1,1,95,0,0.449308," ","integrate(sin(f*x+e)^3*(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","-\frac{16 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} a^{2} - 80 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a^{2} - 15 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2}}{240 \, f}"," ",0,"-1/240*(16*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*a^2 - 80*(cos(f*x + e)^3 - 3*cos(f*x + e))*a^2 - 15*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*a^2)/f","A",0
2,1,143,0,0.428300," ","integrate(sin(f*x+e)^3*(a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","-\frac{192 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} a^{3} - 320 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a^{3} - 5 \, {\left(4 \, \sin\left(2 \, f x + 2 \, e\right)^{3} + 60 \, f x + 60 \, e + 9 \, \sin\left(4 \, f x + 4 \, e\right) - 48 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a^{3} - 90 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a^{3}}{960 \, f}"," ",0,"-1/960*(192*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*a^3 - 320*(cos(f*x + e)^3 - 3*cos(f*x + e))*a^3 - 5*(4*sin(2*f*x + 2*e)^3 + 60*f*x + 60*e + 9*sin(4*f*x + 4*e) - 48*sin(2*f*x + 2*e))*a^3 - 90*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*a^3)/f","A",0
3,1,180,0,0.833601," ","integrate(sin(x)^4/(a+a*sin(x)),x, algorithm=""maxima"")","-\frac{\frac{7 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{39 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{24 \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{24 \, \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{9 \, \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} + \frac{9 \, \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} + 16}{3 \, {\left(a + \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{3 \, a \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{3 \, a \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{3 \, a \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{3 \, a \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} + \frac{a \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} + \frac{a \sin\left(x\right)^{7}}{{\left(\cos\left(x\right) + 1\right)}^{7}}\right)}} - \frac{3 \, \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{a}"," ",0,"-1/3*(7*sin(x)/(cos(x) + 1) + 39*sin(x)^2/(cos(x) + 1)^2 + 24*sin(x)^3/(cos(x) + 1)^3 + 24*sin(x)^4/(cos(x) + 1)^4 + 9*sin(x)^5/(cos(x) + 1)^5 + 9*sin(x)^6/(cos(x) + 1)^6 + 16)/(a + a*sin(x)/(cos(x) + 1) + 3*a*sin(x)^2/(cos(x) + 1)^2 + 3*a*sin(x)^3/(cos(x) + 1)^3 + 3*a*sin(x)^4/(cos(x) + 1)^4 + 3*a*sin(x)^5/(cos(x) + 1)^5 + a*sin(x)^6/(cos(x) + 1)^6 + a*sin(x)^7/(cos(x) + 1)^7) - 3*arctan(sin(x)/(cos(x) + 1))/a","B",0
4,1,128,0,0.648798," ","integrate(sin(x)^3/(a+a*sin(x)),x, algorithm=""maxima"")","\frac{\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{5 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{3 \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + 4}{a + \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{2 \, a \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{2 \, a \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{a \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{a \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}}} + \frac{3 \, \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{a}"," ",0,"(sin(x)/(cos(x) + 1) + 5*sin(x)^2/(cos(x) + 1)^2 + 3*sin(x)^3/(cos(x) + 1)^3 + 3*sin(x)^4/(cos(x) + 1)^4 + 4)/(a + a*sin(x)/(cos(x) + 1) + 2*a*sin(x)^2/(cos(x) + 1)^2 + 2*a*sin(x)^3/(cos(x) + 1)^3 + a*sin(x)^4/(cos(x) + 1)^4 + a*sin(x)^5/(cos(x) + 1)^5) + 3*arctan(sin(x)/(cos(x) + 1))/a","B",0
5,1,78,0,0.491847," ","integrate(sin(x)^2/(a+a*sin(x)),x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 2\right)}}{a + \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{a \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{a \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}}} - \frac{2 \, \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{a}"," ",0,"-2*(sin(x)/(cos(x) + 1) + sin(x)^2/(cos(x) + 1)^2 + 2)/(a + a*sin(x)/(cos(x) + 1) + a*sin(x)^2/(cos(x) + 1)^2 + a*sin(x)^3/(cos(x) + 1)^3) - 2*arctan(sin(x)/(cos(x) + 1))/a","B",0
6,1,32,0,0.823572," ","integrate(sin(x)/(a+a*sin(x)),x, algorithm=""maxima"")","\frac{2 \, \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{a} + \frac{2}{a + \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1}}"," ",0,"2*arctan(sin(x)/(cos(x) + 1))/a + 2/(a + a*sin(x)/(cos(x) + 1))","A",0
7,1,16,0,0.541814," ","integrate(1/(a+a*sin(x)),x, algorithm=""maxima"")","-\frac{2}{a + \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1}}"," ",0,"-2/(a + a*sin(x)/(cos(x) + 1))","A",0
8,1,31,0,0.846549," ","integrate(csc(x)/(a+a*sin(x)),x, algorithm=""maxima"")","\frac{\log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{a} + \frac{2}{a + \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1}}"," ",0,"log(sin(x)/(cos(x) + 1))/a + 2/(a + a*sin(x)/(cos(x) + 1))","A",0
9,1,68,0,0.942215," ","integrate(csc(x)^2/(a+a*sin(x)),x, algorithm=""maxima"")","-\frac{\frac{5 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + 1}{2 \, {\left(\frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{a \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}\right)}} - \frac{\log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{a} + \frac{\sin\left(x\right)}{2 \, a {\left(\cos\left(x\right) + 1\right)}}"," ",0,"-1/2*(5*sin(x)/(cos(x) + 1) + 1)/(a*sin(x)/(cos(x) + 1) + a*sin(x)^2/(cos(x) + 1)^2) - log(sin(x)/(cos(x) + 1))/a + 1/2*sin(x)/(a*(cos(x) + 1))","B",0
10,1,97,0,0.411649," ","integrate(csc(x)^3/(a+a*sin(x)),x, algorithm=""maxima"")","-\frac{\frac{4 \, \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}}{8 \, a} + \frac{\frac{3 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{20 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - 1}{8 \, {\left(\frac{a \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{a \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}}\right)}} + \frac{3 \, \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{2 \, a}"," ",0,"-1/8*(4*sin(x)/(cos(x) + 1) - sin(x)^2/(cos(x) + 1)^2)/a + 1/8*(3*sin(x)/(cos(x) + 1) + 20*sin(x)^2/(cos(x) + 1)^2 - 1)/(a*sin(x)^2/(cos(x) + 1)^2 + a*sin(x)^3/(cos(x) + 1)^3) + 3/2*log(sin(x)/(cos(x) + 1))/a","B",0
11,1,120,0,0.569348," ","integrate(csc(x)^4/(a+a*sin(x)),x, algorithm=""maxima"")","\frac{\frac{21 \, \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{3 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{\sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}}}{24 \, a} + \frac{\frac{2 \, \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{18 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{69 \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} - 1}{24 \, {\left(\frac{a \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{a \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}}\right)}} - \frac{3 \, \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{2 \, a}"," ",0,"1/24*(21*sin(x)/(cos(x) + 1) - 3*sin(x)^2/(cos(x) + 1)^2 + sin(x)^3/(cos(x) + 1)^3)/a + 1/24*(2*sin(x)/(cos(x) + 1) - 18*sin(x)^2/(cos(x) + 1)^2 - 69*sin(x)^3/(cos(x) + 1)^3 - 1)/(a*sin(x)^3/(cos(x) + 1)^3 + a*sin(x)^4/(cos(x) + 1)^4) - 3/2*log(sin(x)/(cos(x) + 1))/a","B",0
12,1,198,0,1.241224," ","integrate(sin(x)^4/(a+a*sin(x))^2,x, algorithm=""maxima"")","\frac{\frac{75 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{97 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{126 \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{98 \, \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{63 \, \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} + \frac{21 \, \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} + 32}{3 \, {\left(a^{2} + \frac{3 \, a^{2} \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{5 \, a^{2} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{7 \, a^{2} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{7 \, a^{2} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{5 \, a^{2} \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} + \frac{3 \, a^{2} \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} + \frac{a^{2} \sin\left(x\right)^{7}}{{\left(\cos\left(x\right) + 1\right)}^{7}}\right)}} + \frac{7 \, \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{a^{2}}"," ",0,"1/3*(75*sin(x)/(cos(x) + 1) + 97*sin(x)^2/(cos(x) + 1)^2 + 126*sin(x)^3/(cos(x) + 1)^3 + 98*sin(x)^4/(cos(x) + 1)^4 + 63*sin(x)^5/(cos(x) + 1)^5 + 21*sin(x)^6/(cos(x) + 1)^6 + 32)/(a^2 + 3*a^2*sin(x)/(cos(x) + 1) + 5*a^2*sin(x)^2/(cos(x) + 1)^2 + 7*a^2*sin(x)^3/(cos(x) + 1)^3 + 7*a^2*sin(x)^4/(cos(x) + 1)^4 + 5*a^2*sin(x)^5/(cos(x) + 1)^5 + 3*a^2*sin(x)^6/(cos(x) + 1)^6 + a^2*sin(x)^7/(cos(x) + 1)^7) + 7*arctan(sin(x)/(cos(x) + 1))/a^2","B",0
13,1,144,0,0.870191," ","integrate(sin(x)^3/(a+a*sin(x))^2,x, algorithm=""maxima"")","-\frac{4 \, {\left(\frac{12 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{11 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{9 \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + 5\right)}}{3 \, {\left(a^{2} + \frac{3 \, a^{2} \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{4 \, a^{2} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{4 \, a^{2} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{3 \, a^{2} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{a^{2} \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}}\right)}} - \frac{4 \, \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{a^{2}}"," ",0,"-4/3*(12*sin(x)/(cos(x) + 1) + 11*sin(x)^2/(cos(x) + 1)^2 + 9*sin(x)^3/(cos(x) + 1)^3 + 3*sin(x)^4/(cos(x) + 1)^4 + 5)/(a^2 + 3*a^2*sin(x)/(cos(x) + 1) + 4*a^2*sin(x)^2/(cos(x) + 1)^2 + 4*a^2*sin(x)^3/(cos(x) + 1)^3 + 3*a^2*sin(x)^4/(cos(x) + 1)^4 + a^2*sin(x)^5/(cos(x) + 1)^5) - 4*arctan(sin(x)/(cos(x) + 1))/a^2","B",0
14,1,90,0,0.967609," ","integrate(sin(x)^2/(a+a*sin(x))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{9 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{3 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 4\right)}}{3 \, {\left(a^{2} + \frac{3 \, a^{2} \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{3 \, a^{2} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}}\right)}} + \frac{2 \, \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{a^{2}}"," ",0,"2/3*(9*sin(x)/(cos(x) + 1) + 3*sin(x)^2/(cos(x) + 1)^2 + 4)/(a^2 + 3*a^2*sin(x)/(cos(x) + 1) + 3*a^2*sin(x)^2/(cos(x) + 1)^2 + a^2*sin(x)^3/(cos(x) + 1)^3) + 2*arctan(sin(x)/(cos(x) + 1))/a^2","B",0
15,1,62,0,0.602540," ","integrate(sin(x)/(a+a*sin(x))^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{3 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + 1\right)}}{3 \, {\left(a^{2} + \frac{3 \, a^{2} \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{3 \, a^{2} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}}\right)}}"," ",0,"-2/3*(3*sin(x)/(cos(x) + 1) + 1)/(a^2 + 3*a^2*sin(x)/(cos(x) + 1) + 3*a^2*sin(x)^2/(cos(x) + 1)^2 + a^2*sin(x)^3/(cos(x) + 1)^3)","B",0
16,1,74,0,0.633581," ","integrate(1/(a+a*sin(x))^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{3 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{3 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 2\right)}}{3 \, {\left(a^{2} + \frac{3 \, a^{2} \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{3 \, a^{2} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}}\right)}}"," ",0,"-2/3*(3*sin(x)/(cos(x) + 1) + 3*sin(x)^2/(cos(x) + 1)^2 + 2)/(a^2 + 3*a^2*sin(x)/(cos(x) + 1) + 3*a^2*sin(x)^2/(cos(x) + 1)^2 + a^2*sin(x)^3/(cos(x) + 1)^3)","B",0
17,1,89,0,0.999072," ","integrate(csc(x)/(a+a*sin(x))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{9 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{6 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 5\right)}}{3 \, {\left(a^{2} + \frac{3 \, a^{2} \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{3 \, a^{2} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}}\right)}} + \frac{\log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{a^{2}}"," ",0,"2/3*(9*sin(x)/(cos(x) + 1) + 6*sin(x)^2/(cos(x) + 1)^2 + 5)/(a^2 + 3*a^2*sin(x)/(cos(x) + 1) + 3*a^2*sin(x)^2/(cos(x) + 1)^2 + a^2*sin(x)^3/(cos(x) + 1)^3) + log(sin(x)/(cos(x) + 1))/a^2","B",0
18,1,126,0,0.922013," ","integrate(csc(x)^2/(a+a*sin(x))^2,x, algorithm=""maxima"")","-\frac{\frac{41 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{69 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{39 \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + 3}{6 \, {\left(\frac{a^{2} \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{3 \, a^{2} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{3 \, a^{2} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{a^{2} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}}\right)}} - \frac{2 \, \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{a^{2}} + \frac{\sin\left(x\right)}{2 \, a^{2} {\left(\cos\left(x\right) + 1\right)}}"," ",0,"-1/6*(41*sin(x)/(cos(x) + 1) + 69*sin(x)^2/(cos(x) + 1)^2 + 39*sin(x)^3/(cos(x) + 1)^3 + 3)/(a^2*sin(x)/(cos(x) + 1) + 3*a^2*sin(x)^2/(cos(x) + 1)^2 + 3*a^2*sin(x)^3/(cos(x) + 1)^3 + a^2*sin(x)^4/(cos(x) + 1)^4) - 2*log(sin(x)/(cos(x) + 1))/a^2 + 1/2*sin(x)/(a^2*(cos(x) + 1))","B",0
19,1,155,0,0.681540," ","integrate(csc(x)^3/(a+a*sin(x))^2,x, algorithm=""maxima"")","\frac{\frac{15 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{239 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{405 \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{216 \, \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} - 3}{24 \, {\left(\frac{a^{2} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{3 \, a^{2} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{3 \, a^{2} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{a^{2} \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}}\right)}} - \frac{\frac{8 \, \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}}{8 \, a^{2}} + \frac{7 \, \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{2 \, a^{2}}"," ",0,"1/24*(15*sin(x)/(cos(x) + 1) + 239*sin(x)^2/(cos(x) + 1)^2 + 405*sin(x)^3/(cos(x) + 1)^3 + 216*sin(x)^4/(cos(x) + 1)^4 - 3)/(a^2*sin(x)^2/(cos(x) + 1)^2 + 3*a^2*sin(x)^3/(cos(x) + 1)^3 + 3*a^2*sin(x)^4/(cos(x) + 1)^4 + a^2*sin(x)^5/(cos(x) + 1)^5) - 1/8*(8*sin(x)/(cos(x) + 1) - sin(x)^2/(cos(x) + 1)^2)/a^2 + 7/2*log(sin(x)/(cos(x) + 1))/a^2","B",0
20,1,178,0,1.040493," ","integrate(csc(x)^4/(a+a*sin(x))^2,x, algorithm=""maxima"")","\frac{\frac{3 \, \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{30 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{342 \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} - \frac{561 \, \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} - \frac{285 \, \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} - 1}{24 \, {\left(\frac{a^{2} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{3 \, a^{2} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{3 \, a^{2} \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} + \frac{a^{2} \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}}\right)}} + \frac{\frac{45 \, \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{6 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{\sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}}}{24 \, a^{2}} - \frac{5 \, \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{a^{2}}"," ",0,"1/24*(3*sin(x)/(cos(x) + 1) - 30*sin(x)^2/(cos(x) + 1)^2 - 342*sin(x)^3/(cos(x) + 1)^3 - 561*sin(x)^4/(cos(x) + 1)^4 - 285*sin(x)^5/(cos(x) + 1)^5 - 1)/(a^2*sin(x)^3/(cos(x) + 1)^3 + 3*a^2*sin(x)^4/(cos(x) + 1)^4 + 3*a^2*sin(x)^5/(cos(x) + 1)^5 + a^2*sin(x)^6/(cos(x) + 1)^6) + 1/24*(45*sin(x)/(cos(x) + 1) - 6*sin(x)^2/(cos(x) + 1)^2 + sin(x)^3/(cos(x) + 1)^3)/a^2 - 5*log(sin(x)/(cos(x) + 1))/a^2","B",0
21,1,306,0,0.844436," ","integrate(sin(x)^6/(a+a*sin(x))^3,x, algorithm=""maxima"")","-\frac{\frac{2375 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{5347 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{9230 \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{12622 \, \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{13340 \, \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} + \frac{11684 \, \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} + \frac{8050 \, \sin\left(x\right)^{7}}{{\left(\cos\left(x\right) + 1\right)}^{7}} + \frac{4370 \, \sin\left(x\right)^{8}}{{\left(\cos\left(x\right) + 1\right)}^{8}} + \frac{1725 \, \sin\left(x\right)^{9}}{{\left(\cos\left(x\right) + 1\right)}^{9}} + \frac{345 \, \sin\left(x\right)^{10}}{{\left(\cos\left(x\right) + 1\right)}^{10}} + 544}{15 \, {\left(a^{3} + \frac{5 \, a^{3} \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{13 \, a^{3} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{25 \, a^{3} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{38 \, a^{3} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{46 \, a^{3} \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} + \frac{46 \, a^{3} \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} + \frac{38 \, a^{3} \sin\left(x\right)^{7}}{{\left(\cos\left(x\right) + 1\right)}^{7}} + \frac{25 \, a^{3} \sin\left(x\right)^{8}}{{\left(\cos\left(x\right) + 1\right)}^{8}} + \frac{13 \, a^{3} \sin\left(x\right)^{9}}{{\left(\cos\left(x\right) + 1\right)}^{9}} + \frac{5 \, a^{3} \sin\left(x\right)^{10}}{{\left(\cos\left(x\right) + 1\right)}^{10}} + \frac{a^{3} \sin\left(x\right)^{11}}{{\left(\cos\left(x\right) + 1\right)}^{11}}\right)}} - \frac{23 \, \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{a^{3}}"," ",0,"-1/15*(2375*sin(x)/(cos(x) + 1) + 5347*sin(x)^2/(cos(x) + 1)^2 + 9230*sin(x)^3/(cos(x) + 1)^3 + 12622*sin(x)^4/(cos(x) + 1)^4 + 13340*sin(x)^5/(cos(x) + 1)^5 + 11684*sin(x)^6/(cos(x) + 1)^6 + 8050*sin(x)^7/(cos(x) + 1)^7 + 4370*sin(x)^8/(cos(x) + 1)^8 + 1725*sin(x)^9/(cos(x) + 1)^9 + 345*sin(x)^10/(cos(x) + 1)^10 + 544)/(a^3 + 5*a^3*sin(x)/(cos(x) + 1) + 13*a^3*sin(x)^2/(cos(x) + 1)^2 + 25*a^3*sin(x)^3/(cos(x) + 1)^3 + 38*a^3*sin(x)^4/(cos(x) + 1)^4 + 46*a^3*sin(x)^5/(cos(x) + 1)^5 + 46*a^3*sin(x)^6/(cos(x) + 1)^6 + 38*a^3*sin(x)^7/(cos(x) + 1)^7 + 25*a^3*sin(x)^8/(cos(x) + 1)^8 + 13*a^3*sin(x)^9/(cos(x) + 1)^9 + 5*a^3*sin(x)^10/(cos(x) + 1)^10 + a^3*sin(x)^11/(cos(x) + 1)^11) - 23*arctan(sin(x)/(cos(x) + 1))/a^3","B",0
22,1,252,0,0.771858," ","integrate(sin(x)^5/(a+a*sin(x))^3,x, algorithm=""maxima"")","\frac{\frac{1325 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{2673 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{3805 \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{4329 \, \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{3575 \, \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} + \frac{2275 \, \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} + \frac{975 \, \sin\left(x\right)^{7}}{{\left(\cos\left(x\right) + 1\right)}^{7}} + \frac{195 \, \sin\left(x\right)^{8}}{{\left(\cos\left(x\right) + 1\right)}^{8}} + 304}{15 \, {\left(a^{3} + \frac{5 \, a^{3} \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{12 \, a^{3} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{20 \, a^{3} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{26 \, a^{3} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{26 \, a^{3} \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} + \frac{20 \, a^{3} \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} + \frac{12 \, a^{3} \sin\left(x\right)^{7}}{{\left(\cos\left(x\right) + 1\right)}^{7}} + \frac{5 \, a^{3} \sin\left(x\right)^{8}}{{\left(\cos\left(x\right) + 1\right)}^{8}} + \frac{a^{3} \sin\left(x\right)^{9}}{{\left(\cos\left(x\right) + 1\right)}^{9}}\right)}} + \frac{13 \, \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{a^{3}}"," ",0,"1/15*(1325*sin(x)/(cos(x) + 1) + 2673*sin(x)^2/(cos(x) + 1)^2 + 3805*sin(x)^3/(cos(x) + 1)^3 + 4329*sin(x)^4/(cos(x) + 1)^4 + 3575*sin(x)^5/(cos(x) + 1)^5 + 2275*sin(x)^6/(cos(x) + 1)^6 + 975*sin(x)^7/(cos(x) + 1)^7 + 195*sin(x)^8/(cos(x) + 1)^8 + 304)/(a^3 + 5*a^3*sin(x)/(cos(x) + 1) + 12*a^3*sin(x)^2/(cos(x) + 1)^2 + 20*a^3*sin(x)^3/(cos(x) + 1)^3 + 26*a^3*sin(x)^4/(cos(x) + 1)^4 + 26*a^3*sin(x)^5/(cos(x) + 1)^5 + 20*a^3*sin(x)^6/(cos(x) + 1)^6 + 12*a^3*sin(x)^7/(cos(x) + 1)^7 + 5*a^3*sin(x)^8/(cos(x) + 1)^8 + a^3*sin(x)^9/(cos(x) + 1)^9) + 13*arctan(sin(x)/(cos(x) + 1))/a^3","B",0
23,1,198,0,0.931286," ","integrate(sin(x)^4/(a+a*sin(x))^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{105 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{189 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{200 \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{160 \, \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{75 \, \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} + \frac{15 \, \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} + 24\right)}}{5 \, {\left(a^{3} + \frac{5 \, a^{3} \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{11 \, a^{3} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{15 \, a^{3} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{15 \, a^{3} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{11 \, a^{3} \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} + \frac{5 \, a^{3} \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} + \frac{a^{3} \sin\left(x\right)^{7}}{{\left(\cos\left(x\right) + 1\right)}^{7}}\right)}} - \frac{6 \, \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{a^{3}}"," ",0,"-2/5*(105*sin(x)/(cos(x) + 1) + 189*sin(x)^2/(cos(x) + 1)^2 + 200*sin(x)^3/(cos(x) + 1)^3 + 160*sin(x)^4/(cos(x) + 1)^4 + 75*sin(x)^5/(cos(x) + 1)^5 + 15*sin(x)^6/(cos(x) + 1)^6 + 24)/(a^3 + 5*a^3*sin(x)/(cos(x) + 1) + 11*a^3*sin(x)^2/(cos(x) + 1)^2 + 15*a^3*sin(x)^3/(cos(x) + 1)^3 + 15*a^3*sin(x)^4/(cos(x) + 1)^4 + 11*a^3*sin(x)^5/(cos(x) + 1)^5 + 5*a^3*sin(x)^6/(cos(x) + 1)^6 + a^3*sin(x)^7/(cos(x) + 1)^7) - 6*arctan(sin(x)/(cos(x) + 1))/a^3","B",0
24,1,144,0,1.024885," ","integrate(sin(x)^3/(a+a*sin(x))^3,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{95 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{145 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{75 \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + 22\right)}}{15 \, {\left(a^{3} + \frac{5 \, a^{3} \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{10 \, a^{3} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}}\right)}} + \frac{2 \, \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{a^{3}}"," ",0,"2/15*(95*sin(x)/(cos(x) + 1) + 145*sin(x)^2/(cos(x) + 1)^2 + 75*sin(x)^3/(cos(x) + 1)^3 + 15*sin(x)^4/(cos(x) + 1)^4 + 22)/(a^3 + 5*a^3*sin(x)/(cos(x) + 1) + 10*a^3*sin(x)^2/(cos(x) + 1)^2 + 10*a^3*sin(x)^3/(cos(x) + 1)^3 + 5*a^3*sin(x)^4/(cos(x) + 1)^4 + a^3*sin(x)^5/(cos(x) + 1)^5) + 2*arctan(sin(x)/(cos(x) + 1))/a^3","B",0
25,1,104,0,0.643659," ","integrate(sin(x)^2/(a+a*sin(x))^3,x, algorithm=""maxima"")","-\frac{4 \, {\left(\frac{5 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{10 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)}}{15 \, {\left(a^{3} + \frac{5 \, a^{3} \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{10 \, a^{3} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}}\right)}}"," ",0,"-4/15*(5*sin(x)/(cos(x) + 1) + 10*sin(x)^2/(cos(x) + 1)^2 + 1)/(a^3 + 5*a^3*sin(x)/(cos(x) + 1) + 10*a^3*sin(x)^2/(cos(x) + 1)^2 + 10*a^3*sin(x)^3/(cos(x) + 1)^3 + 5*a^3*sin(x)^4/(cos(x) + 1)^4 + a^3*sin(x)^5/(cos(x) + 1)^5)","B",0
26,1,116,0,0.688154," ","integrate(sin(x)/(a+a*sin(x))^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{5 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{5 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{5 \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + 1\right)}}{5 \, {\left(a^{3} + \frac{5 \, a^{3} \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{10 \, a^{3} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}}\right)}}"," ",0,"-2/5*(5*sin(x)/(cos(x) + 1) + 5*sin(x)^2/(cos(x) + 1)^2 + 5*sin(x)^3/(cos(x) + 1)^3 + 1)/(a^3 + 5*a^3*sin(x)/(cos(x) + 1) + 10*a^3*sin(x)^2/(cos(x) + 1)^2 + 10*a^3*sin(x)^3/(cos(x) + 1)^3 + 5*a^3*sin(x)^4/(cos(x) + 1)^4 + a^3*sin(x)^5/(cos(x) + 1)^5)","B",0
27,1,128,0,0.456512," ","integrate(1/(a+a*sin(x))^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{20 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{40 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{30 \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + 7\right)}}{15 \, {\left(a^{3} + \frac{5 \, a^{3} \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{10 \, a^{3} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}}\right)}}"," ",0,"-2/15*(20*sin(x)/(cos(x) + 1) + 40*sin(x)^2/(cos(x) + 1)^2 + 30*sin(x)^3/(cos(x) + 1)^3 + 15*sin(x)^4/(cos(x) + 1)^4 + 7)/(a^3 + 5*a^3*sin(x)/(cos(x) + 1) + 10*a^3*sin(x)^2/(cos(x) + 1)^2 + 10*a^3*sin(x)^3/(cos(x) + 1)^3 + 5*a^3*sin(x)^4/(cos(x) + 1)^4 + a^3*sin(x)^5/(cos(x) + 1)^5)","B",0
28,1,143,0,0.861467," ","integrate(csc(x)/(a+a*sin(x))^3,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{115 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{185 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{135 \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{45 \, \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + 32\right)}}{15 \, {\left(a^{3} + \frac{5 \, a^{3} \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{10 \, a^{3} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}}\right)}} + \frac{\log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{a^{3}}"," ",0,"2/15*(115*sin(x)/(cos(x) + 1) + 185*sin(x)^2/(cos(x) + 1)^2 + 135*sin(x)^3/(cos(x) + 1)^3 + 45*sin(x)^4/(cos(x) + 1)^4 + 32)/(a^3 + 5*a^3*sin(x)/(cos(x) + 1) + 10*a^3*sin(x)^2/(cos(x) + 1)^2 + 10*a^3*sin(x)^3/(cos(x) + 1)^3 + 5*a^3*sin(x)^4/(cos(x) + 1)^4 + a^3*sin(x)^5/(cos(x) + 1)^5) + log(sin(x)/(cos(x) + 1))/a^3","B",0
29,1,180,0,0.749503," ","integrate(csc(x)^2/(a+a*sin(x))^3,x, algorithm=""maxima"")","-\frac{\frac{121 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{410 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{610 \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{425 \, \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{125 \, \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} + 5}{10 \, {\left(\frac{a^{3} \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{5 \, a^{3} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{10 \, a^{3} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{5 \, a^{3} \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} + \frac{a^{3} \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}}\right)}} - \frac{3 \, \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{a^{3}} + \frac{\sin\left(x\right)}{2 \, a^{3} {\left(\cos\left(x\right) + 1\right)}}"," ",0,"-1/10*(121*sin(x)/(cos(x) + 1) + 410*sin(x)^2/(cos(x) + 1)^2 + 610*sin(x)^3/(cos(x) + 1)^3 + 425*sin(x)^4/(cos(x) + 1)^4 + 125*sin(x)^5/(cos(x) + 1)^5 + 5)/(a^3*sin(x)/(cos(x) + 1) + 5*a^3*sin(x)^2/(cos(x) + 1)^2 + 10*a^3*sin(x)^3/(cos(x) + 1)^3 + 10*a^3*sin(x)^4/(cos(x) + 1)^4 + 5*a^3*sin(x)^5/(cos(x) + 1)^5 + a^3*sin(x)^6/(cos(x) + 1)^6) - 3*log(sin(x)/(cos(x) + 1))/a^3 + 1/2*sin(x)/(a^3*(cos(x) + 1))","B",0
30,1,209,0,0.687675," ","integrate(csc(x)^3/(a+a*sin(x))^3,x, algorithm=""maxima"")","\frac{\frac{105 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{2782 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{9410 \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{13645 \, \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{9285 \, \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} + \frac{2580 \, \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} - 15}{120 \, {\left(\frac{a^{3} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{5 \, a^{3} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{10 \, a^{3} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{10 \, a^{3} \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} + \frac{5 \, a^{3} \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} + \frac{a^{3} \sin\left(x\right)^{7}}{{\left(\cos\left(x\right) + 1\right)}^{7}}\right)}} - \frac{\frac{12 \, \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}}{8 \, a^{3}} + \frac{13 \, \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{2 \, a^{3}}"," ",0,"1/120*(105*sin(x)/(cos(x) + 1) + 2782*sin(x)^2/(cos(x) + 1)^2 + 9410*sin(x)^3/(cos(x) + 1)^3 + 13645*sin(x)^4/(cos(x) + 1)^4 + 9285*sin(x)^5/(cos(x) + 1)^5 + 2580*sin(x)^6/(cos(x) + 1)^6 - 15)/(a^3*sin(x)^2/(cos(x) + 1)^2 + 5*a^3*sin(x)^3/(cos(x) + 1)^3 + 10*a^3*sin(x)^4/(cos(x) + 1)^4 + 10*a^3*sin(x)^5/(cos(x) + 1)^5 + 5*a^3*sin(x)^6/(cos(x) + 1)^6 + a^3*sin(x)^7/(cos(x) + 1)^7) - 1/8*(12*sin(x)/(cos(x) + 1) - sin(x)^2/(cos(x) + 1)^2)/a^3 + 13/2*log(sin(x)/(cos(x) + 1))/a^3","B",0
31,1,232,0,0.673733," ","integrate(csc(x)^4/(a+a*sin(x))^3,x, algorithm=""maxima"")","\frac{\frac{20 \, \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{230 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{4777 \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} - \frac{15785 \, \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} - \frac{22390 \, \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} - \frac{14940 \, \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} - \frac{4005 \, \sin\left(x\right)^{7}}{{\left(\cos\left(x\right) + 1\right)}^{7}} - 5}{120 \, {\left(\frac{a^{3} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{10 \, a^{3} \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} + \frac{10 \, a^{3} \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} + \frac{5 \, a^{3} \sin\left(x\right)^{7}}{{\left(\cos\left(x\right) + 1\right)}^{7}} + \frac{a^{3} \sin\left(x\right)^{8}}{{\left(\cos\left(x\right) + 1\right)}^{8}}\right)}} + \frac{\frac{81 \, \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{9 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{\sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}}}{24 \, a^{3}} - \frac{23 \, \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{2 \, a^{3}}"," ",0,"1/120*(20*sin(x)/(cos(x) + 1) - 230*sin(x)^2/(cos(x) + 1)^2 - 4777*sin(x)^3/(cos(x) + 1)^3 - 15785*sin(x)^4/(cos(x) + 1)^4 - 22390*sin(x)^5/(cos(x) + 1)^5 - 14940*sin(x)^6/(cos(x) + 1)^6 - 4005*sin(x)^7/(cos(x) + 1)^7 - 5)/(a^3*sin(x)^3/(cos(x) + 1)^3 + 5*a^3*sin(x)^4/(cos(x) + 1)^4 + 10*a^3*sin(x)^5/(cos(x) + 1)^5 + 10*a^3*sin(x)^6/(cos(x) + 1)^6 + 5*a^3*sin(x)^7/(cos(x) + 1)^7 + a^3*sin(x)^8/(cos(x) + 1)^8) + 1/24*(81*sin(x)/(cos(x) + 1) - 9*sin(x)^2/(cos(x) + 1)^2 + sin(x)^3/(cos(x) + 1)^3)/a^3 - 23/2*log(sin(x)/(cos(x) + 1))/a^3","B",0
32,0,0,0,0.000000," ","integrate(sin(d*x+c)^4*(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(d x + c\right) + a} \sin\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate(sqrt(a*sin(d*x + c) + a)*sin(d*x + c)^4, x)","F",0
33,0,0,0,0.000000," ","integrate(sin(d*x+c)^3*(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(d x + c\right) + a} \sin\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate(sqrt(a*sin(d*x + c) + a)*sin(d*x + c)^3, x)","F",0
34,0,0,0,0.000000," ","integrate(sin(d*x+c)^2*(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(d x + c\right) + a} \sin\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate(sqrt(a*sin(d*x + c) + a)*sin(d*x + c)^2, x)","F",0
35,0,0,0,0.000000," ","integrate(sin(d*x+c)*(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(d x + c\right) + a} \sin\left(d x + c\right)\,{d x}"," ",0,"integrate(sqrt(a*sin(d*x + c) + a)*sin(d*x + c), x)","F",0
36,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(a*sin(d*x + c) + a), x)","F",0
37,0,0,0,0.000000," ","integrate(csc(d*x+c)*(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(d x + c\right) + a} \csc\left(d x + c\right)\,{d x}"," ",0,"integrate(sqrt(a*sin(d*x + c) + a)*csc(d*x + c), x)","F",0
38,0,0,0,0.000000," ","integrate(csc(d*x+c)^2*(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(d x + c\right) + a} \csc\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate(sqrt(a*sin(d*x + c) + a)*csc(d*x + c)^2, x)","F",0
39,0,0,0,0.000000," ","integrate(csc(d*x+c)^3*(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(d x + c\right) + a} \csc\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate(sqrt(a*sin(d*x + c) + a)*csc(d*x + c)^3, x)","F",0
40,0,0,0,0.000000," ","integrate(csc(d*x+c)^4*(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(d x + c\right) + a} \csc\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate(sqrt(a*sin(d*x + c) + a)*csc(d*x + c)^4, x)","F",0
41,0,0,0,0.000000," ","integrate(csc(d*x+c)*(a-a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{-a \sin\left(d x + c\right) + a} \csc\left(d x + c\right)\,{d x}"," ",0,"integrate(sqrt(-a*sin(d*x + c) + a)*csc(d*x + c), x)","F",0
42,0,0,0,0.000000," ","integrate(csc(d*x+c)*(-a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(d x + c\right) - a} \csc\left(d x + c\right)\,{d x}"," ",0,"integrate(sqrt(a*sin(d*x + c) - a)*csc(d*x + c), x)","F",0
43,0,0,0,0.000000," ","integrate(csc(d*x+c)*(-a-a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{-a \sin\left(d x + c\right) - a} \csc\left(d x + c\right)\,{d x}"," ",0,"integrate(sqrt(-a*sin(d*x + c) - a)*csc(d*x + c), x)","F",0
44,0,0,0,0.000000," ","integrate(sin(d*x+c)^3*(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sin\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(3/2)*sin(d*x + c)^3, x)","F",0
45,0,0,0,0.000000," ","integrate(sin(d*x+c)^2*(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sin\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(3/2)*sin(d*x + c)^2, x)","F",0
46,0,0,0,0.000000," ","integrate(sin(d*x+c)*(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sin\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(3/2)*sin(d*x + c), x)","F",0
47,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(3/2), x)","F",0
48,0,0,0,0.000000," ","integrate(csc(d*x+c)*(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \csc\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(3/2)*csc(d*x + c), x)","F",0
49,0,0,0,0.000000," ","integrate(csc(d*x+c)^2*(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \csc\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(3/2)*csc(d*x + c)^2, x)","F",0
50,0,0,0,0.000000," ","integrate(csc(d*x+c)^3*(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \csc\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(3/2)*csc(d*x + c)^3, x)","F",0
51,0,0,0,0.000000," ","integrate(csc(d*x+c)^4*(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \csc\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(3/2)*csc(d*x + c)^4, x)","F",0
52,0,0,0,0.000000," ","integrate(sin(d*x+c)^3*(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sin\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(5/2)*sin(d*x + c)^3, x)","F",0
53,0,0,0,0.000000," ","integrate(sin(d*x+c)^2*(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sin\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(5/2)*sin(d*x + c)^2, x)","F",0
54,0,0,0,0.000000," ","integrate(sin(d*x+c)*(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sin\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(5/2)*sin(d*x + c), x)","F",0
55,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(5/2), x)","F",0
56,0,0,0,0.000000," ","integrate(csc(d*x+c)*(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} \csc\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(5/2)*csc(d*x + c), x)","F",0
57,0,0,0,0.000000," ","integrate(csc(d*x+c)^2*(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} \csc\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(5/2)*csc(d*x + c)^2, x)","F",0
58,0,0,0,0.000000," ","integrate(csc(d*x+c)^3*(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} \csc\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(5/2)*csc(d*x + c)^3, x)","F",0
59,0,0,0,0.000000," ","integrate(csc(d*x+c)^4*(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} \csc\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(5/2)*csc(d*x + c)^4, x)","F",0
60,0,0,0,0.000000," ","integrate(csc(d*x+c)^5*(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} \csc\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(5/2)*csc(d*x + c)^5, x)","F",0
61,0,0,0,0.000000," ","integrate(sin(d*x+c)^3/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sin\left(d x + c\right)^{3}}{\sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sin(d*x + c)^3/sqrt(a*sin(d*x + c) + a), x)","F",0
62,0,0,0,0.000000," ","integrate(sin(d*x+c)^2/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sin\left(d x + c\right)^{2}}{\sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sin(d*x + c)^2/sqrt(a*sin(d*x + c) + a), x)","F",0
63,0,0,0,0.000000," ","integrate(sin(d*x+c)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sin\left(d x + c\right)}{\sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sin(d*x + c)/sqrt(a*sin(d*x + c) + a), x)","F",0
64,0,0,0,0.000000," ","integrate(1/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(1/sqrt(a*sin(d*x + c) + a), x)","F",0
65,0,0,0,0.000000," ","integrate(csc(d*x+c)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\csc\left(d x + c\right)}{\sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(csc(d*x + c)/sqrt(a*sin(d*x + c) + a), x)","F",0
66,0,0,0,0.000000," ","integrate(csc(d*x+c)^2/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\csc\left(d x + c\right)^{2}}{\sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(csc(d*x + c)^2/sqrt(a*sin(d*x + c) + a), x)","F",0
67,0,0,0,0.000000," ","integrate(csc(d*x+c)^3/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\csc\left(d x + c\right)^{3}}{\sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(csc(d*x + c)^3/sqrt(a*sin(d*x + c) + a), x)","F",0
68,0,0,0,0.000000," ","integrate(sin(d*x+c)^4/(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\sin\left(d x + c\right)^{4}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sin(d*x + c)^4/(a*sin(d*x + c) + a)^(3/2), x)","F",0
69,0,0,0,0.000000," ","integrate(sin(d*x+c)^3/(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\sin\left(d x + c\right)^{3}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sin(d*x + c)^3/(a*sin(d*x + c) + a)^(3/2), x)","F",0
70,0,0,0,0.000000," ","integrate(sin(d*x+c)^2/(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\sin\left(d x + c\right)^{2}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sin(d*x + c)^2/(a*sin(d*x + c) + a)^(3/2), x)","F",0
71,0,0,0,0.000000," ","integrate(sin(d*x+c)/(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\sin\left(d x + c\right)}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sin(d*x + c)/(a*sin(d*x + c) + a)^(3/2), x)","F",0
72,0,0,0,0.000000," ","integrate(1/(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(-3/2), x)","F",0
73,0,0,0,0.000000," ","integrate(csc(d*x+c)/(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\csc\left(d x + c\right)}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(csc(d*x + c)/(a*sin(d*x + c) + a)^(3/2), x)","F",0
74,0,0,0,0.000000," ","integrate(csc(d*x+c)^2/(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\csc\left(d x + c\right)^{2}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(csc(d*x + c)^2/(a*sin(d*x + c) + a)^(3/2), x)","F",0
75,0,0,0,0.000000," ","integrate(csc(d*x+c)^3/(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\csc\left(d x + c\right)^{3}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(csc(d*x + c)^3/(a*sin(d*x + c) + a)^(3/2), x)","F",0
76,0,0,0,0.000000," ","integrate(sin(d*x+c)^5/(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\sin\left(d x + c\right)^{5}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sin(d*x + c)^5/(a*sin(d*x + c) + a)^(5/2), x)","F",0
77,0,0,0,0.000000," ","integrate(sin(d*x+c)^4/(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\sin\left(d x + c\right)^{4}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sin(d*x + c)^4/(a*sin(d*x + c) + a)^(5/2), x)","F",0
78,0,0,0,0.000000," ","integrate(sin(d*x+c)^3/(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\sin\left(d x + c\right)^{3}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sin(d*x + c)^3/(a*sin(d*x + c) + a)^(5/2), x)","F",0
79,0,0,0,0.000000," ","integrate(sin(d*x+c)^2/(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\sin\left(d x + c\right)^{2}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sin(d*x + c)^2/(a*sin(d*x + c) + a)^(5/2), x)","F",0
80,0,0,0,0.000000," ","integrate(sin(d*x+c)/(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\sin\left(d x + c\right)}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sin(d*x + c)/(a*sin(d*x + c) + a)^(5/2), x)","F",0
81,0,0,0,0.000000," ","integrate(1/(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(-5/2), x)","F",0
82,0,0,0,0.000000," ","integrate(csc(d*x+c)/(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\csc\left(d x + c\right)}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(csc(d*x + c)/(a*sin(d*x + c) + a)^(5/2), x)","F",0
83,0,0,0,0.000000," ","integrate(csc(d*x+c)^2/(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\csc\left(d x + c\right)^{2}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(csc(d*x + c)^2/(a*sin(d*x + c) + a)^(5/2), x)","F",0
84,-1,0,0,0.000000," ","integrate(csc(d*x+c)^3/(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
85,1,210,0,0.930452," ","integrate((a+a*sin(f*x+e))^(1/2)/sin(f*x+e)^(1/2),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{2} \sqrt{a} \left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)^{\frac{3}{2}} - 3 \, \sqrt{2} {\left(\sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}\right)}\right) + \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}\right)}\right)\right)} \sqrt{a} + 6 \, \sqrt{2} \sqrt{a} \sqrt{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}} - \frac{2 \, {\left(\frac{3 \, \sqrt{2} \sqrt{a} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sqrt{2} \sqrt{a} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)}}{\sqrt{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}}}{3 \, f}"," ",0,"-1/3*(2*sqrt(2)*sqrt(a)*(sin(f*x + e)/(cos(f*x + e) + 1))^(3/2) - 3*sqrt(2)*(sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(sin(f*x + e)/(cos(f*x + e) + 1)))) + sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(sin(f*x + e)/(cos(f*x + e) + 1)))))*sqrt(a) + 6*sqrt(2)*sqrt(a)*sqrt(sin(f*x + e)/(cos(f*x + e) + 1)) - 2*(3*sqrt(2)*sqrt(a)*sin(f*x + e)/(cos(f*x + e) + 1) + sqrt(2)*sqrt(a)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)/sqrt(sin(f*x + e)/(cos(f*x + e) + 1)))/f","B",0
86,0,0,0,0.000000," ","integrate((a-a*sin(f*x+e))^(1/2)/(-sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a \sin\left(f x + e\right) + a}}{\sqrt{-\sin\left(f x + e\right)}}\,{d x}"," ",0,"integrate(sqrt(-a*sin(f*x + e) + a)/sqrt(-sin(f*x + e)), x)","F",0
87,0,0,0,0.000000," ","integrate(1/sin(x)^(1/2)/(1+sin(x))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{\sin\left(x\right) + 1} \sqrt{\sin\left(x\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(sin(x) + 1)*sqrt(sin(x))), x)","F",0
