)^{2} - 9 \, a^{5} \sin\left(d x + c\right) + 22 \, a^{3} b^{2} \sin\left(d x + c\right) - 13 \, a b^{4} \sin\left(d x + c\right) + 12 \, a^{4} b - 34 \, a^{2} b^{3} + 28 \, b^{5}\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}} - \frac{16 \, {\left(b \sin\left(d x + c\right) - a\right)}}{a^{2} \sin\left(d x + c\right)}}{16 \, d}"," ",0,"-1/16*(16*b^8*log(abs(b*sin(d*x + c) + a))/(a^8*b - 3*a^6*b^3 + 3*a^4*b^5 - a^2*b^7) - (15*a^2 - 37*a*b + 24*b^2)*log(abs(sin(d*x + c) + 1))/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) + (15*a^2 + 37*a*b + 24*b^2)*log(abs(sin(d*x + c) - 1))/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) + 16*b*log(abs(sin(d*x + c)))/a^2 + 2*(6*a^4*b*sin(d*x + c)^4 - 18*a^2*b^3*sin(d*x + c)^4 + 18*b^5*sin(d*x + c)^4 + 7*a^5*sin(d*x + c)^3 - 18*a^3*b^2*sin(d*x + c)^3 + 11*a*b^4*sin(d*x + c)^3 - 16*a^4*b*sin(d*x + c)^2 + 48*a^2*b^3*sin(d*x + c)^2 - 44*b^5*sin(d*x + c)^2 - 9*a^5*sin(d*x + c) + 22*a^3*b^2*sin(d*x + c) - 13*a*b^4*sin(d*x + c) + 12*a^4*b - 34*a^2*b^3 + 28*b^5)/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(sin(d*x + c)^2 - 1)^2) - 16*(b*sin(d*x + c) - a)/(a^2*sin(d*x + c)))/d","A",0
1369,1,589,0,0.264911," ","integrate(csc(d*x+c)^3*sec(d*x+c)^5/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{16 \, b^{9} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{9} b - 3 \, a^{7} b^{3} + 3 \, a^{5} b^{5} - a^{3} b^{7}} - \frac{{\left(24 \, a^{2} - 57 \, a b + 35 \, b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} - \frac{{\left(24 \, a^{2} + 57 \, a b + 35 \, b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} + \frac{16 \, {\left(3 \, a^{2} + b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) \right|}\right)}{a^{3}} + \frac{2 \, {\left(4 \, b^{8} \sin\left(d x + c\right)^{6} + 15 \, a^{7} b \sin\left(d x + c\right)^{5} - 42 \, a^{5} b^{3} \sin\left(d x + c\right)^{5} + 35 \, a^{3} b^{5} \sin\left(d x + c\right)^{5} - 8 \, a b^{7} \sin\left(d x + c\right)^{5} - 12 \, a^{8} \sin\left(d x + c\right)^{4} + 32 \, a^{6} b^{2} \sin\left(d x + c\right)^{4} - 24 \, a^{4} b^{4} \sin\left(d x + c\right)^{4} + 4 \, a^{2} b^{6} \sin\left(d x + c\right)^{4} - 8 \, b^{8} \sin\left(d x + c\right)^{4} - 25 \, a^{7} b \sin\left(d x + c\right)^{3} + 70 \, a^{5} b^{3} \sin\left(d x + c\right)^{3} - 61 \, a^{3} b^{5} \sin\left(d x + c\right)^{3} + 16 \, a b^{7} \sin\left(d x + c\right)^{3} + 18 \, a^{8} \sin\left(d x + c\right)^{2} - 48 \, a^{6} b^{2} \sin\left(d x + c\right)^{2} + 38 \, a^{4} b^{4} \sin\left(d x + c\right)^{2} - 8 \, a^{2} b^{6} \sin\left(d x + c\right)^{2} + 4 \, b^{8} \sin\left(d x + c\right)^{2} + 8 \, a^{7} b \sin\left(d x + c\right) - 24 \, a^{5} b^{3} \sin\left(d x + c\right) + 24 \, a^{3} b^{5} \sin\left(d x + c\right) - 8 \, a b^{7} \sin\left(d x + c\right) - 4 \, a^{8} + 12 \, a^{6} b^{2} - 12 \, a^{4} b^{4} + 4 \, a^{2} b^{6}\right)}}{{\left(a^{9} - 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} - a^{3} b^{6}\right)} {\left(\sin\left(d x + c\right)^{3} - \sin\left(d x + c\right)\right)}^{2}}}{16 \, d}"," ",0,"1/16*(16*b^9*log(abs(b*sin(d*x + c) + a))/(a^9*b - 3*a^7*b^3 + 3*a^5*b^5 - a^3*b^7) - (24*a^2 - 57*a*b + 35*b^2)*log(abs(sin(d*x + c) + 1))/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) - (24*a^2 + 57*a*b + 35*b^2)*log(abs(sin(d*x + c) - 1))/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) + 16*(3*a^2 + b^2)*log(abs(sin(d*x + c)))/a^3 + 2*(4*b^8*sin(d*x + c)^6 + 15*a^7*b*sin(d*x + c)^5 - 42*a^5*b^3*sin(d*x + c)^5 + 35*a^3*b^5*sin(d*x + c)^5 - 8*a*b^7*sin(d*x + c)^5 - 12*a^8*sin(d*x + c)^4 + 32*a^6*b^2*sin(d*x + c)^4 - 24*a^4*b^4*sin(d*x + c)^4 + 4*a^2*b^6*sin(d*x + c)^4 - 8*b^8*sin(d*x + c)^4 - 25*a^7*b*sin(d*x + c)^3 + 70*a^5*b^3*sin(d*x + c)^3 - 61*a^3*b^5*sin(d*x + c)^3 + 16*a*b^7*sin(d*x + c)^3 + 18*a^8*sin(d*x + c)^2 - 48*a^6*b^2*sin(d*x + c)^2 + 38*a^4*b^4*sin(d*x + c)^2 - 8*a^2*b^6*sin(d*x + c)^2 + 4*b^8*sin(d*x + c)^2 + 8*a^7*b*sin(d*x + c) - 24*a^5*b^3*sin(d*x + c) + 24*a^3*b^5*sin(d*x + c) - 8*a*b^7*sin(d*x + c) - 4*a^8 + 12*a^6*b^2 - 12*a^4*b^4 + 4*a^2*b^6)/((a^9 - 3*a^7*b^2 + 3*a^5*b^4 - a^3*b^6)*(sin(d*x + c)^3 - sin(d*x + c))^2))/d","B",0
1370,0,0,0,0.000000," ","integrate(sin(f*x+e)^4*(g*cos(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\sqrt{g \cos\left(f x + e\right)} \sin\left(f x + e\right)^{4}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(sqrt(g*cos(f*x + e))*sin(f*x + e)^4/(b*sin(f*x + e) + a), x)","F",0
1371,0,0,0,0.000000," ","integrate(sin(f*x+e)^3*(g*cos(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\sqrt{g \cos\left(f x + e\right)} \sin\left(f x + e\right)^{3}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(sqrt(g*cos(f*x + e))*sin(f*x + e)^3/(b*sin(f*x + e) + a), x)","F",0
1372,0,0,0,0.000000," ","integrate(sin(f*x+e)^2*(g*cos(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\sqrt{g \cos\left(f x + e\right)} \sin\left(f x + e\right)^{2}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(sqrt(g*cos(f*x + e))*sin(f*x + e)^2/(b*sin(f*x + e) + a), x)","F",0
1373,0,0,0,0.000000," ","integrate(sin(f*x+e)*(g*cos(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\sqrt{g \cos\left(f x + e\right)} \sin\left(f x + e\right)}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(sqrt(g*cos(f*x + e))*sin(f*x + e)/(b*sin(f*x + e) + a), x)","F",0
1374,0,0,0,0.000000," ","integrate(csc(f*x+e)*(g*cos(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\sqrt{g \cos\left(f x + e\right)} \csc\left(f x + e\right)}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(sqrt(g*cos(f*x + e))*csc(f*x + e)/(b*sin(f*x + e) + a), x)","F",0
1375,0,0,0,0.000000," ","integrate(csc(f*x+e)^2*(g*cos(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\sqrt{g \cos\left(f x + e\right)} \csc\left(f x + e\right)^{2}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(sqrt(g*cos(f*x + e))*csc(f*x + e)^2/(b*sin(f*x + e) + a), x)","F",0
1376,0,0,0,0.000000," ","integrate(csc(f*x+e)^3*(g*cos(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\sqrt{g \cos\left(f x + e\right)} \csc\left(f x + e\right)^{3}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(sqrt(g*cos(f*x + e))*csc(f*x + e)^3/(b*sin(f*x + e) + a), x)","F",0
1377,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*sin(f*x+e)^3/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} \sin\left(f x + e\right)^{3}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*sin(f*x + e)^3/(b*sin(f*x + e) + a), x)","F",0
1378,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*sin(f*x+e)^2/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} \sin\left(f x + e\right)^{2}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*sin(f*x + e)^2/(b*sin(f*x + e) + a), x)","F",0
1379,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*sin(f*x+e)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} \sin\left(f x + e\right)}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*sin(f*x + e)/(b*sin(f*x + e) + a), x)","F",0
1380,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*csc(f*x+e)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} \csc\left(f x + e\right)}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*csc(f*x + e)/(b*sin(f*x + e) + a), x)","F",0
1381,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*csc(f*x+e)^2/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} \csc\left(f x + e\right)^{2}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*csc(f*x + e)^2/(b*sin(f*x + e) + a), x)","F",0
1382,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*csc(f*x+e)^3/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} \csc\left(f x + e\right)^{3}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*csc(f*x + e)^3/(b*sin(f*x + e) + a), x)","F",0
1383,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(5/2)*sin(f*x+e)^3/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{5}{2}} \sin\left(f x + e\right)^{3}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(5/2)*sin(f*x + e)^3/(b*sin(f*x + e) + a), x)","F",0
1384,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(5/2)*sin(f*x+e)^2/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(5/2)*sin(f*x + e)^2/(b*sin(f*x + e) + a), x)","F",0
1385,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(5/2)*sin(f*x+e)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{5}{2}} \sin\left(f x + e\right)}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(5/2)*sin(f*x + e)/(b*sin(f*x + e) + a), x)","F",0
1386,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(5/2)*csc(f*x+e)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{5}{2}} \csc\left(f x + e\right)}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(5/2)*csc(f*x + e)/(b*sin(f*x + e) + a), x)","F",0
1387,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(5/2)*csc(f*x+e)^2/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{5}{2}} \csc\left(f x + e\right)^{2}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(5/2)*csc(f*x + e)^2/(b*sin(f*x + e) + a), x)","F",0
1388,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(5/2)*csc(f*x+e)^3/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{5}{2}} \csc\left(f x + e\right)^{3}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(5/2)*csc(f*x + e)^3/(b*sin(f*x + e) + a), x)","F",0
1389,0,0,0,0.000000," ","integrate(sin(f*x+e)^4/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\sin\left(f x + e\right)^{4}}{\sqrt{g \cos\left(f x + e\right)} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(sin(f*x + e)^4/(sqrt(g*cos(f*x + e))*(b*sin(f*x + e) + a)), x)","F",0
1390,0,0,0,0.000000," ","integrate(sin(f*x+e)^3/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\sin\left(f x + e\right)^{3}}{\sqrt{g \cos\left(f x + e\right)} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(sin(f*x + e)^3/(sqrt(g*cos(f*x + e))*(b*sin(f*x + e) + a)), x)","F",0
1391,0,0,0,0.000000," ","integrate(sin(f*x+e)^2/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\sin\left(f x + e\right)^{2}}{\sqrt{g \cos\left(f x + e\right)} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(sin(f*x + e)^2/(sqrt(g*cos(f*x + e))*(b*sin(f*x + e) + a)), x)","F",0
1392,0,0,0,0.000000," ","integrate(sin(f*x+e)/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\sin\left(f x + e\right)}{\sqrt{g \cos\left(f x + e\right)} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(sin(f*x + e)/(sqrt(g*cos(f*x + e))*(b*sin(f*x + e) + a)), x)","F",0
1393,0,0,0,0.000000," ","integrate(csc(f*x+e)/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\csc\left(f x + e\right)}{\sqrt{g \cos\left(f x + e\right)} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(csc(f*x + e)/(sqrt(g*cos(f*x + e))*(b*sin(f*x + e) + a)), x)","F",0
1394,0,0,0,0.000000," ","integrate(csc(f*x+e)^2/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\csc\left(f x + e\right)^{2}}{\sqrt{g \cos\left(f x + e\right)} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(csc(f*x + e)^2/(sqrt(g*cos(f*x + e))*(b*sin(f*x + e) + a)), x)","F",0
1395,0,0,0,0.000000," ","integrate(csc(f*x+e)^3/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\csc\left(f x + e\right)^{3}}{\sqrt{g \cos\left(f x + e\right)} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(csc(f*x + e)^3/(sqrt(g*cos(f*x + e))*(b*sin(f*x + e) + a)), x)","F",0
1396,0,0,0,0.000000," ","integrate(sin(f*x+e)^4/(g*cos(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\sin\left(f x + e\right)^{4}}{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(sin(f*x + e)^4/((g*cos(f*x + e))^(3/2)*(b*sin(f*x + e) + a)), x)","F",0
1397,0,0,0,0.000000," ","integrate(sin(f*x+e)^3/(g*cos(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\sin\left(f x + e\right)^{3}}{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(sin(f*x + e)^3/((g*cos(f*x + e))^(3/2)*(b*sin(f*x + e) + a)), x)","F",0
1398,0,0,0,0.000000," ","integrate(sin(f*x+e)^2/(g*cos(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\sin\left(f x + e\right)^{2}}{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(sin(f*x + e)^2/((g*cos(f*x + e))^(3/2)*(b*sin(f*x + e) + a)), x)","F",0
1399,0,0,0,0.000000," ","integrate(sin(f*x+e)/(g*cos(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\sin\left(f x + e\right)}{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(sin(f*x + e)/((g*cos(f*x + e))^(3/2)*(b*sin(f*x + e) + a)), x)","F",0
1400,0,0,0,0.000000," ","integrate(csc(f*x+e)/(g*cos(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\csc\left(f x + e\right)}{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(csc(f*x + e)/((g*cos(f*x + e))^(3/2)*(b*sin(f*x + e) + a)), x)","F",0
1401,0,0,0,0.000000," ","integrate(csc(f*x+e)^2/(g*cos(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\csc\left(f x + e\right)^{2}}{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(csc(f*x + e)^2/((g*cos(f*x + e))^(3/2)*(b*sin(f*x + e) + a)), x)","F",0
1402,0,0,0,0.000000," ","integrate(sin(f*x+e)^4/(g*cos(f*x+e))^(5/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\sin\left(f x + e\right)^{4}}{\left(g \cos\left(f x + e\right)\right)^{\frac{5}{2}} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(sin(f*x + e)^4/((g*cos(f*x + e))^(5/2)*(b*sin(f*x + e) + a)), x)","F",0
1403,0,0,0,0.000000," ","integrate(sin(f*x+e)^3/(g*cos(f*x+e))^(5/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\sin\left(f x + e\right)^{3}}{\left(g \cos\left(f x + e\right)\right)^{\frac{5}{2}} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(sin(f*x + e)^3/((g*cos(f*x + e))^(5/2)*(b*sin(f*x + e) + a)), x)","F",0
1404,0,0,0,0.000000," ","integrate(sin(f*x+e)^2/(g*cos(f*x+e))^(5/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\sin\left(f x + e\right)^{2}}{\left(g \cos\left(f x + e\right)\right)^{\frac{5}{2}} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(sin(f*x + e)^2/((g*cos(f*x + e))^(5/2)*(b*sin(f*x + e) + a)), x)","F",0
1405,0,0,0,0.000000," ","integrate(sin(f*x+e)/(g*cos(f*x+e))^(5/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\sin\left(f x + e\right)}{\left(g \cos\left(f x + e\right)\right)^{\frac{5}{2}} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(sin(f*x + e)/((g*cos(f*x + e))^(5/2)*(b*sin(f*x + e) + a)), x)","F",0
1406,0,0,0,0.000000," ","integrate(csc(f*x+e)/(g*cos(f*x+e))^(5/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\csc\left(f x + e\right)}{\left(g \cos\left(f x + e\right)\right)^{\frac{5}{2}} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(csc(f*x + e)/((g*cos(f*x + e))^(5/2)*(b*sin(f*x + e) + a)), x)","F",0
1407,0,0,0,0.000000," ","integrate(csc(f*x+e)^2/(g*cos(f*x+e))^(5/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\csc\left(f x + e\right)^{2}}{\left(g \cos\left(f x + e\right)\right)^{\frac{5}{2}} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(csc(f*x + e)^2/((g*cos(f*x + e))^(5/2)*(b*sin(f*x + e) + a)), x)","F",0
1408,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^(5/2)*(g*cos(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\sqrt{g \cos\left(f x + e\right)} \left(d \sin\left(f x + e\right)\right)^{\frac{5}{2}}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(sqrt(g*cos(f*x + e))*(d*sin(f*x + e))^(5/2)/(b*sin(f*x + e) + a), x)","F",0
1409,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^(3/2)*(g*cos(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\sqrt{g \cos\left(f x + e\right)} \left(d \sin\left(f x + e\right)\right)^{\frac{3}{2}}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(sqrt(g*cos(f*x + e))*(d*sin(f*x + e))^(3/2)/(b*sin(f*x + e) + a), x)","F",0
1410,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^(1/2)*(g*cos(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\sqrt{g \cos\left(f x + e\right)} \sqrt{d \sin\left(f x + e\right)}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(sqrt(g*cos(f*x + e))*sqrt(d*sin(f*x + e))/(b*sin(f*x + e) + a), x)","F",0
1411,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(1/2)/(d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\sqrt{g \cos\left(f x + e\right)}}{{\left(b \sin\left(f x + e\right) + a\right)} \sqrt{d \sin\left(f x + e\right)}}\,{d x}"," ",0,"integrate(sqrt(g*cos(f*x + e))/((b*sin(f*x + e) + a)*sqrt(d*sin(f*x + e))), x)","F",0
1412,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(1/2)/(d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\sqrt{g \cos\left(f x + e\right)}}{{\left(b \sin\left(f x + e\right) + a\right)} \left(d \sin\left(f x + e\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(g*cos(f*x + e))/((b*sin(f*x + e) + a)*(d*sin(f*x + e))^(3/2)), x)","F",0
1413,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(1/2)/(d*sin(f*x+e))^(5/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\sqrt{g \cos\left(f x + e\right)}}{{\left(b \sin\left(f x + e\right) + a\right)} \left(d \sin\left(f x + e\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(g*cos(f*x + e))/((b*sin(f*x + e) + a)*(d*sin(f*x + e))^(5/2)), x)","F",0
1414,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(1/2)/(d*sin(f*x+e))^(7/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\sqrt{g \cos\left(f x + e\right)}}{{\left(b \sin\left(f x + e\right) + a\right)} \left(d \sin\left(f x + e\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sqrt(g*cos(f*x + e))/((b*sin(f*x + e) + a)*(d*sin(f*x + e))^(7/2)), x)","F",0
1415,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(1/2)/(d*sin(f*x+e))^(9/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\sqrt{g \cos\left(f x + e\right)}}{{\left(b \sin\left(f x + e\right) + a\right)} \left(d \sin\left(f x + e\right)\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate(sqrt(g*cos(f*x + e))/((b*sin(f*x + e) + a)*(d*sin(f*x + e))^(9/2)), x)","F",0
1416,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} \left(d \sin\left(f x + e\right)\right)^{\frac{3}{2}}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(d*sin(f*x + e))^(3/2)/(b*sin(f*x + e) + a), x)","F",0
1417,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} \sqrt{d \sin\left(f x + e\right)}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*sqrt(d*sin(f*x + e))/(b*sin(f*x + e) + a), x)","F",0
1418,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)/(d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}}}{{\left(b \sin\left(f x + e\right) + a\right)} \sqrt{d \sin\left(f x + e\right)}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)/((b*sin(f*x + e) + a)*sqrt(d*sin(f*x + e))), x)","F",0