88,0,0,0,0.000000," ","integrate(1/sin(x)^(1/2)/(a+a*sin(x))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{a \sin\left(x\right) + a} \sqrt{\sin\left(x\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(a*sin(x) + a)*sqrt(sin(x))), x)","F",0
89,0,0,0,0.000000," ","integrate(1/(1-sin(x))^(1/2)/sin(x)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-\sin\left(x\right) + 1} \sqrt{\sin\left(x\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(-sin(x) + 1)*sqrt(sin(x))), x)","F",0
90,0,0,0,0.000000," ","integrate(1/sin(x)^(1/2)/(a-a*sin(x))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-a \sin\left(x\right) + a} \sqrt{\sin\left(x\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(-a*sin(x) + a)*sqrt(sin(x))), x)","F",0
91,0,0,0,0.000000," ","integrate(sin(d*x+c)^(1/3)/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\sin\left(d x + c\right)^{\frac{1}{3}}}{{\left(a \sin\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sin(d*x + c)^(1/3)/(a*sin(d*x + c) + a)^2, x)","F",0
92,0,0,0,0.000000," ","integrate(sin(d*x+c)^3*(a+a*sin(d*x+c))^(2/3),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{2}{3}} \sin\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(2/3)*sin(d*x + c)^3, x)","F",0
93,0,0,0,0.000000," ","integrate(sin(d*x+c)^2*(a+a*sin(d*x+c))^(2/3),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{2}{3}} \sin\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(2/3)*sin(d*x + c)^2, x)","F",0
94,0,0,0,0.000000," ","integrate(sin(d*x+c)*(a+a*sin(d*x+c))^(2/3),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{2}{3}} \sin\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(2/3)*sin(d*x + c), x)","F",0
95,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(2/3),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{2}{3}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(2/3), x)","F",0
96,0,0,0,0.000000," ","integrate(csc(d*x+c)*(a+a*sin(d*x+c))^(2/3),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{2}{3}} \csc\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(2/3)*csc(d*x + c), x)","F",0
97,0,0,0,0.000000," ","integrate(csc(d*x+c)^2*(a+a*sin(d*x+c))^(2/3),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{2}{3}} \csc\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(2/3)*csc(d*x + c)^2, x)","F",0
98,0,0,0,0.000000," ","integrate(sin(d*x+c)^3*(a+a*sin(d*x+c))^(4/3),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{4}{3}} \sin\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(4/3)*sin(d*x + c)^3, x)","F",0
99,0,0,0,0.000000," ","integrate(sin(d*x+c)^2*(a+a*sin(d*x+c))^(4/3),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{4}{3}} \sin\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(4/3)*sin(d*x + c)^2, x)","F",0
100,0,0,0,0.000000," ","integrate(sin(d*x+c)*(a+a*sin(d*x+c))^(4/3),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{4}{3}} \sin\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(4/3)*sin(d*x + c), x)","F",0
101,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(4/3),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{4}{3}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(4/3), x)","F",0
102,0,0,0,0.000000," ","integrate(csc(d*x+c)*(a+a*sin(d*x+c))^(4/3),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{4}{3}} \csc\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(4/3)*csc(d*x + c), x)","F",0
103,0,0,0,0.000000," ","integrate(csc(d*x+c)^2*(a+a*sin(d*x+c))^(4/3),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{4}{3}} \csc\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(4/3)*csc(d*x + c)^2, x)","F",0
104,0,0,0,0.000000," ","integrate(sin(d*x+c)^3/(a+a*sin(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{\sin\left(d x + c\right)^{3}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(sin(d*x + c)^3/(a*sin(d*x + c) + a)^(1/3), x)","F",0
105,0,0,0,0.000000," ","integrate(sin(d*x+c)^2/(a+a*sin(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{\sin\left(d x + c\right)^{2}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(sin(d*x + c)^2/(a*sin(d*x + c) + a)^(1/3), x)","F",0
106,0,0,0,0.000000," ","integrate(sin(d*x+c)/(a+a*sin(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{\sin\left(d x + c\right)}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(sin(d*x + c)/(a*sin(d*x + c) + a)^(1/3), x)","F",0
107,0,0,0,0.000000," ","integrate(1/(a+a*sin(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(-1/3), x)","F",0
108,0,0,0,0.000000," ","integrate(csc(d*x+c)/(a+a*sin(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{\csc\left(d x + c\right)}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(csc(d*x + c)/(a*sin(d*x + c) + a)^(1/3), x)","F",0
109,0,0,0,0.000000," ","integrate(csc(d*x+c)^2/(a+a*sin(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{\csc\left(d x + c\right)^{2}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(csc(d*x + c)^2/(a*sin(d*x + c) + a)^(1/3), x)","F",0
110,0,0,0,0.000000," ","integrate(sin(d*x+c)^3/(a+a*sin(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{\sin\left(d x + c\right)^{3}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(sin(d*x + c)^3/(a*sin(d*x + c) + a)^(4/3), x)","F",0
111,0,0,0,0.000000," ","integrate(sin(d*x+c)^2/(a+a*sin(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{\sin\left(d x + c\right)^{2}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(sin(d*x + c)^2/(a*sin(d*x + c) + a)^(4/3), x)","F",0
112,0,0,0,0.000000," ","integrate(sin(d*x+c)/(a+a*sin(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{\sin\left(d x + c\right)}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(sin(d*x + c)/(a*sin(d*x + c) + a)^(4/3), x)","F",0
113,0,0,0,0.000000," ","integrate(1/(a+a*sin(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(-4/3), x)","F",0
114,0,0,0,0.000000," ","integrate(csc(d*x+c)/(a+a*sin(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{\csc\left(d x + c\right)}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(csc(d*x + c)/(a*sin(d*x + c) + a)^(4/3), x)","F",0
115,0,0,0,0.000000," ","integrate(csc(d*x+c)^2/(a+a*sin(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{\csc\left(d x + c\right)^{2}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(csc(d*x + c)^2/(a*sin(d*x + c) + a)^(4/3), x)","F",0
116,0,0,0,0.000000," ","integrate(sin(f*x+e)^n*(1+sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \sin\left(f x + e\right)^{n} {\left(\sin\left(f x + e\right) + 1\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sin(f*x + e)^n*(sin(f*x + e) + 1)^(3/2), x)","F",0
117,0,0,0,0.000000," ","integrate(sin(f*x+e)^n*(1+sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sin\left(f x + e\right)^{n} \sqrt{\sin\left(f x + e\right) + 1}\,{d x}"," ",0,"integrate(sin(f*x + e)^n*sqrt(sin(f*x + e) + 1), x)","F",0
118,0,0,0,0.000000," ","integrate(sin(f*x+e)^n/(1+sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sin\left(f x + e\right)^{n}}{\sqrt{\sin\left(f x + e\right) + 1}}\,{d x}"," ",0,"integrate(sin(f*x + e)^n/sqrt(sin(f*x + e) + 1), x)","F",0
119,0,0,0,0.000000," ","integrate(sin(f*x+e)^n/(1+sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{\sin\left(f x + e\right)^{n}}{{\left(\sin\left(f x + e\right) + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sin(f*x + e)^n/(sin(f*x + e) + 1)^(3/2), x)","F",0
120,0,0,0,0.000000," ","integrate(sin(f*x+e)^n*(a+a*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} \sin\left(f x + e\right)^{n}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(3/2)*sin(f*x + e)^n, x)","F",0
121,0,0,0,0.000000," ","integrate(sin(f*x+e)^n*(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(f x + e\right) + a} \sin\left(f x + e\right)^{n}\,{d x}"," ",0,"integrate(sqrt(a*sin(f*x + e) + a)*sin(f*x + e)^n, x)","F",0
122,0,0,0,0.000000," ","integrate(sin(f*x+e)^n/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sin\left(f x + e\right)^{n}}{\sqrt{a \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate(sin(f*x + e)^n/sqrt(a*sin(f*x + e) + a), x)","F",0
123,0,0,0,0.000000," ","integrate(sin(f*x+e)^n/(a+a*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{\sin\left(f x + e\right)^{n}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sin(f*x + e)^n/(a*sin(f*x + e) + a)^(3/2), x)","F",0
124,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^n*(1+sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \left(d \sin\left(f x + e\right)\right)^{n} {\left(\sin\left(f x + e\right) + 1\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((d*sin(f*x + e))^n*(sin(f*x + e) + 1)^(3/2), x)","F",0
125,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^n*(1+sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \left(d \sin\left(f x + e\right)\right)^{n} \sqrt{\sin\left(f x + e\right) + 1}\,{d x}"," ",0,"integrate((d*sin(f*x + e))^n*sqrt(sin(f*x + e) + 1), x)","F",0
126,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^n/(1+sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(d \sin\left(f x + e\right)\right)^{n}}{\sqrt{\sin\left(f x + e\right) + 1}}\,{d x}"," ",0,"integrate((d*sin(f*x + e))^n/sqrt(sin(f*x + e) + 1), x)","F",0
127,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^n/(1+sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{\left(d \sin\left(f x + e\right)\right)^{n}}{{\left(\sin\left(f x + e\right) + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*sin(f*x + e))^n/(sin(f*x + e) + 1)^(3/2), x)","F",0
128,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^n*(a+a*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} \left(d \sin\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(3/2)*(d*sin(f*x + e))^n, x)","F",0
129,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^n*(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(f x + e\right) + a} \left(d \sin\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate(sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e))^n, x)","F",0
130,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^n/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(d \sin\left(f x + e\right)\right)^{n}}{\sqrt{a \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((d*sin(f*x + e))^n/sqrt(a*sin(f*x + e) + a), x)","F",0
131,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^n/(a+a*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{\left(d \sin\left(f x + e\right)\right)^{n}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*sin(f*x + e))^n/(a*sin(f*x + e) + a)^(3/2), x)","F",0
132,0,0,0,0.000000," ","integrate(sin(f*x+e)^n*(1+sin(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(\sin\left(f x + e\right) + 1\right)}^{m} \sin\left(f x + e\right)^{n}\,{d x}"," ",0,"integrate((sin(f*x + e) + 1)^m*sin(f*x + e)^n, x)","F",0
133,0,0,0,0.000000," ","integrate((1-sin(f*x+e))^m*(-sin(f*x+e))^n,x, algorithm=""maxima"")","\int \left(-\sin\left(f x + e\right)\right)^{n} {\left(-\sin\left(f x + e\right) + 1\right)}^{m}\,{d x}"," ",0,"integrate((-sin(f*x + e))^n*(-sin(f*x + e) + 1)^m, x)","F",0
134,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^n*(1+sin(f*x+e))^m,x, algorithm=""maxima"")","\int \left(d \sin\left(f x + e\right)\right)^{n} {\left(\sin\left(f x + e\right) + 1\right)}^{m}\,{d x}"," ",0,"integrate((d*sin(f*x + e))^n*(sin(f*x + e) + 1)^m, x)","F",0
135,0,0,0,0.000000," ","integrate((1-sin(f*x+e))^m*(d*sin(f*x+e))^n,x, algorithm=""maxima"")","\int \left(d \sin\left(f x + e\right)\right)^{n} {\left(-\sin\left(f x + e\right) + 1\right)}^{m}\,{d x}"," ",0,"integrate((d*sin(f*x + e))^n*(-sin(f*x + e) + 1)^m, x)","F",0
136,0,0,0,0.000000," ","integrate(sin(f*x+e)^n*(a+a*sin(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} \sin\left(f x + e\right)^{n}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*sin(f*x + e)^n, x)","F",0
137,0,0,0,0.000000," ","integrate((-sin(f*x+e))^n*(a-a*sin(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(-a \sin\left(f x + e\right) + a\right)}^{m} \left(-\sin\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((-a*sin(f*x + e) + a)^m*(-sin(f*x + e))^n, x)","F",0
138,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^n*(a+a*sin(f*x+e))^m,x, algorithm=""maxima"")","\int {\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((a*sin(f*x + e) + a)^m*(d*sin(f*x + e))^n, x)","F",0
139,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^n*(a-a*sin(f*x+e))^m,x, algorithm=""maxima"")","\int {\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((-a*sin(f*x + e) + a)^m*(d*sin(f*x + e))^n, x)","F",0
140,0,0,0,0.000000," ","integrate(sin(d*x+c)^4*(a+a*sin(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^n*sin(d*x + c)^4, x)","F",0
141,0,0,0,0.000000," ","integrate(sin(d*x+c)^3*(a+a*sin(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^n*sin(d*x + c)^3, x)","F",0
142,0,0,0,0.000000," ","integrate(sin(d*x+c)^2*(a+a*sin(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^n*sin(d*x + c)^2, x)","F",0
143,0,0,0,0.000000," ","integrate(sin(d*x+c)*(a+a*sin(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^n*sin(d*x + c), x)","F",0
144,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^n, x)","F",0
145,0,0,0,0.000000," ","integrate(csc(d*x+c)*(a+a*sin(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{n} \csc\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^n*csc(d*x + c), x)","F",0
146,0,0,0,0.000000," ","integrate(csc(d*x+c)^2*(a+a*sin(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{n} \csc\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^n*csc(d*x + c)^2, x)","F",0
147,0,0,0,0.000000," ","integrate((1+sin(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(\sin\left(d x + c\right) + 1\right)}^{n}\,{d x}"," ",0,"integrate((sin(d*x + c) + 1)^n, x)","F",0
148,0,0,0,0.000000," ","integrate((1-sin(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(-\sin\left(d x + c\right) + 1\right)}^{n}\,{d x}"," ",0,"integrate((-sin(d*x + c) + 1)^n, x)","F",0
149,1,57,0,1.320756," ","integrate(sin(f*x+e)^3*(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\frac{32 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a + 3 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} b}{96 \, f}"," ",0,"1/96*(32*(cos(f*x + e)^3 - 3*cos(f*x + e))*a + 3*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*b)/f","A",0
150,1,48,0,0.649131," ","integrate(sin(f*x+e)^2*(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\frac{3 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a + 4 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} b}{12 \, f}"," ",0,"1/12*(3*(2*f*x + 2*e - sin(2*f*x + 2*e))*a + 4*(cos(f*x + e)^3 - 3*cos(f*x + e))*b)/f","A",0
151,1,36,0,0.383425," ","integrate(sin(f*x+e)*(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\frac{{\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} b - 4 \, a \cos\left(f x + e\right)}{4 \, f}"," ",0,"1/4*((2*f*x + 2*e - sin(2*f*x + 2*e))*b - 4*a*cos(f*x + e))/f","A",0
152,1,16,0,0.876048," ","integrate(a+b*sin(f*x+e),x, algorithm=""maxima"")","a x - \frac{b \cos\left(f x + e\right)}{f}"," ",0,"a*x - b*cos(f*x + e)/f","A",0
153,1,29,0,0.636164," ","integrate(csc(f*x+e)*(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\frac{{\left(f x + e\right)} b - a \log\left(\cot\left(f x + e\right) + \csc\left(f x + e\right)\right)}{f}"," ",0,"((f*x + e)*b - a*log(cot(f*x + e) + csc(f*x + e)))/f","A",0
154,1,40,0,0.607479," ","integrate(csc(f*x+e)^2*(a+b*sin(f*x+e)),x, algorithm=""maxima"")","-\frac{b {\left(\log\left(\cos\left(f x + e\right) + 1\right) - \log\left(\cos\left(f x + e\right) - 1\right)\right)} + \frac{2 \, a}{\tan\left(f x + e\right)}}{2 \, f}"," ",0,"-1/2*(b*(log(cos(f*x + e) + 1) - log(cos(f*x + e) - 1)) + 2*a/tan(f*x + e))/f","A",0
155,1,60,0,0.822894," ","integrate(csc(f*x+e)^3*(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\frac{a {\left(\frac{2 \, \cos\left(f x + e\right)}{\cos\left(f x + e\right)^{2} - 1} - \log\left(\cos\left(f x + e\right) + 1\right) + \log\left(\cos\left(f x + e\right) - 1\right)\right)} - \frac{4 \, b}{\tan\left(f x + e\right)}}{4 \, f}"," ",0,"1/4*(a*(2*cos(f*x + e)/(cos(f*x + e)^2 - 1) - log(cos(f*x + e) + 1) + log(cos(f*x + e) - 1)) - 4*b/tan(f*x + e))/f","A",0
156,1,73,0,0.303392," ","integrate(csc(f*x+e)^4*(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\frac{3 \, b {\left(\frac{2 \, \cos\left(f x + e\right)}{\cos\left(f x + e\right)^{2} - 1} - \log\left(\cos\left(f x + e\right) + 1\right) + \log\left(\cos\left(f x + e\right) - 1\right)\right)} - \frac{4 \, {\left(3 \, \tan\left(f x + e\right)^{2} + 1\right)} a}{\tan\left(f x + e\right)^{3}}}{12 \, f}"," ",0,"1/12*(3*b*(2*cos(f*x + e)/(cos(f*x + e)^2 - 1) - log(cos(f*x + e) + 1) + log(cos(f*x + e) - 1)) - 4*(3*tan(f*x + e)^2 + 1)*a/tan(f*x + e)^3)/f","A",0
157,1,94,0,0.721719," ","integrate(sin(f*x+e)^3*(a+b*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{80 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a^{2} + 15 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a b - 16 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} b^{2}}{240 \, f}"," ",0,"1/240*(80*(cos(f*x + e)^3 - 3*cos(f*x + e))*a^2 + 15*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*a*b - 16*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*b^2)/f","A",0
158,1,84,0,1.001481," ","integrate(sin(f*x+e)^2*(a+b*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{24 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} + 64 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a b + 3 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} b^{2}}{96 \, f}"," ",0,"1/96*(24*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^2 + 64*(cos(f*x + e)^3 - 3*cos(f*x + e))*a*b + 3*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*b^2)/f","A",0
159,1,62,0,0.643236," ","integrate(sin(f*x+e)*(a+b*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{3 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a b + 2 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} b^{2} - 6 \, a^{2} \cos\left(f x + e\right)}{6 \, f}"," ",0,"1/6*(3*(2*f*x + 2*e - sin(2*f*x + 2*e))*a*b + 2*(cos(f*x + e)^3 - 3*cos(f*x + e))*b^2 - 6*a^2*cos(f*x + e))/f","A",0
160,1,46,0,0.301047," ","integrate((a+b*sin(f*x+e))^2,x, algorithm=""maxima"")","a^{2} x + \frac{{\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} b^{2}}{4 \, f} - \frac{2 \, a b \cos\left(f x + e\right)}{f}"," ",0,"a^2*x + 1/4*(2*f*x + 2*e - sin(2*f*x + 2*e))*b^2/f - 2*a*b*cos(f*x + e)/f","A",0
161,1,44,0,0.640801," ","integrate(csc(f*x+e)*(a+b*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(f x + e\right)} a b - b^{2} \cos\left(f x + e\right) - a^{2} \log\left(\cot\left(f x + e\right) + \csc\left(f x + e\right)\right)}{f}"," ",0,"(2*(f*x + e)*a*b - b^2*cos(f*x + e) - a^2*log(cot(f*x + e) + csc(f*x + e)))/f","A",0
162,1,52,0,0.629254," ","integrate(csc(f*x+e)^2*(a+b*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{{\left(f x + e\right)} b^{2} - a b {\left(\log\left(\cos\left(f x + e\right) + 1\right) - \log\left(\cos\left(f x + e\right) - 1\right)\right)} - \frac{a^{2}}{\tan\left(f x + e\right)}}{f}"," ",0,"((f*x + e)*b^2 - a*b*(log(cos(f*x + e) + 1) - log(cos(f*x + e) - 1)) - a^2/tan(f*x + e))/f","A",0
163,1,89,0,0.307228," ","integrate(csc(f*x+e)^3*(a+b*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{a^{2} {\left(\frac{2 \, \cos\left(f x + e\right)}{\cos\left(f x + e\right)^{2} - 1} - \log\left(\cos\left(f x + e\right) + 1\right) + \log\left(\cos\left(f x + e\right) - 1\right)\right)} - 2 \, b^{2} {\left(\log\left(\cos\left(f x + e\right) + 1\right) - \log\left(\cos\left(f x + e\right) - 1\right)\right)} - \frac{8 \, a b}{\tan\left(f x + e\right)}}{4 \, f}"," ",0,"1/4*(a^2*(2*cos(f*x + e)/(cos(f*x + e)^2 - 1) - log(cos(f*x + e) + 1) + log(cos(f*x + e) - 1)) - 2*b^2*(log(cos(f*x + e) + 1) - log(cos(f*x + e) - 1)) - 8*a*b/tan(f*x + e))/f","A",0
164,1,89,0,0.687990," ","integrate(csc(f*x+e)^4*(a+b*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{3 \, a b {\left(\frac{2 \, \cos\left(f x + e\right)}{\cos\left(f x + e\right)^{2} - 1} - \log\left(\cos\left(f x + e\right) + 1\right) + \log\left(\cos\left(f x + e\right) - 1\right)\right)} - \frac{6 \, b^{2}}{\tan\left(f x + e\right)} - \frac{2 \, {\left(3 \, \tan\left(f x + e\right)^{2} + 1\right)} a^{2}}{\tan\left(f x + e\right)^{3}}}{6 \, f}"," ",0,"1/6*(3*a*b*(2*cos(f*x + e)/(cos(f*x + e)^2 - 1) - log(cos(f*x + e) + 1) + log(cos(f*x + e) - 1)) - 6*b^2/tan(f*x + e) - 2*(3*tan(f*x + e)^2 + 1)*a^2/tan(f*x + e)^3)/f","A",0
165,1,147,0,1.013121," ","integrate(csc(f*x+e)^5*(a+b*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{3 \, a^{2} {\left(\frac{2 \, {\left(3 \, \cos\left(f x + e\right)^{3} - 5 \, \cos\left(f x + e\right)\right)}}{\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1} - 3 \, \log\left(\cos\left(f x + e\right) + 1\right) + 3 \, \log\left(\cos\left(f x + e\right) - 1\right)\right)} + 12 \, b^{2} {\left(\frac{2 \, \cos\left(f x + e\right)}{\cos\left(f x + e\right)^{2} - 1} - \log\left(\cos\left(f x + e\right) + 1\right) + \log\left(\cos\left(f x + e\right) - 1\right)\right)} - \frac{32 \, {\left(3 \, \tan\left(f x + e\right)^{2} + 1\right)} a b}{\tan\left(f x + e\right)^{3}}}{48 \, f}"," ",0,"1/48*(3*a^2*(2*(3*cos(f*x + e)^3 - 5*cos(f*x + e))/(cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1) - 3*log(cos(f*x + e) + 1) + 3*log(cos(f*x + e) - 1)) + 12*b^2*(2*cos(f*x + e)/(cos(f*x + e)^2 - 1) - log(cos(f*x + e) + 1) + log(cos(f*x + e) - 1)) - 32*(3*tan(f*x + e)^2 + 1)*a*b/tan(f*x + e)^3)/f","A",0
166,1,145,0,0.776899," ","integrate(sin(f*x+e)^3*(a+b*sin(f*x+e))^3,x, algorithm=""maxima"")","\frac{320 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a^{3} + 90 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} b - 192 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} a b^{2} + 5 \, {\left(4 \, \sin\left(2 \, f x + 2 \, e\right)^{3} + 60 \, f x + 60 \, e + 9 \, \sin\left(4 \, f x + 4 \, e\right) - 48 \, \sin\left(2 \, f x + 2 \, e\right)\right)} b^{3}}{960 \, f}"," ",0,"1/960*(320*(cos(f*x + e)^3 - 3*cos(f*x + e))*a^3 + 90*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*a^2*b - 192*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*a*b^2 + 5*(4*sin(2*f*x + 2*e)^3 + 60*f*x + 60*e + 9*sin(4*f*x + 4*e) - 48*sin(2*f*x + 2*e))*b^3)/f","A",0
167,1,121,0,1.616664," ","integrate(sin(f*x+e)^2*(a+b*sin(f*x+e))^3,x, algorithm=""maxima"")","\frac{120 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{3} + 480 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a^{2} b + 45 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a b^{2} - 32 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} b^{3}}{480 \, f}"," ",0,"1/480*(120*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^3 + 480*(cos(f*x + e)^3 - 3*cos(f*x + e))*a^2*b + 45*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*a*b^2 - 32*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*b^3)/f","A",0
168,1,97,0,0.509960," ","integrate(sin(f*x+e)*(a+b*sin(f*x+e))^3,x, algorithm=""maxima"")","\frac{24 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} b + 32 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a b^{2} + {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} b^{3} - 32 \, a^{3} \cos\left(f x + e\right)}{32 \, f}"," ",0,"1/32*(24*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^2*b + 32*(cos(f*x + e)^3 - 3*cos(f*x + e))*a*b^2 + (12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*b^3 - 32*a^3*cos(f*x + e))/f","A",0
169,1,74,0,0.647844," ","integrate((a+b*sin(f*x+e))^3,x, algorithm=""maxima"")","a^{3} x + \frac{3 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a b^{2}}{4 \, f} + \frac{{\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} b^{3}}{3 \, f} - \frac{3 \, a^{2} b \cos\left(f x + e\right)}{f}"," ",0,"a^3*x + 3/4*(2*f*x + 2*e - sin(2*f*x + 2*e))*a*b^2/f + 1/3*(cos(f*x + e)^3 - 3*cos(f*x + e))*b^3/f - 3*a^2*b*cos(f*x + e)/f","A",0
170,1,71,0,0.670508," ","integrate(csc(f*x+e)*(a+b*sin(f*x+e))^3,x, algorithm=""maxima"")","\frac{12 \, {\left(f x + e\right)} a^{2} b + {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} b^{3} - 12 \, a b^{2} \cos\left(f x + e\right) - 4 \, a^{3} \log\left(\cot\left(f x + e\right) + \csc\left(f x + e\right)\right)}{4 \, f}"," ",0,"1/4*(12*(f*x + e)*a^2*b + (2*f*x + 2*e - sin(2*f*x + 2*e))*b^3 - 12*a*b^2*cos(f*x + e) - 4*a^3*log(cot(f*x + e) + csc(f*x + e)))/f","A",0
171,1,68,0,0.306625," ","integrate(csc(f*x+e)^2*(a+b*sin(f*x+e))^3,x, algorithm=""maxima"")","\frac{6 \, {\left(f x + e\right)} a b^{2} - 3 \, a^{2} b {\left(\log\left(\cos\left(f x + e\right) + 1\right) - \log\left(\cos\left(f x + e\right) - 1\right)\right)} - 2 \, b^{3} \cos\left(f x + e\right) - \frac{2 \, a^{3}}{\tan\left(f x + e\right)}}{2 \, f}"," ",0,"1/2*(6*(f*x + e)*a*b^2 - 3*a^2*b*(log(cos(f*x + e) + 1) - log(cos(f*x + e) - 1)) - 2*b^3*cos(f*x + e) - 2*a^3/tan(f*x + e))/f","A",0
172,1,102,0,1.282761," ","integrate(csc(f*x+e)^3*(a+b*sin(f*x+e))^3,x, algorithm=""maxima"")","\frac{4 \, {\left(f x + e\right)} b^{3} + a^{3} {\left(\frac{2 \, \cos\left(f x + e\right)}{\cos\left(f x + e\right)^{2} - 1} - \log\left(\cos\left(f x + e\right) + 1\right) + \log\left(\cos\left(f x + e\right) - 1\right)\right)} - 6 \, a b^{2} {\left(\log\left(\cos\left(f x + e\right) + 1\right) - \log\left(\cos\left(f x + e\right) - 1\right)\right)} - \frac{12 \, a^{2} b}{\tan\left(f x + e\right)}}{4 \, f}"," ",0,"1/4*(4*(f*x + e)*b^3 + a^3*(2*cos(f*x + e)/(cos(f*x + e)^2 - 1) - log(cos(f*x + e) + 1) + log(cos(f*x + e) - 1)) - 6*a*b^2*(log(cos(f*x + e) + 1) - log(cos(f*x + e) - 1)) - 12*a^2*b/tan(f*x + e))/f","A",0
173,1,118,0,0.684202," ","integrate(csc(f*x+e)^4*(a+b*sin(f*x+e))^3,x, algorithm=""maxima"")","\frac{9 \, a^{2} b {\left(\frac{2 \, \cos\left(f x + e\right)}{\cos\left(f x + e\right)^{2} - 1} - \log\left(\cos\left(f x + e\right) + 1\right) + \log\left(\cos\left(f x + e\right) - 1\right)\right)} - 6 \, b^{3} {\left(\log\left(\cos\left(f x + e\right) + 1\right) - \log\left(\cos\left(f x + e\right) - 1\right)\right)} - \frac{36 \, a b^{2}}{\tan\left(f x + e\right)} - \frac{4 \, {\left(3 \, \tan\left(f x + e\right)^{2} + 1\right)} a^{3}}{\tan\left(f x + e\right)^{3}}}{12 \, f}"," ",0,"1/12*(9*a^2*b*(2*cos(f*x + e)/(cos(f*x + e)^2 - 1) - log(cos(f*x + e) + 1) + log(cos(f*x + e) - 1)) - 6*b^3*(log(cos(f*x + e) + 1) - log(cos(f*x + e) - 1)) - 36*a*b^2/tan(f*x + e) - 4*(3*tan(f*x + e)^2 + 1)*a^3/tan(f*x + e)^3)/f","A",0
174,1,162,0,1.165064," ","integrate(csc(f*x+e)^5*(a+b*sin(f*x+e))^3,x, algorithm=""maxima"")","\frac{a^{3} {\left(\frac{2 \, {\left(3 \, \cos\left(f x + e\right)^{3} - 5 \, \cos\left(f x + e\right)\right)}}{\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1} - 3 \, \log\left(\cos\left(f x + e\right) + 1\right) + 3 \, \log\left(\cos\left(f x + e\right) - 1\right)\right)} + 12 \, a b^{2} {\left(\frac{2 \, \cos\left(f x + e\right)}{\cos\left(f x + e\right)^{2} - 1} - \log\left(\cos\left(f x + e\right) + 1\right) + \log\left(\cos\left(f x + e\right) - 1\right)\right)} - \frac{16 \, b^{3}}{\tan\left(f x + e\right)} - \frac{16 \, {\left(3 \, \tan\left(f x + e\right)^{2} + 1\right)} a^{2} b}{\tan\left(f x + e\right)^{3}}}{16 \, f}"," ",0,"1/16*(a^3*(2*(3*cos(f*x + e)^3 - 5*cos(f*x + e))/(cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1) - 3*log(cos(f*x + e) + 1) + 3*log(cos(f*x + e) - 1)) + 12*a*b^2*(2*cos(f*x + e)/(cos(f*x + e)^2 - 1) - log(cos(f*x + e) + 1) + log(cos(f*x + e) - 1)) - 16*b^3/tan(f*x + e) - 16*(3*tan(f*x + e)^2 + 1)*a^2*b/tan(f*x + e)^3)/f","A",0
175,1,113,0,1.067526," ","integrate((a+b*sin(f*x+e))^4,x, algorithm=""maxima"")","a^{4} x + \frac{3 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} b^{2}}{2 \, f} + \frac{4 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a b^{3}}{3 \, f} + \frac{{\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} b^{4}}{32 \, f} - \frac{4 \, a^{3} b \cos\left(f x + e\right)}{f}"," ",0,"a^4*x + 3/2*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^2*b^2/f + 4/3*(cos(f*x + e)^3 - 3*cos(f*x + e))*a*b^3/f + 1/32*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*b^4/f - 4*a^3*b*cos(f*x + e)/f","A",0
176,-2,0,0,0.000000," ","integrate(sin(x)^4/(a+b*sin(x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
177,-2,0,0,0.000000," ","integrate(sin(x)^3/(a+b*sin(x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
178,-2,0,0,0.000000," ","integrate(sin(x)^2/(a+b*sin(x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
179,-2,0,0,0.000000," ","integrate(sin(x)/(a+b*sin(x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
180,-2,0,0,0.000000," ","integrate(1/(a+b*sin(x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
181,-2,0,0,0.000000," ","integrate(csc(x)/(a+b*sin(x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
182,-2,0,0,0.000000," ","integrate(csc(x)^2/(a+b*sin(x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
183,-2,0,0,0.000000," ","integrate(csc(x)^3/(a+b*sin(x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
184,-2,0,0,0.000000," ","integrate(csc(x)^4/(a+b*sin(x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
185,-2,0,0,0.000000," ","integrate(sin(x)^4/(a+b*sin(x))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
186,-2,0,0,0.000000," ","integrate(sin(x)^3/(a+b*sin(x))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
187,-2,0,0,0.000000," ","integrate(sin(x)^2/(a+b*sin(x))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
188,-2,0,0,0.000000," ","integrate(sin(x)/(a+b*sin(x))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
189,-2,0,0,0.000000," ","integrate(1/(a+b*sin(x))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
190,-2,0,0,0.000000," ","integrate(csc(x)/(a+b*sin(x))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
191,-2,0,0,0.000000," ","integrate(csc(x)^2/(a+b*sin(x))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
192,-2,0,0,0.000000," ","integrate(csc(x)^3/(a+b*sin(x))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
193,-2,0,0,0.000000," ","integrate(sin(x)^5/(a+b*sin(x))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
194,-2,0,0,0.000000," ","integrate(sin(x)^4/(a+b*sin(x))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
195,-2,0,0,0.000000," ","integrate(sin(x)^3/(a+b*sin(x))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
196,-2,0,0,0.000000," ","integrate(sin(x)^2/(a+b*sin(x))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
197,-2,0,0,0.000000," ","integrate(sin(x)/(a+b*sin(x))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
198,-2,0,0,0.000000," ","integrate(1/(a+b*sin(x))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
199,-2,0,0,0.000000," ","integrate(csc(x)/(a+b*sin(x))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
200,-2,0,0,0.000000," ","integrate(csc(x)^2/(a+b*sin(x))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
201,-2,0,0,0.000000," ","integrate(csc(x)^3/(a+b*sin(x))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
202,-2,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c))^4,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
203,0,0,0,0.000000," ","integrate(sin(f*x+e)*(a+b*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sin\left(f x + e\right) + a} \sin\left(f x + e\right)\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e) + a)*sin(f*x + e), x)","F",0
204,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e) + a), x)","F",0
205,0,0,0,0.000000," ","integrate(csc(f*x+e)*(a+b*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sin\left(f x + e\right) + a} \csc\left(f x + e\right)\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e) + a)*csc(f*x + e), x)","F",0
206,0,0,0,0.000000," ","integrate(csc(f*x+e)^2*(a+b*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sin\left(f x + e\right) + a} \csc\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e) + a)*csc(f*x + e)^2, x)","F",0
207,0,0,0,0.000000," ","integrate(sin(f*x+e)/(a+b*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sin\left(f x + e\right)}{\sqrt{b \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate(sin(f*x + e)/sqrt(b*sin(f*x + e) + a), x)","F",0
208,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate(1/sqrt(b*sin(f*x + e) + a), x)","F",0
209,0,0,0,0.000000," ","integrate(csc(f*x+e)/(a+b*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\csc\left(f x + e\right)}{\sqrt{b \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate(csc(f*x + e)/sqrt(b*sin(f*x + e) + a), x)","F",0
210,0,0,0,0.000000," ","integrate(csc(f*x+e)^2/(a+b*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\csc\left(f x + e\right)^{2}}{\sqrt{b \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate(csc(f*x + e)^2/sqrt(b*sin(f*x + e) + a), x)","F",0
211,0,0,0,0.000000," ","integrate(sin(d*x+c)^(1/2)*(a+b*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sin\left(d x + c\right) + a} \sqrt{\sin\left(d x + c\right)}\,{d x}"," ",0,"integrate(sqrt(b*sin(d*x + c) + a)*sqrt(sin(d*x + c)), x)","F",0
212,0,0,0,0.000000," ","integrate(1/sin(d*x+c)^(1/2)/(a+b*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \sin\left(d x + c\right) + a} \sqrt{\sin\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(b*sin(d*x + c) + a)*sqrt(sin(d*x + c))), x)","F",0
213,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^m*(a+b*sin(f*x+e))^3,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right) + a\right)}^{3} \left(d \sin\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^3*(d*sin(f*x + e))^m, x)","F",0
214,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^m*(a+b*sin(f*x+e))^2,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right) + a\right)}^{2} \left(d \sin\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^2*(d*sin(f*x + e))^m, x)","F",0
215,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^m*(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right) + a\right)} \left(d \sin\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)*(d*sin(f*x + e))^m, x)","F",0
216,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^m/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(d \sin\left(f x + e\right)\right)^{m}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*sin(f*x + e))^m/(b*sin(f*x + e) + a), x)","F",0
217,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^m/(a+b*sin(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{\left(d \sin\left(f x + e\right)\right)^{m}}{{\left(b \sin\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*sin(f*x + e))^m/(b*sin(f*x + e) + a)^2, x)","F",0
218,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^m/(a+b*sin(f*x+e))^3,x, algorithm=""maxima"")","\int \frac{\left(d \sin\left(f x + e\right)\right)^{m}}{{\left(b \sin\left(f x + e\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((d*sin(f*x + e))^m/(b*sin(f*x + e) + a)^3, x)","F",0
219,0,0,0,0.000000," ","integrate(sin(d*x+c)^(-1-a^2/(a^2+b^2))*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{2} \sin\left(d x + c\right)^{-\frac{a^{2}}{a^{2} + b^{2}} - 1}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^2*sin(d*x + c)^(-a^2/(a^2 + b^2) - 1), x)","F",0
220,0,0,0,0.000000," ","integrate((1+2*sin(d*x+c))^2/sin(d*x+c)^(6/5),x, algorithm=""maxima"")","\int \frac{{\left(2 \, \sin\left(d x + c\right) + 1\right)}^{2}}{\sin\left(d x + c\right)^{\frac{6}{5}}}\,{d x}"," ",0,"integrate((2*sin(d*x + c) + 1)^2/sin(d*x + c)^(6/5), x)","F",0
221,0,0,0,0.000000," ","integrate(sin(d*x+c)^m*(a+b*sin(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^n*sin(d*x + c)^m, x)","F",0
222,0,0,0,0.000000," ","integrate(sin(d*x+c)^3*(a+b*sin(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^n*sin(d*x + c)^3, x)","F",0
223,0,0,0,0.000000," ","integrate(sin(d*x+c)^2*(a+b*sin(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^n*sin(d*x + c)^2, x)","F",0
224,0,0,0,0.000000," ","integrate(sin(d*x+c)*(a+b*sin(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^n*sin(d*x + c), x)","F",0
225,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^n, x)","F",0
226,0,0,0,0.000000," ","integrate(csc(d*x+c)*(a+b*sin(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{n} \csc\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^n*csc(d*x + c), x)","F",0
227,1,146,0,0.872173," ","integrate((a+a*sin(f*x+e))*(c-c*sin(f*x+e))^4,x, algorithm=""maxima"")","-\frac{32 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} a c^{4} - 320 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a c^{4} + 45 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a c^{4} - 240 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a c^{4} - 480 \, {\left(f x + e\right)} a c^{4} - 1440 \, a c^{4} \cos\left(f x + e\right)}{480 \, f}"," ",0,"-1/480*(32*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*a*c^4 - 320*(cos(f*x + e)^3 - 3*cos(f*x + e))*a*c^4 + 45*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*a*c^4 - 240*(2*f*x + 2*e - sin(2*f*x + 2*e))*a*c^4 - 480*(f*x + e)*a*c^4 - 1440*a*c^4*cos(f*x + e))/f","A",0
228,1,86,0,1.713999," ","integrate((a+a*sin(f*x+e))*(c-c*sin(f*x+e))^3,x, algorithm=""maxima"")","\frac{64 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a c^{3} - 3 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a c^{3} + 96 \, {\left(f x + e\right)} a c^{3} + 192 \, a c^{3} \cos\left(f x + e\right)}{96 \, f}"," ",0,"1/96*(64*(cos(f*x + e)^3 - 3*cos(f*x + e))*a*c^3 - 3*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*a*c^3 + 96*(f*x + e)*a*c^3 + 192*a*c^3*cos(f*x + e))/f","A",0
229,1,77,0,0.592070," ","integrate((a+a*sin(f*x+e))*(c-c*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{4 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a c^{2} - 3 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a c^{2} + 12 \, {\left(f x + e\right)} a c^{2} + 12 \, a c^{2} \cos\left(f x + e\right)}{12 \, f}"," ",0,"1/12*(4*(cos(f*x + e)^3 - 3*cos(f*x + e))*a*c^2 - 3*(2*f*x + 2*e - sin(2*f*x + 2*e))*a*c^2 + 12*(f*x + e)*a*c^2 + 12*a*c^2*cos(f*x + e))/f","A",0
230,1,37,0,0.513081," ","integrate((a+a*sin(f*x+e))*(c-c*sin(f*x+e)),x, algorithm=""maxima"")","-\frac{{\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a c - 4 \, {\left(f x + e\right)} a c}{4 \, f}"," ",0,"-1/4*((2*f*x + 2*e - sin(2*f*x + 2*e))*a*c - 4*(f*x + e)*a*c)/f","A",0
231,1,82,0,0.919029," ","integrate((a+a*sin(f*x+e))/(c-c*sin(f*x+e)),x, algorithm=""maxima"")","-\frac{2 \, {\left(a {\left(\frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c} - \frac{1}{c - \frac{c \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}\right)} - \frac{a}{c - \frac{c \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}\right)}}{f}"," ",0,"-2*(a*(arctan(sin(f*x + e)/(cos(f*x + e) + 1))/c - 1/(c - c*sin(f*x + e)/(cos(f*x + e) + 1))) - a/(c - c*sin(f*x + e)/(cos(f*x + e) + 1)))/f","B",0
232,1,217,0,0.738549," ","integrate((a+a*sin(f*x+e))/(c-c*sin(f*x+e))^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{a {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - 2\right)}}{c^{2} - \frac{3 \, c^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, c^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{c^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} - \frac{a {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}}{c^{2} - \frac{3 \, c^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, c^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{c^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}\right)}}{3 \, f}"," ",0,"-2/3*(a*(3*sin(f*x + e)/(cos(f*x + e) + 1) - 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 2)/(c^2 - 3*c^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*c^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - c^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) - a*(3*sin(f*x + e)/(cos(f*x + e) + 1) - 1)/(c^2 - 3*c^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*c^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - c^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3))/f","B",0
233,1,389,0,1.050161," ","integrate((a+a*sin(f*x+e))/(c-c*sin(f*x+e))^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{a {\left(\frac{20 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{40 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{30 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - 7\right)}}{c^{3} - \frac{5 \, c^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, c^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{10 \, c^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, c^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{c^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} - \frac{3 \, a {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{5 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - 1\right)}}{c^{3} - \frac{5 \, c^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, c^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{10 \, c^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, c^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{c^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}\right)}}{15 \, f}"," ",0,"-2/15*(a*(20*sin(f*x + e)/(cos(f*x + e) + 1) - 40*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 30*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 7)/(c^3 - 5*c^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*c^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 10*c^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*c^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - c^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) - 3*a*(5*sin(f*x + e)/(cos(f*x + e) + 1) - 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 1)/(c^3 - 5*c^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*c^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 10*c^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*c^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - c^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5))/f","B",0
234,1,561,0,0.551070," ","integrate((a+a*sin(f*x+e))/(c-c*sin(f*x+e))^4,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{a {\left(\frac{91 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{168 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{280 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{175 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{105 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - 13\right)}}{c^{4} - \frac{7 \, c^{4} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{21 \, c^{4} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{35 \, c^{4} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{35 \, c^{4} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{21 \, c^{4} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{7 \, c^{4} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{c^{4} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} - \frac{3 \, a {\left(\frac{49 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{147 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{210 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{210 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{105 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{35 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - 12\right)}}{c^{4} - \frac{7 \, c^{4} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{21 \, c^{4} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{35 \, c^{4} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{35 \, c^{4} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{21 \, c^{4} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{7 \, c^{4} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{c^{4} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}}\right)}}{105 \, f}"," ",0,"2/105*(a*(91*sin(f*x + e)/(cos(f*x + e) + 1) - 168*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 280*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 175*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 105*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 13)/(c^4 - 7*c^4*sin(f*x + e)/(cos(f*x + e) + 1) + 21*c^4*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 35*c^4*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 35*c^4*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 21*c^4*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 7*c^4*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - c^4*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) - 3*a*(49*sin(f*x + e)/(cos(f*x + e) + 1) - 147*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 210*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 210*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 105*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 35*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 12)/(c^4 - 7*c^4*sin(f*x + e)/(cos(f*x + e) + 1) + 21*c^4*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 35*c^4*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 35*c^4*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 21*c^4*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 7*c^4*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - c^4*sin(f*x + e)^7/(cos(f*x + e) + 1)^7))/f","B",0
235,1,733,0,0.609931," ","integrate((a+a*sin(f*x+e))/(c-c*sin(f*x+e))^5,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{a {\left(\frac{432 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{1728 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3612 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{5418 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{5040 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{3360 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{1260 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{315 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - 83\right)}}{c^{5} - \frac{9 \, c^{5} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{36 \, c^{5} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{84 \, c^{5} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{126 \, c^{5} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{126 \, c^{5} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{84 \, c^{5} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{36 \, c^{5} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{9 \, c^{5} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{c^{5} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}} - \frac{5 \, a {\left(\frac{45 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{117 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{273 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{315 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{315 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{147 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{63 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - 5\right)}}{c^{5} - \frac{9 \, c^{5} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{36 \, c^{5} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{84 \, c^{5} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{126 \, c^{5} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{126 \, c^{5} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{84 \, c^{5} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{36 \, c^{5} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{9 \, c^{5} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{c^{5} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}}\right)}}{315 \, f}"," ",0,"-2/315*(a*(432*sin(f*x + e)/(cos(f*x + e) + 1) - 1728*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3612*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 5418*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 5040*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 3360*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 1260*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 315*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 83)/(c^5 - 9*c^5*sin(f*x + e)/(cos(f*x + e) + 1) + 36*c^5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 84*c^5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 126*c^5*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 126*c^5*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 84*c^5*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 36*c^5*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 9*c^5*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - c^5*sin(f*x + e)^9/(cos(f*x + e) + 1)^9) - 5*a*(45*sin(f*x + e)/(cos(f*x + e) + 1) - 117*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 273*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 315*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 315*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 147*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 63*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 5)/(c^5 - 9*c^5*sin(f*x + e)/(cos(f*x + e) + 1) + 36*c^5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 84*c^5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 126*c^5*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 126*c^5*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 84*c^5*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 36*c^5*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 9*c^5*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - c^5*sin(f*x + e)^9/(cos(f*x + e) + 1)^9))/f","B",0
236,1,256,0,0.823598," ","integrate((a+a*sin(f*x+e))^2*(c-c*sin(f*x+e))^5,x, algorithm=""maxima"")","-\frac{192 \, {\left(5 \, \cos\left(f x + e\right)^{7} - 21 \, \cos\left(f x + e\right)^{5} + 35 \, \cos\left(f x + e\right)^{3} - 35 \, \cos\left(f x + e\right)\right)} a^{2} c^{5} - 448 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} a^{2} c^{5} - 11200 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a^{2} c^{5} - 105 \, {\left(4 \, \sin\left(2 \, f x + 2 \, e\right)^{3} + 60 \, f x + 60 \, e + 9 \, \sin\left(4 \, f x + 4 \, e\right) - 48 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c^{5} + 1050 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c^{5} - 1680 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c^{5} - 6720 \, {\left(f x + e\right)} a^{2} c^{5} - 20160 \, a^{2} c^{5} \cos\left(f x + e\right)}{6720 \, f}"," ",0,"-1/6720*(192*(5*cos(f*x + e)^7 - 21*cos(f*x + e)^5 + 35*cos(f*x + e)^3 - 35*cos(f*x + e))*a^2*c^5 - 448*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*a^2*c^5 - 11200*(cos(f*x + e)^3 - 3*cos(f*x + e))*a^2*c^5 - 105*(4*sin(2*f*x + 2*e)^3 + 60*f*x + 60*e + 9*sin(4*f*x + 4*e) - 48*sin(2*f*x + 2*e))*a^2*c^5 + 1050*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*a^2*c^5 - 1680*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^2*c^5 - 6720*(f*x + e)*a^2*c^5 - 20160*a^2*c^5*cos(f*x + e))/f","A",0
237,1,209,0,0.679687," ","integrate((a+a*sin(f*x+e))^2*(c-c*sin(f*x+e))^4,x, algorithm=""maxima"")","\frac{128 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} a^{2} c^{4} + 1280 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a^{2} c^{4} + 5 \, {\left(4 \, \sin\left(2 \, f x + 2 \, e\right)^{3} + 60 \, f x + 60 \, e + 9 \, \sin\left(4 \, f x + 4 \, e\right) - 48 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c^{4} - 30 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c^{4} - 240 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c^{4} + 960 \, {\left(f x + e\right)} a^{2} c^{4} + 1920 \, a^{2} c^{4} \cos\left(f x + e\right)}{960 \, f}"," ",0,"1/960*(128*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*a^2*c^4 + 1280*(cos(f*x + e)^3 - 3*cos(f*x + e))*a^2*c^4 + 5*(4*sin(2*f*x + 2*e)^3 + 60*f*x + 60*e + 9*sin(4*f*x + 4*e) - 48*sin(2*f*x + 2*e))*a^2*c^4 - 30*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*a^2*c^4 - 240*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^2*c^4 + 960*(f*x + e)*a^2*c^4 + 1920*a^2*c^4*cos(f*x + e))/f","A",0
238,1,158,0,0.998064," ","integrate((a+a*sin(f*x+e))^2*(c-c*sin(f*x+e))^3,x, algorithm=""maxima"")","\frac{32 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} a^{2} c^{3} + 320 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a^{2} c^{3} + 15 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c^{3} - 240 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c^{3} + 480 \, {\left(f x + e\right)} a^{2} c^{3} + 480 \, a^{2} c^{3} \cos\left(f x + e\right)}{480 \, f}"," ",0,"1/480*(32*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*a^2*c^3 + 320*(cos(f*x + e)^3 - 3*cos(f*x + e))*a^2*c^3 + 15*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*a^2*c^3 - 240*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^2*c^3 + 480*(f*x + e)*a^2*c^3 + 480*a^2*c^3*cos(f*x + e))/f","B",0
239,1,81,0,0.309748," ","integrate((a+a*sin(f*x+e))^2*(c-c*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{{\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c^{2} - 16 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c^{2} + 32 \, {\left(f x + e\right)} a^{2} c^{2}}{32 \, f}"," ",0,"1/32*((12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*a^2*c^2 - 16*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^2*c^2 + 32*(f*x + e)*a^2*c^2)/f","A",0
240,1,77,0,0.674648," ","integrate((a+a*sin(f*x+e))^2*(c-c*sin(f*x+e)),x, algorithm=""maxima"")","-\frac{4 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a^{2} c + 3 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c - 12 \, {\left(f x + e\right)} a^{2} c + 12 \, a^{2} c \cos\left(f x + e\right)}{12 \, f}"," ",0,"-1/12*(4*(cos(f*x + e)^3 - 3*cos(f*x + e))*a^2*c + 3*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^2*c - 12*(f*x + e)*a^2*c + 12*a^2*c*cos(f*x + e))/f","A",0
241,1,218,0,1.921374," ","integrate((a+a*sin(f*x+e))^2/(c-c*sin(f*x+e)),x, algorithm=""maxima"")","-\frac{2 \, {\left(a^{2} {\left(\frac{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - 2}{c - \frac{c \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{c \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{c \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c}\right)} + 2 \, a^{2} {\left(\frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c} - \frac{1}{c - \frac{c \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}\right)} - \frac{a^{2}}{c - \frac{c \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}\right)}}{f}"," ",0,"-2*(a^2*((sin(f*x + e)/(cos(f*x + e) + 1) - sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 2)/(c - c*sin(f*x + e)/(cos(f*x + e) + 1) + c*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - c*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + arctan(sin(f*x + e)/(cos(f*x + e) + 1))/c) + 2*a^2*(arctan(sin(f*x + e)/(cos(f*x + e) + 1))/c - 1/(c - c*sin(f*x + e)/(cos(f*x + e) + 1))) - a^2/(c - c*sin(f*x + e)/(cos(f*x + e) + 1)))/f","B",0
242,1,364,0,1.182198," ","integrate((a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(a^{2} {\left(\frac{\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - 4}{c^{2} - \frac{3 \, c^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, c^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{c^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c^{2}}\right)} - \frac{a^{2} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - 2\right)}}{c^{2} - \frac{3 \, c^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, c^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{c^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{2 \, a^{2} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}}{c^{2} - \frac{3 \, c^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, c^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{c^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}\right)}}{3 \, f}"," ",0,"2/3*(a^2*((9*sin(f*x + e)/(cos(f*x + e) + 1) - 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 4)/(c^2 - 3*c^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*c^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - c^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/c^2) - a^2*(3*sin(f*x + e)/(cos(f*x + e) + 1) - 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 2)/(c^2 - 3*c^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*c^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - c^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + 2*a^2*(3*sin(f*x + e)/(cos(f*x + e) + 1) - 1)/(c^2 - 3*c^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*c^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - c^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3))/f","B",0
243,1,557,0,2.026674," ","integrate((a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{a^{2} {\left(\frac{20 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{40 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{30 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - 7\right)}}{c^{3} - \frac{5 \, c^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, c^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{10 \, c^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, c^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{c^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} - \frac{6 \, a^{2} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{5 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - 1\right)}}{c^{3} - \frac{5 \, c^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, c^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{10 \, c^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, c^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{c^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{2 \, a^{2} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{10 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - 1\right)}}{c^{3} - \frac{5 \, c^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, c^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{10 \, c^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, c^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{c^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}\right)}}{15 \, f}"," ",0,"-2/15*(a^2*(20*sin(f*x + e)/(cos(f*x + e) + 1) - 40*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 30*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 7)/(c^3 - 5*c^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*c^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 10*c^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*c^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - c^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) - 6*a^2*(5*sin(f*x + e)/(cos(f*x + e) + 1) - 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 1)/(c^3 - 5*c^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*c^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 10*c^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*c^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - c^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 2*a^2*(5*sin(f*x + e)/(cos(f*x + e) + 1) - 10*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 1)/(c^3 - 5*c^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*c^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 10*c^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*c^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - c^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5))/f","B",0
244,1,816,0,0.573242," ","integrate((a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^4,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{2 \, a^{2} {\left(\frac{91 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{168 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{280 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{175 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{105 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - 13\right)}}{c^{4} - \frac{7 \, c^{4} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{21 \, c^{4} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{35 \, c^{4} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{35 \, c^{4} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{21 \, c^{4} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{7 \, c^{4} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{c^{4} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} - \frac{3 \, a^{2} {\left(\frac{49 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{147 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{210 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{210 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{105 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{35 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - 12\right)}}{c^{4} - \frac{7 \, c^{4} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{21 \, c^{4} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{35 \, c^{4} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{35 \, c^{4} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{21 \, c^{4} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{7 \, c^{4} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{c^{4} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} - \frac{4 \, a^{2} {\left(\frac{14 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{42 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{35 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{35 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - 2\right)}}{c^{4} - \frac{7 \, c^{4} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{21 \, c^{4} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{35 \, c^{4} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{35 \, c^{4} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{21 \, c^{4} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{7 \, c^{4} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{c^{4} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}}\right)}}{105 \, f}"," ",0,"2/105*(2*a^2*(91*sin(f*x + e)/(cos(f*x + e) + 1) - 168*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 280*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 175*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 105*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 13)/(c^4 - 7*c^4*sin(f*x + e)/(cos(f*x + e) + 1) + 21*c^4*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 35*c^4*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 35*c^4*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 21*c^4*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 7*c^4*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - c^4*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) - 3*a^2*(49*sin(f*x + e)/(cos(f*x + e) + 1) - 147*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 210*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 210*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 105*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 35*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 12)/(c^4 - 7*c^4*sin(f*x + e)/(cos(f*x + e) + 1) + 21*c^4*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 35*c^4*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 35*c^4*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 21*c^4*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 7*c^4*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - c^4*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) - 4*a^2*(14*sin(f*x + e)/(cos(f*x + e) + 1) - 42*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 35*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 35*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 2)/(c^4 - 7*c^4*sin(f*x + e)/(cos(f*x + e) + 1) + 21*c^4*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 35*c^4*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 35*c^4*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 21*c^4*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 7*c^4*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - c^4*sin(f*x + e)^7/(cos(f*x + e) + 1)^7))/f","B",0
245,1,1073,0,1.193496," ","integrate((a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^5,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{a^{2} {\left(\frac{432 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{1728 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3612 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{5418 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{5040 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{3360 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{1260 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{315 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - 83\right)}}{c^{5} - \frac{9 \, c^{5} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{36 \, c^{5} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{84 \, c^{5} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{126 \, c^{5} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{126 \, c^{5} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{84 \, c^{5} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{36 \, c^{5} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{9 \, c^{5} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{c^{5} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}} - \frac{10 \, a^{2} {\left(\frac{45 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{117 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{273 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{315 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{315 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{147 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{63 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - 5\right)}}{c^{5} - \frac{9 \, c^{5} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{36 \, c^{5} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{84 \, c^{5} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{126 \, c^{5} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{126 \, c^{5} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{84 \, c^{5} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{36 \, c^{5} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{9 \, c^{5} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{c^{5} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}} + \frac{14 \, a^{2} {\left(\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{36 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{54 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{81 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{45 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{30 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - 1\right)}}{c^{5} - \frac{9 \, c^{5} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{36 \, c^{5} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{84 \, c^{5} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{126 \, c^{5} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{126 \, c^{5} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{84 \, c^{5} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{36 \, c^{5} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{9 \, c^{5} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{c^{5} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}}\right)}}{315 \, f}"," ",0,"-2/315*(a^2*(432*sin(f*x + e)/(cos(f*x + e) + 1) - 1728*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3612*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 5418*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 5040*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 3360*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 1260*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 315*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 83)/(c^5 - 9*c^5*sin(f*x + e)/(cos(f*x + e) + 1) + 36*c^5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 84*c^5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 126*c^5*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 126*c^5*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 84*c^5*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 36*c^5*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 9*c^5*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - c^5*sin(f*x + e)^9/(cos(f*x + e) + 1)^9) - 10*a^2*(45*sin(f*x + e)/(cos(f*x + e) + 1) - 117*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 273*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 315*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 315*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 147*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 63*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 5)/(c^5 - 9*c^5*sin(f*x + e)/(cos(f*x + e) + 1) + 36*c^5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 84*c^5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 126*c^5*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 126*c^5*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 84*c^5*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 36*c^5*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 9*c^5*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - c^5*sin(f*x + e)^9/(cos(f*x + e) + 1)^9) + 14*a^2*(9*sin(f*x + e)/(cos(f*x + e) + 1) - 36*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 54*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 81*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 45*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 30*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 1)/(c^5 - 9*c^5*sin(f*x + e)/(cos(f*x + e) + 1) + 36*c^5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 84*c^5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 126*c^5*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 126*c^5*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 84*c^5*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 36*c^5*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 9*c^5*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - c^5*sin(f*x + e)^9/(cos(f*x + e) + 1)^9))/f","B",0
246,1,1332,0,2.362442," ","integrate((a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^6,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{5 \, a^{2} {\left(\frac{913 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{4565 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{12540 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{25080 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{33726 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{33726 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{23100 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{11550 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{3465 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - \frac{693 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - 146\right)}}{c^{6} - \frac{11 \, c^{6} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{55 \, c^{6} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{165 \, c^{6} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{330 \, c^{6} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{462 \, c^{6} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{462 \, c^{6} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{330 \, c^{6} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{165 \, c^{6} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{55 \, c^{6} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{11 \, c^{6} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{c^{6} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}}} - \frac{6 \, a^{2} {\left(\frac{671 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{2200 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{6600 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{10890 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{15246 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{12936 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{9240 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{3465 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{1155 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - 61\right)}}{c^{6} - \frac{11 \, c^{6} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{55 \, c^{6} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{165 \, c^{6} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{330 \, c^{6} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{462 \, c^{6} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{462 \, c^{6} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{330 \, c^{6} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{165 \, c^{6} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{55 \, c^{6} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{11 \, c^{6} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{c^{6} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}}} + \frac{4 \, a^{2} {\left(\frac{253 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{1265 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{2640 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{5280 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{5313 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{5313 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{2310 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{1155 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - 23\right)}}{c^{6} - \frac{11 \, c^{6} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{55 \, c^{6} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{165 \, c^{6} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{330 \, c^{6} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{462 \, c^{6} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{462 \, c^{6} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{330 \, c^{6} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{165 \, c^{6} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{55 \, c^{6} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{11 \, c^{6} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{c^{6} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}}}\right)}}{3465 \, f}"," ",0,"-2/3465*(5*a^2*(913*sin(f*x + e)/(cos(f*x + e) + 1) - 4565*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 12540*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 25080*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 33726*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 33726*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 23100*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 11550*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 3465*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 693*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 146)/(c^6 - 11*c^6*sin(f*x + e)/(cos(f*x + e) + 1) + 55*c^6*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 165*c^6*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 330*c^6*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 462*c^6*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 462*c^6*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 330*c^6*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 165*c^6*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 55*c^6*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 11*c^6*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - c^6*sin(f*x + e)^11/(cos(f*x + e) + 1)^11) - 6*a^2*(671*sin(f*x + e)/(cos(f*x + e) + 1) - 2200*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 6600*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 10890*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 15246*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 12936*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 9240*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 3465*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 1155*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 61)/(c^6 - 11*c^6*sin(f*x + e)/(cos(f*x + e) + 1) + 55*c^6*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 165*c^6*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 330*c^6*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 462*c^6*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 462*c^6*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 330*c^6*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 165*c^6*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 55*c^6*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 11*c^6*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - c^6*sin(f*x + e)^11/(cos(f*x + e) + 1)^11) + 4*a^2*(253*sin(f*x + e)/(cos(f*x + e) + 1) - 1265*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2640*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 5280*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 5313*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 5313*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 2310*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 1155*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 23)/(c^6 - 11*c^6*sin(f*x + e)/(cos(f*x + e) + 1) + 55*c^6*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 165*c^6*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 330*c^6*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 462*c^6*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 462*c^6*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 330*c^6*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 165*c^6*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 55*c^6*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 11*c^6*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - c^6*sin(f*x + e)^11/(cos(f*x + e) + 1)^11))/f","B",0
247,1,301,0,0.329710," ","integrate((a+a*sin(f*x+e))^3*(c-c*sin(f*x+e))^6,x, algorithm=""maxima"")","-\frac{1024 \, {\left(35 \, \cos\left(f x + e\right)^{9} - 180 \, \cos\left(f x + e\right)^{7} + 378 \, \cos\left(f x + e\right)^{5} - 420 \, \cos\left(f x + e\right)^{3} + 315 \, \cos\left(f x + e\right)\right)} a^{3} c^{6} - 129024 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} a^{3} c^{6} - 860160 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a^{3} c^{6} + 315 \, {\left(128 \, \sin\left(2 \, f x + 2 \, e\right)^{3} + 840 \, f x + 840 \, e + 3 \, \sin\left(8 \, f x + 8 \, e\right) + 168 \, \sin\left(4 \, f x + 4 \, e\right) - 768 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a^{3} c^{6} - 13440 \, {\left(4 \, \sin\left(2 \, f x + 2 \, e\right)^{3} + 60 \, f x + 60 \, e + 9 \, \sin\left(4 \, f x + 4 \, e\right) - 48 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a^{3} c^{6} + 60480 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a^{3} c^{6} - 322560 \, {\left(f x + e\right)} a^{3} c^{6} - 967680 \, a^{3} c^{6} \cos\left(f x + e\right)}{322560 \, f}"," ",0,"-1/322560*(1024*(35*cos(f*x + e)^9 - 180*cos(f*x + e)^7 + 378*cos(f*x + e)^5 - 420*cos(f*x + e)^3 + 315*cos(f*x + e))*a^3*c^6 - 129024*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*a^3*c^6 - 860160*(cos(f*x + e)^3 - 3*cos(f*x + e))*a^3*c^6 + 315*(128*sin(2*f*x + 2*e)^3 + 840*f*x + 840*e + 3*sin(8*f*x + 8*e) + 168*sin(4*f*x + 4*e) - 768*sin(2*f*x + 2*e))*a^3*c^6 - 13440*(4*sin(2*f*x + 2*e)^3 + 60*f*x + 60*e + 9*sin(4*f*x + 4*e) - 48*sin(2*f*x + 2*e))*a^3*c^6 + 60480*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*a^3*c^6 - 322560*(f*x + e)*a^3*c^6 - 967680*a^3*c^6*cos(f*x + e))/f","A",0
248,1,282,0,0.768944," ","integrate((a+a*sin(f*x+e))^3*(c-c*sin(f*x+e))^5,x, algorithm=""maxima"")","\frac{6144 \, {\left(5 \, \cos\left(f x + e\right)^{7} - 21 \, \cos\left(f x + e\right)^{5} + 35 \, \cos\left(f x + e\right)^{3} - 35 \, \cos\left(f x + e\right)\right)} a^{3} c^{5} + 43008 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} a^{3} c^{5} + 215040 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a^{3} c^{5} - 35 \, {\left(128 \, \sin\left(2 \, f x + 2 \, e\right)^{3} + 840 \, f x + 840 \, e + 3 \, \sin\left(8 \, f x + 8 \, e\right) + 168 \, \sin\left(4 \, f x + 4 \, e\right) - 768 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a^{3} c^{5} + 1120 \, {\left(4 \, \sin\left(2 \, f x + 2 \, e\right)^{3} + 60 \, f x + 60 \, e + 9 \, \sin\left(4 \, f x + 4 \, e\right) - 48 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a^{3} c^{5} - 53760 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{3} c^{5} + 107520 \, {\left(f x + e\right)} a^{3} c^{5} + 215040 \, a^{3} c^{5} \cos\left(f x + e\right)}{107520 \, f}"," ",0,"1/107520*(6144*(5*cos(f*x + e)^7 - 21*cos(f*x + e)^5 + 35*cos(f*x + e)^3 - 35*cos(f*x + e))*a^3*c^5 + 43008*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*a^3*c^5 + 215040*(cos(f*x + e)^3 - 3*cos(f*x + e))*a^3*c^5 - 35*(128*sin(2*f*x + 2*e)^3 + 840*f*x + 840*e + 3*sin(8*f*x + 8*e) + 168*sin(4*f*x + 4*e) - 768*sin(2*f*x + 2*e))*a^3*c^5 + 1120*(4*sin(2*f*x + 2*e)^3 + 60*f*x + 60*e + 9*sin(4*f*x + 4*e) - 48*sin(2*f*x + 2*e))*a^3*c^5 - 53760*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^3*c^5 + 107520*(f*x + e)*a^3*c^5 + 215040*a^3*c^5*cos(f*x + e))/f","B",0
249,1,256,0,0.532323," ","integrate((a+a*sin(f*x+e))^3*(c-c*sin(f*x+e))^4,x, algorithm=""maxima"")","\frac{192 \, {\left(5 \, \cos\left(f x + e\right)^{7} - 21 \, \cos\left(f x + e\right)^{5} + 35 \, \cos\left(f x + e\right)^{3} - 35 \, \cos\left(f x + e\right)\right)} a^{3} c^{4} + 1344 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} a^{3} c^{4} + 6720 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a^{3} c^{4} - 35 \, {\left(4 \, \sin\left(2 \, f x + 2 \, e\right)^{3} + 60 \, f x + 60 \, e + 9 \, \sin\left(4 \, f x + 4 \, e\right) - 48 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a^{3} c^{4} + 630 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a^{3} c^{4} - 5040 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{3} c^{4} + 6720 \, {\left(f x + e\right)} a^{3} c^{4} + 6720 \, a^{3} c^{4} \cos\left(f x + e\right)}{6720 \, f}"," ",0,"1/6720*(192*(5*cos(f*x + e)^7 - 21*cos(f*x + e)^5 + 35*cos(f*x + e)^3 - 35*cos(f*x + e))*a^3*c^4 + 1344*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*a^3*c^4 + 6720*(cos(f*x + e)^3 - 3*cos(f*x + e))*a^3*c^4 - 35*(4*sin(2*f*x + 2*e)^3 + 60*f*x + 60*e + 9*sin(4*f*x + 4*e) - 48*sin(2*f*x + 2*e))*a^3*c^4 + 630*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*a^3*c^4 - 5040*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^3*c^4 + 6720*(f*x + e)*a^3*c^4 + 6720*a^3*c^4*cos(f*x + e))/f","B",0
250,1,132,0,0.780728," ","integrate((a+a*sin(f*x+e))^3*(c-c*sin(f*x+e))^3,x, algorithm=""maxima"")","-\frac{{\left(4 \, \sin\left(2 \, f x + 2 \, e\right)^{3} + 60 \, f x + 60 \, e + 9 \, \sin\left(4 \, f x + 4 \, e\right) - 48 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a^{3} c^{3} - 18 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a^{3} c^{3} + 144 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{3} c^{3} - 192 \, {\left(f x + e\right)} a^{3} c^{3}}{192 \, f}"," ",0,"-1/192*((4*sin(2*f*x + 2*e)^3 + 60*f*x + 60*e + 9*sin(4*f*x + 4*e) - 48*sin(2*f*x + 2*e))*a^3*c^3 - 18*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*a^3*c^3 + 144*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^3*c^3 - 192*(f*x + e)*a^3*c^3)/f","A",0
251,1,158,0,1.099864," ","integrate((a+a*sin(f*x+e))^3*(c-c*sin(f*x+e))^2,x, algorithm=""maxima"")","-\frac{32 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} a^{3} c^{2} + 320 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a^{3} c^{2} - 15 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a^{3} c^{2} + 240 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{3} c^{2} - 480 \, {\left(f x + e\right)} a^{3} c^{2} + 480 \, a^{3} c^{2} \cos\left(f x + e\right)}{480 \, f}"," ",0,"-1/480*(32*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*a^3*c^2 + 320*(cos(f*x + e)^3 - 3*cos(f*x + e))*a^3*c^2 - 15*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*a^3*c^2 + 240*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^3*c^2 - 480*(f*x + e)*a^3*c^2 + 480*a^3*c^2*cos(f*x + e))/f","B",0
252,1,86,0,0.834158," ","integrate((a+a*sin(f*x+e))^3*(c-c*sin(f*x+e)),x, algorithm=""maxima"")","-\frac{64 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a^{3} c + 3 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a^{3} c - 96 \, {\left(f x + e\right)} a^{3} c + 192 \, a^{3} c \cos\left(f x + e\right)}{96 \, f}"," ",0,"-1/96*(64*(cos(f*x + e)^3 - 3*cos(f*x + e))*a^3*c + 3*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*a^3*c - 96*(f*x + e)*a^3*c + 192*a^3*c*cos(f*x + e))/f","A",0
253,1,433,0,1.776982," ","integrate((a+a*sin(f*x+e))^3/(c-c*sin(f*x+e)),x, algorithm=""maxima"")","-\frac{6 \, a^{3} {\left(\frac{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - 2}{c - \frac{c \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{c \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{c \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c}\right)} + a^{3} {\left(\frac{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{3 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - 4}{c - \frac{c \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{2 \, c \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{2 \, c \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{c \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{c \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c}\right)} + 6 \, a^{3} {\left(\frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c} - \frac{1}{c - \frac{c \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}\right)} - \frac{2 \, a^{3}}{c - \frac{c \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}}{f}"," ",0,"-(6*a^3*((sin(f*x + e)/(cos(f*x + e) + 1) - sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 2)/(c - c*sin(f*x + e)/(cos(f*x + e) + 1) + c*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - c*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + arctan(sin(f*x + e)/(cos(f*x + e) + 1))/c) + a^3*((sin(f*x + e)/(cos(f*x + e) + 1) - 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 4)/(c - c*sin(f*x + e)/(cos(f*x + e) + 1) + 2*c*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 2*c*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + c*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - c*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/c) + 6*a^3*(arctan(sin(f*x + e)/(cos(f*x + e) + 1))/c - 1/(c - c*sin(f*x + e)/(cos(f*x + e) + 1))) - 2*a^3/(c - c*sin(f*x + e)/(cos(f*x + e) + 1)))/f","B",0