1419,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)/(d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}}}{{\left(b \sin\left(f x + e\right) + a\right)} \left(d \sin\left(f x + e\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)/((b*sin(f*x + e) + a)*(d*sin(f*x + e))^(3/2)), x)","F",0
1420,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)/(d*sin(f*x+e))^(5/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}}}{{\left(b \sin\left(f x + e\right) + a\right)} \left(d \sin\left(f x + e\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)/((b*sin(f*x + e) + a)*(d*sin(f*x + e))^(5/2)), x)","F",0
1421,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)/(d*sin(f*x+e))^(7/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}}}{{\left(b \sin\left(f x + e\right) + a\right)} \left(d \sin\left(f x + e\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)/((b*sin(f*x + e) + a)*(d*sin(f*x + e))^(7/2)), x)","F",0
1422,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)/(d*sin(f*x+e))^(9/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}}}{{\left(b \sin\left(f x + e\right) + a\right)} \left(d \sin\left(f x + e\right)\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)/((b*sin(f*x + e) + a)*(d*sin(f*x + e))^(9/2)), x)","F",0
1423,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(5/2)*(d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{5}{2}} \sqrt{d \sin\left(f x + e\right)}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(5/2)*sqrt(d*sin(f*x + e))/(b*sin(f*x + e) + a), x)","F",0
1424,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(5/2)/(d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{5}{2}}}{{\left(b \sin\left(f x + e\right) + a\right)} \sqrt{d \sin\left(f x + e\right)}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(5/2)/((b*sin(f*x + e) + a)*sqrt(d*sin(f*x + e))), x)","F",0
1425,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(5/2)/(d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{5}{2}}}{{\left(b \sin\left(f x + e\right) + a\right)} \left(d \sin\left(f x + e\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(5/2)/((b*sin(f*x + e) + a)*(d*sin(f*x + e))^(3/2)), x)","F",0
1426,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(5/2)/(d*sin(f*x+e))^(5/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{5}{2}}}{{\left(b \sin\left(f x + e\right) + a\right)} \left(d \sin\left(f x + e\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(5/2)/((b*sin(f*x + e) + a)*(d*sin(f*x + e))^(5/2)), x)","F",0
1427,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(5/2)/(d*sin(f*x+e))^(7/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{5}{2}}}{{\left(b \sin\left(f x + e\right) + a\right)} \left(d \sin\left(f x + e\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(5/2)/((b*sin(f*x + e) + a)*(d*sin(f*x + e))^(7/2)), x)","F",0
1428,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(5/2)/(d*sin(f*x+e))^(9/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{5}{2}}}{{\left(b \sin\left(f x + e\right) + a\right)} \left(d \sin\left(f x + e\right)\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(5/2)/((b*sin(f*x + e) + a)*(d*sin(f*x + e))^(9/2)), x)","F",0
1429,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(5/2)/(d*sin(f*x+e))^(11/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{5}{2}}}{{\left(b \sin\left(f x + e\right) + a\right)} \left(d \sin\left(f x + e\right)\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(5/2)/((b*sin(f*x + e) + a)*(d*sin(f*x + e))^(11/2)), x)","F",0
1430,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^(5/2)/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\left(d \sin\left(f x + e\right)\right)^{\frac{5}{2}}}{\sqrt{g \cos\left(f x + e\right)} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate((d*sin(f*x + e))^(5/2)/(sqrt(g*cos(f*x + e))*(b*sin(f*x + e) + a)), x)","F",0
1431,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\left(d \sin\left(f x + e\right)\right)^{\frac{3}{2}}}{\sqrt{g \cos\left(f x + e\right)} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate((d*sin(f*x + e))^(3/2)/(sqrt(g*cos(f*x + e))*(b*sin(f*x + e) + a)), x)","F",0
1432,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{d \sin\left(f x + e\right)}}{\sqrt{g \cos\left(f x + e\right)} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(sqrt(d*sin(f*x + e))/(sqrt(g*cos(f*x + e))*(b*sin(f*x + e) + a)), x)","F",0
1433,0,0,0,0.000000," ","integrate(1/(d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{g \cos\left(f x + e\right)} {\left(b \sin\left(f x + e\right) + a\right)} \sqrt{d \sin\left(f x + e\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(g*cos(f*x + e))*(b*sin(f*x + e) + a)*sqrt(d*sin(f*x + e))), x)","F",0
1434,0,0,0,0.000000," ","integrate(1/(d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{g \cos\left(f x + e\right)} {\left(b \sin\left(f x + e\right) + a\right)} \left(d \sin\left(f x + e\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(g*cos(f*x + e))*(b*sin(f*x + e) + a)*(d*sin(f*x + e))^(3/2)), x)","F",0
1435,0,0,0,0.000000," ","integrate(1/(d*sin(f*x+e))^(5/2)/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{g \cos\left(f x + e\right)} {\left(b \sin\left(f x + e\right) + a\right)} \left(d \sin\left(f x + e\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(g*cos(f*x + e))*(b*sin(f*x + e) + a)*(d*sin(f*x + e))^(5/2)), x)","F",0
1436,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^(5/2)/(g*cos(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(d \sin\left(f x + e\right)\right)^{\frac{5}{2}}}{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate((d*sin(f*x + e))^(5/2)/((g*cos(f*x + e))^(3/2)*(b*sin(f*x + e) + a)), x)","F",0
1437,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^(3/2)/(g*cos(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(d \sin\left(f x + e\right)\right)^{\frac{3}{2}}}{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate((d*sin(f*x + e))^(3/2)/((g*cos(f*x + e))^(3/2)*(b*sin(f*x + e) + a)), x)","F",0
1438,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^(1/2)/(g*cos(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\sqrt{d \sin\left(f x + e\right)}}{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(sqrt(d*sin(f*x + e))/((g*cos(f*x + e))^(3/2)*(b*sin(f*x + e) + a)), x)","F",0
1439,0,0,0,0.000000," ","integrate(1/(g*cos(f*x+e))^(3/2)/(d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{1}{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(b \sin\left(f x + e\right) + a\right)} \sqrt{d \sin\left(f x + e\right)}}\,{d x}"," ",0,"integrate(1/((g*cos(f*x + e))^(3/2)*(b*sin(f*x + e) + a)*sqrt(d*sin(f*x + e))), x)","F",0
1440,0,0,0,0.000000," ","integrate(1/(g*cos(f*x+e))^(3/2)/(d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{1}{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(b \sin\left(f x + e\right) + a\right)} \left(d \sin\left(f x + e\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((g*cos(f*x + e))^(3/2)*(b*sin(f*x + e) + a)*(d*sin(f*x + e))^(3/2)), x)","F",0
1441,0,0,0,0.000000," ","integrate(1/(g*cos(f*x+e))^(3/2)/(d*sin(f*x+e))^(5/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{1}{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(b \sin\left(f x + e\right) + a\right)} \left(d \sin\left(f x + e\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((g*cos(f*x + e))^(3/2)*(b*sin(f*x + e) + a)*(d*sin(f*x + e))^(5/2)), x)","F",0
1442,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)/(a+b*sin(f*x+e))^2/(d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}}}{{\left(b \sin\left(f x + e\right) + a\right)}^{2} \sqrt{d \sin\left(f x + e\right)}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)/((b*sin(f*x + e) + a)^2*sqrt(d*sin(f*x + e))), x)","F",0
1443,1,119,0,0.213964," ","integrate(sec(d*x+c)^2*sin(d*x+c)^4*(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{9 \, {\left(d x + c\right)} a + \frac{12 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} + \frac{2 \, {\left(3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 24 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 10 \, b\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"-1/6*(9*(d*x + c)*a + 12*(a*tan(1/2*d*x + 1/2*c) + b)/(tan(1/2*d*x + 1/2*c)^2 - 1) + 2*(3*a*tan(1/2*d*x + 1/2*c)^5 - 6*b*tan(1/2*d*x + 1/2*c)^4 - 24*b*tan(1/2*d*x + 1/2*c)^2 - 3*a*tan(1/2*d*x + 1/2*c) - 10*b)/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
1444,1,104,0,0.182055," ","integrate(sec(d*x+c)^2*sin(d*x+c)^3*(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{3 \, {\left(d x + c\right)} b + \frac{4 \, {\left(b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} + \frac{2 \, {\left(b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, a\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"-1/2*(3*(d*x + c)*b + 4*(b*tan(1/2*d*x + 1/2*c) + a)/(tan(1/2*d*x + 1/2*c)^2 - 1) + 2*(b*tan(1/2*d*x + 1/2*c)^3 - 2*a*tan(1/2*d*x + 1/2*c)^2 - b*tan(1/2*d*x + 1/2*c) - 2*a)/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","A",0
1445,1,58,0,0.174093," ","integrate(sec(d*x+c)^2*sin(d*x+c)^2*(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{{\left(d x + c\right)} a + \frac{2 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, b\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1}}{d}"," ",0,"-((d*x + c)*a + 2*(a*tan(1/2*d*x + 1/2*c)^3 + a*tan(1/2*d*x + 1/2*c) + 2*b)/(tan(1/2*d*x + 1/2*c)^4 - 1))/d","A",0
1446,1,43,0,0.168213," ","integrate(sec(d*x+c)^2*sin(d*x+c)*(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{{\left(d x + c\right)} b + \frac{2 \, {\left(b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1}}{d}"," ",0,"-((d*x + c)*b + 2*(b*tan(1/2*d*x + 1/2*c) + a)/(tan(1/2*d*x + 1/2*c)^2 - 1))/d","A",0
1447,1,48,0,0.201460," ","integrate(csc(d*x+c)*sec(d*x+c)^2*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{2 \, {\left(b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1}}{d}"," ",0,"(a*log(abs(tan(1/2*d*x + 1/2*c))) - 2*(b*tan(1/2*d*x + 1/2*c) + a)/(tan(1/2*d*x + 1/2*c)^2 - 1))/d","A",0
1448,1,103,0,0.202338," ","integrate(csc(d*x+c)^2*sec(d*x+c)^2*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{6 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 10 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}}{6 \, d}"," ",0,"1/6*(6*b*log(abs(tan(1/2*d*x + 1/2*c))) + 3*a*tan(1/2*d*x + 1/2*c) - (2*b*tan(1/2*d*x + 1/2*c)^3 + 15*a*tan(1/2*d*x + 1/2*c)^2 + 10*b*tan(1/2*d*x + 1/2*c) - 3*a)/(tan(1/2*d*x + 1/2*c)^3 - tan(1/2*d*x + 1/2*c)))/d","B",0
1449,1,116,0,0.203475," ","integrate(csc(d*x+c)^3*sec(d*x+c)^2*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 4 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{16 \, {\left(b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} - \frac{18 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 4 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}}{8 \, d}"," ",0,"1/8*(a*tan(1/2*d*x + 1/2*c)^2 + 12*a*log(abs(tan(1/2*d*x + 1/2*c))) + 4*b*tan(1/2*d*x + 1/2*c) - 16*(b*tan(1/2*d*x + 1/2*c) + a)/(tan(1/2*d*x + 1/2*c)^2 - 1) - (18*a*tan(1/2*d*x + 1/2*c)^2 + 4*b*tan(1/2*d*x + 1/2*c) + a)/tan(1/2*d*x + 1/2*c)^2)/d","A",0
1450,1,172,0,0.224334," ","integrate(sec(d*x+c)^2*sin(d*x+c)^3*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{9 \, {\left(d x + c\right)} a b + \frac{6 \, {\left(2 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} + b^{2}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} + \frac{2 \, {\left(3 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 3 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 6 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a^{2} - 5 \, b^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{3 \, d}"," ",0,"-1/3*(9*(d*x + c)*a*b + 6*(2*a*b*tan(1/2*d*x + 1/2*c) + a^2 + b^2)/(tan(1/2*d*x + 1/2*c)^2 - 1) + 2*(3*a*b*tan(1/2*d*x + 1/2*c)^5 - 3*a^2*tan(1/2*d*x + 1/2*c)^4 - 3*b^2*tan(1/2*d*x + 1/2*c)^4 - 6*a^2*tan(1/2*d*x + 1/2*c)^2 - 12*b^2*tan(1/2*d*x + 1/2*c)^2 - 3*a*b*tan(1/2*d*x + 1/2*c) - 3*a^2 - 5*b^2)/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
1451,1,137,0,0.213848," ","integrate(sec(d*x+c)^2*sin(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{{\left(2 \, a^{2} + 3 \, b^{2}\right)} {\left(d x + c\right)} + \frac{4 \, {\left(a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, a b\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} + \frac{2 \, {\left(b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, a b\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"-1/2*((2*a^2 + 3*b^2)*(d*x + c) + 4*(a^2*tan(1/2*d*x + 1/2*c) + b^2*tan(1/2*d*x + 1/2*c) + 2*a*b)/(tan(1/2*d*x + 1/2*c)^2 - 1) + 2*(b^2*tan(1/2*d*x + 1/2*c)^3 - 4*a*b*tan(1/2*d*x + 1/2*c)^2 - b^2*tan(1/2*d*x + 1/2*c) - 4*a*b)/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","A",0
1452,1,82,0,0.172891," ","integrate(sec(d*x+c)^2*sin(d*x+c)*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{2 \, {\left({\left(d x + c\right)} a b + \frac{2 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} + 2 \, b^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1}\right)}}{d}"," ",0,"-2*((d*x + c)*a*b + (2*a*b*tan(1/2*d*x + 1/2*c)^3 + a^2*tan(1/2*d*x + 1/2*c)^2 + 2*a*b*tan(1/2*d*x + 1/2*c) + a^2 + 2*b^2)/(tan(1/2*d*x + 1/2*c)^4 - 1))/d","A",0
1453,1,57,0,0.212184," ","integrate(csc(d*x+c)*sec(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{2 \, {\left(2 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} + b^{2}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1}}{d}"," ",0,"(a^2*log(abs(tan(1/2*d*x + 1/2*c))) - 2*(2*a*b*tan(1/2*d*x + 1/2*c) + a^2 + b^2)/(tan(1/2*d*x + 1/2*c)^2 - 1))/d","A",0
1454,1,128,0,0.207188," ","integrate(csc(d*x+c)^2*sec(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{12 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{4 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 20 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}}{6 \, d}"," ",0,"1/6*(12*a*b*log(abs(tan(1/2*d*x + 1/2*c))) + 3*a^2*tan(1/2*d*x + 1/2*c) - (4*a*b*tan(1/2*d*x + 1/2*c)^3 + 15*a^2*tan(1/2*d*x + 1/2*c)^2 + 12*b^2*tan(1/2*d*x + 1/2*c)^2 + 20*a*b*tan(1/2*d*x + 1/2*c) - 3*a^2)/(tan(1/2*d*x + 1/2*c)^3 - tan(1/2*d*x + 1/2*c)))/d","B",0
1455,1,157,0,0.229233," ","integrate(csc(d*x+c)^3*sec(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 8 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, {\left(3 \, a^{2} + 2 \, b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{16 \, {\left(2 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} + b^{2}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} - \frac{18 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 8 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}}{8 \, d}"," ",0,"1/8*(a^2*tan(1/2*d*x + 1/2*c)^2 + 8*a*b*tan(1/2*d*x + 1/2*c) + 4*(3*a^2 + 2*b^2)*log(abs(tan(1/2*d*x + 1/2*c))) - 16*(2*a*b*tan(1/2*d*x + 1/2*c) + a^2 + b^2)/(tan(1/2*d*x + 1/2*c)^2 - 1) - (18*a^2*tan(1/2*d*x + 1/2*c)^2 + 12*b^2*tan(1/2*d*x + 1/2*c)^2 + 8*a*b*tan(1/2*d*x + 1/2*c) + a^2)/tan(1/2*d*x + 1/2*c)^2)/d","A",0
1456,1,204,0,0.244110," ","integrate(csc(d*x+c)^4*sec(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 72 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 21 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{48 \, {\left(a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, a b\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} - \frac{132 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 21 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 6 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{24 \, d}"," ",0,"1/24*(a^2*tan(1/2*d*x + 1/2*c)^3 + 6*a*b*tan(1/2*d*x + 1/2*c)^2 + 72*a*b*log(abs(tan(1/2*d*x + 1/2*c))) + 21*a^2*tan(1/2*d*x + 1/2*c) + 12*b^2*tan(1/2*d*x + 1/2*c) - 48*(a^2*tan(1/2*d*x + 1/2*c) + b^2*tan(1/2*d*x + 1/2*c) + 2*a*b)/(tan(1/2*d*x + 1/2*c)^2 - 1) - (132*a*b*tan(1/2*d*x + 1/2*c)^3 + 21*a^2*tan(1/2*d*x + 1/2*c)^2 + 12*b^2*tan(1/2*d*x + 1/2*c)^2 + 6*a*b*tan(1/2*d*x + 1/2*c) + a^2)/tan(1/2*d*x + 1/2*c)^3)/d","A",0
1457,1,336,0,0.235467," ","integrate(sec(d*x+c)^2*sin(d*x+c)^3*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{3 \, {\left(12 \, a^{2} b + 5 \, b^{3}\right)} {\left(d x + c\right)} + \frac{16 \, {\left(3 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3} + 3 \, a b^{2}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} + \frac{2 \, {\left(12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 7 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 8 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 24 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 15 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 24 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 120 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 136 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 7 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, a^{3} - 40 \, a b^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{4}}}{8 \, d}"," ",0,"-1/8*(3*(12*a^2*b + 5*b^3)*(d*x + c) + 16*(3*a^2*b*tan(1/2*d*x + 1/2*c) + b^3*tan(1/2*d*x + 1/2*c) + a^3 + 3*a*b^2)/(tan(1/2*d*x + 1/2*c)^2 - 1) + 2*(12*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 7*b^3*tan(1/2*d*x + 1/2*c)^7 - 8*a^3*tan(1/2*d*x + 1/2*c)^6 - 24*a*b^2*tan(1/2*d*x + 1/2*c)^6 + 12*a^2*b*tan(1/2*d*x + 1/2*c)^5 + 15*b^3*tan(1/2*d*x + 1/2*c)^5 - 24*a^3*tan(1/2*d*x + 1/2*c)^4 - 120*a*b^2*tan(1/2*d*x + 1/2*c)^4 - 12*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 15*b^3*tan(1/2*d*x + 1/2*c)^3 - 24*a^3*tan(1/2*d*x + 1/2*c)^2 - 136*a*b^2*tan(1/2*d*x + 1/2*c)^2 - 12*a^2*b*tan(1/2*d*x + 1/2*c) - 7*b^3*tan(1/2*d*x + 1/2*c) - 8*a^3 - 40*a*b^2)/(tan(1/2*d*x + 1/2*c)^2 + 1)^4)/d","A",0