254,1,594,0,1.500220," ","integrate((a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(2 \, a^{3} {\left(\frac{\frac{12 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{11 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{9 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{3 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - 5}{c^{2} - \frac{3 \, c^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{4 \, c^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{4 \, c^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, c^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{c^{2} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c^{2}}\right)} + 3 \, a^{3} {\left(\frac{\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - 4}{c^{2} - \frac{3 \, c^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, c^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{c^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c^{2}}\right)} - \frac{a^{3} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - 2\right)}}{c^{2} - \frac{3 \, c^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, c^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{c^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{3 \, a^{3} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}}{c^{2} - \frac{3 \, c^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, c^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{c^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}\right)}}{3 \, f}"," ",0,"2/3*(2*a^3*((12*sin(f*x + e)/(cos(f*x + e) + 1) - 11*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 9*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 5)/(c^2 - 3*c^2*sin(f*x + e)/(cos(f*x + e) + 1) + 4*c^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 4*c^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*c^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - c^2*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/c^2) + 3*a^3*((9*sin(f*x + e)/(cos(f*x + e) + 1) - 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 4)/(c^2 - 3*c^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*c^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - c^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/c^2) - a^3*(3*sin(f*x + e)/(cos(f*x + e) + 1) - 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 2)/(c^2 - 3*c^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*c^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - c^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + 3*a^3*(3*sin(f*x + e)/(cos(f*x + e) + 1) - 1)/(c^2 - 3*c^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*c^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - c^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3))/f","B",0
255,1,785,0,1.760996," ","integrate((a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(a^{3} {\left(\frac{\frac{95 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{145 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{75 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - 22}{c^{3} - \frac{5 \, c^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, c^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{10 \, c^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, c^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{c^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{15 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c^{3}}\right)} + \frac{a^{3} {\left(\frac{20 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{40 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{30 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - 7\right)}}{c^{3} - \frac{5 \, c^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, c^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{10 \, c^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, c^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{c^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} - \frac{9 \, a^{3} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{5 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - 1\right)}}{c^{3} - \frac{5 \, c^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, c^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{10 \, c^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, c^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{c^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{6 \, a^{3} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{10 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - 1\right)}}{c^{3} - \frac{5 \, c^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, c^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{10 \, c^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, c^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{c^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}\right)}}{15 \, f}"," ",0,"-2/15*(a^3*((95*sin(f*x + e)/(cos(f*x + e) + 1) - 145*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 75*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 22)/(c^3 - 5*c^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*c^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 10*c^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*c^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - c^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 15*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/c^3) + a^3*(20*sin(f*x + e)/(cos(f*x + e) + 1) - 40*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 30*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 7)/(c^3 - 5*c^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*c^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 10*c^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*c^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - c^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) - 9*a^3*(5*sin(f*x + e)/(cos(f*x + e) + 1) - 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 1)/(c^3 - 5*c^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*c^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 10*c^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*c^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - c^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 6*a^3*(5*sin(f*x + e)/(cos(f*x + e) + 1) - 10*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 1)/(c^3 - 5*c^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*c^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 10*c^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*c^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - c^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5))/f","B",0
256,1,1045,0,0.888711," ","integrate((a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^4,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{a^{3} {\left(\frac{91 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{168 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{280 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{175 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{105 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - 13\right)}}{c^{4} - \frac{7 \, c^{4} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{21 \, c^{4} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{35 \, c^{4} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{35 \, c^{4} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{21 \, c^{4} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{7 \, c^{4} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{c^{4} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} - \frac{a^{3} {\left(\frac{49 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{147 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{210 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{210 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{105 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{35 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - 12\right)}}{c^{4} - \frac{7 \, c^{4} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{21 \, c^{4} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{35 \, c^{4} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{35 \, c^{4} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{21 \, c^{4} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{7 \, c^{4} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{c^{4} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} - \frac{4 \, a^{3} {\left(\frac{14 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{42 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{35 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{35 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - 2\right)}}{c^{4} - \frac{7 \, c^{4} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{21 \, c^{4} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{35 \, c^{4} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{35 \, c^{4} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{21 \, c^{4} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{7 \, c^{4} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{c^{4} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} + \frac{2 \, a^{3} {\left(\frac{7 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{21 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{35 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - 1\right)}}{c^{4} - \frac{7 \, c^{4} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{21 \, c^{4} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{35 \, c^{4} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{35 \, c^{4} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{21 \, c^{4} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{7 \, c^{4} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{c^{4} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}}\right)}}{35 \, f}"," ",0,"2/35*(a^3*(91*sin(f*x + e)/(cos(f*x + e) + 1) - 168*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 280*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 175*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 105*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 13)/(c^4 - 7*c^4*sin(f*x + e)/(cos(f*x + e) + 1) + 21*c^4*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 35*c^4*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 35*c^4*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 21*c^4*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 7*c^4*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - c^4*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) - a^3*(49*sin(f*x + e)/(cos(f*x + e) + 1) - 147*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 210*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 210*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 105*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 35*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 12)/(c^4 - 7*c^4*sin(f*x + e)/(cos(f*x + e) + 1) + 21*c^4*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 35*c^4*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 35*c^4*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 21*c^4*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 7*c^4*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - c^4*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) - 4*a^3*(14*sin(f*x + e)/(cos(f*x + e) + 1) - 42*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 35*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 35*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 2)/(c^4 - 7*c^4*sin(f*x + e)/(cos(f*x + e) + 1) + 21*c^4*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 35*c^4*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 35*c^4*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 21*c^4*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 7*c^4*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - c^4*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) + 2*a^3*(7*sin(f*x + e)/(cos(f*x + e) + 1) - 21*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 35*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 1)/(c^4 - 7*c^4*sin(f*x + e)/(cos(f*x + e) + 1) + 21*c^4*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 35*c^4*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 35*c^4*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 21*c^4*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 7*c^4*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - c^4*sin(f*x + e)^7/(cos(f*x + e) + 1)^7))/f","B",0
257,1,1389,0,0.809530," ","integrate((a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^5,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{a^{3} {\left(\frac{432 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{1728 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3612 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{5418 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{5040 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{3360 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{1260 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{315 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - 83\right)}}{c^{5} - \frac{9 \, c^{5} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{36 \, c^{5} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{84 \, c^{5} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{126 \, c^{5} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{126 \, c^{5} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{84 \, c^{5} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{36 \, c^{5} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{9 \, c^{5} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{c^{5} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}} - \frac{15 \, a^{3} {\left(\frac{45 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{117 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{273 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{315 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{315 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{147 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{63 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - 5\right)}}{c^{5} - \frac{9 \, c^{5} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{36 \, c^{5} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{84 \, c^{5} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{126 \, c^{5} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{126 \, c^{5} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{84 \, c^{5} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{36 \, c^{5} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{9 \, c^{5} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{c^{5} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}} - \frac{10 \, a^{3} {\left(\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{36 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{84 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{63 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{63 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - 1\right)}}{c^{5} - \frac{9 \, c^{5} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{36 \, c^{5} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{84 \, c^{5} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{126 \, c^{5} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{126 \, c^{5} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{84 \, c^{5} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{36 \, c^{5} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{9 \, c^{5} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{c^{5} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}} + \frac{42 \, a^{3} {\left(\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{36 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{54 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{81 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{45 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{30 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - 1\right)}}{c^{5} - \frac{9 \, c^{5} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{36 \, c^{5} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{84 \, c^{5} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{126 \, c^{5} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{126 \, c^{5} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{84 \, c^{5} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{36 \, c^{5} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{9 \, c^{5} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{c^{5} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}}\right)}}{315 \, f}"," ",0,"-2/315*(a^3*(432*sin(f*x + e)/(cos(f*x + e) + 1) - 1728*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3612*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 5418*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 5040*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 3360*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 1260*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 315*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 83)/(c^5 - 9*c^5*sin(f*x + e)/(cos(f*x + e) + 1) + 36*c^5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 84*c^5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 126*c^5*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 126*c^5*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 84*c^5*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 36*c^5*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 9*c^5*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - c^5*sin(f*x + e)^9/(cos(f*x + e) + 1)^9) - 15*a^3*(45*sin(f*x + e)/(cos(f*x + e) + 1) - 117*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 273*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 315*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 315*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 147*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 63*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 5)/(c^5 - 9*c^5*sin(f*x + e)/(cos(f*x + e) + 1) + 36*c^5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 84*c^5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 126*c^5*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 126*c^5*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 84*c^5*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 36*c^5*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 9*c^5*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - c^5*sin(f*x + e)^9/(cos(f*x + e) + 1)^9) - 10*a^3*(9*sin(f*x + e)/(cos(f*x + e) + 1) - 36*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 84*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 63*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 63*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 1)/(c^5 - 9*c^5*sin(f*x + e)/(cos(f*x + e) + 1) + 36*c^5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 84*c^5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 126*c^5*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 126*c^5*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 84*c^5*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 36*c^5*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 9*c^5*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - c^5*sin(f*x + e)^9/(cos(f*x + e) + 1)^9) + 42*a^3*(9*sin(f*x + e)/(cos(f*x + e) + 1) - 36*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 54*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 81*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 45*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 30*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 1)/(c^5 - 9*c^5*sin(f*x + e)/(cos(f*x + e) + 1) + 36*c^5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 84*c^5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 126*c^5*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 126*c^5*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 84*c^5*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 36*c^5*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 9*c^5*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - c^5*sin(f*x + e)^9/(cos(f*x + e) + 1)^9))/f","B",0
258,1,1734,0,1.249880," ","integrate((a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^6,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{5 \, a^{3} {\left(\frac{913 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{4565 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{12540 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{25080 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{33726 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{33726 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{23100 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{11550 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{3465 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - \frac{693 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - 146\right)}}{c^{6} - \frac{11 \, c^{6} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{55 \, c^{6} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{165 \, c^{6} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{330 \, c^{6} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{462 \, c^{6} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{462 \, c^{6} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{330 \, c^{6} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{165 \, c^{6} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{55 \, c^{6} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{11 \, c^{6} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{c^{6} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}}} - \frac{9 \, a^{3} {\left(\frac{671 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{2200 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{6600 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{10890 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{15246 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{12936 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{9240 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{3465 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{1155 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - 61\right)}}{c^{6} - \frac{11 \, c^{6} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{55 \, c^{6} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{165 \, c^{6} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{330 \, c^{6} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{462 \, c^{6} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{462 \, c^{6} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{330 \, c^{6} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{165 \, c^{6} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{55 \, c^{6} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{11 \, c^{6} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{c^{6} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}}} - \frac{2 \, a^{3} {\left(\frac{341 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{1705 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{5115 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{6765 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{9471 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{4851 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{3465 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - 31\right)}}{c^{6} - \frac{11 \, c^{6} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{55 \, c^{6} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{165 \, c^{6} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{330 \, c^{6} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{462 \, c^{6} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{462 \, c^{6} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{330 \, c^{6} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{165 \, c^{6} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{55 \, c^{6} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{11 \, c^{6} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{c^{6} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}}} + \frac{12 \, a^{3} {\left(\frac{253 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{1265 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{2640 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{5280 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{5313 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{5313 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{2310 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{1155 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - 23\right)}}{c^{6} - \frac{11 \, c^{6} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{55 \, c^{6} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{165 \, c^{6} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{330 \, c^{6} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{462 \, c^{6} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{462 \, c^{6} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{330 \, c^{6} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{165 \, c^{6} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{55 \, c^{6} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{11 \, c^{6} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{c^{6} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}}}\right)}}{3465 \, f}"," ",0,"-2/3465*(5*a^3*(913*sin(f*x + e)/(cos(f*x + e) + 1) - 4565*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 12540*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 25080*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 33726*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 33726*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 23100*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 11550*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 3465*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 693*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 146)/(c^6 - 11*c^6*sin(f*x + e)/(cos(f*x + e) + 1) + 55*c^6*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 165*c^6*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 330*c^6*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 462*c^6*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 462*c^6*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 330*c^6*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 165*c^6*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 55*c^6*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 11*c^6*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - c^6*sin(f*x + e)^11/(cos(f*x + e) + 1)^11) - 9*a^3*(671*sin(f*x + e)/(cos(f*x + e) + 1) - 2200*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 6600*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 10890*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 15246*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 12936*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 9240*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 3465*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 1155*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 61)/(c^6 - 11*c^6*sin(f*x + e)/(cos(f*x + e) + 1) + 55*c^6*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 165*c^6*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 330*c^6*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 462*c^6*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 462*c^6*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 330*c^6*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 165*c^6*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 55*c^6*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 11*c^6*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - c^6*sin(f*x + e)^11/(cos(f*x + e) + 1)^11) - 2*a^3*(341*sin(f*x + e)/(cos(f*x + e) + 1) - 1705*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 5115*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 6765*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 9471*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 4851*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 3465*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 31)/(c^6 - 11*c^6*sin(f*x + e)/(cos(f*x + e) + 1) + 55*c^6*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 165*c^6*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 330*c^6*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 462*c^6*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 462*c^6*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 330*c^6*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 165*c^6*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 55*c^6*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 11*c^6*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - c^6*sin(f*x + e)^11/(cos(f*x + e) + 1)^11) + 12*a^3*(253*sin(f*x + e)/(cos(f*x + e) + 1) - 1265*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2640*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 5280*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 5313*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 5313*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 2310*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 1155*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 23)/(c^6 - 11*c^6*sin(f*x + e)/(cos(f*x + e) + 1) + 55*c^6*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 165*c^6*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 330*c^6*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 462*c^6*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 462*c^6*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 330*c^6*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 165*c^6*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 55*c^6*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 11*c^6*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - c^6*sin(f*x + e)^11/(cos(f*x + e) + 1)^11))/f","B",0
259,1,2078,0,0.878488," ","integrate((a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^7,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{2 \, a^{3} {\left(\frac{4771 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{28626 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{74932 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{187330 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{265122 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{353496 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{276276 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{207207 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{75075 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - \frac{30030 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - 367\right)}}{c^{7} - \frac{13 \, c^{7} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{78 \, c^{7} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{286 \, c^{7} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{715 \, c^{7} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{1287 \, c^{7} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{1716 \, c^{7} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{1716 \, c^{7} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{1287 \, c^{7} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{715 \, c^{7} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{286 \, c^{7} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{78 \, c^{7} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} + \frac{13 \, c^{7} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - \frac{c^{7} \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}}} + \frac{5 \, a^{3} {\left(\frac{3796 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{22776 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{77506 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{193765 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{339768 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{453024 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{444444 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{333333 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{180180 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - \frac{72072 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{18018 \, \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} - \frac{3003 \, \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - 523\right)}}{c^{7} - \frac{13 \, c^{7} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{78 \, c^{7} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{286 \, c^{7} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{715 \, c^{7} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{1287 \, c^{7} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{1716 \, c^{7} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{1716 \, c^{7} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{1287 \, c^{7} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{715 \, c^{7} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{286 \, c^{7} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{78 \, c^{7} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} + \frac{13 \, c^{7} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - \frac{c^{7} \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}}} - \frac{35 \, a^{3} {\left(\frac{611 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{2379 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{8723 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{18590 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{33462 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{40326 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{40326 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{27027 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{15015 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - \frac{4719 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{1287 \, \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} - 47\right)}}{c^{7} - \frac{13 \, c^{7} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{78 \, c^{7} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{286 \, c^{7} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{715 \, c^{7} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{1287 \, c^{7} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{1716 \, c^{7} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{1716 \, c^{7} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{1287 \, c^{7} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{715 \, c^{7} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{286 \, c^{7} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{78 \, c^{7} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} + \frac{13 \, c^{7} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - \frac{c^{7} \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}}} - \frac{154 \, a^{3} {\left(\frac{13 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{78 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{286 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{520 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{936 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{858 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{858 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{351 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{195 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - 1\right)}}{c^{7} - \frac{13 \, c^{7} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{78 \, c^{7} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{286 \, c^{7} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{715 \, c^{7} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{1287 \, c^{7} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{1716 \, c^{7} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{1716 \, c^{7} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{1287 \, c^{7} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{715 \, c^{7} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{286 \, c^{7} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{78 \, c^{7} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} + \frac{13 \, c^{7} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - \frac{c^{7} \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}}}\right)}}{15015 \, f}"," ",0,"-2/15015*(2*a^3*(4771*sin(f*x + e)/(cos(f*x + e) + 1) - 28626*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 74932*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 187330*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 265122*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 353496*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 276276*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 207207*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 75075*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 30030*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 367)/(c^7 - 13*c^7*sin(f*x + e)/(cos(f*x + e) + 1) + 78*c^7*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 286*c^7*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 715*c^7*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 1287*c^7*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 1716*c^7*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 1716*c^7*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 1287*c^7*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 715*c^7*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 286*c^7*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 78*c^7*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 + 13*c^7*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - c^7*sin(f*x + e)^13/(cos(f*x + e) + 1)^13) + 5*a^3*(3796*sin(f*x + e)/(cos(f*x + e) + 1) - 22776*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 77506*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 193765*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 339768*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 453024*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 444444*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 333333*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 180180*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 72072*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 18018*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 - 3003*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - 523)/(c^7 - 13*c^7*sin(f*x + e)/(cos(f*x + e) + 1) + 78*c^7*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 286*c^7*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 715*c^7*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 1287*c^7*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 1716*c^7*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 1716*c^7*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 1287*c^7*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 715*c^7*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 286*c^7*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 78*c^7*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 + 13*c^7*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - c^7*sin(f*x + e)^13/(cos(f*x + e) + 1)^13) - 35*a^3*(611*sin(f*x + e)/(cos(f*x + e) + 1) - 2379*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 8723*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 18590*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 33462*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 40326*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 40326*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 27027*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 15015*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 4719*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 1287*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 - 47)/(c^7 - 13*c^7*sin(f*x + e)/(cos(f*x + e) + 1) + 78*c^7*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 286*c^7*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 715*c^7*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 1287*c^7*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 1716*c^7*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 1716*c^7*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 1287*c^7*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 715*c^7*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 286*c^7*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 78*c^7*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 + 13*c^7*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - c^7*sin(f*x + e)^13/(cos(f*x + e) + 1)^13) - 154*a^3*(13*sin(f*x + e)/(cos(f*x + e) + 1) - 78*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 286*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 520*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 936*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 858*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 858*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 351*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 195*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 1)/(c^7 - 13*c^7*sin(f*x + e)/(cos(f*x + e) + 1) + 78*c^7*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 286*c^7*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 715*c^7*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 1287*c^7*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 1716*c^7*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 1716*c^7*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 1287*c^7*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 715*c^7*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 286*c^7*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 78*c^7*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 + 13*c^7*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - c^7*sin(f*x + e)^13/(cos(f*x + e) + 1)^13))/f","B",0
260,1,2422,0,0.935974," ","integrate((a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^8,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{3 \, a^{3} {\left(\frac{17715 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{78960 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{342160 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{891345 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{1960959 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{3043040 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{3912480 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{3687255 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{2867865 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - \frac{1585584 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{720720 \, \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} - \frac{195195 \, \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} + \frac{45045 \, \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}} - 1181\right)}}{c^{8} - \frac{15 \, c^{8} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{105 \, c^{8} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{455 \, c^{8} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{1365 \, c^{8} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{3003 \, c^{8} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{5005 \, c^{8} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{6435 \, c^{8} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{6435 \, c^{8} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{5005 \, c^{8} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{3003 \, c^{8} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{1365 \, c^{8} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} + \frac{455 \, c^{8} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - \frac{105 \, c^{8} \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}} + \frac{15 \, c^{8} \sin\left(f x + e\right)^{14}}{{\left(\cos\left(f x + e\right) + 1\right)}^{14}} - \frac{c^{8} \sin\left(f x + e\right)^{15}}{{\left(\cos\left(f x + e\right) + 1\right)}^{15}}} - \frac{7 \, a^{3} {\left(\frac{7845 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{54915 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{222950 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{668850 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{1444443 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{2407405 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{3063060 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{3063060 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{2357355 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - \frac{1414413 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{630630 \, \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} - \frac{210210 \, \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} + \frac{45045 \, \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}} - \frac{6435 \, \sin\left(f x + e\right)^{14}}{{\left(\cos\left(f x + e\right) + 1\right)}^{14}} - 952\right)}}{c^{8} - \frac{15 \, c^{8} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{105 \, c^{8} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{455 \, c^{8} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{1365 \, c^{8} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{3003 \, c^{8} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{5005 \, c^{8} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{6435 \, c^{8} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{6435 \, c^{8} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{5005 \, c^{8} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{3003 \, c^{8} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{1365 \, c^{8} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} + \frac{455 \, c^{8} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - \frac{105 \, c^{8} \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}} + \frac{15 \, c^{8} \sin\left(f x + e\right)^{14}}{{\left(\cos\left(f x + e\right) + 1\right)}^{14}} - \frac{c^{8} \sin\left(f x + e\right)^{15}}{{\left(\cos\left(f x + e\right) + 1\right)}^{15}}} - \frac{12 \, a^{3} {\left(\frac{1740 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{12180 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{37765 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{113295 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{204204 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{340340 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{373230 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{373230 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{240240 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - \frac{144144 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{45045 \, \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} - \frac{15015 \, \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - 116\right)}}{c^{8} - \frac{15 \, c^{8} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{105 \, c^{8} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{455 \, c^{8} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{1365 \, c^{8} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{3003 \, c^{8} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{5005 \, c^{8} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{6435 \, c^{8} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{6435 \, c^{8} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{5005 \, c^{8} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{3003 \, c^{8} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{1365 \, c^{8} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} + \frac{455 \, c^{8} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - \frac{105 \, c^{8} \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}} + \frac{15 \, c^{8} \sin\left(f x + e\right)^{14}}{{\left(\cos\left(f x + e\right) + 1\right)}^{14}} - \frac{c^{8} \sin\left(f x + e\right)^{15}}{{\left(\cos\left(f x + e\right) + 1\right)}^{15}}} + \frac{6 \, a^{3} {\left(\frac{675 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{4725 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{20475 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{46410 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{102102 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{130130 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{167310 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{122265 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{95095 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - \frac{33033 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{15015 \, \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} - 45\right)}}{c^{8} - \frac{15 \, c^{8} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{105 \, c^{8} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{455 \, c^{8} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{1365 \, c^{8} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{3003 \, c^{8} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{5005 \, c^{8} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{6435 \, c^{8} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{6435 \, c^{8} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{5005 \, c^{8} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{3003 \, c^{8} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{1365 \, c^{8} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} + \frac{455 \, c^{8} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - \frac{105 \, c^{8} \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}} + \frac{15 \, c^{8} \sin\left(f x + e\right)^{14}}{{\left(\cos\left(f x + e\right) + 1\right)}^{14}} - \frac{c^{8} \sin\left(f x + e\right)^{15}}{{\left(\cos\left(f x + e\right) + 1\right)}^{15}}}\right)}}{45045 \, f}"," ",0,"2/45045*(3*a^3*(17715*sin(f*x + e)/(cos(f*x + e) + 1) - 78960*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 342160*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 891345*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 1960959*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 3043040*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 3912480*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 3687255*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 2867865*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 1585584*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 720720*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 - 195195*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 + 45045*sin(f*x + e)^13/(cos(f*x + e) + 1)^13 - 1181)/(c^8 - 15*c^8*sin(f*x + e)/(cos(f*x + e) + 1) + 105*c^8*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 455*c^8*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 1365*c^8*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 3003*c^8*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 5005*c^8*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 6435*c^8*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 6435*c^8*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 5005*c^8*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 3003*c^8*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 1365*c^8*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 + 455*c^8*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - 105*c^8*sin(f*x + e)^13/(cos(f*x + e) + 1)^13 + 15*c^8*sin(f*x + e)^14/(cos(f*x + e) + 1)^14 - c^8*sin(f*x + e)^15/(cos(f*x + e) + 1)^15) - 7*a^3*(7845*sin(f*x + e)/(cos(f*x + e) + 1) - 54915*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 222950*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 668850*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 1444443*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 2407405*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 3063060*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 3063060*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 2357355*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 1414413*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 630630*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 - 210210*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 + 45045*sin(f*x + e)^13/(cos(f*x + e) + 1)^13 - 6435*sin(f*x + e)^14/(cos(f*x + e) + 1)^14 - 952)/(c^8 - 15*c^8*sin(f*x + e)/(cos(f*x + e) + 1) + 105*c^8*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 455*c^8*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 1365*c^8*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 3003*c^8*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 5005*c^8*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 6435*c^8*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 6435*c^8*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 5005*c^8*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 3003*c^8*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 1365*c^8*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 + 455*c^8*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - 105*c^8*sin(f*x + e)^13/(cos(f*x + e) + 1)^13 + 15*c^8*sin(f*x + e)^14/(cos(f*x + e) + 1)^14 - c^8*sin(f*x + e)^15/(cos(f*x + e) + 1)^15) - 12*a^3*(1740*sin(f*x + e)/(cos(f*x + e) + 1) - 12180*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 37765*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 113295*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 204204*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 340340*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 373230*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 373230*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 240240*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 144144*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 45045*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 - 15015*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - 116)/(c^8 - 15*c^8*sin(f*x + e)/(cos(f*x + e) + 1) + 105*c^8*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 455*c^8*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 1365*c^8*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 3003*c^8*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 5005*c^8*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 6435*c^8*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 6435*c^8*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 5005*c^8*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 3003*c^8*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 1365*c^8*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 + 455*c^8*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - 105*c^8*sin(f*x + e)^13/(cos(f*x + e) + 1)^13 + 15*c^8*sin(f*x + e)^14/(cos(f*x + e) + 1)^14 - c^8*sin(f*x + e)^15/(cos(f*x + e) + 1)^15) + 6*a^3*(675*sin(f*x + e)/(cos(f*x + e) + 1) - 4725*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 20475*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 46410*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 102102*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 130130*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 167310*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 122265*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 95095*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 33033*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 15015*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 - 45)/(c^8 - 15*c^8*sin(f*x + e)/(cos(f*x + e) + 1) + 105*c^8*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 455*c^8*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 1365*c^8*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 3003*c^8*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 5005*c^8*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 6435*c^8*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 6435*c^8*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 5005*c^8*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 3003*c^8*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 1365*c^8*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 + 455*c^8*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - 105*c^8*sin(f*x + e)^13/(cos(f*x + e) + 1)^13 + 15*c^8*sin(f*x + e)^14/(cos(f*x + e) + 1)^14 - c^8*sin(f*x + e)^15/(cos(f*x + e) + 1)^15))/f","B",0
261,1,720,0,0.911608," ","integrate((c-c*sin(f*x+e))^4/(a+a*sin(f*x+e)),x, algorithm=""maxima"")","-\frac{c^{4} {\left(\frac{\frac{7 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{39 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{24 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{24 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{9 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{9 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + 16}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3 \, a \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, a \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{3 \, a \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{a \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{a \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} + \frac{9 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a}\right)} + 12 \, c^{4} {\left(\frac{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 4}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{2 \, a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{2 \, a \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{a \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a}\right)} + 36 \, c^{4} {\left(\frac{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 2}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a}\right)} + 24 \, c^{4} {\left(\frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a} + \frac{1}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}\right)} + \frac{6 \, c^{4}}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}}{3 \, f}"," ",0,"-1/3*(c^4*((7*sin(f*x + e)/(cos(f*x + e) + 1) + 39*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 24*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 24*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 9*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 9*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 16)/(a + a*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3*a*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*a*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 3*a*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + a*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + a*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) + 9*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a) + 12*c^4*((sin(f*x + e)/(cos(f*x + e) + 1) + 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 4)/(a + a*sin(f*x + e)/(cos(f*x + e) + 1) + 2*a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2*a*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + a*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a) + 36*c^4*((sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2)/(a + a*sin(f*x + e)/(cos(f*x + e) + 1) + a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a) + 24*c^4*(arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a + 1/(a + a*sin(f*x + e)/(cos(f*x + e) + 1))) + 6*c^4/(a + a*sin(f*x + e)/(cos(f*x + e) + 1)))/f","B",0
262,1,424,0,1.130383," ","integrate((c-c*sin(f*x+e))^3/(a+a*sin(f*x+e)),x, algorithm=""maxima"")","-\frac{c^{3} {\left(\frac{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 4}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{2 \, a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{2 \, a \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{a \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a}\right)} + 6 \, c^{3} {\left(\frac{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 2}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a}\right)} + 6 \, c^{3} {\left(\frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a} + \frac{1}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}\right)} + \frac{2 \, c^{3}}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}}{f}"," ",0,"-(c^3*((sin(f*x + e)/(cos(f*x + e) + 1) + 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 4)/(a + a*sin(f*x + e)/(cos(f*x + e) + 1) + 2*a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2*a*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + a*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a) + 6*c^3*((sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2)/(a + a*sin(f*x + e)/(cos(f*x + e) + 1) + a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a) + 6*c^3*(arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a + 1/(a + a*sin(f*x + e)/(cos(f*x + e) + 1))) + 2*c^3/(a + a*sin(f*x + e)/(cos(f*x + e) + 1)))/f","B",0
263,1,210,0,0.874111," ","integrate((c-c*sin(f*x+e))^2/(a+a*sin(f*x+e)),x, algorithm=""maxima"")","-\frac{2 \, {\left(c^{2} {\left(\frac{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 2}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a}\right)} + 2 \, c^{2} {\left(\frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a} + \frac{1}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}\right)} + \frac{c^{2}}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}\right)}}{f}"," ",0,"-2*(c^2*((sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2)/(a + a*sin(f*x + e)/(cos(f*x + e) + 1) + a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a) + 2*c^2*(arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a + 1/(a + a*sin(f*x + e)/(cos(f*x + e) + 1))) + c^2/(a + a*sin(f*x + e)/(cos(f*x + e) + 1)))/f","B",0
264,1,77,0,0.857550," ","integrate((c-c*sin(f*x+e))/(a+a*sin(f*x+e)),x, algorithm=""maxima"")","-\frac{2 \, {\left(c {\left(\frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a} + \frac{1}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}\right)} + \frac{c}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}\right)}}{f}"," ",0,"-2*(c*(arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a + 1/(a + a*sin(f*x + e)/(cos(f*x + e) + 1))) + c/(a + a*sin(f*x + e)/(cos(f*x + e) + 1)))/f","B",0
265,1,16,0,0.305158," ","integrate(1/(a+a*sin(f*x+e))/(c-c*sin(f*x+e)),x, algorithm=""maxima"")","\frac{\tan\left(f x + e\right)}{a c f}"," ",0,"tan(f*x + e)/(a*c*f)","A",0
266,1,142,0,0.711002," ","integrate(1/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + 1\right)}}{3 \, {\left(a c^{2} - \frac{2 \, a c^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{2 \, a c^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{a c^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}}\right)} f}"," ",0,"2/3*(sin(f*x + e)/(cos(f*x + e) + 1) - 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 1)/((a*c^2 - 2*a*c^2*sin(f*x + e)/(cos(f*x + e) + 1) + 2*a*c^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - a*c^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4)*f)","B",0
267,1,211,0,1.581187," ","integrate(1/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{10 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{10 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{5 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - 2\right)}}{5 \, {\left(a c^{3} - \frac{4 \, a c^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, a c^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{5 \, a c^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{4 \, a c^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{a c^{3} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}}\right)} f}"," ",0,"-2/5*(3*sin(f*x + e)/(cos(f*x + e) + 1) - 10*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 10*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 5*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 2)/((a*c^3 - 4*a*c^3*sin(f*x + e)/(cos(f*x + e) + 1) + 5*a*c^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 5*a*c^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 4*a*c^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - a*c^3*sin(f*x + e)^6/(cos(f*x + e) + 1)^6)*f)","B",0
268,1,319,0,0.676247," ","integrate(1/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^4,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{43 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{77 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{7 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{105 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{175 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{105 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{35 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - 13\right)}}{35 \, {\left(a c^{4} - \frac{6 \, a c^{4} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{14 \, a c^{4} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{14 \, a c^{4} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{14 \, a c^{4} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{14 \, a c^{4} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{6 \, a c^{4} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{a c^{4} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}}\right)} f}"," ",0,"-2/35*(43*sin(f*x + e)/(cos(f*x + e) + 1) - 77*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 7*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 105*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 175*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 105*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 35*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 13)/((a*c^4 - 6*a*c^4*sin(f*x + e)/(cos(f*x + e) + 1) + 14*a*c^4*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 14*a*c^4*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 14*a*c^4*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 14*a*c^4*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 6*a*c^4*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - a*c^4*sin(f*x + e)^8/(cos(f*x + e) + 1)^8)*f)","B",0
269,1,1304,0,1.116832," ","integrate((c-c*sin(f*x+e))^5/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{5 \, c^{5} {\left(\frac{\frac{75 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{97 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{126 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{98 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{63 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{21 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + 32}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{7 \, a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{7 \, a^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{5 \, a^{2} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{a^{2} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} + \frac{21 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} + 2 \, c^{5} {\left(\frac{\frac{57 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{99 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{155 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{153 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{135 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{85 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{45 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{15 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + 24}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{6 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{12 \, a^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{12 \, a^{2} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{10 \, a^{2} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{6 \, a^{2} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{a^{2} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}} + \frac{15 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} + 40 \, c^{5} {\left(\frac{\frac{12 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{11 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{9 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 5}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{4 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{4 \, a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{2} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} + 20 \, c^{5} {\left(\frac{\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 4}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} - \frac{2 \, c^{5} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 2\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{10 \, c^{5} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}}{3 \, f}"," ",0,"1/3*(5*c^5*((75*sin(f*x + e)/(cos(f*x + e) + 1) + 97*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 126*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 98*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 63*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 21*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 32)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 5*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 7*a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 7*a^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 5*a^2*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 3*a^2*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + a^2*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) + 21*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) + 2*c^5*((57*sin(f*x + e)/(cos(f*x + e) + 1) + 99*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 155*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 153*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 135*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 85*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 45*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 15*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 24)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 6*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 12*a^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 12*a^2*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 10*a^2*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 6*a^2*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 3*a^2*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + a^2*sin(f*x + e)^9/(cos(f*x + e) + 1)^9) + 15*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) + 40*c^5*((12*sin(f*x + e)/(cos(f*x + e) + 1) + 11*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 9*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 5)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 4*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4*a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*a^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^2*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) + 20*c^5*((9*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) - 2*c^5*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + 10*c^5*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 1)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3))/f","B",0
270,1,903,0,0.873193," ","integrate((c-c*sin(f*x+e))^4/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{c^{4} {\left(\frac{\frac{75 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{97 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{126 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{98 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{63 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{21 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + 32}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{7 \, a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{7 \, a^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{5 \, a^{2} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{a^{2} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} + \frac{21 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} + 16 \, c^{4} {\left(\frac{\frac{12 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{11 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{9 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 5}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{4 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{4 \, a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{2} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} + 12 \, c^{4} {\left(\frac{\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 4}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} - \frac{2 \, c^{4} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 2\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{8 \, c^{4} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}}{3 \, f}"," ",0,"1/3*(c^4*((75*sin(f*x + e)/(cos(f*x + e) + 1) + 97*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 126*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 98*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 63*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 21*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 32)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 5*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 7*a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 7*a^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 5*a^2*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 3*a^2*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + a^2*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) + 21*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) + 16*c^4*((12*sin(f*x + e)/(cos(f*x + e) + 1) + 11*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 9*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 5)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 4*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4*a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*a^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^2*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) + 12*c^4*((9*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) - 2*c^4*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + 8*c^4*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 1)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3))/f","B",0
271,1,590,0,0.924839," ","integrate((c-c*sin(f*x+e))^3/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(2 \, c^{3} {\left(\frac{\frac{12 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{11 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{9 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 5}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{4 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{4 \, a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{2} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} + 3 \, c^{3} {\left(\frac{\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 4}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} - \frac{c^{3} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 2\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{3 \, c^{3} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}\right)}}{3 \, f}"," ",0,"2/3*(2*c^3*((12*sin(f*x + e)/(cos(f*x + e) + 1) + 11*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 9*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 5)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 4*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4*a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*a^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^2*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) + 3*c^3*((9*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) - c^3*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + 3*c^3*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 1)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3))/f","B",0
272,1,361,0,0.754333," ","integrate((c-c*sin(f*x+e))^2/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(c^{2} {\left(\frac{\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 4}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} - \frac{c^{2} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 2\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{2 \, c^{2} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}\right)}}{3 \, f}"," ",0,"2/3*(c^2*((9*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) - c^2*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + 2*c^2*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 1)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3))/f","B",0
273,1,215,0,0.704147," ","integrate((c-c*sin(f*x+e))/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{c {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 2\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} - \frac{c {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}\right)}}{3 \, f}"," ",0,"-2/3*(c*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) - c*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 1)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3))/f","B",0
274,1,142,0,0.721801," ","integrate(1/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e)),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - 1\right)}}{3 \, {\left(a^{2} c + \frac{2 \, a^{2} c \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{2 \, a^{2} c \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{a^{2} c \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}}\right)} f}"," ",0,"2/3*(sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 1)/((a^2*c + 2*a^2*c*sin(f*x + e)/(cos(f*x + e) + 1) - 2*a^2*c*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - a^2*c*sin(f*x + e)^4/(cos(f*x + e) + 1)^4)*f)","B",0
275,1,28,0,0.670550," ","integrate(1/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)}{3 \, a^{2} c^{2} f}"," ",0,"1/3*(tan(f*x + e)^3 + 3*tan(f*x + e))/(a^2*c^2*f)","A",0
276,1,335,0,0.974508," ","integrate(1/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^3,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{21 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{13 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{25 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{5 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{15 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{15 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + 3\right)}}{15 \, {\left(a^{2} c^{3} - \frac{2 \, a^{2} c^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{2 \, a^{2} c^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{6 \, a^{2} c^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{6 \, a^{2} c^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{2 \, a^{2} c^{3} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{2 \, a^{2} c^{3} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{a^{2} c^{3} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}}\right)} f}"," ",0,"2/15*(9*sin(f*x + e)/(cos(f*x + e) + 1) - 21*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 13*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 25*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 5*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 15*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 15*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 3)/((a^2*c^3 - 2*a^2*c^3*sin(f*x + e)/(cos(f*x + e) + 1) - 2*a^2*c^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 6*a^2*c^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 6*a^2*c^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 2*a^2*c^3*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 2*a^2*c^3*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - a^2*c^3*sin(f*x + e)^8/(cos(f*x + e) + 1)^8)*f)","B",0
277,1,427,0,0.942028," ","integrate(1/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^4,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{24 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{76 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{28 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{42 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{56 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{28 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{42 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{21 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - 6\right)}}{21 \, {\left(a^{2} c^{4} - \frac{4 \, a^{2} c^{4} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} c^{4} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{8 \, a^{2} c^{4} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{14 \, a^{2} c^{4} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{14 \, a^{2} c^{4} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{8 \, a^{2} c^{4} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{3 \, a^{2} c^{4} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{4 \, a^{2} c^{4} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - \frac{a^{2} c^{4} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}}\right)} f}"," ",0,"-2/21*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 24*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 76*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 28*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 42*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 56*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 28*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 42*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 21*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 6)/((a^2*c^4 - 4*a^2*c^4*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*c^4*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 8*a^2*c^4*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 14*a^2*c^4*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 14*a^2*c^4*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 8*a^2*c^4*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 3*a^2*c^4*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 4*a^2*c^4*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - a^2*c^4*sin(f*x + e)^10/(cos(f*x + e) + 1)^10)*f)","B",0
278,1,519,0,0.814147," ","integrate(1/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^5,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{51 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{39 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{235 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{450 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{306 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{294 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{378 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{63 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{273 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{189 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{63 \, \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} - 19\right)}}{63 \, {\left(a^{2} c^{5} - \frac{6 \, a^{2} c^{5} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{12 \, a^{2} c^{5} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{2 \, a^{2} c^{5} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{27 \, a^{2} c^{5} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{36 \, a^{2} c^{5} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{36 \, a^{2} c^{5} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{27 \, a^{2} c^{5} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{2 \, a^{2} c^{5} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - \frac{12 \, a^{2} c^{5} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{6 \, a^{2} c^{5} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} - \frac{a^{2} c^{5} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}}\right)} f}"," ",0,"-2/63*(51*sin(f*x + e)/(cos(f*x + e) + 1) - 39*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 235*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 450*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 306*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 294*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 378*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 63*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 273*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 189*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 63*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 - 19)/((a^2*c^5 - 6*a^2*c^5*sin(f*x + e)/(cos(f*x + e) + 1) + 12*a^2*c^5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 2*a^2*c^5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 27*a^2*c^5*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 36*a^2*c^5*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 36*a^2*c^5*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 27*a^2*c^5*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 2*a^2*c^5*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 12*a^2*c^5*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 6*a^2*c^5*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 - a^2*c^5*sin(f*x + e)^12/(cos(f*x + e) + 1)^12)*f)","B",0