1458,1,207,0,0.204323," ","integrate(sec(d*x+c)^2*sin(d*x+c)^2*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{3 \, {\left(2 \, a^{3} + 9 \, a b^{2}\right)} {\left(d x + c\right)} + \frac{12 \, {\left(a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a^{2} b + b^{3}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} + \frac{2 \, {\left(9 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 6 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 36 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 24 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 18 \, a^{2} b - 10 \, b^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"-1/6*(3*(2*a^3 + 9*a*b^2)*(d*x + c) + 12*(a^3*tan(1/2*d*x + 1/2*c) + 3*a*b^2*tan(1/2*d*x + 1/2*c) + 3*a^2*b + b^3)/(tan(1/2*d*x + 1/2*c)^2 - 1) + 2*(9*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 18*a^2*b*tan(1/2*d*x + 1/2*c)^4 - 6*b^3*tan(1/2*d*x + 1/2*c)^4 - 36*a^2*b*tan(1/2*d*x + 1/2*c)^2 - 24*b^3*tan(1/2*d*x + 1/2*c)^2 - 9*a*b^2*tan(1/2*d*x + 1/2*c) - 18*a^2*b - 10*b^3)/(tan(1/2*d*x + 1/2*c)^2 + 1)^3)/d","A",0
1459,1,148,0,0.198027," ","integrate(sec(d*x+c)^2*sin(d*x+c)*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{3 \, {\left(2 \, a^{2} b + b^{3}\right)} {\left(d x + c\right)} + \frac{4 \, {\left(3 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3} + 3 \, a b^{2}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} + \frac{2 \, {\left(b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, a b^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}}}{2 \, d}"," ",0,"-1/2*(3*(2*a^2*b + b^3)*(d*x + c) + 4*(3*a^2*b*tan(1/2*d*x + 1/2*c) + b^3*tan(1/2*d*x + 1/2*c) + a^3 + 3*a*b^2)/(tan(1/2*d*x + 1/2*c)^2 - 1) + 2*(b^3*tan(1/2*d*x + 1/2*c)^3 - 6*a*b^2*tan(1/2*d*x + 1/2*c)^2 - b^3*tan(1/2*d*x + 1/2*c) - 6*a*b^2)/(tan(1/2*d*x + 1/2*c)^2 + 1)^2)/d","B",0
1460,1,86,0,0.210539," ","integrate(csc(d*x+c)*sec(d*x+c)^2*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{{\left(d x + c\right)} b^{3} - a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + \frac{2 \, {\left(3 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3} + 3 \, a b^{2}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1}}{d}"," ",0,"-((d*x + c)*b^3 - a^3*log(abs(tan(1/2*d*x + 1/2*c))) + 2*(3*a^2*b*tan(1/2*d*x + 1/2*c) + b^3*tan(1/2*d*x + 1/2*c) + a^3 + 3*a*b^2)/(tan(1/2*d*x + 1/2*c)^2 - 1))/d","A",0
1461,1,148,0,0.219772," ","integrate(csc(d*x+c)^2*sec(d*x+c)^2*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{6 \, a^{2} b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{2 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 10 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}}{2 \, d}"," ",0,"1/2*(6*a^2*b*log(abs(tan(1/2*d*x + 1/2*c))) + a^3*tan(1/2*d*x + 1/2*c) - (2*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 5*a^3*tan(1/2*d*x + 1/2*c)^2 + 12*a*b^2*tan(1/2*d*x + 1/2*c)^2 + 10*a^2*b*tan(1/2*d*x + 1/2*c) + 4*b^3*tan(1/2*d*x + 1/2*c) - a^3)/(tan(1/2*d*x + 1/2*c)^3 - tan(1/2*d*x + 1/2*c)))/d","A",0
1462,1,179,0,0.257167," ","integrate(csc(d*x+c)^3*sec(d*x+c)^2*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, {\left(a^{3} + 2 \, a b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{16 \, {\left(3 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3} + 3 \, a b^{2}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} - \frac{18 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 36 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}}{8 \, d}"," ",0,"1/8*(a^3*tan(1/2*d*x + 1/2*c)^2 + 12*a^2*b*tan(1/2*d*x + 1/2*c) + 12*(a^3 + 2*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c))) - 16*(3*a^2*b*tan(1/2*d*x + 1/2*c) + b^3*tan(1/2*d*x + 1/2*c) + a^3 + 3*a*b^2)/(tan(1/2*d*x + 1/2*c)^2 - 1) - (18*a^3*tan(1/2*d*x + 1/2*c)^2 + 36*a*b^2*tan(1/2*d*x + 1/2*c)^2 + 12*a^2*b*tan(1/2*d*x + 1/2*c) + a^3)/tan(1/2*d*x + 1/2*c)^2)/d","A",0
1463,1,245,0,0.274805," ","integrate(csc(d*x+c)^4*sec(d*x+c)^2*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 9 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 21 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, {\left(9 \, a^{2} b + 2 \, b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{48 \, {\left(a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a^{2} b + b^{3}\right)}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} - \frac{198 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 44 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 21 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 36 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 9 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{24 \, d}"," ",0,"1/24*(a^3*tan(1/2*d*x + 1/2*c)^3 + 9*a^2*b*tan(1/2*d*x + 1/2*c)^2 + 21*a^3*tan(1/2*d*x + 1/2*c) + 36*a*b^2*tan(1/2*d*x + 1/2*c) + 12*(9*a^2*b + 2*b^3)*log(abs(tan(1/2*d*x + 1/2*c))) - 48*(a^3*tan(1/2*d*x + 1/2*c) + 3*a*b^2*tan(1/2*d*x + 1/2*c) + 3*a^2*b + b^3)/(tan(1/2*d*x + 1/2*c)^2 - 1) - (198*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 44*b^3*tan(1/2*d*x + 1/2*c)^3 + 21*a^3*tan(1/2*d*x + 1/2*c)^2 + 36*a*b^2*tan(1/2*d*x + 1/2*c)^2 + 9*a^2*b*tan(1/2*d*x + 1/2*c) + a^3)/tan(1/2*d*x + 1/2*c)^3)/d","A",0
1464,1,264,0,0.268946," ","integrate(sec(d*x+c)^2*sin(d*x+c)^4/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(a^{5} - 4 \, a^{3} b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} \sqrt{a^{2} - b^{2}}} - \frac{2 \, {\left(2 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{4} - 2 \, a^{2} b^{2}\right)}}{{\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a\right)}} - \frac{d x + c}{b^{2}}}{d}"," ",0,"(2*(a^5 - 4*a^3*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/((a^4*b^2 - 2*a^2*b^4 + b^6)*sqrt(a^2 - b^2)) - 2*(2*a^3*b*tan(1/2*d*x + 1/2*c)^3 + a*b^3*tan(1/2*d*x + 1/2*c)^3 + a^4*tan(1/2*d*x + 1/2*c)^2 + 2*b^4*tan(1/2*d*x + 1/2*c)^2 - 3*a*b^3*tan(1/2*d*x + 1/2*c) - a^4 - 2*a^2*b^2)/((a^4*b - 2*a^2*b^3 + b^5)*(a*tan(1/2*d*x + 1/2*c)^4 + 2*b*tan(1/2*d*x + 1/2*c)^3 - 2*b*tan(1/2*d*x + 1/2*c) - a)) - (d*x + c)/b^2)/d","A",0
1465,1,222,0,0.237528," ","integrate(sec(d*x+c)^2*sin(d*x+c)^3/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{3 \, {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} a^{2} b}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} - b^{2}}} + \frac{3 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, a^{3} - a b^{2}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a\right)} {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)}}\right)}}{d}"," ",0,"2*(3*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))*a^2*b/((a^4 - 2*a^2*b^2 + b^4)*sqrt(a^2 - b^2)) + (3*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 3*a*b^2*tan(1/2*d*x + 1/2*c)^2 - a^2*b*tan(1/2*d*x + 1/2*c) - 2*b^3*tan(1/2*d*x + 1/2*c) - 2*a^3 - a*b^2)/((a*tan(1/2*d*x + 1/2*c)^4 + 2*b*tan(1/2*d*x + 1/2*c)^3 - 2*b*tan(1/2*d*x + 1/2*c) - a)*(a^4 - 2*a^2*b^2 + b^4)))/d","A",0
1466,1,251,0,0.235400," ","integrate(sec(d*x+c)^2*sin(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{{\left(a^{3} + 2 \, a b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} - b^{2}}} + \frac{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a^{2} b}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a\right)} {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)}}\right)}}{d}"," ",0,"-2*((a^3 + 2*a*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/((a^4 - 2*a^2*b^2 + b^4)*sqrt(a^2 - b^2)) + (a^3*tan(1/2*d*x + 1/2*c)^3 + 2*a*b^2*tan(1/2*d*x + 1/2*c)^3 + a^2*b*tan(1/2*d*x + 1/2*c)^2 + 2*b^3*tan(1/2*d*x + 1/2*c)^2 + a^3*tan(1/2*d*x + 1/2*c) - 4*a*b^2*tan(1/2*d*x + 1/2*c) - 3*a^2*b)/((a*tan(1/2*d*x + 1/2*c)^4 + 2*b*tan(1/2*d*x + 1/2*c)^3 - 2*b*tan(1/2*d*x + 1/2*c) - a)*(a^4 - 2*a^2*b^2 + b^4)))/d","A",0
1467,1,243,0,0.224492," ","integrate(sec(d*x+c)^2*sin(d*x+c)/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{{\left(2 \, a^{2} b + b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} - b^{2}}} + \frac{2 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 4 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{3} - 2 \, a b^{2}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a\right)} {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)}}\right)}}{d}"," ",0,"2*((2*a^2*b + b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/((a^4 - 2*a^2*b^2 + b^4)*sqrt(a^2 - b^2)) + (2*a^2*b*tan(1/2*d*x + 1/2*c)^3 + b^3*tan(1/2*d*x + 1/2*c)^3 - a^3*tan(1/2*d*x + 1/2*c)^2 + 4*a*b^2*tan(1/2*d*x + 1/2*c)^2 - 3*b^3*tan(1/2*d*x + 1/2*c) - a^3 - 2*a*b^2)/((a*tan(1/2*d*x + 1/2*c)^4 + 2*b*tan(1/2*d*x + 1/2*c)^3 - 2*b*tan(1/2*d*x + 1/2*c) - a)*(a^4 - 2*a^2*b^2 + b^4)))/d","A",0
1468,1,314,0,0.236696," ","integrate(csc(d*x+c)*sec(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(4 \, a^{2} b^{3} - b^{5}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} \sqrt{a^{2} - b^{2}}} + \frac{2 \, {\left(2 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{5} - a^{3} b^{2} - a b^{4}\right)}}{{\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a\right)}} + \frac{\log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{2}}}{d}"," ",0,"(2*(4*a^2*b^3 - b^5)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/((a^6 - 2*a^4*b^2 + a^2*b^4)*sqrt(a^2 - b^2)) + 2*(2*a^4*b*tan(1/2*d*x + 1/2*c)^3 + b^5*tan(1/2*d*x + 1/2*c)^3 - a^5*tan(1/2*d*x + 1/2*c)^2 + 3*a^3*b^2*tan(1/2*d*x + 1/2*c)^2 + a*b^4*tan(1/2*d*x + 1/2*c)^2 - 2*a^2*b^3*tan(1/2*d*x + 1/2*c) - b^5*tan(1/2*d*x + 1/2*c) - a^5 - a^3*b^2 - a*b^4)/((a^6 - 2*a^4*b^2 + a^2*b^4)*(a*tan(1/2*d*x + 1/2*c)^4 + 2*b*tan(1/2*d*x + 1/2*c)^3 - 2*b*tan(1/2*d*x + 1/2*c) - a)) + log(abs(tan(1/2*d*x + 1/2*c)))/a^2)/d","A",0
1469,1,523,0,0.256291," ","integrate(csc(d*x+c)^2*sec(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{20 \, {\left(5 \, a^{2} b^{4} - 2 \, b^{6}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} \sqrt{a^{2} - b^{2}}} - \frac{4 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 8 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 25 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 2 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 21 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 12 \, b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 10 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 20 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 30 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 20 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 52 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 16 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 46 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 26 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, a^{6} - 10 \, a^{4} b^{2} + 5 \, a^{2} b^{4}}{{\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}} + \frac{20 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}} - \frac{5 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{2}}}{10 \, d}"," ",0,"-1/10*(20*(5*a^2*b^4 - 2*b^6)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/((a^7 - 2*a^5*b^2 + a^3*b^4)*sqrt(a^2 - b^2)) - (4*a^5*b*tan(1/2*d*x + 1/2*c)^5 - 8*a^3*b^3*tan(1/2*d*x + 1/2*c)^5 + 4*a*b^5*tan(1/2*d*x + 1/2*c)^5 - 25*a^6*tan(1/2*d*x + 1/2*c)^4 - 2*a^4*b^2*tan(1/2*d*x + 1/2*c)^4 - 21*a^2*b^4*tan(1/2*d*x + 1/2*c)^4 - 12*b^6*tan(1/2*d*x + 1/2*c)^4 - 10*a^5*b*tan(1/2*d*x + 1/2*c)^3 - 20*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 - 30*a*b^5*tan(1/2*d*x + 1/2*c)^3 - 20*a^6*tan(1/2*d*x + 1/2*c)^2 + 52*a^4*b^2*tan(1/2*d*x + 1/2*c)^2 + 16*a^2*b^4*tan(1/2*d*x + 1/2*c)^2 + 12*b^6*tan(1/2*d*x + 1/2*c)^2 + 46*a^5*b*tan(1/2*d*x + 1/2*c) - 12*a^3*b^3*tan(1/2*d*x + 1/2*c) + 26*a*b^5*tan(1/2*d*x + 1/2*c) + 5*a^6 - 10*a^4*b^2 + 5*a^2*b^4)/((a^7 - 2*a^5*b^2 + a^3*b^4)*(a*tan(1/2*d*x + 1/2*c)^5 + 2*b*tan(1/2*d*x + 1/2*c)^4 - 2*b*tan(1/2*d*x + 1/2*c)^2 - a*tan(1/2*d*x + 1/2*c))) + 20*b*log(abs(tan(1/2*d*x + 1/2*c)))/a^3 - 5*tan(1/2*d*x + 1/2*c)/a^2)/d","B",0
1470,1,423,0,0.262223," ","integrate(csc(d*x+c)^3*sec(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{48 \, {\left(2 \, a^{2} b^{5} - b^{7}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{8} - 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} \sqrt{a^{2} - b^{2}}} + \frac{16 \, {\left(2 \, a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{7} - a^{5} b^{2} - a b^{6}\right)}}{{\left(a^{8} - 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a\right)}} + \frac{12 \, {\left(a^{2} + 2 \, b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{4}} + \frac{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{4}} - \frac{18 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 36 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2}}{a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}}{8 \, d}"," ",0,"1/8*(48*(2*a^2*b^5 - b^7)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/((a^8 - 2*a^6*b^2 + a^4*b^4)*sqrt(a^2 - b^2)) + 16*(2*a^6*b*tan(1/2*d*x + 1/2*c)^3 + b^7*tan(1/2*d*x + 1/2*c)^3 - a^7*tan(1/2*d*x + 1/2*c)^2 + 3*a^5*b^2*tan(1/2*d*x + 1/2*c)^2 + a*b^6*tan(1/2*d*x + 1/2*c)^2 - 2*a^4*b^3*tan(1/2*d*x + 1/2*c) - b^7*tan(1/2*d*x + 1/2*c) - a^7 - a^5*b^2 - a*b^6)/((a^8 - 2*a^6*b^2 + a^4*b^4)*(a*tan(1/2*d*x + 1/2*c)^4 + 2*b*tan(1/2*d*x + 1/2*c)^3 - 2*b*tan(1/2*d*x + 1/2*c) - a)) + 12*(a^2 + 2*b^2)*log(abs(tan(1/2*d*x + 1/2*c)))/a^4 + (a^2*tan(1/2*d*x + 1/2*c)^2 - 8*a*b*tan(1/2*d*x + 1/2*c))/a^4 - (18*a^2*tan(1/2*d*x + 1/2*c)^2 + 36*b^2*tan(1/2*d*x + 1/2*c)^2 - 8*a*b*tan(1/2*d*x + 1/2*c) + a^2)/(a^4*tan(1/2*d*x + 1/2*c)^2))/d","A",0
1471,1,351,0,0.351146," ","integrate(sec(d*x+c)^2*sin(d*x+c)^4/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(a^{4} + 4 \, a^{2} b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \sqrt{a^{2} - b^{2}}} + \frac{2 \, {\left(a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a^{2} b - b^{3}\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}} + \frac{a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 7 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 14 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 22 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 7 \, a^{4} b}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}^{2}}}{d}"," ",0,"-(3*(a^4 + 4*a^2*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*sqrt(a^2 - b^2)) + 2*(a^3*tan(1/2*d*x + 1/2*c) + 3*a*b^2*tan(1/2*d*x + 1/2*c) - 3*a^2*b - b^3)/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(tan(1/2*d*x + 1/2*c)^2 - 1)) + (a^5*tan(1/2*d*x + 1/2*c)^3 + 6*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 + 7*a^4*b*tan(1/2*d*x + 1/2*c)^2 + 14*a^2*b^3*tan(1/2*d*x + 1/2*c)^2 - a^5*tan(1/2*d*x + 1/2*c) + 22*a^3*b^2*tan(1/2*d*x + 1/2*c) + 7*a^4*b)/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)^2))/d","A",0
1472,1,377,0,0.314300," ","integrate(sec(d*x+c)^2*sin(d*x+c)^3/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(3 \, a^{3} b + 2 \, a b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \sqrt{a^{2} - b^{2}}} + \frac{2 \, {\left(3 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{3} - 3 \, a b^{2}\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}} + \frac{3 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 9 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 10 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 5 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 16 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, a^{5} + 5 \, a^{3} b^{2}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}^{2}}}{d}"," ",0,"(3*(3*a^3*b + 2*a*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*sqrt(a^2 - b^2)) + 2*(3*a^2*b*tan(1/2*d*x + 1/2*c) + b^3*tan(1/2*d*x + 1/2*c) - a^3 - 3*a*b^2)/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(tan(1/2*d*x + 1/2*c)^2 - 1)) + (3*a^4*b*tan(1/2*d*x + 1/2*c)^3 + 4*a^2*b^3*tan(1/2*d*x + 1/2*c)^3 + 2*a^5*tan(1/2*d*x + 1/2*c)^2 + 9*a^3*b^2*tan(1/2*d*x + 1/2*c)^2 + 10*a*b^4*tan(1/2*d*x + 1/2*c)^2 + 5*a^4*b*tan(1/2*d*x + 1/2*c) + 16*a^2*b^3*tan(1/2*d*x + 1/2*c) + 2*a^5 + 5*a^3*b^2)/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)^2))/d","A",0
1473,1,384,0,0.311733," ","integrate(sec(d*x+c)^2*sin(d*x+c)^2/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{{\left(2 \, a^{4} + 11 \, a^{2} b^{2} + 2 \, b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \sqrt{a^{2} - b^{2}}} + \frac{2 \, {\left(a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a^{2} b - b^{3}\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}} + \frac{5 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 11 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 6 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 11 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 10 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, a^{4} b + 3 \, a^{2} b^{3}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}^{2}}}{d}"," ",0,"-((2*a^4 + 11*a^2*b^2 + 2*b^4)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*sqrt(a^2 - b^2)) + 2*(a^3*tan(1/2*d*x + 1/2*c) + 3*a*b^2*tan(1/2*d*x + 1/2*c) - 3*a^2*b - b^3)/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(tan(1/2*d*x + 1/2*c)^2 - 1)) + (5*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 + 2*a*b^4*tan(1/2*d*x + 1/2*c)^3 + 4*a^4*b*tan(1/2*d*x + 1/2*c)^2 + 11*a^2*b^3*tan(1/2*d*x + 1/2*c)^2 + 6*b^5*tan(1/2*d*x + 1/2*c)^2 + 11*a^3*b^2*tan(1/2*d*x + 1/2*c) + 10*a*b^4*tan(1/2*d*x + 1/2*c) + 4*a^4*b + 3*a^2*b^3)/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)^2))/d","A",0
1474,1,365,0,0.316093," ","integrate(sec(d*x+c)^2*sin(d*x+c)/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(2 \, a^{3} b + 3 \, a b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \sqrt{a^{2} - b^{2}}} + \frac{2 \, {\left(3 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{3} - 3 \, a b^{2}\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}} + \frac{7 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 13 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 17 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, a^{4} b^{2} + a^{2} b^{4}}{{\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}^{2}}}{d}"," ",0,"(3*(2*a^3*b + 3*a*b^3)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*sqrt(a^2 - b^2)) + 2*(3*a^2*b*tan(1/2*d*x + 1/2*c) + b^3*tan(1/2*d*x + 1/2*c) - a^3 - 3*a*b^2)/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(tan(1/2*d*x + 1/2*c)^2 - 1)) + (7*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 + 6*a^4*b^2*tan(1/2*d*x + 1/2*c)^2 + 13*a^2*b^4*tan(1/2*d*x + 1/2*c)^2 + 2*b^6*tan(1/2*d*x + 1/2*c)^2 + 17*a^3*b^3*tan(1/2*d*x + 1/2*c) + 4*a*b^5*tan(1/2*d*x + 1/2*c) + 6*a^4*b^2 + a^2*b^4)/((a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*(a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)^2))/d","A",0
1475,1,411,0,0.296606," ","integrate(csc(d*x+c)*sec(d*x+c)^2/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{{\left(20 \, a^{4} b^{3} - 7 \, a^{2} b^{5} + 2 \, b^{7}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{9} - 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} - a^{3} b^{6}\right)} \sqrt{a^{2} - b^{2}}} + \frac{2 \, {\left(3 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{3} - 3 \, a b^{2}\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}} + \frac{11 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 10 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 17 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 6 \, b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 29 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 10 \, a^{4} b^{4} - 3 \, a^{2} b^{6}}{{\left(a^{9} - 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} - a^{3} b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}^{2}} + \frac{\log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{3}}}{d}"," ",0,"((20*a^4*b^3 - 7*a^2*b^5 + 2*b^7)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/((a^9 - 3*a^7*b^2 + 3*a^5*b^4 - a^3*b^6)*sqrt(a^2 - b^2)) + 2*(3*a^2*b*tan(1/2*d*x + 1/2*c) + b^3*tan(1/2*d*x + 1/2*c) - a^3 - 3*a*b^2)/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(tan(1/2*d*x + 1/2*c)^2 - 1)) + (11*a^3*b^5*tan(1/2*d*x + 1/2*c)^3 - 4*a*b^7*tan(1/2*d*x + 1/2*c)^3 + 10*a^4*b^4*tan(1/2*d*x + 1/2*c)^2 + 17*a^2*b^6*tan(1/2*d*x + 1/2*c)^2 - 6*b^8*tan(1/2*d*x + 1/2*c)^2 + 29*a^3*b^5*tan(1/2*d*x + 1/2*c) - 8*a*b^7*tan(1/2*d*x + 1/2*c) + 10*a^4*b^4 - 3*a^2*b^6)/((a^9 - 3*a^7*b^2 + 3*a^5*b^4 - a^3*b^6)*(a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)^2) + log(abs(tan(1/2*d*x + 1/2*c)))/a^3)/d","A",0
1476,1,633,0,0.298015," ","integrate(csc(d*x+c)^2*sec(d*x+c)^2/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{6 \, {\left(10 \, a^{4} b^{4} - 7 \, a^{2} b^{6} + 2 \, b^{8}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{10} - 3 \, a^{8} b^{2} + 3 \, a^{6} b^{4} - a^{4} b^{6}\right)} \sqrt{a^{2} - b^{2}}} - \frac{2 \, a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 10 \, a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 10 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}}{{\left(a^{10} - 3 \, a^{8} b^{2} + 3 \, a^{6} b^{4} - a^{4} b^{6}\right)} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}} + \frac{2 \, {\left(13 \, a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 19 \, a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 10 \, b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 35 \, a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 14 \, a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, a^{4} b^{5} - 5 \, a^{2} b^{7}\right)}}{{\left(a^{10} - 3 \, a^{8} b^{2} + 3 \, a^{6} b^{4} - a^{4} b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}^{2}} + \frac{6 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{4}} - \frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3}}}{2 \, d}"," ",0,"-1/2*(6*(10*a^4*b^4 - 7*a^2*b^6 + 2*b^8)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/((a^10 - 3*a^8*b^2 + 3*a^6*b^4 - a^4*b^6)*sqrt(a^2 - b^2)) - (2*a^6*b*tan(1/2*d*x + 1/2*c)^3 - 6*a^4*b^3*tan(1/2*d*x + 1/2*c)^3 + 6*a^2*b^5*tan(1/2*d*x + 1/2*c)^3 - 2*b^7*tan(1/2*d*x + 1/2*c)^3 - 5*a^7*tan(1/2*d*x + 1/2*c)^2 - 9*a^5*b^2*tan(1/2*d*x + 1/2*c)^2 - 3*a^3*b^4*tan(1/2*d*x + 1/2*c)^2 + a*b^6*tan(1/2*d*x + 1/2*c)^2 + 10*a^6*b*tan(1/2*d*x + 1/2*c) + 10*a^4*b^3*tan(1/2*d*x + 1/2*c) - 6*a^2*b^5*tan(1/2*d*x + 1/2*c) + 2*b^7*tan(1/2*d*x + 1/2*c) + a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)/((a^10 - 3*a^8*b^2 + 3*a^6*b^4 - a^4*b^6)*(tan(1/2*d*x + 1/2*c)^3 - tan(1/2*d*x + 1/2*c))) + 2*(13*a^3*b^6*tan(1/2*d*x + 1/2*c)^3 - 6*a*b^8*tan(1/2*d*x + 1/2*c)^3 + 12*a^4*b^5*tan(1/2*d*x + 1/2*c)^2 + 19*a^2*b^7*tan(1/2*d*x + 1/2*c)^2 - 10*b^9*tan(1/2*d*x + 1/2*c)^2 + 35*a^3*b^6*tan(1/2*d*x + 1/2*c) - 14*a*b^8*tan(1/2*d*x + 1/2*c) + 12*a^4*b^5 - 5*a^2*b^7)/((a^10 - 3*a^8*b^2 + 3*a^6*b^4 - a^4*b^6)*(a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)^2) + 6*b*log(abs(tan(1/2*d*x + 1/2*c)))/a^4 - tan(1/2*d*x + 1/2*c)/a^3)/d","A",0
1477,1,900,0,0.371212," ","integrate(csc(d*x+c)^3*sec(d*x+c)^2/(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{24 \, {\left(14 \, a^{4} b^{5} - 13 \, a^{2} b^{7} + 4 \, b^{9}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{11} - 3 \, a^{9} b^{2} + 3 \, a^{7} b^{4} - a^{5} b^{6}\right)} \sqrt{a^{2} - b^{2}}} + \frac{16 \, {\left(3 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{3} - 3 \, a b^{2}\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}} - \frac{6 \, a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 6 \, a^{8} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 54 \, a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 66 \, a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 24 \, a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 12 \, a^{9} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 60 \, a^{7} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 252 \, a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 156 \, a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 32 \, a b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 13 \, a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 15 \, a^{8} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 63 \, a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 341 \, a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 96 \, a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 16 \, b^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 4 \, a^{9} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, a^{7} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 132 \, a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 188 \, a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 112 \, a b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, a^{10} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 44 \, a^{8} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 84 \, a^{6} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 180 \, a^{4} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 76 \, a^{2} b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, a^{9} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, a^{7} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, a^{5} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8 \, a^{3} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{10} - 3 \, a^{8} b^{2} + 3 \, a^{6} b^{4} - a^{4} b^{6}}{{\left(a^{11} - 3 \, a^{9} b^{2} + 3 \, a^{7} b^{4} - a^{5} b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}^{2}} + \frac{12 \, {\left(a^{2} + 4 \, b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{a^{5}} + \frac{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{6}}}{8 \, d}"," ",0,"1/8*(24*(14*a^4*b^5 - 13*a^2*b^7 + 4*b^9)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/((a^11 - 3*a^9*b^2 + 3*a^7*b^4 - a^5*b^6)*sqrt(a^2 - b^2)) + 16*(3*a^2*b*tan(1/2*d*x + 1/2*c) + b^3*tan(1/2*d*x + 1/2*c) - a^3 - 3*a*b^2)/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(tan(1/2*d*x + 1/2*c)^2 - 1)) - (6*a^10*tan(1/2*d*x + 1/2*c)^6 + 6*a^8*b^2*tan(1/2*d*x + 1/2*c)^6 - 54*a^6*b^4*tan(1/2*d*x + 1/2*c)^6 + 66*a^4*b^6*tan(1/2*d*x + 1/2*c)^6 - 24*a^2*b^8*tan(1/2*d*x + 1/2*c)^6 + 12*a^9*b*tan(1/2*d*x + 1/2*c)^5 + 60*a^7*b^3*tan(1/2*d*x + 1/2*c)^5 - 252*a^5*b^5*tan(1/2*d*x + 1/2*c)^5 + 156*a^3*b^7*tan(1/2*d*x + 1/2*c)^5 - 32*a*b^9*tan(1/2*d*x + 1/2*c)^5 + 13*a^10*tan(1/2*d*x + 1/2*c)^4 - 15*a^8*b^2*tan(1/2*d*x + 1/2*c)^4 + 63*a^6*b^4*tan(1/2*d*x + 1/2*c)^4 - 341*a^4*b^6*tan(1/2*d*x + 1/2*c)^4 + 96*a^2*b^8*tan(1/2*d*x + 1/2*c)^4 + 16*b^10*tan(1/2*d*x + 1/2*c)^4 + 4*a^9*b*tan(1/2*d*x + 1/2*c)^3 + 36*a^7*b^3*tan(1/2*d*x + 1/2*c)^3 - 132*a^5*b^5*tan(1/2*d*x + 1/2*c)^3 - 188*a^3*b^7*tan(1/2*d*x + 1/2*c)^3 + 112*a*b^9*tan(1/2*d*x + 1/2*c)^3 + 8*a^10*tan(1/2*d*x + 1/2*c)^2 - 44*a^8*b^2*tan(1/2*d*x + 1/2*c)^2 + 84*a^6*b^4*tan(1/2*d*x + 1/2*c)^2 - 180*a^4*b^6*tan(1/2*d*x + 1/2*c)^2 + 76*a^2*b^8*tan(1/2*d*x + 1/2*c)^2 - 8*a^9*b*tan(1/2*d*x + 1/2*c) + 24*a^7*b^3*tan(1/2*d*x + 1/2*c) - 24*a^5*b^5*tan(1/2*d*x + 1/2*c) + 8*a^3*b^7*tan(1/2*d*x + 1/2*c) + a^10 - 3*a^8*b^2 + 3*a^6*b^4 - a^4*b^6)/((a^11 - 3*a^9*b^2 + 3*a^7*b^4 - a^5*b^6)*(a*tan(1/2*d*x + 1/2*c)^3 + 2*b*tan(1/2*d*x + 1/2*c)^2 + a*tan(1/2*d*x + 1/2*c))^2) + 12*(a^2 + 4*b^2)*log(abs(tan(1/2*d*x + 1/2*c)))/a^5 + (a^3*tan(1/2*d*x + 1/2*c)^2 - 12*a^2*b*tan(1/2*d*x + 1/2*c))/a^6)/d","B",0
1478,0,0,0,0.000000," ","integrate(sec(f*x+e)^2*(a+b*sin(f*x+e))^(1/2)/(d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{b \sin\left(f x + e\right) + a} \sec\left(f x + e\right)^{2}}{\sqrt{d \sin\left(f x + e\right)}}\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e) + a)*sec(f*x + e)^2/sqrt(d*sin(f*x + e)), x)","F",0
1479,0,0,0,0.000000," ","integrate(sec(f*x+e)^2*(a+b*sin(f*x+e))^(3/2)/(d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} \sec\left(f x + e\right)^{2}}{\sqrt{d \sin\left(f x + e\right)}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^(3/2)*sec(f*x + e)^2/sqrt(d*sin(f*x + e)), x)","F",0
1480,0,0,0,0.000000," ","integrate(sec(f*x+e)^4*(a+b*sin(f*x+e))^(5/2)/(d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} \sec\left(f x + e\right)^{4}}{\sqrt{d \sin\left(f x + e\right)}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^(5/2)*sec(f*x + e)^4/sqrt(d*sin(f*x + e)), x)","F",0
1481,1,135,0,0.289697," ","integrate(sec(d*x+c)^5*sin(d*x+c)^7*(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{16 \, b \sin\left(d x + c\right)^{3} + 24 \, a \sin\left(d x + c\right)^{2} + 3 \, {\left(24 \, a - 35 \, b\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) + 3 \, {\left(24 \, a + 35 \, b\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) + 144 \, b \sin\left(d x + c\right) - \frac{6 \, {\left(18 \, a \sin\left(d x + c\right)^{4} + 13 \, b \sin\left(d x + c\right)^{3} - 24 \, a \sin\left(d x + c\right)^{2} - 11 \, b \sin\left(d x + c\right) + 8 \, a\right)}}{{\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{48 \, d}"," ",0,"-1/48*(16*b*sin(d*x + c)^3 + 24*a*sin(d*x + c)^2 + 3*(24*a - 35*b)*log(abs(sin(d*x + c) + 1)) + 3*(24*a + 35*b)*log(abs(sin(d*x + c) - 1)) + 144*b*sin(d*x + c) - 6*(18*a*sin(d*x + c)^4 + 13*b*sin(d*x + c)^3 - 24*a*sin(d*x + c)^2 - 11*b*sin(d*x + c) + 8*a)/(sin(d*x + c)^2 - 1)^2)/d","A",0
1482,1,124,0,0.281235," ","integrate(sec(d*x+c)^5*sin(d*x+c)^6*(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{8 \, b \sin\left(d x + c\right)^{2} - 3 \, {\left(5 \, a - 8 \, b\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) + 3 \, {\left(5 \, a + 8 \, b\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) + 16 \, a \sin\left(d x + c\right) - \frac{2 \, {\left(18 \, b \sin\left(d x + c\right)^{4} + 9 \, a \sin\left(d x + c\right)^{3} - 24 \, b \sin\left(d x + c\right)^{2} - 7 \, a \sin\left(d x + c\right) + 8 \, b\right)}}{{\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{16 \, d}"," ",0,"-1/16*(8*b*sin(d*x + c)^2 - 3*(5*a - 8*b)*log(abs(sin(d*x + c) + 1)) + 3*(5*a + 8*b)*log(abs(sin(d*x + c) - 1)) + 16*a*sin(d*x + c) - 2*(18*b*sin(d*x + c)^4 + 9*a*sin(d*x + c)^3 - 24*b*sin(d*x + c)^2 - 7*a*sin(d*x + c) + 8*b)/(sin(d*x + c)^2 - 1)^2)/d","A",0
1483,1,108,0,0.265477," ","integrate(sec(d*x+c)^5*sin(d*x+c)^5*(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{{\left(8 \, a - 15 \, b\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) + {\left(8 \, a + 15 \, b\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) + 16 \, b \sin\left(d x + c\right) - \frac{2 \, {\left(6 \, a \sin\left(d x + c\right)^{4} + 9 \, b \sin\left(d x + c\right)^{3} - 4 \, a \sin\left(d x + c\right)^{2} - 7 \, b \sin\left(d x + c\right)\right)}}{{\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{16 \, d}"," ",0,"-1/16*((8*a - 15*b)*log(abs(sin(d*x + c) + 1)) + (8*a + 15*b)*log(abs(sin(d*x + c) - 1)) + 16*b*sin(d*x + c) - 2*(6*a*sin(d*x + c)^4 + 9*b*sin(d*x + c)^3 - 4*a*sin(d*x + c)^2 - 7*b*sin(d*x + c))/(sin(d*x + c)^2 - 1)^2)/d","A",0
1484,1,100,0,0.289840," ","integrate(sec(d*x+c)^5*sin(d*x+c)^4*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{{\left(3 \, a - 8 \, b\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - {\left(3 \, a + 8 \, b\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) + \frac{2 \, {\left(6 \, b \sin\left(d x + c\right)^{4} + 5 \, a \sin\left(d x + c\right)^{3} - 4 \, b \sin\left(d x + c\right)^{2} - 3 \, a \sin\left(d x + c\right)\right)}}{{\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{16 \, d}"," ",0,"1/16*((3*a - 8*b)*log(abs(sin(d*x + c) + 1)) - (3*a + 8*b)*log(abs(sin(d*x + c) - 1)) + 2*(6*b*sin(d*x + c)^4 + 5*a*sin(d*x + c)^3 - 4*b*sin(d*x + c)^2 - 3*a*sin(d*x + c))/(sin(d*x + c)^2 - 1)^2)/d","A",0
1485,1,81,0,0.274241," ","integrate(sec(d*x+c)^5*sin(d*x+c)^3*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{3 \, b \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - 3 \, b \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) + \frac{2 \, {\left(5 \, b \sin\left(d x + c\right)^{3} + 4 \, a \sin\left(d x + c\right)^{2} - 3 \, b \sin\left(d x + c\right) - 2 \, a\right)}}{{\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{16 \, d}"," ",0,"1/16*(3*b*log(abs(sin(d*x + c) + 1)) - 3*b*log(abs(sin(d*x + c) - 1)) + 2*(5*b*sin(d*x + c)^3 + 4*a*sin(d*x + c)^2 - 3*b*sin(d*x + c) - 2*a)/(sin(d*x + c)^2 - 1)^2)/d","A",0
1486,1,78,0,0.373354," ","integrate(sec(d*x+c)^5*sin(d*x+c)^2*(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{a \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - a \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - \frac{2 \, {\left(a \sin\left(d x + c\right)^{3} + 4 \, b \sin\left(d x + c\right)^{2} + a \sin\left(d x + c\right) - 2 \, b\right)}}{{\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{16 \, d}"," ",0,"-1/16*(a*log(abs(sin(d*x + c) + 1)) - a*log(abs(sin(d*x + c) - 1)) - 2*(a*sin(d*x + c)^3 + 4*b*sin(d*x + c)^2 + a*sin(d*x + c) - 2*b)/(sin(d*x + c)^2 - 1)^2)/d","A",0
1487,1,67,0,0.225528," ","integrate(sec(d*x+c)^5*sin(d*x+c)*(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{b \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - b \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - \frac{2 \, {\left(b \sin\left(d x + c\right)^{3} + b \sin\left(d x + c\right) + 2 \, a\right)}}{{\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{16 \, d}"," ",0,"-1/16*(b*log(abs(sin(d*x + c) + 1)) - b*log(abs(sin(d*x + c) - 1)) - 2*(b*sin(d*x + c)^3 + b*sin(d*x + c) + 2*a)/(sin(d*x + c)^2 - 1)^2)/d","A",0
1488,1,113,0,0.241554," ","integrate(csc(d*x+c)*sec(d*x+c)^5*(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{{\left(8 \, a - 3 \, b\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) + {\left(8 \, a + 3 \, b\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - 16 \, a \log\left({\left| \sin\left(d x + c\right) \right|}\right) - \frac{2 \, {\left(6 \, a \sin\left(d x + c\right)^{4} - 3 \, b \sin\left(d x + c\right)^{3} - 16 \, a \sin\left(d x + c\right)^{2} + 5 \, b \sin\left(d x + c\right) + 12 \, a\right)}}{{\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{16 \, d}"," ",0,"-1/16*((8*a - 3*b)*log(abs(sin(d*x + c) + 1)) + (8*a + 3*b)*log(abs(sin(d*x + c) - 1)) - 16*a*log(abs(sin(d*x + c))) - 2*(6*a*sin(d*x + c)^4 - 3*b*sin(d*x + c)^3 - 16*a*sin(d*x + c)^2 + 5*b*sin(d*x + c) + 12*a)/(sin(d*x + c)^2 - 1)^2)/d","A",0
1489,1,134,0,0.289313," ","integrate(csc(d*x+c)^2*sec(d*x+c)^5*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{{\left(15 \, a - 8 \, b\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - {\left(15 \, a + 8 \, b\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) + 16 \, b \log\left({\left| \sin\left(d x + c\right) \right|}\right) - \frac{16 \, {\left(b \sin\left(d x + c\right) + a\right)}}{\sin\left(d x + c\right)} + \frac{2 \, {\left(6 \, b \sin\left(d x + c\right)^{4} - 7 \, a \sin\left(d x + c\right)^{3} - 16 \, b \sin\left(d x + c\right)^{2} + 9 \, a \sin\left(d x + c\right) + 12 \, b\right)}}{{\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{16 \, d}"," ",0,"1/16*((15*a - 8*b)*log(abs(sin(d*x + c) + 1)) - (15*a + 8*b)*log(abs(sin(d*x + c) - 1)) + 16*b*log(abs(sin(d*x + c))) - 16*(b*sin(d*x + c) + a)/sin(d*x + c) + 2*(6*b*sin(d*x + c)^4 - 7*a*sin(d*x + c)^3 - 16*b*sin(d*x + c)^2 + 9*a*sin(d*x + c) + 12*b)/(sin(d*x + c)^2 - 1)^2)/d","A",0
1490,1,133,0,0.320662," ","integrate(csc(d*x+c)^3*sec(d*x+c)^5*(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{3 \, {\left(8 \, a - 5 \, b\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) + 3 \, {\left(8 \, a + 5 \, b\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - 48 \, a \log\left({\left| \sin\left(d x + c\right) \right|}\right) + \frac{2 \, {\left(15 \, b \sin\left(d x + c\right)^{5} + 12 \, a \sin\left(d x + c\right)^{4} - 25 \, b \sin\left(d x + c\right)^{3} - 18 \, a \sin\left(d x + c\right)^{2} + 8 \, b \sin\left(d x + c\right) + 4 \, a\right)}}{{\left(\sin\left(d x + c\right)^{3} - \sin\left(d x + c\right)\right)}^{2}}}{16 \, d}"," ",0,"-1/16*(3*(8*a - 5*b)*log(abs(sin(d*x + c) + 1)) + 3*(8*a + 5*b)*log(abs(sin(d*x + c) - 1)) - 48*a*log(abs(sin(d*x + c))) + 2*(15*b*sin(d*x + c)^5 + 12*a*sin(d*x + c)^4 - 25*b*sin(d*x + c)^3 - 18*a*sin(d*x + c)^2 + 8*b*sin(d*x + c) + 4*a)/(sin(d*x + c)^3 - sin(d*x + c))^2)/d","A",0
1491,1,160,0,0.298438," ","integrate(csc(d*x+c)^4*sec(d*x+c)^5*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{3 \, {\left(35 \, a - 24 \, b\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - 3 \, {\left(35 \, a + 24 \, b\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) + 144 \, b \log\left({\left| \sin\left(d x + c\right) \right|}\right) + \frac{6 \, {\left(18 \, b \sin\left(d x + c\right)^{4} - 11 \, a \sin\left(d x + c\right)^{3} - 44 \, b \sin\left(d x + c\right)^{2} + 13 \, a \sin\left(d x + c\right) + 28 \, b\right)}}{{\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}} - \frac{8 \, {\left(33 \, b \sin\left(d x + c\right)^{3} + 18 \, a \sin\left(d x + c\right)^{2} + 3 \, b \sin\left(d x + c\right) + 2 \, a\right)}}{\sin\left(d x + c\right)^{3}}}{48 \, d}"," ",0,"1/48*(3*(35*a - 24*b)*log(abs(sin(d*x + c) + 1)) - 3*(35*a + 24*b)*log(abs(sin(d*x + c) - 1)) + 144*b*log(abs(sin(d*x + c))) + 6*(18*b*sin(d*x + c)^4 - 11*a*sin(d*x + c)^3 - 44*b*sin(d*x + c)^2 + 13*a*sin(d*x + c) + 28*b)/(sin(d*x + c)^2 - 1)^2 - 8*(33*b*sin(d*x + c)^3 + 18*a*sin(d*x + c)^2 + 3*b*sin(d*x + c) + 2*a)/sin(d*x + c)^3)/d","A",0