279,1,1496,0,1.486205," ","integrate((c-c*sin(f*x+e))^5/(a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","-\frac{c^{5} {\left(\frac{\frac{1325 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{2673 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3805 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{4329 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{3575 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{2275 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{975 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{195 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + 304}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{12 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{20 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{26 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{26 \, a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{20 \, a^{3} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{12 \, a^{3} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{a^{3} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}} + \frac{195 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{3}}\right)} + 30 \, c^{5} {\left(\frac{\frac{105 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{189 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{200 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{160 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{75 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{15 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + 24}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{11 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{15 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{11 \, a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{a^{3} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} + \frac{15 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{3}}\right)} + 20 \, c^{5} {\left(\frac{\frac{95 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{145 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{75 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 22}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{15 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{3}}\right)} + \frac{2 \, c^{5} {\left(\frac{20 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{40 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{30 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 7\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{40 \, c^{5} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} - \frac{30 \, c^{5} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{5 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}}{15 \, f}"," ",0,"-1/15*(c^5*((1325*sin(f*x + e)/(cos(f*x + e) + 1) + 2673*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3805*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 4329*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 3575*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 2275*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 975*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 195*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 304)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 12*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 20*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 26*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 26*a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 20*a^3*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 12*a^3*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 5*a^3*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + a^3*sin(f*x + e)^9/(cos(f*x + e) + 1)^9) + 195*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^3) + 30*c^5*((105*sin(f*x + e)/(cos(f*x + e) + 1) + 189*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 200*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 160*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 75*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 15*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 24)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 11*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 15*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 11*a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 5*a^3*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + a^3*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) + 15*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^3) + 20*c^5*((95*sin(f*x + e)/(cos(f*x + e) + 1) + 145*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 75*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 22)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 15*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^3) + 2*c^5*(20*sin(f*x + e)/(cos(f*x + e) + 1) + 40*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 30*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 7)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 40*c^5*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 10*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) - 30*c^5*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5))/f","B",0
280,1,1096,0,0.970271," ","integrate((c-c*sin(f*x+e))^4/(a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(3 \, c^{4} {\left(\frac{\frac{105 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{189 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{200 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{160 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{75 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{15 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + 24}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{11 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{15 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{11 \, a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{a^{3} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} + \frac{15 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{3}}\right)} + 4 \, c^{4} {\left(\frac{\frac{95 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{145 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{75 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 22}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{15 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{3}}\right)} + \frac{c^{4} {\left(\frac{20 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{40 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{30 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 7\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{12 \, c^{4} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} - \frac{12 \, c^{4} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{5 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}\right)}}{15 \, f}"," ",0,"-2/15*(3*c^4*((105*sin(f*x + e)/(cos(f*x + e) + 1) + 189*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 200*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 160*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 75*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 15*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 24)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 11*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 15*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 11*a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 5*a^3*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + a^3*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) + 15*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^3) + 4*c^4*((95*sin(f*x + e)/(cos(f*x + e) + 1) + 145*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 75*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 22)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 15*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^3) + c^4*(20*sin(f*x + e)/(cos(f*x + e) + 1) + 40*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 30*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 7)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 12*c^4*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 10*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) - 12*c^4*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5))/f","B",0
281,1,781,0,1.459535," ","integrate((c-c*sin(f*x+e))^3/(a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(c^{3} {\left(\frac{\frac{95 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{145 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{75 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 22}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{15 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{3}}\right)} + \frac{c^{3} {\left(\frac{20 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{40 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{30 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 7\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{6 \, c^{3} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} - \frac{9 \, c^{3} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{5 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}\right)}}{15 \, f}"," ",0,"-2/15*(c^3*((95*sin(f*x + e)/(cos(f*x + e) + 1) + 145*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 75*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 22)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 15*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^3) + c^3*(20*sin(f*x + e)/(cos(f*x + e) + 1) + 40*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 30*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 7)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 6*c^3*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 10*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) - 9*c^3*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5))/f","B",0
282,1,554,0,0.712626," ","integrate((c-c*sin(f*x+e))^2/(a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{c^{2} {\left(\frac{20 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{40 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{30 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 7\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{2 \, c^{2} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} - \frac{6 \, c^{2} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{5 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}\right)}}{15 \, f}"," ",0,"-2/15*(c^2*(20*sin(f*x + e)/(cos(f*x + e) + 1) + 40*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 30*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 7)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 2*c^2*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 10*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) - 6*c^2*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5))/f","B",0
283,1,387,0,0.982861," ","integrate((c-c*sin(f*x+e))/(a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{c {\left(\frac{20 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{40 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{30 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 7\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} - \frac{3 \, c {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{5 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}\right)}}{15 \, f}"," ",0,"-2/15*(c*(20*sin(f*x + e)/(cos(f*x + e) + 1) + 40*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 30*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 7)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) - 3*c*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5))/f","B",0
284,1,211,0,0.651947," ","integrate(1/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e)),x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{10 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{10 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{5 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + 2\right)}}{5 \, {\left(a^{3} c + \frac{4 \, a^{3} c \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, a^{3} c \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{5 \, a^{3} c \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{4 \, a^{3} c \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{a^{3} c \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}}\right)} f}"," ",0,"-2/5*(3*sin(f*x + e)/(cos(f*x + e) + 1) - 10*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 10*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 5*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 2)/((a^3*c + 4*a^3*c*sin(f*x + e)/(cos(f*x + e) + 1) + 5*a^3*c*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 5*a^3*c*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 4*a^3*c*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - a^3*c*sin(f*x + e)^6/(cos(f*x + e) + 1)^6)*f)","B",0
285,1,335,0,1.117407," ","integrate(1/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{21 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{13 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{25 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{5 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{15 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{15 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - 3\right)}}{15 \, {\left(a^{3} c^{2} + \frac{2 \, a^{3} c^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{2 \, a^{3} c^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{6 \, a^{3} c^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{6 \, a^{3} c^{2} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{2 \, a^{3} c^{2} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{2 \, a^{3} c^{2} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{a^{3} c^{2} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}}\right)} f}"," ",0,"2/15*(9*sin(f*x + e)/(cos(f*x + e) + 1) + 21*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 13*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 25*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 5*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 15*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 15*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 3)/((a^3*c^2 + 2*a^3*c^2*sin(f*x + e)/(cos(f*x + e) + 1) - 2*a^3*c^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 6*a^3*c^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 6*a^3*c^2*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 2*a^3*c^2*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 2*a^3*c^2*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - a^3*c^2*sin(f*x + e)^8/(cos(f*x + e) + 1)^8)*f)","B",0
286,1,40,0,0.667642," ","integrate(1/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^3,x, algorithm=""maxima"")","\frac{3 \, \tan\left(f x + e\right)^{5} + 10 \, \tan\left(f x + e\right)^{3} + 15 \, \tan\left(f x + e\right)}{15 \, a^{3} c^{3} f}"," ",0,"1/15*(3*tan(f*x + e)^5 + 10*tan(f*x + e)^3 + 15*tan(f*x + e))/(a^3*c^3*f)","A",0
287,1,519,0,1.019124," ","integrate(1/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^4,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{25 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{55 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{15 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{130 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{26 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{182 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{126 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{105 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{35 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - \frac{35 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{35 \, \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} + 5\right)}}{35 \, {\left(a^{3} c^{4} - \frac{2 \, a^{3} c^{4} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{4 \, a^{3} c^{4} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} c^{4} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} c^{4} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{20 \, a^{3} c^{4} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{20 \, a^{3} c^{4} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{5 \, a^{3} c^{4} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{10 \, a^{3} c^{4} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{4 \, a^{3} c^{4} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{2 \, a^{3} c^{4} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} - \frac{a^{3} c^{4} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}}\right)} f}"," ",0,"2/35*(25*sin(f*x + e)/(cos(f*x + e) + 1) - 55*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 15*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 130*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 26*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 182*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 126*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 105*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 35*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 35*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 35*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 + 5)/((a^3*c^4 - 2*a^3*c^4*sin(f*x + e)/(cos(f*x + e) + 1) - 4*a^3*c^4*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*c^4*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*c^4*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 20*a^3*c^4*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 20*a^3*c^4*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 5*a^3*c^4*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 10*a^3*c^4*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 4*a^3*c^4*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 2*a^3*c^4*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 - a^3*c^4*sin(f*x + e)^12/(cos(f*x + e) + 1)^12)*f)","B",0
288,1,610,0,0.440482," ","integrate(1/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^5,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{80 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{190 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{50 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{269 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{96 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{516 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{354 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{69 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{240 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{30 \, \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} - \frac{90 \, \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} + \frac{45 \, \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}} + 10\right)}}{45 \, {\left(a^{3} c^{5} - \frac{4 \, a^{3} c^{5} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{a^{3} c^{5} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{16 \, a^{3} c^{5} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{19 \, a^{3} c^{5} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{20 \, a^{3} c^{5} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{45 \, a^{3} c^{5} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{45 \, a^{3} c^{5} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{20 \, a^{3} c^{5} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{19 \, a^{3} c^{5} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{16 \, a^{3} c^{5} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} - \frac{a^{3} c^{5} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} + \frac{4 \, a^{3} c^{5} \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}} - \frac{a^{3} c^{5} \sin\left(f x + e\right)^{14}}{{\left(\cos\left(f x + e\right) + 1\right)}^{14}}\right)} f}"," ",0,"2/45*(5*sin(f*x + e)/(cos(f*x + e) + 1) - 80*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 190*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 50*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 269*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 96*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 516*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 354*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 69*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 240*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 30*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 - 90*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 + 45*sin(f*x + e)^13/(cos(f*x + e) + 1)^13 + 10)/((a^3*c^5 - 4*a^3*c^5*sin(f*x + e)/(cos(f*x + e) + 1) + a^3*c^5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 16*a^3*c^5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 19*a^3*c^5*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 20*a^3*c^5*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 45*a^3*c^5*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 45*a^3*c^5*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 20*a^3*c^5*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 19*a^3*c^5*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 16*a^3*c^5*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 - a^3*c^5*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 + 4*a^3*c^5*sin(f*x + e)^13/(cos(f*x + e) + 1)^13 - a^3*c^5*sin(f*x + e)^14/(cos(f*x + e) + 1)^14)*f)","B",0
289,1,703,0,0.730786," ","integrate(1/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^6,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{255 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{235 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{3065 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3775 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{667 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{8217 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{2035 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{8745 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{11715 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{33 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{4917 \, \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} - \frac{2475 \, \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - \frac{1815 \, \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}} + \frac{1485 \, \sin\left(f x + e\right)^{14}}{{\left(\cos\left(f x + e\right) + 1\right)}^{14}} - \frac{495 \, \sin\left(f x + e\right)^{15}}{{\left(\cos\left(f x + e\right) + 1\right)}^{15}} - 125\right)}}{495 \, {\left(a^{3} c^{6} - \frac{6 \, a^{3} c^{6} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} c^{6} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} c^{6} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{50 \, a^{3} c^{6} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{34 \, a^{3} c^{6} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{66 \, a^{3} c^{6} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{110 \, a^{3} c^{6} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{110 \, a^{3} c^{6} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - \frac{66 \, a^{3} c^{6} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{34 \, a^{3} c^{6} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} + \frac{50 \, a^{3} c^{6} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - \frac{10 \, a^{3} c^{6} \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}} - \frac{10 \, a^{3} c^{6} \sin\left(f x + e\right)^{14}}{{\left(\cos\left(f x + e\right) + 1\right)}^{14}} + \frac{6 \, a^{3} c^{6} \sin\left(f x + e\right)^{15}}{{\left(\cos\left(f x + e\right) + 1\right)}^{15}} - \frac{a^{3} c^{6} \sin\left(f x + e\right)^{16}}{{\left(\cos\left(f x + e\right) + 1\right)}^{16}}\right)} f}"," ",0,"-2/495*(255*sin(f*x + e)/(cos(f*x + e) + 1) + 235*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 3065*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3775*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 667*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 8217*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 2035*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 8745*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 11715*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 33*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 4917*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 - 2475*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - 1815*sin(f*x + e)^13/(cos(f*x + e) + 1)^13 + 1485*sin(f*x + e)^14/(cos(f*x + e) + 1)^14 - 495*sin(f*x + e)^15/(cos(f*x + e) + 1)^15 - 125)/((a^3*c^6 - 6*a^3*c^6*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*c^6*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*c^6*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 50*a^3*c^6*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 34*a^3*c^6*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 66*a^3*c^6*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 110*a^3*c^6*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 110*a^3*c^6*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 66*a^3*c^6*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 34*a^3*c^6*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 + 50*a^3*c^6*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - 10*a^3*c^6*sin(f*x + e)^13/(cos(f*x + e) + 1)^13 - 10*a^3*c^6*sin(f*x + e)^14/(cos(f*x + e) + 1)^14 + 6*a^3*c^6*sin(f*x + e)^15/(cos(f*x + e) + 1)^15 - a^3*c^6*sin(f*x + e)^16/(cos(f*x + e) + 1)^16)*f)","B",0
290,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(c-c*sin(f*x+e))^(7/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)*(-c*sin(f*x + e) + c)^(7/2), x)","F",0
291,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)*(-c*sin(f*x + e) + c)^(5/2), x)","F",0
292,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)*(-c*sin(f*x + e) + c)^(3/2), x)","F",0
293,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)} \sqrt{-c \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c), x)","F",0
294,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{a \sin\left(f x + e\right) + a}{\sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)/sqrt(-c*sin(f*x + e) + c), x)","F",0
295,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{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((a*sin(f*x + e) + a)/(-c*sin(f*x + e) + c)^(3/2), x)","F",0
296,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{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((a*sin(f*x + e) + a)/(-c*sin(f*x + e) + c)^(5/2), x)","F",0
297,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(7/2),x, algorithm=""maxima"")","\int \frac{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((a*sin(f*x + e) + a)/(-c*sin(f*x + e) + c)^(7/2), x)","F",0
298,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2*(c-c*sin(f*x+e))^(7/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^2*(-c*sin(f*x + e) + c)^(7/2), x)","F",0
299,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2*(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\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)^2*(-c*sin(f*x + e) + c)^(5/2), x)","F",0
300,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2*(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\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)^2*(-c*sin(f*x + e) + c)^(3/2), x)","F",0
301,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2*(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{2} \sqrt{-c \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^2*sqrt(-c*sin(f*x + e) + c), x)","F",0
302,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{2}}{\sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^2/sqrt(-c*sin(f*x + e) + c), x)","F",0
303,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\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)^2/(-c*sin(f*x + e) + c)^(3/2), x)","F",0
304,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\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)^2/(-c*sin(f*x + e) + c)^(5/2), x)","F",0
305,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{2}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^2/(-c*sin(f*x + e) + c)^(7/2), x)","F",0
306,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{2}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^2/(-c*sin(f*x + e) + c)^(9/2), x)","F",0
307,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3*(c-c*sin(f*x+e))^(7/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^3*(-c*sin(f*x + e) + c)^(7/2), x)","F",0
308,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3*(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^3*(-c*sin(f*x + e) + c)^(5/2), x)","F",0
309,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3*(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^3*(-c*sin(f*x + e) + c)^(3/2), x)","F",0
310,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3*(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{3} \sqrt{-c \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^3*sqrt(-c*sin(f*x + e) + c), x)","F",0
311,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{3}}{\sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^3/sqrt(-c*sin(f*x + e) + c), x)","F",0
312,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{3}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^3/(-c*sin(f*x + e) + c)^(3/2), x)","F",0
313,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{3}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^3/(-c*sin(f*x + e) + c)^(5/2), x)","F",0
314,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{3}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^3/(-c*sin(f*x + e) + c)^(7/2), x)","F",0
315,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{3}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^3/(-c*sin(f*x + e) + c)^(9/2), x)","F",0
316,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^(11/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{3}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^3/(-c*sin(f*x + e) + c)^(11/2), x)","F",0
317,1,238,0,1.801756," ","integrate((c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e)),x, algorithm=""maxima"")","\frac{2 \, {\left(91 \, c^{\frac{7}{2}} + \frac{86 \, c^{\frac{7}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{336 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{266 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{490 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{266 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{336 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{86 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{91 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}}\right)}}{5 \, {\left(a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)} f {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{7}{2}}}"," ",0,"2/5*(91*c^(7/2) + 86*c^(7/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 336*c^(7/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 266*c^(7/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 490*c^(7/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 266*c^(7/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 336*c^(7/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 86*c^(7/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 91*c^(7/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8)/((a + a*sin(f*x + e)/(cos(f*x + e) + 1))*f*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(7/2))","B",0
318,1,192,0,0.661301," ","integrate((c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e)),x, algorithm=""maxima"")","\frac{2 \, {\left(23 \, c^{\frac{5}{2}} + \frac{20 \, c^{\frac{5}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{65 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{40 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{65 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{20 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{23 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}}\right)}}{3 \, {\left(a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)} f {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{5}{2}}}"," ",0,"2/3*(23*c^(5/2) + 20*c^(5/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 65*c^(5/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 40*c^(5/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 65*c^(5/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 20*c^(5/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 23*c^(5/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6)/((a + a*sin(f*x + e)/(cos(f*x + e) + 1))*f*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(5/2))","B",0
319,1,146,0,0.920421," ","integrate((c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e)),x, algorithm=""maxima"")","\frac{2 \, {\left(3 \, c^{\frac{3}{2}} + \frac{2 \, c^{\frac{3}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{6 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{2 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}}\right)}}{{\left(a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)} f {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{3}{2}}}"," ",0,"2*(3*c^(3/2) + 2*c^(3/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 6*c^(3/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2*c^(3/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*c^(3/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4)/((a + a*sin(f*x + e)/(cos(f*x + e) + 1))*f*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(3/2))","B",0
320,1,76,0,0.778338," ","integrate((c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e)),x, algorithm=""maxima"")","\frac{2 \, {\left(\sqrt{c} + \frac{\sqrt{c} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)}}{{\left(a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)} f \sqrt{\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1}}"," ",0,"2*(sqrt(c) + sqrt(c)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)/((a + a*sin(f*x + e)/(cos(f*x + e) + 1))*f*sqrt(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1))","B",0
321,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sin\left(f x + e\right) + a\right)} \sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(1/((a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)), x)","F",0
322,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sin\left(f x + e\right) + a\right)} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((a*sin(f*x + e) + a)*(-c*sin(f*x + e) + c)^(3/2)), x)","F",0
323,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sin\left(f x + e\right) + a\right)} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((a*sin(f*x + e) + a)*(-c*sin(f*x + e) + c)^(5/2)), x)","F",0
324,1,380,0,1.020766," ","integrate((c-c*sin(f*x+e))^(9/2)/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(723 \, c^{\frac{9}{2}} + \frac{2184 \, c^{\frac{9}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5370 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10696 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15021 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{21168 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{20748 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{21168 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{15021 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{10696 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{5370 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{2184 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} + \frac{723 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}}\right)}}{15 \, {\left(a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)} f {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{9}{2}}}"," ",0,"-2/15*(723*c^(9/2) + 2184*c^(9/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 5370*c^(9/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10696*c^(9/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15021*c^(9/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 21168*c^(9/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 20748*c^(9/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 21168*c^(9/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 15021*c^(9/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 10696*c^(9/2)*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 5370*c^(9/2)*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 2184*c^(9/2)*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 + 723*c^(9/2)*sin(f*x + e)^12/(cos(f*x + e) + 1)^12)/((a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3)*f*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(9/2))","B",0
325,1,334,0,0.823412," ","integrate((c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(45 \, c^{\frac{7}{2}} + \frac{138 \, c^{\frac{7}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{285 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{544 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{630 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{812 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{630 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{544 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{285 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{138 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{45 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}}\right)}}{3 \, {\left(a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)} f {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{7}{2}}}"," ",0,"-2/3*(45*c^(7/2) + 138*c^(7/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 285*c^(7/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 544*c^(7/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 630*c^(7/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 812*c^(7/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 630*c^(7/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 544*c^(7/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 285*c^(7/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 138*c^(7/2)*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 45*c^(7/2)*sin(f*x + e)^10/(cos(f*x + e) + 1)^10)/((a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3)*f*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(7/2))","B",0
326,1,288,0,1.177083," ","integrate((c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(11 \, c^{\frac{5}{2}} + \frac{36 \, c^{\frac{5}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{56 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{108 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{90 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{108 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{56 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{36 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{11 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}}\right)}}{3 \, {\left(a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)} f {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{5}{2}}}"," ",0,"-2/3*(11*c^(5/2) + 36*c^(5/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 56*c^(5/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 108*c^(5/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 90*c^(5/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 108*c^(5/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 56*c^(5/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 36*c^(5/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 11*c^(5/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8)/((a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3)*f*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(5/2))","B",0
327,1,239,0,0.427227," ","integrate((c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(c^{\frac{3}{2}} + \frac{6 \, c^{\frac{3}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{12 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{6 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{c^{\frac{3}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}}\right)}}{3 \, {\left(a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)} f {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{3}{2}}}"," ",0,"-2/3*(c^(3/2) + 6*c^(3/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 3*c^(3/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 12*c^(3/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*c^(3/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 6*c^(3/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + c^(3/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6)/((a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3)*f*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(3/2))","B",0
328,1,149,0,0.983596," ","integrate((c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(\sqrt{c} + \frac{2 \, \sqrt{c} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{\sqrt{c} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}}\right)}}{3 \, {\left(a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)} f \sqrt{\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1}}"," ",0,"2/3*(sqrt(c) + 2*sqrt(c)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + sqrt(c)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4)/((a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3)*f*sqrt(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1))","B",0
329,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sin\left(f x + e\right) + a\right)}^{2} \sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(1/((a*sin(f*x + e) + a)^2*sqrt(-c*sin(f*x + e) + c)), x)","F",0
330,-1,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
331,-1,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
332,1,472,0,0.836944," ","integrate((c-c*sin(f*x+e))^(9/2)/(a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","\frac{2 \, {\left(363 \, c^{\frac{9}{2}} + \frac{1800 \, c^{\frac{9}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5301 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{11600 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{21343 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{30200 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{40065 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{40800 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{40065 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{30200 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{21343 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{11600 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} + \frac{5301 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} + \frac{1800 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}} + \frac{363 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{14}}{{\left(\cos\left(f x + e\right) + 1\right)}^{14}}\right)}}{15 \, {\left(a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)} f {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{9}{2}}}"," ",0,"2/15*(363*c^(9/2) + 1800*c^(9/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 5301*c^(9/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 11600*c^(9/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 21343*c^(9/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 30200*c^(9/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 40065*c^(9/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 40800*c^(9/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 40065*c^(9/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 30200*c^(9/2)*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 21343*c^(9/2)*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 11600*c^(9/2)*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 + 5301*c^(9/2)*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 + 1800*c^(9/2)*sin(f*x + e)^13/(cos(f*x + e) + 1)^13 + 363*c^(9/2)*sin(f*x + e)^14/(cos(f*x + e) + 1)^14)/((a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)*f*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(9/2))","B",0