1492,1,198,0,0.306362," ","integrate(sec(d*x+c)^5*sin(d*x+c)^6*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{16 \, b^{2} \sin\left(d x + c\right)^{3} + 48 \, a b \sin\left(d x + c\right)^{2} + 48 \, a^{2} \sin\left(d x + c\right) + 144 \, b^{2} \sin\left(d x + c\right) - 3 \, {\left(15 \, a^{2} - 48 \, a b + 35 \, b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) + 3 \, {\left(15 \, a^{2} + 48 \, a b + 35 \, b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - \frac{6 \, {\left(36 \, a b \sin\left(d x + c\right)^{4} + 9 \, a^{2} \sin\left(d x + c\right)^{3} + 13 \, b^{2} \sin\left(d x + c\right)^{3} - 48 \, a b \sin\left(d x + c\right)^{2} - 7 \, a^{2} \sin\left(d x + c\right) - 11 \, b^{2} \sin\left(d x + c\right) + 16 \, a b\right)}}{{\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{48 \, d}"," ",0,"-1/48*(16*b^2*sin(d*x + c)^3 + 48*a*b*sin(d*x + c)^2 + 48*a^2*sin(d*x + c) + 144*b^2*sin(d*x + c) - 3*(15*a^2 - 48*a*b + 35*b^2)*log(abs(sin(d*x + c) + 1)) + 3*(15*a^2 + 48*a*b + 35*b^2)*log(abs(sin(d*x + c) - 1)) - 6*(36*a*b*sin(d*x + c)^4 + 9*a^2*sin(d*x + c)^3 + 13*b^2*sin(d*x + c)^3 - 48*a*b*sin(d*x + c)^2 - 7*a^2*sin(d*x + c) - 11*b^2*sin(d*x + c) + 16*a*b)/(sin(d*x + c)^2 - 1)^2)/d","A",0
1493,1,175,0,0.314881," ","integrate(sec(d*x+c)^5*sin(d*x+c)^5*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{4 \, b^{2} \sin\left(d x + c\right)^{2} + 16 \, a b \sin\left(d x + c\right) + {\left(4 \, a^{2} - 15 \, a b + 12 \, b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) + {\left(4 \, a^{2} + 15 \, a b + 12 \, b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - \frac{2 \, {\left(3 \, a^{2} \sin\left(d x + c\right)^{4} + 9 \, b^{2} \sin\left(d x + c\right)^{4} + 9 \, a b \sin\left(d x + c\right)^{3} - 2 \, a^{2} \sin\left(d x + c\right)^{2} - 12 \, b^{2} \sin\left(d x + c\right)^{2} - 7 \, a b \sin\left(d x + c\right) + 4 \, b^{2}\right)}}{{\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{8 \, d}"," ",0,"-1/8*(4*b^2*sin(d*x + c)^2 + 16*a*b*sin(d*x + c) + (4*a^2 - 15*a*b + 12*b^2)*log(abs(sin(d*x + c) + 1)) + (4*a^2 + 15*a*b + 12*b^2)*log(abs(sin(d*x + c) - 1)) - 2*(3*a^2*sin(d*x + c)^4 + 9*b^2*sin(d*x + c)^4 + 9*a*b*sin(d*x + c)^3 - 2*a^2*sin(d*x + c)^2 - 12*b^2*sin(d*x + c)^2 - 7*a*b*sin(d*x + c) + 4*b^2)/(sin(d*x + c)^2 - 1)^2)/d","A",0
1494,1,157,0,0.290082," ","integrate(sec(d*x+c)^5*sin(d*x+c)^4*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{16 \, b^{2} \sin\left(d x + c\right) - {\left(3 \, a^{2} - 16 \, a b + 15 \, b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) + {\left(3 \, a^{2} + 16 \, a b + 15 \, b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - \frac{2 \, {\left(12 \, a b \sin\left(d x + c\right)^{4} + 5 \, a^{2} \sin\left(d x + c\right)^{3} + 9 \, b^{2} \sin\left(d x + c\right)^{3} - 8 \, a b \sin\left(d x + c\right)^{2} - 3 \, a^{2} \sin\left(d x + c\right) - 7 \, b^{2} \sin\left(d x + c\right)\right)}}{{\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{16 \, d}"," ",0,"-1/16*(16*b^2*sin(d*x + c) - (3*a^2 - 16*a*b + 15*b^2)*log(abs(sin(d*x + c) + 1)) + (3*a^2 + 16*a*b + 15*b^2)*log(abs(sin(d*x + c) - 1)) - 2*(12*a*b*sin(d*x + c)^4 + 5*a^2*sin(d*x + c)^3 + 9*b^2*sin(d*x + c)^3 - 8*a*b*sin(d*x + c)^2 - 3*a^2*sin(d*x + c) - 7*b^2*sin(d*x + c))/(sin(d*x + c)^2 - 1)^2)/d","A",0
1495,1,130,0,0.282159," ","integrate(sec(d*x+c)^5*sin(d*x+c)^3*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{{\left(3 \, a b - 4 \, b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - {\left(3 \, a b + 4 \, b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) + \frac{2 \, {\left(3 \, b^{2} \sin\left(d x + c\right)^{4} + 5 \, a b \sin\left(d x + c\right)^{3} + 2 \, a^{2} \sin\left(d x + c\right)^{2} - 2 \, b^{2} \sin\left(d x + c\right)^{2} - 3 \, a b \sin\left(d x + c\right) - a^{2}\right)}}{{\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{8 \, d}"," ",0,"1/8*((3*a*b - 4*b^2)*log(abs(sin(d*x + c) + 1)) - (3*a*b + 4*b^2)*log(abs(sin(d*x + c) - 1)) + 2*(3*b^2*sin(d*x + c)^4 + 5*a*b*sin(d*x + c)^3 + 2*a^2*sin(d*x + c)^2 - 2*b^2*sin(d*x + c)^2 - 3*a*b*sin(d*x + c) - a^2)/(sin(d*x + c)^2 - 1)^2)/d","A",0
1496,1,124,0,0.264698," ","integrate(sec(d*x+c)^5*sin(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{{\left(a^{2} - 3 \, b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - {\left(a^{2} - 3 \, b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - \frac{2 \, {\left(a^{2} \sin\left(d x + c\right)^{3} + 5 \, b^{2} \sin\left(d x + c\right)^{3} + 8 \, a b \sin\left(d x + c\right)^{2} + a^{2} \sin\left(d x + c\right) - 3 \, b^{2} \sin\left(d x + c\right) - 4 \, a b\right)}}{{\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{16 \, d}"," ",0,"-1/16*((a^2 - 3*b^2)*log(abs(sin(d*x + c) + 1)) - (a^2 - 3*b^2)*log(abs(sin(d*x + c) - 1)) - 2*(a^2*sin(d*x + c)^3 + 5*b^2*sin(d*x + c)^3 + 8*a*b*sin(d*x + c)^2 + a^2*sin(d*x + c) - 3*b^2*sin(d*x + c) - 4*a*b)/(sin(d*x + c)^2 - 1)^2)/d","A",0
1497,1,89,0,0.240295," ","integrate(sec(d*x+c)^5*sin(d*x+c)*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{a b \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - a b \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - \frac{2 \, {\left(a b \sin\left(d x + c\right)^{3} + 2 \, b^{2} \sin\left(d x + c\right)^{2} + a b \sin\left(d x + c\right) + a^{2} - b^{2}\right)}}{{\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{8 \, d}"," ",0,"-1/8*(a*b*log(abs(sin(d*x + c) + 1)) - a*b*log(abs(sin(d*x + c) - 1)) - 2*(a*b*sin(d*x + c)^3 + 2*b^2*sin(d*x + c)^2 + a*b*sin(d*x + c) + a^2 - b^2)/(sin(d*x + c)^2 - 1)^2)/d","A",0
1498,1,134,0,0.251513," ","integrate(csc(d*x+c)*sec(d*x+c)^5*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{8 \, a^{2} \log\left({\left| \sin\left(d x + c\right) \right|}\right) - {\left(4 \, a^{2} - 3 \, a b\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - {\left(4 \, a^{2} + 3 \, a b\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) + \frac{2 \, {\left(3 \, a^{2} \sin\left(d x + c\right)^{4} - 3 \, a b \sin\left(d x + c\right)^{3} - 8 \, a^{2} \sin\left(d x + c\right)^{2} + 5 \, a b \sin\left(d x + c\right) + 6 \, a^{2} + b^{2}\right)}}{{\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{8 \, d}"," ",0,"1/8*(8*a^2*log(abs(sin(d*x + c))) - (4*a^2 - 3*a*b)*log(abs(sin(d*x + c) + 1)) - (4*a^2 + 3*a*b)*log(abs(sin(d*x + c) - 1)) + 2*(3*a^2*sin(d*x + c)^4 - 3*a*b*sin(d*x + c)^3 - 8*a^2*sin(d*x + c)^2 + 5*a*b*sin(d*x + c) + 6*a^2 + b^2)/(sin(d*x + c)^2 - 1)^2)/d","A",0
1499,1,186,0,0.330010," ","integrate(csc(d*x+c)^2*sec(d*x+c)^5*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{32 \, a b \log\left({\left| \sin\left(d x + c\right) \right|}\right) + {\left(15 \, a^{2} - 16 \, a b + 3 \, b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - {\left(15 \, a^{2} + 16 \, a b + 3 \, b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - \frac{16 \, {\left(2 \, a b \sin\left(d x + c\right) + a^{2}\right)}}{\sin\left(d x + c\right)} + \frac{2 \, {\left(12 \, a b \sin\left(d x + c\right)^{4} - 7 \, a^{2} \sin\left(d x + c\right)^{3} - 3 \, b^{2} \sin\left(d x + c\right)^{3} - 32 \, a b \sin\left(d x + c\right)^{2} + 9 \, a^{2} \sin\left(d x + c\right) + 5 \, b^{2} \sin\left(d x + c\right) + 24 \, a b\right)}}{{\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{16 \, d}"," ",0,"1/16*(32*a*b*log(abs(sin(d*x + c))) + (15*a^2 - 16*a*b + 3*b^2)*log(abs(sin(d*x + c) + 1)) - (15*a^2 + 16*a*b + 3*b^2)*log(abs(sin(d*x + c) - 1)) - 16*(2*a*b*sin(d*x + c) + a^2)/sin(d*x + c) + 2*(12*a*b*sin(d*x + c)^4 - 7*a^2*sin(d*x + c)^3 - 3*b^2*sin(d*x + c)^3 - 32*a*b*sin(d*x + c)^2 + 9*a^2*sin(d*x + c) + 5*b^2*sin(d*x + c) + 24*a*b)/(sin(d*x + c)^2 - 1)^2)/d","A",0
1500,1,190,0,0.334917," ","integrate(csc(d*x+c)^3*sec(d*x+c)^5*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{{\left(12 \, a^{2} - 15 \, a b + 4 \, b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) + {\left(12 \, a^{2} + 15 \, a b + 4 \, b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - 8 \, {\left(3 \, a^{2} + b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) \right|}\right) + \frac{2 \, {\left(15 \, a b \sin\left(d x + c\right)^{5} + 6 \, a^{2} \sin\left(d x + c\right)^{4} + 2 \, b^{2} \sin\left(d x + c\right)^{4} - 25 \, a b \sin\left(d x + c\right)^{3} - 9 \, a^{2} \sin\left(d x + c\right)^{2} - 3 \, b^{2} \sin\left(d x + c\right)^{2} + 8 \, a b \sin\left(d x + c\right) + 2 \, a^{2}\right)}}{{\left(\sin\left(d x + c\right)^{3} - \sin\left(d x + c\right)\right)}^{2}}}{8 \, d}"," ",0,"-1/8*((12*a^2 - 15*a*b + 4*b^2)*log(abs(sin(d*x + c) + 1)) + (12*a^2 + 15*a*b + 4*b^2)*log(abs(sin(d*x + c) - 1)) - 8*(3*a^2 + b^2)*log(abs(sin(d*x + c))) + 2*(15*a*b*sin(d*x + c)^5 + 6*a^2*sin(d*x + c)^4 + 2*b^2*sin(d*x + c)^4 - 25*a*b*sin(d*x + c)^3 - 9*a^2*sin(d*x + c)^2 - 3*b^2*sin(d*x + c)^2 + 8*a*b*sin(d*x + c) + 2*a^2)/(sin(d*x + c)^3 - sin(d*x + c))^2)/d","A",0
1501,1,251,0,0.344302," ","integrate(sec(d*x+c)^5*sin(d*x+c)^5*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{16 \, b^{3} \sin\left(d x + c\right)^{3} + 72 \, a b^{2} \sin\left(d x + c\right)^{2} + 144 \, a^{2} b \sin\left(d x + c\right) + 144 \, b^{3} \sin\left(d x + c\right) + 3 \, {\left(8 \, a^{3} - 45 \, a^{2} b + 72 \, a b^{2} - 35 \, b^{3}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) + 3 \, {\left(8 \, a^{3} + 45 \, a^{2} b + 72 \, a b^{2} + 35 \, b^{3}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - \frac{6 \, {\left(6 \, a^{3} \sin\left(d x + c\right)^{4} + 54 \, a b^{2} \sin\left(d x + c\right)^{4} + 27 \, a^{2} b \sin\left(d x + c\right)^{3} + 13 \, b^{3} \sin\left(d x + c\right)^{3} - 4 \, a^{3} \sin\left(d x + c\right)^{2} - 72 \, a b^{2} \sin\left(d x + c\right)^{2} - 21 \, a^{2} b \sin\left(d x + c\right) - 11 \, b^{3} \sin\left(d x + c\right) + 24 \, a b^{2}\right)}}{{\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{48 \, d}"," ",0,"-1/48*(16*b^3*sin(d*x + c)^3 + 72*a*b^2*sin(d*x + c)^2 + 144*a^2*b*sin(d*x + c) + 144*b^3*sin(d*x + c) + 3*(8*a^3 - 45*a^2*b + 72*a*b^2 - 35*b^3)*log(abs(sin(d*x + c) + 1)) + 3*(8*a^3 + 45*a^2*b + 72*a*b^2 + 35*b^3)*log(abs(sin(d*x + c) - 1)) - 6*(6*a^3*sin(d*x + c)^4 + 54*a*b^2*sin(d*x + c)^4 + 27*a^2*b*sin(d*x + c)^3 + 13*b^3*sin(d*x + c)^3 - 4*a^3*sin(d*x + c)^2 - 72*a*b^2*sin(d*x + c)^2 - 21*a^2*b*sin(d*x + c) - 11*b^3*sin(d*x + c) + 24*a*b^2)/(sin(d*x + c)^2 - 1)^2)/d","A",0
1502,1,221,0,0.315752," ","integrate(sec(d*x+c)^5*sin(d*x+c)^4*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{8 \, b^{3} \sin\left(d x + c\right)^{2} + 48 \, a b^{2} \sin\left(d x + c\right) - 3 \, {\left(a^{3} - 8 \, a^{2} b + 15 \, a b^{2} - 8 \, b^{3}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) + 3 \, {\left(a^{3} + 8 \, a^{2} b + 15 \, a b^{2} + 8 \, b^{3}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - \frac{2 \, {\left(18 \, a^{2} b \sin\left(d x + c\right)^{4} + 18 \, b^{3} \sin\left(d x + c\right)^{4} + 5 \, a^{3} \sin\left(d x + c\right)^{3} + 27 \, a b^{2} \sin\left(d x + c\right)^{3} - 12 \, a^{2} b \sin\left(d x + c\right)^{2} - 24 \, b^{3} \sin\left(d x + c\right)^{2} - 3 \, a^{3} \sin\left(d x + c\right) - 21 \, a b^{2} \sin\left(d x + c\right) + 8 \, b^{3}\right)}}{{\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{16 \, d}"," ",0,"-1/16*(8*b^3*sin(d*x + c)^2 + 48*a*b^2*sin(d*x + c) - 3*(a^3 - 8*a^2*b + 15*a*b^2 - 8*b^3)*log(abs(sin(d*x + c) + 1)) + 3*(a^3 + 8*a^2*b + 15*a*b^2 + 8*b^3)*log(abs(sin(d*x + c) - 1)) - 2*(18*a^2*b*sin(d*x + c)^4 + 18*b^3*sin(d*x + c)^4 + 5*a^3*sin(d*x + c)^3 + 27*a*b^2*sin(d*x + c)^3 - 12*a^2*b*sin(d*x + c)^2 - 24*b^3*sin(d*x + c)^2 - 3*a^3*sin(d*x + c) - 21*a*b^2*sin(d*x + c) + 8*b^3)/(sin(d*x + c)^2 - 1)^2)/d","A",0
1503,1,188,0,0.293112," ","integrate(sec(d*x+c)^5*sin(d*x+c)^3*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{16 \, b^{3} \sin\left(d x + c\right) - 3 \, {\left(3 \, a^{2} b - 8 \, a b^{2} + 5 \, b^{3}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) + 3 \, {\left(3 \, a^{2} b + 8 \, a b^{2} + 5 \, b^{3}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - \frac{2 \, {\left(18 \, a b^{2} \sin\left(d x + c\right)^{4} + 15 \, a^{2} b \sin\left(d x + c\right)^{3} + 9 \, b^{3} \sin\left(d x + c\right)^{3} + 4 \, a^{3} \sin\left(d x + c\right)^{2} - 12 \, a b^{2} \sin\left(d x + c\right)^{2} - 9 \, a^{2} b \sin\left(d x + c\right) - 7 \, b^{3} \sin\left(d x + c\right) - 2 \, a^{3}\right)}}{{\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{16 \, d}"," ",0,"-1/16*(16*b^3*sin(d*x + c) - 3*(3*a^2*b - 8*a*b^2 + 5*b^3)*log(abs(sin(d*x + c) + 1)) + 3*(3*a^2*b + 8*a*b^2 + 5*b^3)*log(abs(sin(d*x + c) - 1)) - 2*(18*a*b^2*sin(d*x + c)^4 + 15*a^2*b*sin(d*x + c)^3 + 9*b^3*sin(d*x + c)^3 + 4*a^3*sin(d*x + c)^2 - 12*a*b^2*sin(d*x + c)^2 - 9*a^2*b*sin(d*x + c) - 7*b^3*sin(d*x + c) - 2*a^3)/(sin(d*x + c)^2 - 1)^2)/d","A",0
1504,1,168,0,0.273307," ","integrate(sec(d*x+c)^5*sin(d*x+c)^2*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{{\left(a^{3} - 9 \, a b^{2} + 8 \, b^{3}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - {\left(a^{3} - 9 \, a b^{2} - 8 \, b^{3}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - \frac{2 \, {\left(6 \, b^{3} \sin\left(d x + c\right)^{4} + a^{3} \sin\left(d x + c\right)^{3} + 15 \, a b^{2} \sin\left(d x + c\right)^{3} + 12 \, a^{2} b \sin\left(d x + c\right)^{2} - 4 \, b^{3} \sin\left(d x + c\right)^{2} + a^{3} \sin\left(d x + c\right) - 9 \, a b^{2} \sin\left(d x + c\right) - 6 \, a^{2} b\right)}}{{\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{16 \, d}"," ",0,"-1/16*((a^3 - 9*a*b^2 + 8*b^3)*log(abs(sin(d*x + c) + 1)) - (a^3 - 9*a*b^2 - 8*b^3)*log(abs(sin(d*x + c) - 1)) - 2*(6*b^3*sin(d*x + c)^4 + a^3*sin(d*x + c)^3 + 15*a*b^2*sin(d*x + c)^3 + 12*a^2*b*sin(d*x + c)^2 - 4*b^3*sin(d*x + c)^2 + a^3*sin(d*x + c) - 9*a*b^2*sin(d*x + c) - 6*a^2*b)/(sin(d*x + c)^2 - 1)^2)/d","A",0
1505,1,142,0,0.255997," ","integrate(sec(d*x+c)^5*sin(d*x+c)*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{3 \, {\left(a^{2} b - b^{3}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - 3 \, {\left(a^{2} b - b^{3}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - \frac{2 \, {\left(3 \, a^{2} b \sin\left(d x + c\right)^{3} + 5 \, b^{3} \sin\left(d x + c\right)^{3} + 12 \, a b^{2} \sin\left(d x + c\right)^{2} + 3 \, a^{2} b \sin\left(d x + c\right) - 3 \, b^{3} \sin\left(d x + c\right) + 2 \, a^{3} - 6 \, a b^{2}\right)}}{{\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{16 \, d}"," ",0,"-1/16*(3*(a^2*b - b^3)*log(abs(sin(d*x + c) + 1)) - 3*(a^2*b - b^3)*log(abs(sin(d*x + c) - 1)) - 2*(3*a^2*b*sin(d*x + c)^3 + 5*b^3*sin(d*x + c)^3 + 12*a*b^2*sin(d*x + c)^2 + 3*a^2*b*sin(d*x + c) - 3*b^3*sin(d*x + c) + 2*a^3 - 6*a*b^2)/(sin(d*x + c)^2 - 1)^2)/d","A",0
1506,1,175,0,0.352162," ","integrate(csc(d*x+c)*sec(d*x+c)^5*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{16 \, a^{3} \log\left({\left| \sin\left(d x + c\right) \right|}\right) - {\left(8 \, a^{3} - 9 \, a^{2} b + b^{3}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - {\left(8 \, a^{3} + 9 \, a^{2} b - b^{3}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) + \frac{2 \, {\left(6 \, a^{3} \sin\left(d x + c\right)^{4} - 9 \, a^{2} b \sin\left(d x + c\right)^{3} + b^{3} \sin\left(d x + c\right)^{3} - 16 \, a^{3} \sin\left(d x + c\right)^{2} + 15 \, a^{2} b \sin\left(d x + c\right) + b^{3} \sin\left(d x + c\right) + 12 \, a^{3} + 6 \, a b^{2}\right)}}{{\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{16 \, d}"," ",0,"1/16*(16*a^3*log(abs(sin(d*x + c))) - (8*a^3 - 9*a^2*b + b^3)*log(abs(sin(d*x + c) + 1)) - (8*a^3 + 9*a^2*b - b^3)*log(abs(sin(d*x + c) - 1)) + 2*(6*a^3*sin(d*x + c)^4 - 9*a^2*b*sin(d*x + c)^3 + b^3*sin(d*x + c)^3 - 16*a^3*sin(d*x + c)^2 + 15*a^2*b*sin(d*x + c) + b^3*sin(d*x + c) + 12*a^3 + 6*a*b^2)/(sin(d*x + c)^2 - 1)^2)/d","A",0
1507,1,210,0,0.297158," ","integrate(csc(d*x+c)^2*sec(d*x+c)^5*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{48 \, a^{2} b \log\left({\left| \sin\left(d x + c\right) \right|}\right) + 3 \, {\left(5 \, a^{3} - 8 \, a^{2} b + 3 \, a b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - 3 \, {\left(5 \, a^{3} + 8 \, a^{2} b + 3 \, a b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - \frac{16 \, {\left(3 \, a^{2} b \sin\left(d x + c\right) + a^{3}\right)}}{\sin\left(d x + c\right)} + \frac{2 \, {\left(18 \, a^{2} b \sin\left(d x + c\right)^{4} - 7 \, a^{3} \sin\left(d x + c\right)^{3} - 9 \, a b^{2} \sin\left(d x + c\right)^{3} - 48 \, a^{2} b \sin\left(d x + c\right)^{2} + 9 \, a^{3} \sin\left(d x + c\right) + 15 \, a b^{2} \sin\left(d x + c\right) + 36 \, a^{2} b + 2 \, b^{3}\right)}}{{\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{16 \, d}"," ",0,"1/16*(48*a^2*b*log(abs(sin(d*x + c))) + 3*(5*a^3 - 8*a^2*b + 3*a*b^2)*log(abs(sin(d*x + c) + 1)) - 3*(5*a^3 + 8*a^2*b + 3*a*b^2)*log(abs(sin(d*x + c) - 1)) - 16*(3*a^2*b*sin(d*x + c) + a^3)/sin(d*x + c) + 2*(18*a^2*b*sin(d*x + c)^4 - 7*a^3*sin(d*x + c)^3 - 9*a*b^2*sin(d*x + c)^3 - 48*a^2*b*sin(d*x + c)^2 + 9*a^3*sin(d*x + c) + 15*a*b^2*sin(d*x + c) + 36*a^2*b + 2*b^3)/(sin(d*x + c)^2 - 1)^2)/d","A",0
1508,1,240,0,0.346070," ","integrate(csc(d*x+c)^3*sec(d*x+c)^5*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{3 \, {\left(8 \, a^{3} - 15 \, a^{2} b + 8 \, a b^{2} - b^{3}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) + 3 \, {\left(8 \, a^{3} + 15 \, a^{2} b + 8 \, a b^{2} + b^{3}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - 48 \, {\left(a^{3} + a b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) \right|}\right) + \frac{2 \, {\left(45 \, a^{2} b \sin\left(d x + c\right)^{5} + 3 \, b^{3} \sin\left(d x + c\right)^{5} + 12 \, a^{3} \sin\left(d x + c\right)^{4} + 12 \, a b^{2} \sin\left(d x + c\right)^{4} - 75 \, a^{2} b \sin\left(d x + c\right)^{3} - 5 \, b^{3} \sin\left(d x + c\right)^{3} - 18 \, a^{3} \sin\left(d x + c\right)^{2} - 18 \, a b^{2} \sin\left(d x + c\right)^{2} + 24 \, a^{2} b \sin\left(d x + c\right) + 4 \, a^{3}\right)}}{{\left(\sin\left(d x + c\right)^{3} - \sin\left(d x + c\right)\right)}^{2}}}{16 \, d}"," ",0,"-1/16*(3*(8*a^3 - 15*a^2*b + 8*a*b^2 - b^3)*log(abs(sin(d*x + c) + 1)) + 3*(8*a^3 + 15*a^2*b + 8*a*b^2 + b^3)*log(abs(sin(d*x + c) - 1)) - 48*(a^3 + a*b^2)*log(abs(sin(d*x + c))) + 2*(45*a^2*b*sin(d*x + c)^5 + 3*b^3*sin(d*x + c)^5 + 12*a^3*sin(d*x + c)^4 + 12*a*b^2*sin(d*x + c)^4 - 75*a^2*b*sin(d*x + c)^3 - 5*b^3*sin(d*x + c)^3 - 18*a^3*sin(d*x + c)^2 - 18*a*b^2*sin(d*x + c)^2 + 24*a^2*b*sin(d*x + c) + 4*a^3)/(sin(d*x + c)^3 - sin(d*x + c))^2)/d","A",0