333,1,426,0,1.001578," ","integrate((c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","\frac{2 \, {\left(23 \, c^{\frac{7}{2}} + \frac{110 \, c^{\frac{7}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{318 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{590 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{1065 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{1220 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{1540 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{1220 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{1065 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{590 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{318 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{110 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} + \frac{23 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}}\right)}}{5 \, {\left(a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)} f {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{7}{2}}}"," ",0,"2/5*(23*c^(7/2) + 110*c^(7/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 318*c^(7/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 590*c^(7/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 1065*c^(7/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 1220*c^(7/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 1540*c^(7/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 1220*c^(7/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 1065*c^(7/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 590*c^(7/2)*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 318*c^(7/2)*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 110*c^(7/2)*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 + 23*c^(7/2)*sin(f*x + e)^12/(cos(f*x + e) + 1)^12)/((a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)*f*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(7/2))","B",0
334,1,380,0,1.086165," ","integrate((c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","\frac{2 \, {\left(7 \, c^{\frac{5}{2}} + \frac{20 \, c^{\frac{5}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{95 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{80 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{250 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{120 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{250 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{80 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{95 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{20 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{7 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}}\right)}}{15 \, {\left(a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)} f {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{5}{2}}}"," ",0,"2/15*(7*c^(5/2) + 20*c^(5/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 95*c^(5/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 80*c^(5/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 250*c^(5/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 120*c^(5/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 250*c^(5/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 80*c^(5/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 95*c^(5/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 20*c^(5/2)*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 7*c^(5/2)*sin(f*x + e)^10/(cos(f*x + e) + 1)^10)/((a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)*f*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(5/2))","B",0
335,1,331,0,0.853156," ","integrate((c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","\frac{2 \, {\left(c^{\frac{3}{2}} - \frac{10 \, c^{\frac{3}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{4 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{30 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{6 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{30 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{4 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{10 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{c^{\frac{3}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}}\right)}}{15 \, {\left(a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)} f {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{3}{2}}}"," ",0,"2/15*(c^(3/2) - 10*c^(3/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 4*c^(3/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 30*c^(3/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 6*c^(3/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 30*c^(3/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 4*c^(3/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 10*c^(3/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + c^(3/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8)/((a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)*f*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(3/2))","B",0
336,1,218,0,1.134044," ","integrate((c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","\frac{2 \, {\left(\sqrt{c} + \frac{3 \, \sqrt{c} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3 \, \sqrt{c} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{\sqrt{c} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}}\right)}}{5 \, {\left(a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)} f \sqrt{\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1}}"," ",0,"2/5*(sqrt(c) + 3*sqrt(c)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3*sqrt(c)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + sqrt(c)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6)/((a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)*f*sqrt(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1))","B",0
337,-1,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
338,-1,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
339,-1,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
340,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)*(c-c*sin(f*x+e))^(7/2),x, algorithm=""maxima"")","\int \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(sqrt(a*sin(f*x + e) + a)*(-c*sin(f*x + e) + c)^(7/2), x)","F",0
341,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)*(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \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(sqrt(a*sin(f*x + e) + a)*(-c*sin(f*x + e) + c)^(5/2), x)","F",0
342,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)*(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \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(sqrt(a*sin(f*x + e) + a)*(-c*sin(f*x + e) + c)^(3/2), x)","F",0
343,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)*(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate(sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c), x)","F",0
344,1,63,0,0.917399," ","integrate((a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\frac{\frac{2 \, \sqrt{a} \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{\sqrt{c}} - \frac{\sqrt{a} \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}{\sqrt{c}}}{f}"," ",0,"(2*sqrt(a)*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/sqrt(c) - sqrt(a)*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/sqrt(c))/f","A",0
345,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{\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(sqrt(a*sin(f*x + e) + a)/(-c*sin(f*x + e) + c)^(3/2), x)","F",0
346,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{\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(sqrt(a*sin(f*x + e) + a)/(-c*sin(f*x + e) + c)^(5/2), x)","F",0
347,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(7/2),x, algorithm=""maxima"")","\int \frac{\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(sqrt(a*sin(f*x + e) + a)/(-c*sin(f*x + e) + c)^(7/2), x)","F",0
348,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(7/2),x, algorithm=""maxima"")","\int {\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((a*sin(f*x + e) + a)^(3/2)*(-c*sin(f*x + e) + c)^(7/2), x)","F",0
349,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int {\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((a*sin(f*x + e) + a)^(3/2)*(-c*sin(f*x + e) + c)^(5/2), x)","F",0
350,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\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((a*sin(f*x + e) + a)^(3/2)*(-c*sin(f*x + e) + c)^(3/2), x)","F",0
351,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int {\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((a*sin(f*x + e) + a)^(3/2)*sqrt(-c*sin(f*x + e) + c), x)","F",0
352,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\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((a*sin(f*x + e) + a)^(3/2)/sqrt(-c*sin(f*x + e) + c), x)","F",0
353,1,137,0,0.897881," ","integrate((a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","-\frac{\frac{2 \, a^{\frac{3}{2}} \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{c^{\frac{3}{2}}} - \frac{a^{\frac{3}{2}} \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}{c^{\frac{3}{2}}} + \frac{4 \, a^{\frac{3}{2}} \sqrt{c} \sin\left(f x + e\right)}{{\left(c^{2} - \frac{2 \, c^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{c^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)} {\left(\cos\left(f x + e\right) + 1\right)}}}{f}"," ",0,"-(2*a^(3/2)*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/c^(3/2) - a^(3/2)*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/c^(3/2) + 4*a^(3/2)*sqrt(c)*sin(f*x + e)/((c^2 - 2*c^2*sin(f*x + e)/(cos(f*x + e) + 1) + c^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)*(cos(f*x + e) + 1)))/f","A",0
354,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\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((a*sin(f*x + e) + a)^(3/2)/(-c*sin(f*x + e) + c)^(5/2), x)","F",0
355,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(7/2),x, algorithm=""maxima"")","\int \frac{{\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((a*sin(f*x + e) + a)^(3/2)/(-c*sin(f*x + e) + c)^(7/2), x)","F",0
356,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(3/2)/(-c*sin(f*x + e) + c)^(9/2), x)","F",0
357,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(11/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(3/2)/(-c*sin(f*x + e) + c)^(11/2), x)","F",0
358,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(7/2),x, algorithm=""maxima"")","\int {\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((a*sin(f*x + e) + a)^(5/2)*(-c*sin(f*x + e) + c)^(7/2), x)","F",0
359,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int {\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((a*sin(f*x + e) + a)^(5/2)*(-c*sin(f*x + e) + c)^(5/2), x)","F",0
360,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\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((a*sin(f*x + e) + a)^(5/2)*(-c*sin(f*x + e) + c)^(3/2), x)","F",0
361,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int {\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((a*sin(f*x + e) + a)^(5/2)*sqrt(-c*sin(f*x + e) + c), x)","F",0
362,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\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((a*sin(f*x + e) + a)^(5/2)/sqrt(-c*sin(f*x + e) + c), x)","F",0
363,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\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((a*sin(f*x + e) + a)^(5/2)/(-c*sin(f*x + e) + c)^(3/2), x)","F",0
364,1,184,0,1.923356," ","integrate((a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","-\frac{\frac{8 \, a^{\frac{5}{2}} \sqrt{c} \sin\left(f x + e\right)^{2}}{{\left(c^{3} - \frac{4 \, c^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{6 \, c^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{4 \, c^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{c^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}}\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{2 \, a^{\frac{5}{2}} \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{c^{\frac{5}{2}}} + \frac{a^{\frac{5}{2}} \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}{c^{\frac{5}{2}}}}{f}"," ",0,"-(8*a^(5/2)*sqrt(c)*sin(f*x + e)^2/((c^3 - 4*c^3*sin(f*x + e)/(cos(f*x + e) + 1) + 6*c^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 4*c^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + c^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4)*(cos(f*x + e) + 1)^2) - 2*a^(5/2)*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/c^(5/2) + a^(5/2)*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/c^(5/2))/f","A",0
365,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(7/2),x, algorithm=""maxima"")","\int \frac{{\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((a*sin(f*x + e) + a)^(5/2)/(-c*sin(f*x + e) + c)^(7/2), x)","F",0
366,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(5/2)/(-c*sin(f*x + e) + c)^(9/2), x)","F",0
367,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(11/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(5/2)/(-c*sin(f*x + e) + c)^(11/2), x)","F",0
368,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(13/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{13}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(5/2)/(-c*sin(f*x + e) + c)^(13/2), x)","F",0
369,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(9/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{7}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{9}{2}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(7/2)*(-c*sin(f*x + e) + c)^(9/2), x)","F",0
370,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(7/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{7}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(7/2)*(-c*sin(f*x + e) + c)^(7/2), x)","F",0
371,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{7}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(7/2)*(-c*sin(f*x + e) + c)^(5/2), x)","F",0
372,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\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((a*sin(f*x + e) + a)^(7/2)*(-c*sin(f*x + e) + c)^(3/2), x)","F",0
373,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int {\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((a*sin(f*x + e) + a)^(7/2)*sqrt(-c*sin(f*x + e) + c), x)","F",0
374,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\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((a*sin(f*x + e) + a)^(7/2)/sqrt(-c*sin(f*x + e) + c), x)","F",0
375,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\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((a*sin(f*x + e) + a)^(7/2)/(-c*sin(f*x + e) + c)^(3/2), x)","F",0
376,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{7}{2}}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(7/2)/(-c*sin(f*x + e) + c)^(5/2), x)","F",0
377,1,336,0,1.005248," ","integrate((a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(7/2),x, algorithm=""maxima"")","-\frac{\frac{6 \, a^{\frac{7}{2}} \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{c^{\frac{7}{2}}} - \frac{3 \, a^{\frac{7}{2}} \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}{c^{\frac{7}{2}}} + \frac{4 \, {\left(\frac{3 \, a^{\frac{7}{2}} \sqrt{c} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{6 \, a^{\frac{7}{2}} \sqrt{c} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{22 \, a^{\frac{7}{2}} \sqrt{c} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{6 \, a^{\frac{7}{2}} \sqrt{c} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{3 \, a^{\frac{7}{2}} \sqrt{c} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{c^{4} - \frac{6 \, c^{4} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{15 \, c^{4} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{20 \, c^{4} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, c^{4} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{6 \, c^{4} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{c^{4} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}}}}{3 \, f}"," ",0,"-1/3*(6*a^(7/2)*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/c^(7/2) - 3*a^(7/2)*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/c^(7/2) + 4*(3*a^(7/2)*sqrt(c)*sin(f*x + e)/(cos(f*x + e) + 1) - 6*a^(7/2)*sqrt(c)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 22*a^(7/2)*sqrt(c)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 6*a^(7/2)*sqrt(c)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 3*a^(7/2)*sqrt(c)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/(c^4 - 6*c^4*sin(f*x + e)/(cos(f*x + e) + 1) + 15*c^4*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 20*c^4*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*c^4*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 6*c^4*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + c^4*sin(f*x + e)^6/(cos(f*x + e) + 1)^6))/f","A",0
378,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{7}{2}}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(7/2)/(-c*sin(f*x + e) + c)^(9/2), x)","F",0
379,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(11/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{7}{2}}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(7/2)/(-c*sin(f*x + e) + c)^(11/2), x)","F",0
380,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(13/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{7}{2}}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{13}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(7/2)/(-c*sin(f*x + e) + c)^(13/2), x)","F",0
381,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(15/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{7}{2}}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{15}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(7/2)/(-c*sin(f*x + e) + c)^(15/2), x)","F",0
382,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(17/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
383,0,0,0,0.000000," ","integrate((c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}{\sqrt{a \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((-c*sin(f*x + e) + c)^(5/2)/sqrt(a*sin(f*x + e) + a), x)","F",0
384,0,0,0,0.000000," ","integrate((c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{\sqrt{a \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((-c*sin(f*x + e) + c)^(3/2)/sqrt(a*sin(f*x + e) + a), x)","F",0
385,1,64,0,0.601669," ","integrate((c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{\frac{2 \, \sqrt{c} \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{\sqrt{a}} - \frac{\sqrt{c} \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}{\sqrt{a}}}{f}"," ",0,"-(2*sqrt(c)*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/sqrt(a) - sqrt(c)*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/sqrt(a))/f","A",0
386,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(1/(sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)), x)","F",0
387,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{\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(1/(sqrt(a*sin(f*x + e) + a)*(-c*sin(f*x + e) + c)^(3/2)), x)","F",0
388,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{\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(1/(sqrt(a*sin(f*x + e) + a)*(-c*sin(f*x + e) + c)^(5/2)), x)","F",0
389,0,0,0,0.000000," ","integrate((c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((-c*sin(f*x + e) + c)^(7/2)/(a*sin(f*x + e) + a)^(3/2), x)","F",0
390,0,0,0,0.000000," ","integrate((c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((-c*sin(f*x + e) + c)^(5/2)/(a*sin(f*x + e) + a)^(3/2), x)","F",0
391,1,136,0,1.000975," ","integrate((c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\frac{\frac{2 \, c^{\frac{3}{2}} \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{\frac{3}{2}}} - \frac{c^{\frac{3}{2}} \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}{a^{\frac{3}{2}}} - \frac{4 \, \sqrt{a} c^{\frac{3}{2}} \sin\left(f x + e\right)}{{\left(a^{2} + \frac{2 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)} {\left(\cos\left(f x + e\right) + 1\right)}}}{f}"," ",0,"(2*c^(3/2)*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^(3/2) - c^(3/2)*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/a^(3/2) - 4*sqrt(a)*c^(3/2)*sin(f*x + e)/((a^2 + 2*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)*(cos(f*x + e) + 1)))/f","A",0
392,0,0,0,0.000000," ","integrate((c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-c \sin\left(f x + e\right) + c}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-c*sin(f*x + e) + c)/(a*sin(f*x + e) + a)^(3/2), x)","F",0
393,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\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(1/((a*sin(f*x + e) + a)^(3/2)*sqrt(-c*sin(f*x + e) + c)), x)","F",0
394,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\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(1/((a*sin(f*x + e) + a)^(3/2)*(-c*sin(f*x + e) + c)^(3/2)), x)","F",0
395,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\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(1/((a*sin(f*x + e) + a)^(3/2)*(-c*sin(f*x + e) + c)^(5/2)), x)","F",0
396,0,0,0,0.000000," ","integrate((c-c*sin(f*x+e))^(9/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{9}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((-c*sin(f*x + e) + c)^(9/2)/(a*sin(f*x + e) + a)^(5/2), x)","F",0
397,0,0,0,0.000000," ","integrate((c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((-c*sin(f*x + e) + c)^(7/2)/(a*sin(f*x + e) + a)^(5/2), x)","F",0
398,1,183,0,0.435774," ","integrate((c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\frac{\frac{8 \, \sqrt{a} c^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(a^{3} + \frac{4 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{6 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{4 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}}\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{2 \, c^{\frac{5}{2}} \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{\frac{5}{2}}} + \frac{c^{\frac{5}{2}} \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}{a^{\frac{5}{2}}}}{f}"," ",0,"(8*sqrt(a)*c^(5/2)*sin(f*x + e)^2/((a^3 + 4*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 6*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4)*(cos(f*x + e) + 1)^2) - 2*c^(5/2)*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^(5/2) + c^(5/2)*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/a^(5/2))/f","A",0
399,0,0,0,0.000000," ","integrate((c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((-c*sin(f*x + e) + c)^(3/2)/(a*sin(f*x + e) + a)^(5/2), x)","F",0
400,0,0,0,0.000000," ","integrate((c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-c \sin\left(f x + e\right) + c}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(-c*sin(f*x + e) + c)/(a*sin(f*x + e) + a)^(5/2), x)","F",0
401,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\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(1/((a*sin(f*x + e) + a)^(5/2)*sqrt(-c*sin(f*x + e) + c)), x)","F",0
402,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\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(1/((a*sin(f*x + e) + a)^(5/2)*(-c*sin(f*x + e) + c)^(3/2)), x)","F",0
403,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\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(1/((a*sin(f*x + e) + a)^(5/2)*(-c*sin(f*x + e) + c)^(5/2)), x)","F",0
404,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x, algorithm=""maxima"")","\int {\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((a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^n, x)","F",0
405,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^3,x, algorithm=""maxima"")","-\int {\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((c*sin(f*x + e) - c)^3*(a*sin(f*x + e) + a)^m, x)","F",0
406,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^2,x, algorithm=""maxima"")","\int {\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((c*sin(f*x + e) - c)^2*(a*sin(f*x + e) + a)^m, x)","F",0
407,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e)),x, algorithm=""maxima"")","-\int {\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((c*sin(f*x + e) - c)*(a*sin(f*x + e) + a)^m, x)","F",0
408,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m/(c-c*sin(f*x+e)),x, algorithm=""maxima"")","-\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m}}{c \sin\left(f x + e\right) - c}\,{d x}"," ",0,"-integrate((a*sin(f*x + e) + a)^m/(c*sin(f*x + e) - c), x)","F",0
409,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{{\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((a*sin(f*x + e) + a)^m/(c*sin(f*x + e) - c)^2, x)","F",0
410,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^3,x, algorithm=""maxima"")","-\int \frac{{\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((a*sin(f*x + e) + a)^m/(c*sin(f*x + e) - c)^3, x)","F",0
411,1,290,0,0.466337," ","integrate((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","-\frac{2 \, {\left({\left(4 \, m^{2} + 24 \, m + 43\right)} a^{m} c^{\frac{5}{2}} - \frac{{\left(12 \, m^{2} + 40 \, m - 15\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{2 \, {\left(4 \, m^{2} + 8 \, m + 35\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{2 \, {\left(4 \, m^{2} + 8 \, m + 35\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{{\left(12 \, m^{2} + 40 \, m - 15\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{{\left(4 \, m^{2} + 24 \, m + 43\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)} e^{\left(2 \, m \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right) - m \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)\right)}}{{\left(8 \, m^{3} + 36 \, m^{2} + 46 \, m + 15\right)} f {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{5}{2}}}"," ",0,"-2*((4*m^2 + 24*m + 43)*a^m*c^(5/2) - (12*m^2 + 40*m - 15)*a^m*c^(5/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 2*(4*m^2 + 8*m + 35)*a^m*c^(5/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2*(4*m^2 + 8*m + 35)*a^m*c^(5/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - (12*m^2 + 40*m - 15)*a^m*c^(5/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + (4*m^2 + 24*m + 43)*a^m*c^(5/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)*e^(2*m*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1) - m*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1))/((8*m^3 + 36*m^2 + 46*m + 15)*f*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(5/2))","A",0
412,1,193,0,0.444594," ","integrate((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(a^{m} c^{\frac{3}{2}} {\left(2 \, m + 5\right)} - \frac{a^{m} c^{\frac{3}{2}} {\left(2 \, m - 3\right)} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{a^{m} c^{\frac{3}{2}} {\left(2 \, m - 3\right)} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{m} c^{\frac{3}{2}} {\left(2 \, m + 5\right)} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)} e^{\left(2 \, m \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right) - m \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)\right)}}{{\left(4 \, m^{2} + 8 \, m + 3\right)} f {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{3}{2}}}"," ",0,"-2*(a^m*c^(3/2)*(2*m + 5) - a^m*c^(3/2)*(2*m - 3)*sin(f*x + e)/(cos(f*x + e) + 1) - a^m*c^(3/2)*(2*m - 3)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^m*c^(3/2)*(2*m + 5)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3)*e^(2*m*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1) - m*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1))/((4*m^2 + 8*m + 3)*f*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(3/2))","B",0
413,1,116,0,0.450197," ","integrate((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(a^{m} \sqrt{c} + \frac{a^{m} \sqrt{c} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)} e^{\left(2 \, m \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right) - m \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)\right)}}{f {\left(2 \, m + 1\right)} \sqrt{\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1}}"," ",0,"-2*(a^m*sqrt(c) + a^m*sqrt(c)*sin(f*x + e)/(cos(f*x + e) + 1))*e^(2*m*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1) - m*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1))/(f*(2*m + 1)*sqrt(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1))","B",0
414,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m}}{\sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m/sqrt(-c*sin(f*x + e) + c), x)","F",0
415,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\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((a*sin(f*x + e) + a)^m/(-c*sin(f*x + e) + c)^(3/2), x)","F",0
416,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\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((a*sin(f*x + e) + a)^m/(-c*sin(f*x + e) + c)^(5/2), x)","F",0
417,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m}}{\sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m/sqrt(-c*sin(f*x + e) + c), x)","F",0
418,0,0,0,0.000000," ","integrate((c+c*sin(f*x+e))^m/(a-a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(c \sin\left(f x + e\right) + c\right)}^{m}}{\sqrt{-a \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((c*sin(f*x + e) + c)^m/sqrt(-a*sin(f*x + e) + a), x)","F",0
419,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-3-m),x, algorithm=""maxima"")","\int {\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((a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m - 3), x)","F",0
420,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-2-m),x, algorithm=""maxima"")","\int {\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((a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m - 2), x)","F",0
421,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-1-m),x, algorithm=""maxima"")","\int {\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((a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m - 1), x)","F",0
422,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m/((c-c*sin(f*x+e))^m),x, algorithm=""maxima"")","\int \frac{{\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((a*sin(f*x + e) + a)^m/(-c*sin(f*x + e) + c)^m, x)","F",0
423,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(1-m),x, algorithm=""maxima"")","\int {\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((a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m + 1), x)","F",0
424,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(2-m),x, algorithm=""maxima"")","\int {\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((a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m + 2), x)","F",0
425,1,250,0,0.386357," ","integrate((a+a*sin(f*x+e))*(c+d*sin(f*x+e))^4,x, algorithm=""maxima"")","\frac{480 \, {\left(f x + e\right)} a c^{4} + 480 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a c^{3} d + 960 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a c^{2} d^{2} + 720 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a c^{2} d^{2} + 640 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a c d^{3} + 60 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a c d^{3} - 32 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} a d^{4} + 15 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a d^{4} - 480 \, a c^{4} \cos\left(f x + e\right) - 1920 \, a c^{3} d \cos\left(f x + e\right)}{480 \, f}"," ",0,"1/480*(480*(f*x + e)*a*c^4 + 480*(2*f*x + 2*e - sin(2*f*x + 2*e))*a*c^3*d + 960*(cos(f*x + e)^3 - 3*cos(f*x + e))*a*c^2*d^2 + 720*(2*f*x + 2*e - sin(2*f*x + 2*e))*a*c^2*d^2 + 640*(cos(f*x + e)^3 - 3*cos(f*x + e))*a*c*d^3 + 60*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*a*c*d^3 - 32*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*a*d^4 + 15*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*a*d^4 - 480*a*c^4*cos(f*x + e) - 1920*a*c^3*d*cos(f*x + e))/f","A",0
426,1,175,0,0.329806," ","integrate((a+a*sin(f*x+e))*(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\frac{96 \, {\left(f x + e\right)} a c^{3} + 72 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a c^{2} d + 96 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a c d^{2} + 72 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a c d^{2} + 32 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a d^{3} + 3 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a d^{3} - 96 \, a c^{3} \cos\left(f x + e\right) - 288 \, a c^{2} d \cos\left(f x + e\right)}{96 \, f}"," ",0,"1/96*(96*(f*x + e)*a*c^3 + 72*(2*f*x + 2*e - sin(2*f*x + 2*e))*a*c^2*d + 96*(cos(f*x + e)^3 - 3*cos(f*x + e))*a*c*d^2 + 72*(2*f*x + 2*e - sin(2*f*x + 2*e))*a*c*d^2 + 32*(cos(f*x + e)^3 - 3*cos(f*x + e))*a*d^3 + 3*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*a*d^3 - 96*a*c^3*cos(f*x + e) - 288*a*c^2*d*cos(f*x + e))/f","A",0
427,1,112,0,0.309120," ","integrate((a+a*sin(f*x+e))*(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{12 \, {\left(f x + e\right)} a c^{2} + 6 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a c d + 4 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a d^{2} + 3 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a d^{2} - 12 \, a c^{2} \cos\left(f x + e\right) - 24 \, a c d \cos\left(f x + e\right)}{12 \, f}"," ",0,"1/12*(12*(f*x + e)*a*c^2 + 6*(2*f*x + 2*e - sin(2*f*x + 2*e))*a*c*d + 4*(cos(f*x + e)^3 - 3*cos(f*x + e))*a*d^2 + 3*(2*f*x + 2*e - sin(2*f*x + 2*e))*a*d^2 - 12*a*c^2*cos(f*x + e) - 24*a*c*d*cos(f*x + e))/f","A",0
428,1,57,0,0.309664," ","integrate((a+a*sin(f*x+e))*(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\frac{4 \, {\left(f x + e\right)} a c + {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a d - 4 \, a c \cos\left(f x + e\right) - 4 \, a d \cos\left(f x + e\right)}{4 \, f}"," ",0,"1/4*(4*(f*x + e)*a*c + (2*f*x + 2*e - sin(2*f*x + 2*e))*a*d - 4*a*c*cos(f*x + e) - 4*a*d*cos(f*x + e))/f","A",0
429,1,16,0,0.318435," ","integrate(a+a*sin(f*x+e),x, algorithm=""maxima"")","a x - \frac{a \cos\left(f x + e\right)}{f}"," ",0,"a*x - a*cos(f*x + e)/f","A",0
430,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))/(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
431,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))/(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
432,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))/(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
433,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))/(c+d*sin(f*x+e))^4,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
434,1,451,0,0.346680," ","integrate((a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^4,x, algorithm=""maxima"")","\frac{240 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c^{4} + 960 \, {\left(f x + e\right)} a^{2} c^{4} + 1280 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a^{2} c^{3} d + 1920 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c^{3} d + 3840 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a^{2} c^{2} d^{2} + 180 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c^{2} d^{2} + 1440 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c^{2} d^{2} - 256 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} a^{2} c d^{3} + 1280 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a^{2} c d^{3} + 240 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c d^{3} - 128 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} a^{2} d^{4} + 5 \, {\left(4 \, \sin\left(2 \, f x + 2 \, e\right)^{3} + 60 \, f x + 60 \, e + 9 \, \sin\left(4 \, f x + 4 \, e\right) - 48 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} d^{4} + 30 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} d^{4} - 1920 \, a^{2} c^{4} \cos\left(f x + e\right) - 3840 \, a^{2} c^{3} d \cos\left(f x + e\right)}{960 \, f}"," ",0,"1/960*(240*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^2*c^4 + 960*(f*x + e)*a^2*c^4 + 1280*(cos(f*x + e)^3 - 3*cos(f*x + e))*a^2*c^3*d + 1920*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^2*c^3*d + 3840*(cos(f*x + e)^3 - 3*cos(f*x + e))*a^2*c^2*d^2 + 180*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*a^2*c^2*d^2 + 1440*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^2*c^2*d^2 - 256*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*a^2*c*d^3 + 1280*(cos(f*x + e)^3 - 3*cos(f*x + e))*a^2*c*d^3 + 240*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*a^2*c*d^3 - 128*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*a^2*d^4 + 5*(4*sin(2*f*x + 2*e)^3 + 60*f*x + 60*e + 9*sin(4*f*x + 4*e) - 48*sin(2*f*x + 2*e))*a^2*d^4 + 30*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*a^2*d^4 - 1920*a^2*c^4*cos(f*x + e) - 3840*a^2*c^3*d*cos(f*x + e))/f","A",0
435,1,318,0,0.332131," ","integrate((a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\frac{120 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c^{3} + 480 \, {\left(f x + e\right)} a^{2} c^{3} + 480 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a^{2} c^{2} d + 720 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c^{2} d + 960 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a^{2} c d^{2} + 45 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c d^{2} + 360 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c d^{2} - 32 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} a^{2} d^{3} + 160 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a^{2} d^{3} + 30 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} d^{3} - 960 \, a^{2} c^{3} \cos\left(f x + e\right) - 1440 \, a^{2} c^{2} d \cos\left(f x + e\right)}{480 \, f}"," ",0,"1/480*(120*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^2*c^3 + 480*(f*x + e)*a^2*c^3 + 480*(cos(f*x + e)^3 - 3*cos(f*x + e))*a^2*c^2*d + 720*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^2*c^2*d + 960*(cos(f*x + e)^3 - 3*cos(f*x + e))*a^2*c*d^2 + 45*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*a^2*c*d^2 + 360*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^2*c*d^2 - 32*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*a^2*d^3 + 160*(cos(f*x + e)^3 - 3*cos(f*x + e))*a^2*d^3 + 30*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*a^2*d^3 - 960*a^2*c^3*cos(f*x + e) - 1440*a^2*c^2*d*cos(f*x + e))/f","A",0
436,1,211,0,0.329578," ","integrate((a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{24 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c^{2} + 96 \, {\left(f x + e\right)} a^{2} c^{2} + 64 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a^{2} c d + 96 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c d + 64 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a^{2} d^{2} + 3 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} d^{2} + 24 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} d^{2} - 192 \, a^{2} c^{2} \cos\left(f x + e\right) - 192 \, a^{2} c d \cos\left(f x + e\right)}{96 \, f}"," ",0,"1/96*(24*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^2*c^2 + 96*(f*x + e)*a^2*c^2 + 64*(cos(f*x + e)^3 - 3*cos(f*x + e))*a^2*c*d + 96*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^2*c*d + 64*(cos(f*x + e)^3 - 3*cos(f*x + e))*a^2*d^2 + 3*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*a^2*d^2 + 24*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^2*d^2 - 192*a^2*c^2*cos(f*x + e) - 192*a^2*c*d*cos(f*x + e))/f","A",0
437,1,114,0,0.311607," ","integrate((a+a*sin(f*x+e))^2*(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\frac{3 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c + 12 \, {\left(f x + e\right)} a^{2} c + 4 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a^{2} d + 6 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} d - 24 \, a^{2} c \cos\left(f x + e\right) - 12 \, a^{2} d \cos\left(f x + e\right)}{12 \, f}"," ",0,"1/12*(3*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^2*c + 12*(f*x + e)*a^2*c + 4*(cos(f*x + e)^3 - 3*cos(f*x + e))*a^2*d + 6*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^2*d - 24*a^2*c*cos(f*x + e) - 12*a^2*d*cos(f*x + e))/f","A",0
438,1,47,0,0.302976," ","integrate((a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","a^{2} x + \frac{{\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2}}{4 \, f} - \frac{2 \, a^{2} \cos\left(f x + e\right)}{f}"," ",0,"a^2*x + 1/4*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^2/f - 2*a^2*cos(f*x + e)/f","A",0
439,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2/(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
440,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2/(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
441,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2/(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
442,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2/(c+d*sin(f*x+e))^4,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
443,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2/(c+d*sin(f*x+e))^5,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
444,1,469,0,0.361280," ","integrate((a+a*sin(f*x+e))^3*(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\frac{320 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a^{3} c^{3} + 720 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{3} c^{3} + 960 \, {\left(f x + e\right)} a^{3} c^{3} + 2880 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a^{3} c^{2} d + 90 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a^{3} c^{2} d + 2160 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{3} c^{2} d - 192 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} a^{3} c d^{2} + 2880 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a^{3} c d^{2} + 270 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a^{3} c d^{2} + 720 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{3} c d^{2} - 192 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} a^{3} d^{3} + 320 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a^{3} d^{3} + 5 \, {\left(4 \, \sin\left(2 \, f x + 2 \, e\right)^{3} + 60 \, f x + 60 \, e + 9 \, \sin\left(4 \, f x + 4 \, e\right) - 48 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a^{3} d^{3} + 90 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a^{3} d^{3} - 2880 \, a^{3} c^{3} \cos\left(f x + e\right) - 2880 \, a^{3} c^{2} d \cos\left(f x + e\right)}{960 \, f}"," ",0,"1/960*(320*(cos(f*x + e)^3 - 3*cos(f*x + e))*a^3*c^3 + 720*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^3*c^3 + 960*(f*x + e)*a^3*c^3 + 2880*(cos(f*x + e)^3 - 3*cos(f*x + e))*a^3*c^2*d + 90*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*a^3*c^2*d + 2160*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^3*c^2*d - 192*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*a^3*c*d^2 + 2880*(cos(f*x + e)^3 - 3*cos(f*x + e))*a^3*c*d^2 + 270*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*a^3*c*d^2 + 720*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^3*c*d^2 - 192*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*a^3*d^3 + 320*(cos(f*x + e)^3 - 3*cos(f*x + e))*a^3*d^3 + 5*(4*sin(2*f*x + 2*e)^3 + 60*f*x + 60*e + 9*sin(4*f*x + 4*e) - 48*sin(2*f*x + 2*e))*a^3*d^3 + 90*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*a^3*d^3 - 2880*a^3*c^3*cos(f*x + e) - 2880*a^3*c^2*d*cos(f*x + e))/f","B",0