1509,0,0,0,0.000000," ","integrate(sec(d*x+c)^5*sin(d*x+c)^n*(a+b*sin(d*x+c))^4,x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{4} \sin\left(d x + c\right)^{n} \sec\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^4*sin(d*x + c)^n*sec(d*x + c)^5, x)","F",0
1510,0,0,0,0.000000," ","integrate(sec(d*x+c)^5*sin(d*x+c)^n*(a+b*sin(d*x+c))^3,x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{3} \sin\left(d x + c\right)^{n} \sec\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^3*sin(d*x + c)^n*sec(d*x + c)^5, x)","F",0
1511,0,0,0,0.000000," ","integrate(sec(d*x+c)^5*sin(d*x+c)^n*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{2} \sin\left(d x + c\right)^{n} \sec\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^2*sin(d*x + c)^n*sec(d*x + c)^5, x)","F",0
1512,0,0,0,0.000000," ","integrate(sec(d*x+c)^5*sin(d*x+c)^n*(a+b*sin(d*x+c)),x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)} \sin\left(d x + c\right)^{n} \sec\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)*sin(d*x + c)^n*sec(d*x + c)^5, x)","F",0
1513,0,0,0,0.000000," ","integrate(sec(d*x+c)^5*sin(d*x+c)^n/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\int \frac{\sin\left(d x + c\right)^{n} \sec\left(d x + c\right)^{5}}{b \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sin(d*x + c)^n*sec(d*x + c)^5/(b*sin(d*x + c) + a), x)","F",0
1514,0,0,0,0.000000," ","integrate(sec(d*x+c)^5*sin(d*x+c)^n*(a+b*sin(d*x+c))^p,x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{p} \sin\left(d x + c\right)^{n} \sec\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^p*sin(d*x + c)^n*sec(d*x + c)^5, x)","F",0
1515,0,0,0,0.000000," ","integrate(sec(f*x+e)^6*(a+b*sin(f*x+e))^(9/2)/(d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{9}{2}} \sec\left(f x + e\right)^{6}}{\sqrt{d \sin\left(f x + e\right)}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^(9/2)*sec(f*x + e)^6/sqrt(d*sin(f*x + e)), x)","F",0
1516,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+b*sin(f*x+e))^2*(c+d*sin(f*x+e))^(4/3),x, algorithm=""giac"")","\int {\left(b \sin\left(f x + e\right) + a\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{4}{3}} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^2*(d*sin(f*x + e) + c)^(4/3)*cos(f*x + e)^2, x)","F",0
1517,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+b*sin(f*x+e))*(c+d*sin(f*x+e))^(4/3),x, algorithm=""giac"")","\int {\left(b \sin\left(f x + e\right) + a\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{4}{3}} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^(4/3)*cos(f*x + e)^2, x)","F",0
1518,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c+d*sin(f*x+e))^(4/3),x, algorithm=""giac"")","\int {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{4}{3}} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(4/3)*cos(f*x + e)^2, x)","F",0
1519,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c+d*sin(f*x+e))^(4/3)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{4}{3}} \cos\left(f x + e\right)^{2}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(4/3)*cos(f*x + e)^2/(b*sin(f*x + e) + a), x)","F",0
1520,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c+d*sin(f*x+e))^(4/3)/(a+b*sin(f*x+e))^2,x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{4}{3}} \cos\left(f x + e\right)^{2}}{{\left(b \sin\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(4/3)*cos(f*x + e)^2/(b*sin(f*x + e) + a)^2, x)","F",0
1521,-1,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+b*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1522,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+b*sin(f*x+e))^m*(c+d*sin(f*x+e))^(4/3),x, algorithm=""giac"")","\int {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{4}{3}} {\left(b \sin\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(4/3)*(b*sin(f*x + e) + a)^m*cos(f*x + e)^2, x)","F",0
1523,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+b*sin(f*x+e))^2*(c+d*sin(f*x+e))^n,x, algorithm=""giac"")","\int {\left(b \sin\left(f x + e\right) + a\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^2*(d*sin(f*x + e) + c)^n*cos(f*x + e)^2, x)","F",0
1524,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+b*sin(f*x+e))*(c+d*sin(f*x+e))^n,x, algorithm=""giac"")","\int {\left(b \sin\left(f x + e\right) + a\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^n*cos(f*x + e)^2, x)","F",0
1525,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c+d*sin(f*x+e))^n,x, algorithm=""giac"")","\int {\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^n*cos(f*x + e)^2, x)","F",0
1526,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c+d*sin(f*x+e))^n/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{2}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^n*cos(f*x + e)^2/(b*sin(f*x + e) + a), x)","F",0
1527,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c+d*sin(f*x+e))^n/(a+b*sin(f*x+e))^2,x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{2}}{{\left(b \sin\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^n*cos(f*x + e)^2/(b*sin(f*x + e) + a)^2, x)","F",0
1528,1,182,0,0.314829," ","integrate(cos(d*x+c)^7*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""giac"")","-\frac{B b \sin\left(9 \, d x + 9 \, c\right)}{2304 \, d} + \frac{7 \, A a \sin\left(3 \, d x + 3 \, c\right)}{64 \, d} - \frac{{\left(B a + A b\right)} \cos\left(8 \, d x + 8 \, c\right)}{1024 \, d} - \frac{{\left(B a + A b\right)} \cos\left(6 \, d x + 6 \, c\right)}{128 \, d} - \frac{7 \, {\left(B a + A b\right)} \cos\left(4 \, d x + 4 \, c\right)}{256 \, d} - \frac{7 \, {\left(B a + A b\right)} \cos\left(2 \, d x + 2 \, c\right)}{128 \, d} + \frac{{\left(4 \, A a - 5 \, B b\right)} \sin\left(7 \, d x + 7 \, c\right)}{1792 \, d} + \frac{{\left(7 \, A a - 2 \, B b\right)} \sin\left(5 \, d x + 5 \, c\right)}{320 \, d} + \frac{7 \, {\left(10 \, A a + B b\right)} \sin\left(d x + c\right)}{128 \, d}"," ",0,"-1/2304*B*b*sin(9*d*x + 9*c)/d + 7/64*A*a*sin(3*d*x + 3*c)/d - 1/1024*(B*a + A*b)*cos(8*d*x + 8*c)/d - 1/128*(B*a + A*b)*cos(6*d*x + 6*c)/d - 7/256*(B*a + A*b)*cos(4*d*x + 4*c)/d - 7/128*(B*a + A*b)*cos(2*d*x + 2*c)/d + 1/1792*(4*A*a - 5*B*b)*sin(7*d*x + 7*c)/d + 1/320*(7*A*a - 2*B*b)*sin(5*d*x + 5*c)/d + 7/128*(10*A*a + B*b)*sin(d*x + c)/d","A",0
1529,1,145,0,0.241776," ","integrate(cos(d*x+c)^5*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""giac"")","-\frac{B b \sin\left(7 \, d x + 7 \, c\right)}{448 \, d} - \frac{{\left(B a + A b\right)} \cos\left(6 \, d x + 6 \, c\right)}{192 \, d} - \frac{{\left(B a + A b\right)} \cos\left(4 \, d x + 4 \, c\right)}{32 \, d} - \frac{5 \, {\left(B a + A b\right)} \cos\left(2 \, d x + 2 \, c\right)}{64 \, d} + \frac{{\left(4 \, A a - 3 \, B b\right)} \sin\left(5 \, d x + 5 \, c\right)}{320 \, d} + \frac{{\left(20 \, A a - B b\right)} \sin\left(3 \, d x + 3 \, c\right)}{192 \, d} + \frac{5 \, {\left(8 \, A a + B b\right)} \sin\left(d x + c\right)}{64 \, d}"," ",0,"-1/448*B*b*sin(7*d*x + 7*c)/d - 1/192*(B*a + A*b)*cos(6*d*x + 6*c)/d - 1/32*(B*a + A*b)*cos(4*d*x + 4*c)/d - 5/64*(B*a + A*b)*cos(2*d*x + 2*c)/d + 1/320*(4*A*a - 3*B*b)*sin(5*d*x + 5*c)/d + 1/192*(20*A*a - B*b)*sin(3*d*x + 3*c)/d + 5/64*(8*A*a + B*b)*sin(d*x + c)/d","A",0
1530,1,100,0,0.202467," ","integrate(cos(d*x+c)^3*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""giac"")","-\frac{12 \, B b \sin\left(d x + c\right)^{5} + 15 \, B a \sin\left(d x + c\right)^{4} + 15 \, A b \sin\left(d x + c\right)^{4} + 20 \, A a \sin\left(d x + c\right)^{3} - 20 \, B b \sin\left(d x + c\right)^{3} - 30 \, B a \sin\left(d x + c\right)^{2} - 30 \, A b \sin\left(d x + c\right)^{2} - 60 \, A a \sin\left(d x + c\right)}{60 \, d}"," ",0,"-1/60*(12*B*b*sin(d*x + c)^5 + 15*B*a*sin(d*x + c)^4 + 15*A*b*sin(d*x + c)^4 + 20*A*a*sin(d*x + c)^3 - 20*B*b*sin(d*x + c)^3 - 30*B*a*sin(d*x + c)^2 - 30*A*b*sin(d*x + c)^2 - 60*A*a*sin(d*x + c))/d","A",0
1531,1,52,0,0.158114," ","integrate(cos(d*x+c)*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""giac"")","\frac{2 \, B b \sin\left(d x + c\right)^{3} + 3 \, B a \sin\left(d x + c\right)^{2} + 3 \, A b \sin\left(d x + c\right)^{2} + 6 \, A a \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(2*B*b*sin(d*x + c)^3 + 3*B*a*sin(d*x + c)^2 + 3*A*b*sin(d*x + c)^2 + 6*A*a*sin(d*x + c))/d","A",0
1532,1,67,0,0.171925," ","integrate(sec(d*x+c)*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""giac"")","-\frac{2 \, B b \sin\left(d x + c\right) - {\left(A a - B a - A b + B b\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) + {\left(A a + B a + A b + B b\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{2 \, d}"," ",0,"-1/2*(2*B*b*sin(d*x + c) - (A*a - B*a - A*b + B*b)*log(abs(sin(d*x + c) + 1)) + (A*a + B*a + A*b + B*b)*log(abs(sin(d*x + c) - 1)))/d","A",0
1533,1,84,0,0.211662," ","integrate(sec(d*x+c)^3*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""giac"")","\frac{{\left(A a - B b\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - {\left(A a - B b\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - \frac{2 \, {\left(A a \sin\left(d x + c\right) + B b \sin\left(d x + c\right) + B a + A b\right)}}{\sin\left(d x + c\right)^{2} - 1}}{4 \, d}"," ",0,"1/4*((A*a - B*b)*log(abs(sin(d*x + c) + 1)) - (A*a - B*b)*log(abs(sin(d*x + c) - 1)) - 2*(A*a*sin(d*x + c) + B*b*sin(d*x + c) + B*a + A*b)/(sin(d*x + c)^2 - 1))/d","A",0
1534,1,114,0,0.225202," ","integrate(sec(d*x+c)^5*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""giac"")","\frac{{\left(3 \, A a - B b\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - {\left(3 \, A a - B b\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - \frac{2 \, {\left(3 \, A a \sin\left(d x + c\right)^{3} - B b \sin\left(d x + c\right)^{3} - 5 \, A a \sin\left(d x + c\right) - B b \sin\left(d x + c\right) - 2 \, B a - 2 \, A b\right)}}{{\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{16 \, d}"," ",0,"1/16*((3*A*a - B*b)*log(abs(sin(d*x + c) + 1)) - (3*A*a - B*b)*log(abs(sin(d*x + c) - 1)) - 2*(3*A*a*sin(d*x + c)^3 - B*b*sin(d*x + c)^3 - 5*A*a*sin(d*x + c) - B*b*sin(d*x + c) - 2*B*a - 2*A*b)/(sin(d*x + c)^2 - 1)^2)/d","A",0
1535,1,139,0,0.261997," ","integrate(sec(d*x+c)^7*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""giac"")","\frac{3 \, {\left(5 \, A a - B b\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - 3 \, {\left(5 \, A a - B b\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - \frac{2 \, {\left(15 \, A a \sin\left(d x + c\right)^{5} - 3 \, B b \sin\left(d x + c\right)^{5} - 40 \, A a \sin\left(d x + c\right)^{3} + 8 \, B b \sin\left(d x + c\right)^{3} + 33 \, A a \sin\left(d x + c\right) + 3 \, B b \sin\left(d x + c\right) + 8 \, B a + 8 \, A b\right)}}{{\left(\sin\left(d x + c\right)^{2} - 1\right)}^{3}}}{96 \, d}"," ",0,"1/96*(3*(5*A*a - B*b)*log(abs(sin(d*x + c) + 1)) - 3*(5*A*a - B*b)*log(abs(sin(d*x + c) - 1)) - 2*(15*A*a*sin(d*x + c)^5 - 3*B*b*sin(d*x + c)^5 - 40*A*a*sin(d*x + c)^3 + 8*B*b*sin(d*x + c)^3 + 33*A*a*sin(d*x + c) + 3*B*b*sin(d*x + c) + 8*B*a + 8*A*b)/(sin(d*x + c)^2 - 1)^3)/d","A",0
1536,1,279,0,0.501081," ","integrate(cos(d*x+c)^7*(a+b*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""giac"")","\frac{B b^{2} \cos\left(10 \, d x + 10 \, c\right)}{5120 \, d} + \frac{7 \, A a^{2} \sin\left(3 \, d x + 3 \, c\right)}{64 \, d} - \frac{{\left(B a^{2} + 2 \, A a b - B b^{2}\right)} \cos\left(8 \, d x + 8 \, c\right)}{1024 \, d} - \frac{{\left(8 \, B a^{2} + 16 \, A a b - B b^{2}\right)} \cos\left(6 \, d x + 6 \, c\right)}{1024 \, d} - \frac{{\left(7 \, B a^{2} + 14 \, A a b + B b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)}{256 \, d} - \frac{7 \, {\left(4 \, B a^{2} + 8 \, A a b + B b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)}{512 \, d} - \frac{{\left(2 \, B a b + A b^{2}\right)} \sin\left(9 \, d x + 9 \, c\right)}{2304 \, d} + \frac{{\left(4 \, A a^{2} - 10 \, B a b - 5 \, A b^{2}\right)} \sin\left(7 \, d x + 7 \, c\right)}{1792 \, d} + \frac{{\left(7 \, A a^{2} - 4 \, B a b - 2 \, A b^{2}\right)} \sin\left(5 \, d x + 5 \, c\right)}{320 \, d} + \frac{7 \, {\left(10 \, A a^{2} + 2 \, B a b + A b^{2}\right)} \sin\left(d x + c\right)}{128 \, d}"," ",0,"1/5120*B*b^2*cos(10*d*x + 10*c)/d + 7/64*A*a^2*sin(3*d*x + 3*c)/d - 1/1024*(B*a^2 + 2*A*a*b - B*b^2)*cos(8*d*x + 8*c)/d - 1/1024*(8*B*a^2 + 16*A*a*b - B*b^2)*cos(6*d*x + 6*c)/d - 1/256*(7*B*a^2 + 14*A*a*b + B*b^2)*cos(4*d*x + 4*c)/d - 7/512*(4*B*a^2 + 8*A*a*b + B*b^2)*cos(2*d*x + 2*c)/d - 1/2304*(2*B*a*b + A*b^2)*sin(9*d*x + 9*c)/d + 1/1792*(4*A*a^2 - 10*B*a*b - 5*A*b^2)*sin(7*d*x + 7*c)/d + 1/320*(7*A*a^2 - 4*B*a*b - 2*A*b^2)*sin(5*d*x + 5*c)/d + 7/128*(10*A*a^2 + 2*B*a*b + A*b^2)*sin(d*x + c)/d","A",0
1537,1,231,0,0.383502," ","integrate(cos(d*x+c)^5*(a+b*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""giac"")","\frac{B b^{2} \cos\left(8 \, d x + 8 \, c\right)}{1024 \, d} - \frac{{\left(2 \, B a^{2} + 4 \, A a b - B b^{2}\right)} \cos\left(6 \, d x + 6 \, c\right)}{384 \, d} - \frac{{\left(8 \, B a^{2} + 16 \, A a b + B b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)}{256 \, d} - \frac{{\left(10 \, B a^{2} + 20 \, A a b + 3 \, B b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)}{128 \, d} - \frac{{\left(2 \, B a b + A b^{2}\right)} \sin\left(7 \, d x + 7 \, c\right)}{448 \, d} + \frac{{\left(4 \, A a^{2} - 6 \, B a b - 3 \, A b^{2}\right)} \sin\left(5 \, d x + 5 \, c\right)}{320 \, d} + \frac{{\left(20 \, A a^{2} - 2 \, B a b - A b^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)}{192 \, d} + \frac{5 \, {\left(8 \, A a^{2} + 2 \, B a b + A b^{2}\right)} \sin\left(d x + c\right)}{64 \, d}"," ",0,"1/1024*B*b^2*cos(8*d*x + 8*c)/d - 1/384*(2*B*a^2 + 4*A*a*b - B*b^2)*cos(6*d*x + 6*c)/d - 1/256*(8*B*a^2 + 16*A*a*b + B*b^2)*cos(4*d*x + 4*c)/d - 1/128*(10*B*a^2 + 20*A*a*b + 3*B*b^2)*cos(2*d*x + 2*c)/d - 1/448*(2*B*a*b + A*b^2)*sin(7*d*x + 7*c)/d + 1/320*(4*A*a^2 - 6*B*a*b - 3*A*b^2)*sin(5*d*x + 5*c)/d + 1/192*(20*A*a^2 - 2*B*a*b - A*b^2)*sin(3*d*x + 3*c)/d + 5/64*(8*A*a^2 + 2*B*a*b + A*b^2)*sin(d*x + c)/d","A",0
1538,1,168,0,0.266027," ","integrate(cos(d*x+c)^3*(a+b*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""giac"")","-\frac{10 \, B b^{2} \sin\left(d x + c\right)^{6} + 24 \, B a b \sin\left(d x + c\right)^{5} + 12 \, A b^{2} \sin\left(d x + c\right)^{5} + 15 \, B a^{2} \sin\left(d x + c\right)^{4} + 30 \, A a b \sin\left(d x + c\right)^{4} - 15 \, B b^{2} \sin\left(d x + c\right)^{4} + 20 \, A a^{2} \sin\left(d x + c\right)^{3} - 40 \, B a b \sin\left(d x + c\right)^{3} - 20 \, A b^{2} \sin\left(d x + c\right)^{3} - 30 \, B a^{2} \sin\left(d x + c\right)^{2} - 60 \, A a b \sin\left(d x + c\right)^{2} - 60 \, A a^{2} \sin\left(d x + c\right)}{60 \, d}"," ",0,"-1/60*(10*B*b^2*sin(d*x + c)^6 + 24*B*a*b*sin(d*x + c)^5 + 12*A*b^2*sin(d*x + c)^5 + 15*B*a^2*sin(d*x + c)^4 + 30*A*a*b*sin(d*x + c)^4 - 15*B*b^2*sin(d*x + c)^4 + 20*A*a^2*sin(d*x + c)^3 - 40*B*a*b*sin(d*x + c)^3 - 20*A*b^2*sin(d*x + c)^3 - 30*B*a^2*sin(d*x + c)^2 - 60*A*a*b*sin(d*x + c)^2 - 60*A*a^2*sin(d*x + c))/d","A",0
1539,1,86,0,0.172223," ","integrate(cos(d*x+c)*(a+b*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""giac"")","\frac{3 \, B b^{2} \sin\left(d x + c\right)^{4} + 8 \, B a b \sin\left(d x + c\right)^{3} + 4 \, A b^{2} \sin\left(d x + c\right)^{3} + 6 \, B a^{2} \sin\left(d x + c\right)^{2} + 12 \, A a b \sin\left(d x + c\right)^{2} + 12 \, A a^{2} \sin\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(3*B*b^2*sin(d*x + c)^4 + 8*B*a*b*sin(d*x + c)^3 + 4*A*b^2*sin(d*x + c)^3 + 6*B*a^2*sin(d*x + c)^2 + 12*A*a*b*sin(d*x + c)^2 + 12*A*a^2*sin(d*x + c))/d","A",0
1540,1,129,0,0.196419," ","integrate(sec(d*x+c)*(a+b*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""giac"")","-\frac{B b^{2} \sin\left(d x + c\right)^{2} + 4 \, B a b \sin\left(d x + c\right) + 2 \, A b^{2} \sin\left(d x + c\right) - {\left(A a^{2} - B a^{2} - 2 \, A a b + 2 \, B a b + A b^{2} - B b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) + {\left(A a^{2} + B a^{2} + 2 \, A a b + 2 \, B a b + A b^{2} + B b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{2 \, d}"," ",0,"-1/2*(B*b^2*sin(d*x + c)^2 + 4*B*a*b*sin(d*x + c) + 2*A*b^2*sin(d*x + c) - (A*a^2 - B*a^2 - 2*A*a*b + 2*B*a*b + A*b^2 - B*b^2)*log(abs(sin(d*x + c) + 1)) + (A*a^2 + B*a^2 + 2*A*a*b + 2*B*a*b + A*b^2 + B*b^2)*log(abs(sin(d*x + c) - 1)))/d","A",0
1541,1,146,0,0.257389," ","integrate(sec(d*x+c)^3*(a+b*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""giac"")","\frac{{\left(A a^{2} - 2 \, B a b - A b^{2} + 2 \, B b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - {\left(A a^{2} - 2 \, B a b - A b^{2} - 2 \, B b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - \frac{2 \, {\left(B b^{2} \sin\left(d x + c\right)^{2} + A a^{2} \sin\left(d x + c\right) + 2 \, B a b \sin\left(d x + c\right) + A b^{2} \sin\left(d x + c\right) + B a^{2} + 2 \, A a b\right)}}{\sin\left(d x + c\right)^{2} - 1}}{4 \, d}"," ",0,"1/4*((A*a^2 - 2*B*a*b - A*b^2 + 2*B*b^2)*log(abs(sin(d*x + c) + 1)) - (A*a^2 - 2*B*a*b - A*b^2 - 2*B*b^2)*log(abs(sin(d*x + c) - 1)) - 2*(B*b^2*sin(d*x + c)^2 + A*a^2*sin(d*x + c) + 2*B*a*b*sin(d*x + c) + A*b^2*sin(d*x + c) + B*a^2 + 2*A*a*b)/(sin(d*x + c)^2 - 1))/d","A",0
1542,1,187,0,0.273993," ","integrate(sec(d*x+c)^5*(a+b*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""giac"")","\frac{{\left(3 \, A a^{2} - 2 \, B a b - A b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - {\left(3 \, A a^{2} - 2 \, B a b - A b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - \frac{2 \, {\left(3 \, A a^{2} \sin\left(d x + c\right)^{3} - 2 \, B a b \sin\left(d x + c\right)^{3} - A b^{2} \sin\left(d x + c\right)^{3} - 4 \, B b^{2} \sin\left(d x + c\right)^{2} - 5 \, A a^{2} \sin\left(d x + c\right) - 2 \, B a b \sin\left(d x + c\right) - A b^{2} \sin\left(d x + c\right) - 2 \, B a^{2} - 4 \, A a b + 2 \, B b^{2}\right)}}{{\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{16 \, d}"," ",0,"1/16*((3*A*a^2 - 2*B*a*b - A*b^2)*log(abs(sin(d*x + c) + 1)) - (3*A*a^2 - 2*B*a*b - A*b^2)*log(abs(sin(d*x + c) - 1)) - 2*(3*A*a^2*sin(d*x + c)^3 - 2*B*a*b*sin(d*x + c)^3 - A*b^2*sin(d*x + c)^3 - 4*B*b^2*sin(d*x + c)^2 - 5*A*a^2*sin(d*x + c) - 2*B*a*b*sin(d*x + c) - A*b^2*sin(d*x + c) - 2*B*a^2 - 4*A*a*b + 2*B*b^2)/(sin(d*x + c)^2 - 1)^2)/d","A",0
1543,1,229,0,0.268908," ","integrate(sec(d*x+c)^7*(a+b*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""giac"")","\frac{3 \, {\left(5 \, A a^{2} - 2 \, B a b - A b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right) - 3 \, {\left(5 \, A a^{2} - 2 \, B a b - A b^{2}\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right) - \frac{2 \, {\left(15 \, A a^{2} \sin\left(d x + c\right)^{5} - 6 \, B a b \sin\left(d x + c\right)^{5} - 3 \, A b^{2} \sin\left(d x + c\right)^{5} - 40 \, A a^{2} \sin\left(d x + c\right)^{3} + 16 \, B a b \sin\left(d x + c\right)^{3} + 8 \, A b^{2} \sin\left(d x + c\right)^{3} + 12 \, B b^{2} \sin\left(d x + c\right)^{2} + 33 \, A a^{2} \sin\left(d x + c\right) + 6 \, B a b \sin\left(d x + c\right) + 3 \, A b^{2} \sin\left(d x + c\right) + 8 \, B a^{2} + 16 \, A a b - 4 \, B b^{2}\right)}}{{\left(\sin\left(d x + c\right)^{2} - 1\right)}^{3}}}{96 \, d}"," ",0,"1/96*(3*(5*A*a^2 - 2*B*a*b - A*b^2)*log(abs(sin(d*x + c) + 1)) - 3*(5*A*a^2 - 2*B*a*b - A*b^2)*log(abs(sin(d*x + c) - 1)) - 2*(15*A*a^2*sin(d*x + c)^5 - 6*B*a*b*sin(d*x + c)^5 - 3*A*b^2*sin(d*x + c)^5 - 40*A*a^2*sin(d*x + c)^3 + 16*B*a*b*sin(d*x + c)^3 + 8*A*b^2*sin(d*x + c)^3 + 12*B*b^2*sin(d*x + c)^2 + 33*A*a^2*sin(d*x + c) + 6*B*a*b*sin(d*x + c) + 3*A*b^2*sin(d*x + c) + 8*B*a^2 + 16*A*a*b - 4*B*b^2)/(sin(d*x + c)^2 - 1)^3)/d","A",0
1544,1,511,0,0.243294," ","integrate(cos(d*x+c)^7*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{60 \, B b^{6} \sin\left(d x + c\right)^{7} - 70 \, B a b^{5} \sin\left(d x + c\right)^{6} + 70 \, A b^{6} \sin\left(d x + c\right)^{6} + 84 \, B a^{2} b^{4} \sin\left(d x + c\right)^{5} - 84 \, A a b^{5} \sin\left(d x + c\right)^{5} - 252 \, B b^{6} \sin\left(d x + c\right)^{5} - 105 \, B a^{3} b^{3} \sin\left(d x + c\right)^{4} + 105 \, A a^{2} b^{4} \sin\left(d x + c\right)^{4} + 315 \, B a b^{5} \sin\left(d x + c\right)^{4} - 315 \, A b^{6} \sin\left(d x + c\right)^{4} + 140 \, B a^{4} b^{2} \sin\left(d x + c\right)^{3} - 140 \, A a^{3} b^{3} \sin\left(d x + c\right)^{3} - 420 \, B a^{2} b^{4} \sin\left(d x + c\right)^{3} + 420 \, A a b^{5} \sin\left(d x + c\right)^{3} + 420 \, B b^{6} \sin\left(d x + c\right)^{3} - 210 \, B a^{5} b \sin\left(d x + c\right)^{2} + 210 \, A a^{4} b^{2} \sin\left(d x + c\right)^{2} + 630 \, B a^{3} b^{3} \sin\left(d x + c\right)^{2} - 630 \, A a^{2} b^{4} \sin\left(d x + c\right)^{2} - 630 \, B a b^{5} \sin\left(d x + c\right)^{2} + 630 \, A b^{6} \sin\left(d x + c\right)^{2} + 420 \, B a^{6} \sin\left(d x + c\right) - 420 \, A a^{5} b \sin\left(d x + c\right) - 1260 \, B a^{4} b^{2} \sin\left(d x + c\right) + 1260 \, A a^{3} b^{3} \sin\left(d x + c\right) + 1260 \, B a^{2} b^{4} \sin\left(d x + c\right) - 1260 \, A a b^{5} \sin\left(d x + c\right) - 420 \, B b^{6} \sin\left(d x + c\right)}{b^{7}} - \frac{420 \, {\left(B a^{7} - A a^{6} b - 3 \, B a^{5} b^{2} + 3 \, A a^{4} b^{3} + 3 \, B a^{3} b^{4} - 3 \, A a^{2} b^{5} - B a b^{6} + A b^{7}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{b^{8}}}{420 \, d}"," ",0,"-1/420*((60*B*b^6*sin(d*x + c)^7 - 70*B*a*b^5*sin(d*x + c)^6 + 70*A*b^6*sin(d*x + c)^6 + 84*B*a^2*b^4*sin(d*x + c)^5 - 84*A*a*b^5*sin(d*x + c)^5 - 252*B*b^6*sin(d*x + c)^5 - 105*B*a^3*b^3*sin(d*x + c)^4 + 105*A*a^2*b^4*sin(d*x + c)^4 + 315*B*a*b^5*sin(d*x + c)^4 - 315*A*b^6*sin(d*x + c)^4 + 140*B*a^4*b^2*sin(d*x + c)^3 - 140*A*a^3*b^3*sin(d*x + c)^3 - 420*B*a^2*b^4*sin(d*x + c)^3 + 420*A*a*b^5*sin(d*x + c)^3 + 420*B*b^6*sin(d*x + c)^3 - 210*B*a^5*b*sin(d*x + c)^2 + 210*A*a^4*b^2*sin(d*x + c)^2 + 630*B*a^3*b^3*sin(d*x + c)^2 - 630*A*a^2*b^4*sin(d*x + c)^2 - 630*B*a*b^5*sin(d*x + c)^2 + 630*A*b^6*sin(d*x + c)^2 + 420*B*a^6*sin(d*x + c) - 420*A*a^5*b*sin(d*x + c) - 1260*B*a^4*b^2*sin(d*x + c) + 1260*A*a^3*b^3*sin(d*x + c) + 1260*B*a^2*b^4*sin(d*x + c) - 1260*A*a*b^5*sin(d*x + c) - 420*B*b^6*sin(d*x + c))/b^7 - 420*(B*a^7 - A*a^6*b - 3*B*a^5*b^2 + 3*A*a^4*b^3 + 3*B*a^3*b^4 - 3*A*a^2*b^5 - B*a*b^6 + A*b^7)*log(abs(b*sin(d*x + c) + a))/b^8)/d","A",0
1545,1,286,0,0.203827," ","integrate(cos(d*x+c)^5*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{12 \, B b^{4} \sin\left(d x + c\right)^{5} - 15 \, B a b^{3} \sin\left(d x + c\right)^{4} + 15 \, A b^{4} \sin\left(d x + c\right)^{4} + 20 \, B a^{2} b^{2} \sin\left(d x + c\right)^{3} - 20 \, A a b^{3} \sin\left(d x + c\right)^{3} - 40 \, B b^{4} \sin\left(d x + c\right)^{3} - 30 \, B a^{3} b \sin\left(d x + c\right)^{2} + 30 \, A a^{2} b^{2} \sin\left(d x + c\right)^{2} + 60 \, B a b^{3} \sin\left(d x + c\right)^{2} - 60 \, A b^{4} \sin\left(d x + c\right)^{2} + 60 \, B a^{4} \sin\left(d x + c\right) - 60 \, A a^{3} b \sin\left(d x + c\right) - 120 \, B a^{2} b^{2} \sin\left(d x + c\right) + 120 \, A a b^{3} \sin\left(d x + c\right) + 60 \, B b^{4} \sin\left(d x + c\right)}{b^{5}} - \frac{60 \, {\left(B a^{5} - A a^{4} b - 2 \, B a^{3} b^{2} + 2 \, A a^{2} b^{3} + B a b^{4} - A b^{5}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{b^{6}}}{60 \, d}"," ",0,"1/60*((12*B*b^4*sin(d*x + c)^5 - 15*B*a*b^3*sin(d*x + c)^4 + 15*A*b^4*sin(d*x + c)^4 + 20*B*a^2*b^2*sin(d*x + c)^3 - 20*A*a*b^3*sin(d*x + c)^3 - 40*B*b^4*sin(d*x + c)^3 - 30*B*a^3*b*sin(d*x + c)^2 + 30*A*a^2*b^2*sin(d*x + c)^2 + 60*B*a*b^3*sin(d*x + c)^2 - 60*A*b^4*sin(d*x + c)^2 + 60*B*a^4*sin(d*x + c) - 60*A*a^3*b*sin(d*x + c) - 120*B*a^2*b^2*sin(d*x + c) + 120*A*a*b^3*sin(d*x + c) + 60*B*b^4*sin(d*x + c))/b^5 - 60*(B*a^5 - A*a^4*b - 2*B*a^3*b^2 + 2*A*a^2*b^3 + B*a*b^4 - A*b^5)*log(abs(b*sin(d*x + c) + a))/b^6)/d","A",0
1546,1,129,0,0.201385," ","integrate(cos(d*x+c)^3*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{2 \, B b^{2} \sin\left(d x + c\right)^{3} - 3 \, B a b \sin\left(d x + c\right)^{2} + 3 \, A b^{2} \sin\left(d x + c\right)^{2} + 6 \, B a^{2} \sin\left(d x + c\right) - 6 \, A a b \sin\left(d x + c\right) - 6 \, B b^{2} \sin\left(d x + c\right)}{b^{3}} - \frac{6 \, {\left(B a^{3} - A a^{2} b - B a b^{2} + A b^{3}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{b^{4}}}{6 \, d}"," ",0,"-1/6*((2*B*b^2*sin(d*x + c)^3 - 3*B*a*b*sin(d*x + c)^2 + 3*A*b^2*sin(d*x + c)^2 + 6*B*a^2*sin(d*x + c) - 6*A*a*b*sin(d*x + c) - 6*B*b^2*sin(d*x + c))/b^3 - 6*(B*a^3 - A*a^2*b - B*a*b^2 + A*b^3)*log(abs(b*sin(d*x + c) + a))/b^4)/d","A",0
1547,1,41,0,0.153122," ","integrate(cos(d*x+c)*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{B \sin\left(d x + c\right)}{b} - \frac{{\left(B a - A b\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{b^{2}}}{d}"," ",0,"(B*sin(d*x + c)/b - (B*a - A*b)*log(abs(b*sin(d*x + c) + a))/b^2)/d","A",0
1548,1,87,0,0.203195," ","integrate(sec(d*x+c)*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{2 \, {\left(B a b - A b^{2}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{2} b - b^{3}} + \frac{{\left(A - B\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a - b} - \frac{{\left(A + B\right)} \log\left({\left| \sin\left(d x + c\right) - 1 \right|}\right)}{a + b}}{2 \, d}"," ",0,"1/2*(2*(B*a*b - A*b^2)*log(abs(b*sin(d*x + c) + a))/(a^2*b - b^3) + (A - B)*log(abs(sin(d*x + c) + 1))/(a - b) - (A + B)*log(abs(sin(d*x + c) - 1))/(a + b))/d","A",0
1549,1,260,0,0.315227," ","integrate(sec(d*x+c)^3*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{4 \, {\left(B a b^{3} - A b^{4}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{4} b - 2 \, a^{2} b^{3} + b^{5}} + \frac{{\left(A a + 2 \, A b + B b\right)} \log\left({\left| -\sin\left(d x + c\right) + 1 \right|}\right)}{a^{2} + 2 \, a b + b^{2}} - \frac{{\left(A a - 2 \, A b + B b\right)} \log\left({\left| -\sin\left(d x + c\right) - 1 \right|}\right)}{a^{2} - 2 \, a b + b^{2}} + \frac{2 \, {\left(B a b^{2} \sin\left(d x + c\right)^{2} - A b^{3} \sin\left(d x + c\right)^{2} + A a^{3} \sin\left(d x + c\right) - B a^{2} b \sin\left(d x + c\right) - A a b^{2} \sin\left(d x + c\right) + B b^{3} \sin\left(d x + c\right) + B a^{3} - A a^{2} b - 2 \, B a b^{2} + 2 \, A b^{3}\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(\sin\left(d x + c\right)^{2} - 1\right)}}}{4 \, d}"," ",0,"-1/4*(4*(B*a*b^3 - A*b^4)*log(abs(b*sin(d*x + c) + a))/(a^4*b - 2*a^2*b^3 + b^5) + (A*a + 2*A*b + B*b)*log(abs(-sin(d*x + c) + 1))/(a^2 + 2*a*b + b^2) - (A*a - 2*A*b + B*b)*log(abs(-sin(d*x + c) - 1))/(a^2 - 2*a*b + b^2) + 2*(B*a*b^2*sin(d*x + c)^2 - A*b^3*sin(d*x + c)^2 + A*a^3*sin(d*x + c) - B*a^2*b*sin(d*x + c) - A*a*b^2*sin(d*x + c) + B*b^3*sin(d*x + c) + B*a^3 - A*a^2*b - 2*B*a*b^2 + 2*A*b^3)/((a^4 - 2*a^2*b^2 + b^4)*(sin(d*x + c)^2 - 1)))/d","A",0
1550,1,539,0,0.403213," ","integrate(sec(d*x+c)^5*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x, algorithm=""giac"")","\frac{\frac{16 \, {\left(B a b^{5} - A b^{6}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}} - \frac{{\left(3 \, A a^{2} + 9 \, A a b + B a b + 8 \, A b^{2} + 3 \, B b^{2}\right)} \log\left({\left| -\sin\left(d x + c\right) + 1 \right|}\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} + \frac{{\left(3 \, A a^{2} - 9 \, A a b + B a b + 8 \, A b^{2} - 3 \, B b^{2}\right)} \log\left({\left| -\sin\left(d x + c\right) - 1 \right|}\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} + \frac{2 \, {\left(6 \, B a b^{4} \sin\left(d x + c\right)^{4} - 6 \, A b^{5} \sin\left(d x + c\right)^{4} - 3 \, A a^{5} \sin\left(d x + c\right)^{3} - B a^{4} b \sin\left(d x + c\right)^{3} + 10 \, A a^{3} b^{2} \sin\left(d x + c\right)^{3} - 2 \, B a^{2} b^{3} \sin\left(d x + c\right)^{3} - 7 \, A a b^{4} \sin\left(d x + c\right)^{3} + 3 \, B b^{5} \sin\left(d x + c\right)^{3} + 4 \, B a^{3} b^{2} \sin\left(d x + c\right)^{2} - 4 \, A a^{2} b^{3} \sin\left(d x + c\right)^{2} - 16 \, B a b^{4} \sin\left(d x + c\right)^{2} + 16 \, A b^{5} \sin\left(d x + c\right)^{2} + 5 \, A a^{5} \sin\left(d x + c\right) - B a^{4} b \sin\left(d x + c\right) - 14 \, A a^{3} b^{2} \sin\left(d x + c\right) + 6 \, B a^{2} b^{3} \sin\left(d x + c\right) + 9 \, A a b^{4} \sin\left(d x + c\right) - 5 \, B b^{5} \sin\left(d x + c\right) + 2 \, B a^{5} - 2 \, A a^{4} b - 8 \, B a^{3} b^{2} + 8 \, A a^{2} b^{3} + 12 \, B a b^{4} - 12 \, A b^{5}\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{16 \, d}"," ",0,"1/16*(16*(B*a*b^5 - A*b^6)*log(abs(b*sin(d*x + c) + a))/(a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7) - (3*A*a^2 + 9*A*a*b + B*a*b + 8*A*b^2 + 3*B*b^2)*log(abs(-sin(d*x + c) + 1))/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) + (3*A*a^2 - 9*A*a*b + B*a*b + 8*A*b^2 - 3*B*b^2)*log(abs(-sin(d*x + c) - 1))/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) + 2*(6*B*a*b^4*sin(d*x + c)^4 - 6*A*b^5*sin(d*x + c)^4 - 3*A*a^5*sin(d*x + c)^3 - B*a^4*b*sin(d*x + c)^3 + 10*A*a^3*b^2*sin(d*x + c)^3 - 2*B*a^2*b^3*sin(d*x + c)^3 - 7*A*a*b^4*sin(d*x + c)^3 + 3*B*b^5*sin(d*x + c)^3 + 4*B*a^3*b^2*sin(d*x + c)^2 - 4*A*a^2*b^3*sin(d*x + c)^2 - 16*B*a*b^4*sin(d*x + c)^2 + 16*A*b^5*sin(d*x + c)^2 + 5*A*a^5*sin(d*x + c) - B*a^4*b*sin(d*x + c) - 14*A*a^3*b^2*sin(d*x + c) + 6*B*a^2*b^3*sin(d*x + c) + 9*A*a*b^4*sin(d*x + c) - 5*B*b^5*sin(d*x + c) + 2*B*a^5 - 2*A*a^4*b - 8*B*a^3*b^2 + 8*A*a^2*b^3 + 12*B*a*b^4 - 12*A*b^5)/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(sin(d*x + c)^2 - 1)^2))/d","B",0
1551,1,907,0,0.323214," ","integrate(sec(d*x+c)^7*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{96 \, {\left(B a b^{7} - A b^{8}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{8} b - 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} - 4 \, a^{2} b^{7} + b^{9}} + \frac{3 \, {\left(5 \, A a^{3} + 20 \, A a^{2} b + B a^{2} b + 29 \, A a b^{2} + 4 \, B a b^{2} + 16 \, A b^{3} + 5 \, B b^{3}\right)} \log\left({\left| -\sin\left(d x + c\right) + 1 \right|}\right)}{a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}} - \frac{3 \, {\left(5 \, A a^{3} - 20 \, A a^{2} b + B a^{2} b + 29 \, A a b^{2} - 4 \, B a b^{2} - 16 \, A b^{3} + 5 \, B b^{3}\right)} \log\left({\left| -\sin\left(d x + c\right) - 1 \right|}\right)}{a^{4} - 4 \, a^{3} b + 6 \, a^{2} b^{2} - 4 \, a b^{3} + b^{4}} + \frac{2 \, {\left(44 \, B a b^{6} \sin\left(d x + c\right)^{6} - 44 \, A b^{7} \sin\left(d x + c\right)^{6} + 15 \, A a^{7} \sin\left(d x + c\right)^{5} + 3 \, B a^{6} b \sin\left(d x + c\right)^{5} - 63 \, A a^{5} b^{2} \sin\left(d x + c\right)^{5} - 15 \, B a^{4} b^{3} \sin\left(d x + c\right)^{5} + 105 \, A a^{3} b^{4} \sin\left(d x + c\right)^{5} - 3 \, B a^{2} b^{5} \sin\left(d x + c\right)^{5} - 57 \, A a b^{6} \sin\left(d x + c\right)^{5} + 15 \, B b^{7} \sin\left(d x + c\right)^{5} + 24 \, B a^{3} b^{4} \sin\left(d x + c\right)^{4} - 24 \, A a^{2} b^{5} \sin\left(d x + c\right)^{4} - 156 \, B a b^{6} \sin\left(d x + c\right)^{4} + 156 \, A b^{7} \sin\left(d x + c\right)^{4} - 40 \, A a^{7} \sin\left(d x + c\right)^{3} - 8 \, B a^{6} b \sin\left(d x + c\right)^{3} + 168 \, A a^{5} b^{2} \sin\left(d x + c\right)^{3} + 24 \, B a^{4} b^{3} \sin\left(d x + c\right)^{3} - 264 \, A a^{3} b^{4} \sin\left(d x + c\right)^{3} + 24 \, B a^{2} b^{5} \sin\left(d x + c\right)^{3} + 136 \, A a b^{6} \sin\left(d x + c\right)^{3} - 40 \, B b^{7} \sin\left(d x + c\right)^{3} + 12 \, B a^{5} b^{2} \sin\left(d x + c\right)^{2} - 12 \, A a^{4} b^{3} \sin\left(d x + c\right)^{2} - 72 \, B a^{3} b^{4} \sin\left(d x + c\right)^{2} + 72 \, A a^{2} b^{5} \sin\left(d x + c\right)^{2} + 192 \, B a b^{6} \sin\left(d x + c\right)^{2} - 192 \, A b^{7} \sin\left(d x + c\right)^{2} + 33 \, A a^{7} \sin\left(d x + c\right) - 3 \, B a^{6} b \sin\left(d x + c\right) - 129 \, A a^{5} b^{2} \sin\left(d x + c\right) + 15 \, B a^{4} b^{3} \sin\left(d x + c\right) + 183 \, A a^{3} b^{4} \sin\left(d x + c\right) - 45 \, B a^{2} b^{5} \sin\left(d x + c\right) - 87 \, A a b^{6} \sin\left(d x + c\right) + 33 \, B b^{7} \sin\left(d x + c\right) + 8 \, B a^{7} - 8 \, A a^{6} b - 36 \, B a^{5} b^{2} + 36 \, A a^{4} b^{3} + 72 \, B a^{3} b^{4} - 72 \, A a^{2} b^{5} - 88 \, B a b^{6} + 88 \, A b^{7}\right)}}{{\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} {\left(\sin\left(d x + c\right)^{2} - 1\right)}^{3}}}{96 \, d}"," ",0,"-1/96*(96*(B*a*b^7 - A*b^8)*log(abs(b*sin(d*x + c) + a))/(a^8*b - 4*a^6*b^3 + 6*a^4*b^5 - 4*a^2*b^7 + b^9) + 3*(5*A*a^3 + 20*A*a^2*b + B*a^2*b + 29*A*a*b^2 + 4*B*a*b^2 + 16*A*b^3 + 5*B*b^3)*log(abs(-sin(d*x + c) + 1))/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4) - 3*(5*A*a^3 - 20*A*a^2*b + B*a^2*b + 29*A*a*b^2 - 4*B*a*b^2 - 16*A*b^3 + 5*B*b^3)*log(abs(-sin(d*x + c) - 1))/(a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4) + 2*(44*B*a*b^6*sin(d*x + c)^6 - 44*A*b^7*sin(d*x + c)^6 + 15*A*a^7*sin(d*x + c)^5 + 3*B*a^6*b*sin(d*x + c)^5 - 63*A*a^5*b^2*sin(d*x + c)^5 - 15*B*a^4*b^3*sin(d*x + c)^5 + 105*A*a^3*b^4*sin(d*x + c)^5 - 3*B*a^2*b^5*sin(d*x + c)^5 - 57*A*a*b^6*sin(d*x + c)^5 + 15*B*b^7*sin(d*x + c)^5 + 24*B*a^3*b^4*sin(d*x + c)^4 - 24*A*a^2*b^5*sin(d*x + c)^4 - 156*B*a*b^6*sin(d*x + c)^4 + 156*A*b^7*sin(d*x + c)^4 - 40*A*a^7*sin(d*x + c)^3 - 8*B*a^6*b*sin(d*x + c)^3 + 168*A*a^5*b^2*sin(d*x + c)^3 + 24*B*a^4*b^3*sin(d*x + c)^3 - 264*A*a^3*b^4*sin(d*x + c)^3 + 24*B*a^2*b^5*sin(d*x + c)^3 + 136*A*a*b^6*sin(d*x + c)^3 - 40*B*b^7*sin(d*x + c)^3 + 12*B*a^5*b^2*sin(d*x + c)^2 - 12*A*a^4*b^3*sin(d*x + c)^2 - 72*B*a^3*b^4*sin(d*x + c)^2 + 72*A*a^2*b^5*sin(d*x + c)^2 + 192*B*a*b^6*sin(d*x + c)^2 - 192*A*b^7*sin(d*x + c)^2 + 33*A*a^7*sin(d*x + c) - 3*B*a^6*b*sin(d*x + c) - 129*A*a^5*b^2*sin(d*x + c) + 15*B*a^4*b^3*sin(d*x + c) + 183*A*a^3*b^4*sin(d*x + c) - 45*B*a^2*b^5*sin(d*x + c) - 87*A*a*b^6*sin(d*x + c) + 33*B*b^7*sin(d*x + c) + 8*B*a^7 - 8*A*a^6*b - 36*B*a^5*b^2 + 36*A*a^4*b^3 + 72*B*a^3*b^4 - 72*A*a^2*b^5 - 88*B*a*b^6 + 88*A*b^7)/((a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*(sin(d*x + c)^2 - 1)^3))/d","B",0
1552,1,570,0,0.266028," ","integrate(cos(d*x+c)^7*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{60 \, {\left(7 \, B a^{6} - 6 \, A a^{5} b - 15 \, B a^{4} b^{2} + 12 \, A a^{3} b^{3} + 9 \, B a^{2} b^{4} - 6 \, A a b^{5} - B b^{6}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{b^{8}} - \frac{60 \, {\left(7 \, B a^{6} b \sin\left(d x + c\right) - 6 \, A a^{5} b^{2} \sin\left(d x + c\right) - 15 \, B a^{4} b^{3} \sin\left(d x + c\right) + 12 \, A a^{3} b^{4} \sin\left(d x + c\right) + 9 \, B a^{2} b^{5} \sin\left(d x + c\right) - 6 \, A a b^{6} \sin\left(d x + c\right) - B b^{7} \sin\left(d x + c\right) + 6 \, B a^{7} - 5 \, A a^{6} b - 12 \, B a^{5} b^{2} + 9 \, A a^{4} b^{3} + 6 \, B a^{3} b^{4} - 3 \, A a^{2} b^{5} - A b^{7}\right)}}{{\left(b \sin\left(d x + c\right) + a\right)} b^{8}} + \frac{10 \, B b^{10} \sin\left(d x + c\right)^{6} - 24 \, B a b^{9} \sin\left(d x + c\right)^{5} + 12 \, A b^{10} \sin\left(d x + c\right)^{5} + 45 \, B a^{2} b^{8} \sin\left(d x + c\right)^{4} - 30 \, A a b^{9} \sin\left(d x + c\right)^{4} - 45 \, B b^{10} \sin\left(d x + c\right)^{4} - 80 \, B a^{3} b^{7} \sin\left(d x + c\right)^{3} + 60 \, A a^{2} b^{8} \sin\left(d x + c\right)^{3} + 120 \, B a b^{9} \sin\left(d x + c\right)^{3} - 60 \, A b^{10} \sin\left(d x + c\right)^{3} + 150 \, B a^{4} b^{6} \sin\left(d x + c\right)^{2} - 120 \, A a^{3} b^{7} \sin\left(d x + c\right)^{2} - 270 \, B a^{2} b^{8} \sin\left(d x + c\right)^{2} + 180 \, A a b^{9} \sin\left(d x + c\right)^{2} + 90 \, B b^{10} \sin\left(d x + c\right)^{2} - 360 \, B a^{5} b^{5} \sin\left(d x + c\right) + 300 \, A a^{4} b^{6} \sin\left(d x + c\right) + 720 \, B a^{3} b^{7} \sin\left(d x + c\right) - 540 \, A a^{2} b^{8} \sin\left(d x + c\right) - 360 \, B a b^{9} \sin\left(d x + c\right) + 180 \, A b^{10} \sin\left(d x + c\right)}{b^{12}}}{60 \, d}"," ",0,"-1/60*(60*(7*B*a^6 - 6*A*a^5*b - 15*B*a^4*b^2 + 12*A*a^3*b^3 + 9*B*a^2*b^4 - 6*A*a*b^5 - B*b^6)*log(abs(b*sin(d*x + c) + a))/b^8 - 60*(7*B*a^6*b*sin(d*x + c) - 6*A*a^5*b^2*sin(d*x + c) - 15*B*a^4*b^3*sin(d*x + c) + 12*A*a^3*b^4*sin(d*x + c) + 9*B*a^2*b^5*sin(d*x + c) - 6*A*a*b^6*sin(d*x + c) - B*b^7*sin(d*x + c) + 6*B*a^7 - 5*A*a^6*b - 12*B*a^5*b^2 + 9*A*a^4*b^3 + 6*B*a^3*b^4 - 3*A*a^2*b^5 - A*b^7)/((b*sin(d*x + c) + a)*b^8) + (10*B*b^10*sin(d*x + c)^6 - 24*B*a*b^9*sin(d*x + c)^5 + 12*A*b^10*sin(d*x + c)^5 + 45*B*a^2*b^8*sin(d*x + c)^4 - 30*A*a*b^9*sin(d*x + c)^4 - 45*B*b^10*sin(d*x + c)^4 - 80*B*a^3*b^7*sin(d*x + c)^3 + 60*A*a^2*b^8*sin(d*x + c)^3 + 120*B*a*b^9*sin(d*x + c)^3 - 60*A*b^10*sin(d*x + c)^3 + 150*B*a^4*b^6*sin(d*x + c)^2 - 120*A*a^3*b^7*sin(d*x + c)^2 - 270*B*a^2*b^8*sin(d*x + c)^2 + 180*A*a*b^9*sin(d*x + c)^2 + 90*B*b^10*sin(d*x + c)^2 - 360*B*a^5*b^5*sin(d*x + c) + 300*A*a^4*b^6*sin(d*x + c) + 720*B*a^3*b^7*sin(d*x + c) - 540*A*a^2*b^8*sin(d*x + c) - 360*B*a*b^9*sin(d*x + c) + 180*A*b^10*sin(d*x + c))/b^12)/d","A",0
1553,1,328,0,0.245301," ","integrate(cos(d*x+c)^5*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{12 \, {\left(5 \, B a^{4} - 4 \, A a^{3} b - 6 \, B a^{2} b^{2} + 4 \, A a b^{3} + B b^{4}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{b^{6}} - \frac{12 \, {\left(5 \, B a^{4} b \sin\left(d x + c\right) - 4 \, A a^{3} b^{2} \sin\left(d x + c\right) - 6 \, B a^{2} b^{3} \sin\left(d x + c\right) + 4 \, A a b^{4} \sin\left(d x + c\right) + B b^{5} \sin\left(d x + c\right) + 4 \, B a^{5} - 3 \, A a^{4} b - 4 \, B a^{3} b^{2} + 2 \, A a^{2} b^{3} + A b^{5}\right)}}{{\left(b \sin\left(d x + c\right) + a\right)} b^{6}} + \frac{3 \, B b^{6} \sin\left(d x + c\right)^{4} - 8 \, B a b^{5} \sin\left(d x + c\right)^{3} + 4 \, A b^{6} \sin\left(d x + c\right)^{3} + 18 \, B a^{2} b^{4} \sin\left(d x + c\right)^{2} - 12 \, A a b^{5} \sin\left(d x + c\right)^{2} - 12 \, B b^{6} \sin\left(d x + c\right)^{2} - 48 \, B a^{3} b^{3} \sin\left(d x + c\right) + 36 \, A a^{2} b^{4} \sin\left(d x + c\right) + 48 \, B a b^{5} \sin\left(d x + c\right) - 24 \, A b^{6} \sin\left(d x + c\right)}{b^{8}}}{12 \, d}"," ",0,"1/12*(12*(5*B*a^4 - 4*A*a^3*b - 6*B*a^2*b^2 + 4*A*a*b^3 + B*b^4)*log(abs(b*sin(d*x + c) + a))/b^6 - 12*(5*B*a^4*b*sin(d*x + c) - 4*A*a^3*b^2*sin(d*x + c) - 6*B*a^2*b^3*sin(d*x + c) + 4*A*a*b^4*sin(d*x + c) + B*b^5*sin(d*x + c) + 4*B*a^5 - 3*A*a^4*b - 4*B*a^3*b^2 + 2*A*a^2*b^3 + A*b^5)/((b*sin(d*x + c) + a)*b^6) + (3*B*b^6*sin(d*x + c)^4 - 8*B*a*b^5*sin(d*x + c)^3 + 4*A*b^6*sin(d*x + c)^3 + 18*B*a^2*b^4*sin(d*x + c)^2 - 12*A*a*b^5*sin(d*x + c)^2 - 12*B*b^6*sin(d*x + c)^2 - 48*B*a^3*b^3*sin(d*x + c) + 36*A*a^2*b^4*sin(d*x + c) + 48*B*a*b^5*sin(d*x + c) - 24*A*b^6*sin(d*x + c))/b^8)/d","A",0
1554,1,188,0,0.228456," ","integrate(cos(d*x+c)^3*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{{\left(b \sin\left(d x + c\right) + a\right)}^{2} {\left(B - \frac{2 \, {\left(3 \, B a b - A b^{2}\right)}}{{\left(b \sin\left(d x + c\right) + a\right)} b}\right)}}{b^{4}} - \frac{2 \, {\left(3 \, B a^{2} - 2 \, A a b - B b^{2}\right)} \log\left(\frac{{\left| b \sin\left(d x + c\right) + a \right|}}{{\left(b \sin\left(d x + c\right) + a\right)}^{2} {\left| b \right|}}\right)}{b^{4}} + \frac{2 \, {\left(\frac{B a^{3} b^{2}}{b \sin\left(d x + c\right) + a} - \frac{A a^{2} b^{3}}{b \sin\left(d x + c\right) + a} - \frac{B a b^{4}}{b \sin\left(d x + c\right) + a} + \frac{A b^{5}}{b \sin\left(d x + c\right) + a}\right)}}{b^{6}}}{2 \, d}"," ",0,"-1/2*((b*sin(d*x + c) + a)^2*(B - 2*(3*B*a*b - A*b^2)/((b*sin(d*x + c) + a)*b))/b^4 - 2*(3*B*a^2 - 2*A*a*b - B*b^2)*log(abs(b*sin(d*x + c) + a)/((b*sin(d*x + c) + a)^2*abs(b)))/b^4 + 2*(B*a^3*b^2/(b*sin(d*x + c) + a) - A*a^2*b^3/(b*sin(d*x + c) + a) - B*a*b^4/(b*sin(d*x + c) + a) + A*b^5/(b*sin(d*x + c) + a))/b^6)/d","A",0
1555,1,80,0,0.169780," ","integrate(cos(d*x+c)*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{B {\left(\frac{\log\left(\frac{{\left| b \sin\left(d x + c\right) + a \right|}}{{\left(b \sin\left(d x + c\right) + a\right)}^{2} {\left| b \right|}}\right)}{b} - \frac{a}{{\left(b \sin\left(d x + c\right) + a\right)} b}\right)}}{b} + \frac{A}{{\left(b \sin\left(d x + c\right) + a\right)} b}}{d}"," ",0,"-(B*(log(abs(b*sin(d*x + c) + a)/((b*sin(d*x + c) + a)^2*abs(b)))/b - a/((b*sin(d*x + c) + a)*b))/b + A/((b*sin(d*x + c) + a)*b))/d","A",0
1556,1,205,0,0.230197," ","integrate(sec(d*x+c)*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(B a^{2} b - 2 \, A a b^{2} + B b^{3}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{4} b - 2 \, a^{2} b^{3} + b^{5}} - \frac{{\left(A + B\right)} \log\left({\left| -\sin\left(d x + c\right) + 1 \right|}\right)}{a^{2} + 2 \, a b + b^{2}} + \frac{{\left(A - B\right)} \log\left({\left| -\sin\left(d x + c\right) - 1 \right|}\right)}{a^{2} - 2 \, a b + b^{2}} - \frac{2 \, {\left(B a^{2} b \sin\left(d x + c\right) - 2 \, A a b^{2} \sin\left(d x + c\right) + B b^{3} \sin\left(d x + c\right) + 2 \, B a^{3} - 3 \, A a^{2} b + A b^{3}\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(b \sin\left(d x + c\right) + a\right)}}}{2 \, d}"," ",0,"1/2*(2*(B*a^2*b - 2*A*a*b^2 + B*b^3)*log(abs(b*sin(d*x + c) + a))/(a^4*b - 2*a^2*b^3 + b^5) - (A + B)*log(abs(-sin(d*x + c) + 1))/(a^2 + 2*a*b + b^2) + (A - B)*log(abs(-sin(d*x + c) - 1))/(a^2 - 2*a*b + b^2) - 2*(B*a^2*b*sin(d*x + c) - 2*A*a*b^2*sin(d*x + c) + B*b^3*sin(d*x + c) + 2*B*a^3 - 3*A*a^2*b + A*b^3)/((a^4 - 2*a^2*b^2 + b^4)*(b*sin(d*x + c) + a)))/d","A",0
1557,1,335,0,0.291944," ","integrate(sec(d*x+c)^3*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{4 \, {\left(3 \, B a^{2} b^{3} - 4 \, A a b^{4} + B b^{5}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}} - \frac{{\left(A a - 3 \, A b + 2 \, B b\right)} \log\left({\left| \sin\left(d x + c\right) + 1 \right|}\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} + \frac{{\left(A a + 3 \, A b + 2 \, B b\right)} \log\left({\left| -\sin\left(d x + c\right) + 1 \right|}\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} + \frac{2 \, {\left(A a^{2} b \sin\left(d x + c\right)^{2} - 4 \, B a b^{2} \sin\left(d x + c\right)^{2} + 3 \, A b^{3} \sin\left(d x + c\right)^{2} + A a^{3} \sin\left(d x + c\right) - B a^{2} b \sin\left(d x + c\right) - A a b^{2} \sin\left(d x + c\right) + B b^{3} \sin\left(d x + c\right) + B a^{3} - 2 \, A a^{2} b + 3 \, B a b^{2} - 2 \, A b^{3}\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(b \sin\left(d x + c\right)^{3} + a \sin\left(d x + c\right)^{2} - b \sin\left(d x + c\right) - a\right)}}}{4 \, d}"," ",0,"-1/4*(4*(3*B*a^2*b^3 - 4*A*a*b^4 + B*b^5)*log(abs(b*sin(d*x + c) + a))/(a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7) - (A*a - 3*A*b + 2*B*b)*log(abs(sin(d*x + c) + 1))/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) + (A*a + 3*A*b + 2*B*b)*log(abs(-sin(d*x + c) + 1))/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) + 2*(A*a^2*b*sin(d*x + c)^2 - 4*B*a*b^2*sin(d*x + c)^2 + 3*A*b^3*sin(d*x + c)^2 + A*a^3*sin(d*x + c) - B*a^2*b*sin(d*x + c) - A*a*b^2*sin(d*x + c) + B*b^3*sin(d*x + c) + B*a^3 - 2*A*a^2*b + 3*B*a*b^2 - 2*A*b^3)/((a^4 - 2*a^2*b^2 + b^4)*(b*sin(d*x + c)^3 + a*sin(d*x + c)^2 - b*sin(d*x + c) - a)))/d","A",0
1558,1,761,0,0.342217," ","integrate(sec(d*x+c)^5*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{16 \, {\left(5 \, B a^{2} b^{5} - 6 \, A a b^{6} + B b^{7}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{8} b - 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} - 4 \, a^{2} b^{7} + b^{9}} - \frac{{\left(3 \, A a^{2} + 12 \, A a b + 2 \, B a b + 15 \, A b^{2} + 8 \, B b^{2}\right)} \log\left({\left| -\sin\left(d x + c\right) + 1 \right|}\right)}{a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}} + \frac{{\left(3 \, A a^{2} - 12 \, A a b + 2 \, B a b + 15 \, A b^{2} - 8 \, B b^{2}\right)} \log\left({\left| -\sin\left(d x + c\right) - 1 \right|}\right)}{a^{4} - 4 \, a^{3} b + 6 \, a^{2} b^{2} - 4 \, a b^{3} + b^{4}} - \frac{16 \, {\left(5 \, B a^{2} b^{5} \sin\left(d x + c\right) - 6 \, A a b^{6} \sin\left(d x + c\right) + B b^{7} \sin\left(d x + c\right) + 6 \, B a^{3} b^{4} - 7 \, A a^{2} b^{5} + A b^{7}\right)}}{{\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} {\left(b \sin\left(d x + c\right) + a\right)}} + \frac{2 \, {\left(30 \, B a^{2} b^{4} \sin\left(d x + c\right)^{4} - 36 \, A a b^{5} \sin\left(d x + c\right)^{4} + 6 \, B b^{6} \sin\left(d x + c\right)^{4} - 3 \, A a^{6} \sin\left(d x + c\right)^{3} - 2 \, B a^{5} b \sin\left(d x + c\right)^{3} + 15 \, A a^{4} b^{2} \sin\left(d x + c\right)^{3} - 12 \, B a^{3} b^{3} \sin\left(d x + c\right)^{3} - 5 \, A a^{2} b^{4} \sin\left(d x + c\right)^{3} + 14 \, B a b^{5} \sin\left(d x + c\right)^{3} - 7 \, A b^{6} \sin\left(d x + c\right)^{3} + 12 \, B a^{4} b^{2} \sin\left(d x + c\right)^{2} - 16 \, A a^{3} b^{3} \sin\left(d x + c\right)^{2} - 68 \, B a^{2} b^{4} \sin\left(d x + c\right)^{2} + 88 \, A a b^{5} \sin\left(d x + c\right)^{2} - 16 \, B b^{6} \sin\left(d x + c\right)^{2} + 5 \, A a^{6} \sin\left(d x + c\right) - 2 \, B a^{5} b \sin\left(d x + c\right) - 17 \, A a^{4} b^{2} \sin\left(d x + c\right) + 20 \, B a^{3} b^{3} \sin\left(d x + c\right) + 3 \, A a^{2} b^{4} \sin\left(d x + c\right) - 18 \, B a b^{5} \sin\left(d x + c\right) + 9 \, A b^{6} \sin\left(d x + c\right) + 2 \, B a^{6} - 4 \, A a^{5} b - 14 \, B a^{4} b^{2} + 24 \, A a^{3} b^{3} + 36 \, B a^{2} b^{4} - 56 \, A a b^{5} + 12 \, B b^{6}\right)}}{{\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} {\left(\sin\left(d x + c\right)^{2} - 1\right)}^{2}}}{16 \, d}"," ",0,"1/16*(16*(5*B*a^2*b^5 - 6*A*a*b^6 + B*b^7)*log(abs(b*sin(d*x + c) + a))/(a^8*b - 4*a^6*b^3 + 6*a^4*b^5 - 4*a^2*b^7 + b^9) - (3*A*a^2 + 12*A*a*b + 2*B*a*b + 15*A*b^2 + 8*B*b^2)*log(abs(-sin(d*x + c) + 1))/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4) + (3*A*a^2 - 12*A*a*b + 2*B*a*b + 15*A*b^2 - 8*B*b^2)*log(abs(-sin(d*x + c) - 1))/(a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4) - 16*(5*B*a^2*b^5*sin(d*x + c) - 6*A*a*b^6*sin(d*x + c) + B*b^7*sin(d*x + c) + 6*B*a^3*b^4 - 7*A*a^2*b^5 + A*b^7)/((a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*(b*sin(d*x + c) + a)) + 2*(30*B*a^2*b^4*sin(d*x + c)^4 - 36*A*a*b^5*sin(d*x + c)^4 + 6*B*b^6*sin(d*x + c)^4 - 3*A*a^6*sin(d*x + c)^3 - 2*B*a^5*b*sin(d*x + c)^3 + 15*A*a^4*b^2*sin(d*x + c)^3 - 12*B*a^3*b^3*sin(d*x + c)^3 - 5*A*a^2*b^4*sin(d*x + c)^3 + 14*B*a*b^5*sin(d*x + c)^3 - 7*A*b^6*sin(d*x + c)^3 + 12*B*a^4*b^2*sin(d*x + c)^2 - 16*A*a^3*b^3*sin(d*x + c)^2 - 68*B*a^2*b^4*sin(d*x + c)^2 + 88*A*a*b^5*sin(d*x + c)^2 - 16*B*b^6*sin(d*x + c)^2 + 5*A*a^6*sin(d*x + c) - 2*B*a^5*b*sin(d*x + c) - 17*A*a^4*b^2*sin(d*x + c) + 20*B*a^3*b^3*sin(d*x + c) + 3*A*a^2*b^4*sin(d*x + c) - 18*B*a*b^5*sin(d*x + c) + 9*A*b^6*sin(d*x + c) + 2*B*a^6 - 4*A*a^5*b - 14*B*a^4*b^2 + 24*A*a^3*b^3 + 36*B*a^2*b^4 - 56*A*a*b^5 + 12*B*b^6)/((a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*(sin(d*x + c)^2 - 1)^2))/d","B",0
1559,1,1185,0,0.429119," ","integrate(sec(d*x+c)^7*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{96 \, {\left(7 \, B a^{2} b^{7} - 8 \, A a b^{8} + B b^{9}\right)} \log\left({\left| b \sin\left(d x + c\right) + a \right|}\right)}{a^{10} b - 5 \, a^{8} b^{3} + 10 \, a^{6} b^{5} - 10 \, a^{4} b^{7} + 5 \, a^{2} b^{9} - b^{11}} + \frac{3 \, {\left(5 \, A a^{3} + 25 \, A a^{2} b + 2 \, B a^{2} b + 47 \, A a b^{2} + 10 \, B a b^{2} + 35 \, A b^{3} + 16 \, B b^{3}\right)} \log\left({\left| -\sin\left(d x + c\right) + 1 \right|}\right)}{a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}} - \frac{3 \, {\left(5 \, A a^{3} - 25 \, A a^{2} b + 2 \, B a^{2} b + 47 \, A a b^{2} - 10 \, B a b^{2} - 35 \, A b^{3} + 16 \, B b^{3}\right)} \log\left({\left| -\sin\left(d x + c\right) - 1 \right|}\right)}{a^{5} - 5 \, a^{4} b + 10 \, a^{3} b^{2} - 10 \, a^{2} b^{3} + 5 \, a b^{4} - b^{5}} - \frac{96 \, {\left(7 \, B a^{2} b^{7} \sin\left(d x + c\right) - 8 \, A a b^{8} \sin\left(d x + c\right) + B b^{9} \sin\left(d x + c\right) + 8 \, B a^{3} b^{6} - 9 \, A a^{2} b^{7} + A b^{9}\right)}}{{\left(a^{10} - 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} - 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} - b^{10}\right)} {\left(b \sin\left(d x + c\right) + a\right)}} + \frac{2 \, {\left(308 \, B a^{2} b^{6} \sin\left(d x + c\right)^{6} - 352 \, A a b^{7} \sin\left(d x + c\right)^{6} + 44 \, B b^{8} \sin\left(d x + c\right)^{6} + 15 \, A a^{8} \sin\left(d x + c\right)^{5} + 6 \, B a^{7} b \sin\left(d x + c\right)^{5} - 84 \, A a^{6} b^{2} \sin\left(d x + c\right)^{5} - 42 \, B a^{5} b^{3} \sin\left(d x + c\right)^{5} + 210 \, A a^{4} b^{4} \sin\left(d x + c\right)^{5} - 78 \, B a^{3} b^{5} \sin\left(d x + c\right)^{5} - 84 \, A a^{2} b^{6} \sin\left(d x + c\right)^{5} + 114 \, B a b^{7} \sin\left(d x + c\right)^{5} - 57 \, A b^{8} \sin\left(d x + c\right)^{5} + 120 \, B a^{4} b^{4} \sin\left(d x + c\right)^{4} - 144 \, A a^{3} b^{5} \sin\left(d x + c\right)^{4} - 1020 \, B a^{2} b^{6} \sin\left(d x + c\right)^{4} + 1200 \, A a b^{7} \sin\left(d x + c\right)^{4} - 156 \, B b^{8} \sin\left(d x + c\right)^{4} - 40 \, A a^{8} \sin\left(d x + c\right)^{3} - 16 \, B a^{7} b \sin\left(d x + c\right)^{3} + 224 \, A a^{6} b^{2} \sin\left(d x + c\right)^{3} + 48 \, B a^{5} b^{3} \sin\left(d x + c\right)^{3} - 480 \, A a^{4} b^{4} \sin\left(d x + c\right)^{3} + 240 \, B a^{3} b^{5} \sin\left(d x + c\right)^{3} + 160 \, A a^{2} b^{6} \sin\left(d x + c\right)^{3} - 272 \, B a b^{7} \sin\left(d x + c\right)^{3} + 136 \, A b^{8} \sin\left(d x + c\right)^{3} + 36 \, B a^{6} b^{2} \sin\left(d x + c\right)^{2} - 48 \, A a^{5} b^{3} \sin\left(d x + c\right)^{2} - 300 \, B a^{4} b^{4} \sin\left(d x + c\right)^{2} + 384 \, A a^{3} b^{5} \sin\left(d x + c\right)^{2} + 1128 \, B a^{2} b^{6} \sin\left(d x + c\right)^{2} - 1392 \, A a b^{7} \sin\left(d x + c\right)^{2} + 192 \, B b^{8} \sin\left(d x + c\right)^{2} + 33 \, A a^{8} \sin\left(d x + c\right) - 6 \, B a^{7} b \sin\left(d x + c\right) - 156 \, A a^{6} b^{2} \sin\left(d x + c\right) + 42 \, B a^{5} b^{3} \sin\left(d x + c\right) + 270 \, A a^{4} b^{4} \sin\left(d x + c\right) - 210 \, B a^{3} b^{5} \sin\left(d x + c\right) - 60 \, A a^{2} b^{6} \sin\left(d x + c\right) + 174 \, B a b^{7} \sin\left(d x + c\right) - 87 \, A b^{8} \sin\left(d x + c\right) + 8 \, B a^{8} - 16 \, A a^{7} b - 52 \, B a^{6} b^{2} + 96 \, A a^{5} b^{3} + 180 \, B a^{4} b^{4} - 288 \, A a^{3} b^{5} - 400 \, B a^{2} b^{6} + 560 \, A a b^{7} - 88 \, B b^{8}\right)}}{{\left(a^{10} - 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} - 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} - b^{10}\right)} {\left(\sin\left(d x + c\right)^{2} - 1\right)}^{3}}}{96 \, d}"," ",0,"-1/96*(96*(7*B*a^2*b^7 - 8*A*a*b^8 + B*b^9)*log(abs(b*sin(d*x + c) + a))/(a^10*b - 5*a^8*b^3 + 10*a^6*b^5 - 10*a^4*b^7 + 5*a^2*b^9 - b^11) + 3*(5*A*a^3 + 25*A*a^2*b + 2*B*a^2*b + 47*A*a*b^2 + 10*B*a*b^2 + 35*A*b^3 + 16*B*b^3)*log(abs(-sin(d*x + c) + 1))/(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5) - 3*(5*A*a^3 - 25*A*a^2*b + 2*B*a^2*b + 47*A*a*b^2 - 10*B*a*b^2 - 35*A*b^3 + 16*B*b^3)*log(abs(-sin(d*x + c) - 1))/(a^5 - 5*a^4*b + 10*a^3*b^2 - 10*a^2*b^3 + 5*a*b^4 - b^5) - 96*(7*B*a^2*b^7*sin(d*x + c) - 8*A*a*b^8*sin(d*x + c) + B*b^9*sin(d*x + c) + 8*B*a^3*b^6 - 9*A*a^2*b^7 + A*b^9)/((a^10 - 5*a^8*b^2 + 10*a^6*b^4 - 10*a^4*b^6 + 5*a^2*b^8 - b^10)*(b*sin(d*x + c) + a)) + 2*(308*B*a^2*b^6*sin(d*x + c)^6 - 352*A*a*b^7*sin(d*x + c)^6 + 44*B*b^8*sin(d*x + c)^6 + 15*A*a^8*sin(d*x + c)^5 + 6*B*a^7*b*sin(d*x + c)^5 - 84*A*a^6*b^2*sin(d*x + c)^5 - 42*B*a^5*b^3*sin(d*x + c)^5 + 210*A*a^4*b^4*sin(d*x + c)^5 - 78*B*a^3*b^5*sin(d*x + c)^5 - 84*A*a^2*b^6*sin(d*x + c)^5 + 114*B*a*b^7*sin(d*x + c)^5 - 57*A*b^8*sin(d*x + c)^5 + 120*B*a^4*b^4*sin(d*x + c)^4 - 144*A*a^3*b^5*sin(d*x + c)^4 - 1020*B*a^2*b^6*sin(d*x + c)^4 + 1200*A*a*b^7*sin(d*x + c)^4 - 156*B*b^8*sin(d*x + c)^4 - 40*A*a^8*sin(d*x + c)^3 - 16*B*a^7*b*sin(d*x + c)^3 + 224*A*a^6*b^2*sin(d*x + c)^3 + 48*B*a^5*b^3*sin(d*x + c)^3 - 480*A*a^4*b^4*sin(d*x + c)^3 + 240*B*a^3*b^5*sin(d*x + c)^3 + 160*A*a^2*b^6*sin(d*x + c)^3 - 272*B*a*b^7*sin(d*x + c)^3 + 136*A*b^8*sin(d*x + c)^3 + 36*B*a^6*b^2*sin(d*x + c)^2 - 48*A*a^5*b^3*sin(d*x + c)^2 - 300*B*a^4*b^4*sin(d*x + c)^2 + 384*A*a^3*b^5*sin(d*x + c)^2 + 1128*B*a^2*b^6*sin(d*x + c)^2 - 1392*A*a*b^7*sin(d*x + c)^2 + 192*B*b^8*sin(d*x + c)^2 + 33*A*a^8*sin(d*x + c) - 6*B*a^7*b*sin(d*x + c) - 156*A*a^6*b^2*sin(d*x + c) + 42*B*a^5*b^3*sin(d*x + c) + 270*A*a^4*b^4*sin(d*x + c) - 210*B*a^3*b^5*sin(d*x + c) - 60*A*a^2*b^6*sin(d*x + c) + 174*B*a*b^7*sin(d*x + c) - 87*A*b^8*sin(d*x + c) + 8*B*a^8 - 16*A*a^7*b - 52*B*a^6*b^2 + 96*A*a^5*b^3 + 180*B*a^4*b^4 - 288*A*a^3*b^5 - 400*B*a^2*b^6 + 560*A*a*b^7 - 88*B*b^8)/((a^10 - 5*a^8*b^2 + 10*a^6*b^4 - 10*a^4*b^6 + 5*a^2*b^8 - b^10)*(sin(d*x + c)^2 - 1)^3))/d","B",0
1560,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(-1-m)*(a+b*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""giac"")","\int {\left(B \sin\left(f x + e\right) + A\right)} \left(g \cos\left(f x + e\right)\right)^{-m - 1} {\left(b \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(g*cos(f*x + e))^(-m - 1)*(b*sin(f*x + e) + a)^m, x)","F",0
1561,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^p/(a+b*sin(f*x+e))/(c+d*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{p}}{{\left(b \sin\left(f x + e\right) + a\right)} {\left(d \sin\left(f x + e\right) + c\right)}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^p/((b*sin(f*x + e) + a)*(d*sin(f*x + e) + c)), x)","F",0
1562,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^p/(a+b*sin(f*x+e))/(c+d*sin(f*x+e))^2,x, algorithm=""giac"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{p}}{{\left(b \sin\left(f x + e\right) + a\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{2}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^p/((b*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^2), x)","F",0
1563,0,0,0,0.000000," ","integrate((g*sec(f*x+e))^p/(a+b*sin(f*x+e))/(c+d*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(g \sec\left(f x + e\right)\right)^{p}}{{\left(b \sin\left(f x + e\right) + a\right)} {\left(d \sin\left(f x + e\right) + c\right)}}\,{d x}"," ",0,"integrate((g*sec(f*x + e))^p/((b*sin(f*x + e) + a)*(d*sin(f*x + e) + c)), x)","F",0