445,1,308,0,0.353261," ","integrate((a+a*sin(f*x+e))^3*(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{160 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a^{3} c^{2} + 360 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{3} c^{2} + 480 \, {\left(f x + e\right)} a^{3} c^{2} + 960 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a^{3} c d + 30 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a^{3} c d + 720 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{3} c d - 32 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} a^{3} d^{2} + 480 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a^{3} d^{2} + 45 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a^{3} d^{2} + 120 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{3} d^{2} - 1440 \, a^{3} c^{2} \cos\left(f x + e\right) - 960 \, a^{3} c d \cos\left(f x + e\right)}{480 \, f}"," ",0,"1/480*(160*(cos(f*x + e)^3 - 3*cos(f*x + e))*a^3*c^2 + 360*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^3*c^2 + 480*(f*x + e)*a^3*c^2 + 960*(cos(f*x + e)^3 - 3*cos(f*x + e))*a^3*c*d + 30*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*a^3*c*d + 720*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^3*c*d - 32*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*a^3*d^2 + 480*(cos(f*x + e)^3 - 3*cos(f*x + e))*a^3*d^2 + 45*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*a^3*d^2 + 120*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^3*d^2 - 1440*a^3*c^2*cos(f*x + e) - 960*a^3*c*d*cos(f*x + e))/f","A",0
446,1,171,0,0.345435," ","integrate((a+a*sin(f*x+e))^3*(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\frac{32 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a^{3} c + 72 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{3} c + 96 \, {\left(f x + e\right)} a^{3} c + 96 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a^{3} d + 3 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a^{3} d + 72 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{3} d - 288 \, a^{3} c \cos\left(f x + e\right) - 96 \, a^{3} d \cos\left(f x + e\right)}{96 \, f}"," ",0,"1/96*(32*(cos(f*x + e)^3 - 3*cos(f*x + e))*a^3*c + 72*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^3*c + 96*(f*x + e)*a^3*c + 96*(cos(f*x + e)^3 - 3*cos(f*x + e))*a^3*d + 3*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*a^3*d + 72*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^3*d - 288*a^3*c*cos(f*x + e) - 96*a^3*d*cos(f*x + e))/f","A",0
447,1,72,0,0.316505," ","integrate((a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","a^{3} x + \frac{{\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a^{3}}{3 \, f} + \frac{3 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{3}}{4 \, f} - \frac{3 \, a^{3} \cos\left(f x + e\right)}{f}"," ",0,"a^3*x + 1/3*(cos(f*x + e)^3 - 3*cos(f*x + e))*a^3/f + 3/4*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^3/f - 3*a^3*cos(f*x + e)/f","A",0
448,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3/(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
449,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
450,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
451,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^4,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
452,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^5,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
453,1,725,0,0.444404," ","integrate((c+d*sin(f*x+e))^4/(a+a*sin(f*x+e)),x, algorithm=""maxima"")","-\frac{d^{4} {\left(\frac{\frac{7 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{39 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{24 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{24 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{9 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{9 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + 16}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3 \, a \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, a \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{3 \, a \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{a \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{a \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} + \frac{9 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a}\right)} - 12 \, c d^{3} {\left(\frac{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 4}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{2 \, a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{2 \, a \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{a \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a}\right)} + 36 \, c^{2} d^{2} {\left(\frac{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 2}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a}\right)} - 24 \, c^{3} d {\left(\frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a} + \frac{1}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}\right)} + \frac{6 \, c^{4}}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}}{3 \, f}"," ",0,"-1/3*(d^4*((7*sin(f*x + e)/(cos(f*x + e) + 1) + 39*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 24*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 24*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 9*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 9*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 16)/(a + a*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3*a*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*a*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 3*a*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + a*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + a*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) + 9*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a) - 12*c*d^3*((sin(f*x + e)/(cos(f*x + e) + 1) + 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 4)/(a + a*sin(f*x + e)/(cos(f*x + e) + 1) + 2*a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2*a*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + a*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a) + 36*c^2*d^2*((sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2)/(a + a*sin(f*x + e)/(cos(f*x + e) + 1) + a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a) - 24*c^3*d*(arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a + 1/(a + a*sin(f*x + e)/(cos(f*x + e) + 1))) + 6*c^4/(a + a*sin(f*x + e)/(cos(f*x + e) + 1)))/f","B",0
454,1,425,0,0.439467," ","integrate((c+d*sin(f*x+e))^3/(a+a*sin(f*x+e)),x, algorithm=""maxima"")","\frac{d^{3} {\left(\frac{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 4}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{2 \, a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{2 \, a \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{a \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a}\right)} - 6 \, c d^{2} {\left(\frac{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 2}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a}\right)} + 6 \, c^{2} d {\left(\frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a} + \frac{1}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}\right)} - \frac{2 \, c^{3}}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}}{f}"," ",0,"(d^3*((sin(f*x + e)/(cos(f*x + e) + 1) + 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 4)/(a + a*sin(f*x + e)/(cos(f*x + e) + 1) + 2*a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2*a*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + a*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a) - 6*c*d^2*((sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2)/(a + a*sin(f*x + e)/(cos(f*x + e) + 1) + a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a) + 6*c^2*d*(arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a + 1/(a + a*sin(f*x + e)/(cos(f*x + e) + 1))) - 2*c^3/(a + a*sin(f*x + e)/(cos(f*x + e) + 1)))/f","B",0
455,1,209,0,0.447163," ","integrate((c+d*sin(f*x+e))^2/(a+a*sin(f*x+e)),x, algorithm=""maxima"")","-\frac{2 \, {\left(d^{2} {\left(\frac{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 2}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a}\right)} - 2 \, c d {\left(\frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a} + \frac{1}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}\right)} + \frac{c^{2}}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}\right)}}{f}"," ",0,"-2*(d^2*((sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2)/(a + a*sin(f*x + e)/(cos(f*x + e) + 1) + a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a) - 2*c*d*(arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a + 1/(a + a*sin(f*x + e)/(cos(f*x + e) + 1))) + c^2/(a + a*sin(f*x + e)/(cos(f*x + e) + 1)))/f","B",0
456,1,78,0,0.428807," ","integrate((c+d*sin(f*x+e))/(a+a*sin(f*x+e)),x, algorithm=""maxima"")","\frac{2 \, {\left(d {\left(\frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a} + \frac{1}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}\right)} - \frac{c}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}\right)}}{f}"," ",0,"2*(d*(arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a + 1/(a + a*sin(f*x + e)/(cos(f*x + e) + 1))) - c/(a + a*sin(f*x + e)/(cos(f*x + e) + 1)))/f","B",0
457,1,27,0,0.308443," ","integrate(1/(a+a*sin(f*x+e)),x, algorithm=""maxima"")","-\frac{2}{{\left(a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)} f}"," ",0,"-2/((a + a*sin(f*x + e)/(cos(f*x + e) + 1))*f)","A",0
458,-2,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))/(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
459,-2,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))/(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
460,-2,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))/(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
461,1,1312,0,0.475476," ","integrate((c+d*sin(f*x+e))^5/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{5 \, c d^{4} {\left(\frac{\frac{75 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{97 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{126 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{98 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{63 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{21 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + 32}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{7 \, a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{7 \, a^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{5 \, a^{2} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{a^{2} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} + \frac{21 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} - 2 \, d^{5} {\left(\frac{\frac{57 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{99 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{155 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{153 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{135 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{85 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{45 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{15 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + 24}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{6 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{12 \, a^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{12 \, a^{2} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{10 \, a^{2} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{6 \, a^{2} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{a^{2} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}} + \frac{15 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} - 40 \, c^{2} d^{3} {\left(\frac{\frac{12 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{11 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{9 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 5}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{4 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{4 \, a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{2} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} + 20 \, c^{3} d^{2} {\left(\frac{\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 4}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} - \frac{2 \, c^{5} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 2\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} - \frac{10 \, c^{4} d {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}}{3 \, f}"," ",0,"1/3*(5*c*d^4*((75*sin(f*x + e)/(cos(f*x + e) + 1) + 97*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 126*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 98*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 63*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 21*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 32)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 5*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 7*a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 7*a^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 5*a^2*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 3*a^2*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + a^2*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) + 21*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) - 2*d^5*((57*sin(f*x + e)/(cos(f*x + e) + 1) + 99*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 155*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 153*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 135*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 85*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 45*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 15*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 24)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 6*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 12*a^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 12*a^2*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 10*a^2*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 6*a^2*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 3*a^2*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + a^2*sin(f*x + e)^9/(cos(f*x + e) + 1)^9) + 15*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) - 40*c^2*d^3*((12*sin(f*x + e)/(cos(f*x + e) + 1) + 11*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 9*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 5)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 4*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4*a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*a^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^2*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) + 20*c^3*d^2*((9*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) - 2*c^5*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) - 10*c^4*d*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 1)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3))/f","B",0
462,1,908,0,0.454171," ","integrate((c+d*sin(f*x+e))^4/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{d^{4} {\left(\frac{\frac{75 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{97 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{126 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{98 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{63 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{21 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + 32}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{7 \, a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{7 \, a^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{5 \, a^{2} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{a^{2} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} + \frac{21 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} - 16 \, c d^{3} {\left(\frac{\frac{12 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{11 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{9 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 5}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{4 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{4 \, a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{2} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} + 12 \, c^{2} d^{2} {\left(\frac{\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 4}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} - \frac{2 \, c^{4} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 2\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} - \frac{8 \, c^{3} d {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}}{3 \, f}"," ",0,"1/3*(d^4*((75*sin(f*x + e)/(cos(f*x + e) + 1) + 97*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 126*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 98*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 63*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 21*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 32)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 5*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 7*a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 7*a^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 5*a^2*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 3*a^2*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + a^2*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) + 21*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) - 16*c*d^3*((12*sin(f*x + e)/(cos(f*x + e) + 1) + 11*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 9*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 5)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 4*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4*a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*a^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^2*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) + 12*c^2*d^2*((9*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) - 2*c^4*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) - 8*c^3*d*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 1)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3))/f","B",0
463,1,591,0,0.436339," ","integrate((c+d*sin(f*x+e))^3/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(2 \, d^{3} {\left(\frac{\frac{12 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{11 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{9 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 5}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{4 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{4 \, a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{2} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} - 3 \, c d^{2} {\left(\frac{\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 4}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} + \frac{c^{3} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 2\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{3 \, c^{2} d {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}\right)}}{3 \, f}"," ",0,"-2/3*(2*d^3*((12*sin(f*x + e)/(cos(f*x + e) + 1) + 11*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 9*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 5)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 4*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4*a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*a^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^2*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) - 3*c*d^2*((9*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) + c^3*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + 3*c^2*d*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 1)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3))/f","B",0
464,1,360,0,0.430308," ","integrate((c+d*sin(f*x+e))^2/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(d^{2} {\left(\frac{\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 4}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} - \frac{c^{2} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 2\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} - \frac{2 \, c d {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}\right)}}{3 \, f}"," ",0,"2/3*(d^2*((9*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) - c^2*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) - 2*c*d*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 1)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3))/f","B",0
465,1,214,0,0.332257," ","integrate((c+d*sin(f*x+e))/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{c {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 2\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{d {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}\right)}}{3 \, f}"," ",0,"-2/3*(c*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + d*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 1)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3))/f","B",0
466,1,117,0,0.319045," ","integrate(1/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 2\right)}}{3 \, {\left(a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)} f}"," ",0,"-2/3*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2)/((a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3)*f)","B",0
467,-2,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^2/(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
468,-2,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^2/(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
469,-2,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^2/(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
470,1,1993,0,0.836947," ","integrate((c+d*sin(f*x+e))^6/(a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","-\frac{d^{6} {\left(\frac{\frac{2375 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5347 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{9230 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{12622 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{13340 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{11684 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{8050 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{4370 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{1725 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{345 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + 544}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{13 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{25 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{38 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{46 \, a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{46 \, a^{3} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{38 \, a^{3} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{25 \, a^{3} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{13 \, a^{3} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{a^{3} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}}} + \frac{345 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{3}}\right)} - 6 \, c d^{5} {\left(\frac{\frac{1325 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{2673 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3805 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{4329 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{3575 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{2275 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{975 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{195 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + 304}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{12 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{20 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{26 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{26 \, a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{20 \, a^{3} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{12 \, a^{3} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{a^{3} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}} + \frac{195 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{3}}\right)} + 90 \, c^{2} d^{4} {\left(\frac{\frac{105 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{189 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{200 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{160 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{75 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{15 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + 24}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{11 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{15 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{11 \, a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{a^{3} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} + \frac{15 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{3}}\right)} - 40 \, c^{3} d^{3} {\left(\frac{\frac{95 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{145 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{75 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 22}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{15 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{3}}\right)} + \frac{2 \, c^{6} {\left(\frac{20 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{40 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{30 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 7\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{60 \, c^{4} d^{2} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{36 \, c^{5} d {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{5 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}}{15 \, f}"," ",0,"-1/15*(d^6*((2375*sin(f*x + e)/(cos(f*x + e) + 1) + 5347*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 9230*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 12622*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 13340*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 11684*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 8050*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 4370*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 1725*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 345*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 544)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 13*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 25*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 38*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 46*a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 46*a^3*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 38*a^3*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 25*a^3*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 13*a^3*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 5*a^3*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + a^3*sin(f*x + e)^11/(cos(f*x + e) + 1)^11) + 345*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^3) - 6*c*d^5*((1325*sin(f*x + e)/(cos(f*x + e) + 1) + 2673*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3805*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 4329*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 3575*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 2275*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 975*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 195*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 304)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 12*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 20*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 26*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 26*a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 20*a^3*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 12*a^3*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 5*a^3*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + a^3*sin(f*x + e)^9/(cos(f*x + e) + 1)^9) + 195*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^3) + 90*c^2*d^4*((105*sin(f*x + e)/(cos(f*x + e) + 1) + 189*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 200*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 160*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 75*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 15*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 24)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 11*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 15*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 11*a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 5*a^3*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + a^3*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) + 15*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^3) - 40*c^3*d^3*((95*sin(f*x + e)/(cos(f*x + e) + 1) + 145*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 75*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 22)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 15*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^3) + 2*c^6*(20*sin(f*x + e)/(cos(f*x + e) + 1) + 40*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 30*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 7)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 60*c^4*d^2*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 10*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 36*c^5*d*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5))/f","B",0
471,1,1504,0,0.486289," ","integrate((c+d*sin(f*x+e))^5/(a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","\frac{d^{5} {\left(\frac{\frac{1325 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{2673 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3805 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{4329 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{3575 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{2275 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{975 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{195 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + 304}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{12 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{20 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{26 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{26 \, a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{20 \, a^{3} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{12 \, a^{3} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{a^{3} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}} + \frac{195 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{3}}\right)} - 30 \, c d^{4} {\left(\frac{\frac{105 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{189 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{200 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{160 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{75 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{15 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + 24}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{11 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{15 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{11 \, a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{a^{3} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} + \frac{15 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{3}}\right)} + 20 \, c^{2} d^{3} {\left(\frac{\frac{95 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{145 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{75 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 22}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{15 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{3}}\right)} - \frac{2 \, c^{5} {\left(\frac{20 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{40 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{30 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 7\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} - \frac{40 \, c^{3} d^{2} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} - \frac{30 \, c^{4} d {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{5 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}}{15 \, f}"," ",0,"1/15*(d^5*((1325*sin(f*x + e)/(cos(f*x + e) + 1) + 2673*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3805*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 4329*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 3575*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 2275*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 975*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 195*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 304)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 12*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 20*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 26*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 26*a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 20*a^3*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 12*a^3*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 5*a^3*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + a^3*sin(f*x + e)^9/(cos(f*x + e) + 1)^9) + 195*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^3) - 30*c*d^4*((105*sin(f*x + e)/(cos(f*x + e) + 1) + 189*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 200*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 160*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 75*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 15*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 24)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 11*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 15*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 11*a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 5*a^3*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + a^3*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) + 15*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^3) + 20*c^2*d^3*((95*sin(f*x + e)/(cos(f*x + e) + 1) + 145*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 75*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 22)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 15*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^3) - 2*c^5*(20*sin(f*x + e)/(cos(f*x + e) + 1) + 40*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 30*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 7)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) - 40*c^3*d^2*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 10*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) - 30*c^4*d*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5))/f","B",0
472,1,1101,0,0.453866," ","integrate((c+d*sin(f*x+e))^4/(a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(3 \, d^{4} {\left(\frac{\frac{105 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{189 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{200 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{160 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{75 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{15 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + 24}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{11 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{15 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{11 \, a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{a^{3} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} + \frac{15 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{3}}\right)} - 4 \, c d^{3} {\left(\frac{\frac{95 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{145 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{75 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 22}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{15 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{3}}\right)} + \frac{c^{4} {\left(\frac{20 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{40 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{30 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 7\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{12 \, c^{2} d^{2} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{12 \, c^{3} d {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{5 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}\right)}}{15 \, f}"," ",0,"-2/15*(3*d^4*((105*sin(f*x + e)/(cos(f*x + e) + 1) + 189*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 200*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 160*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 75*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 15*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 24)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 11*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 15*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 11*a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 5*a^3*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + a^3*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) + 15*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^3) - 4*c*d^3*((95*sin(f*x + e)/(cos(f*x + e) + 1) + 145*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 75*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 22)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 15*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^3) + c^4*(20*sin(f*x + e)/(cos(f*x + e) + 1) + 40*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 30*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 7)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 12*c^2*d^2*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 10*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 12*c^3*d*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5))/f","B",0
473,1,784,0,0.438459," ","integrate((c+d*sin(f*x+e))^3/(a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","\frac{2 \, {\left(d^{3} {\left(\frac{\frac{95 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{145 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{75 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 22}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{15 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{3}}\right)} - \frac{c^{3} {\left(\frac{20 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{40 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{30 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 7\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} - \frac{6 \, c d^{2} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} - \frac{9 \, c^{2} d {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{5 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}\right)}}{15 \, f}"," ",0,"2/15*(d^3*((95*sin(f*x + e)/(cos(f*x + e) + 1) + 145*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 75*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 22)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 15*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^3) - c^3*(20*sin(f*x + e)/(cos(f*x + e) + 1) + 40*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 30*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 7)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) - 6*c*d^2*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 10*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) - 9*c^2*d*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5))/f","B",0
474,1,553,0,0.341397," ","integrate((c+d*sin(f*x+e))^2/(a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{c^{2} {\left(\frac{20 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{40 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{30 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 7\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{2 \, d^{2} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{6 \, c d {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{5 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}\right)}}{15 \, f}"," ",0,"-2/15*(c^2*(20*sin(f*x + e)/(cos(f*x + e) + 1) + 40*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 30*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 7)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 2*d^2*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 10*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 6*c*d*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5))/f","B",0
475,1,387,0,0.329517," ","integrate((c+d*sin(f*x+e))/(a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{c {\left(\frac{20 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{40 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{30 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 7\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{3 \, d {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{5 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}\right)}}{15 \, f}"," ",0,"-2/15*(c*(20*sin(f*x + e)/(cos(f*x + e) + 1) + 40*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 30*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 7)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 3*d*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5))/f","B",0
476,1,203,0,0.335691," ","integrate(1/(a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{20 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{40 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{30 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 7\right)}}{15 \, {\left(a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)} f}"," ",0,"-2/15*(20*sin(f*x + e)/(cos(f*x + e) + 1) + 40*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 30*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 7)/((a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)*f)","B",0
477,-2,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^3/(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
478,-2,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
479,-2,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
480,1,309,0,0.325171," ","integrate((A+B*sin(x))/(1+sin(x))^4,x, algorithm=""maxima"")","-\frac{2 \, B {\left(\frac{91 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{168 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{280 \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{175 \, \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{105 \, \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} + 13\right)}}{105 \, {\left(\frac{7 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{21 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{35 \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{35 \, \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{21 \, \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} + \frac{7 \, \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} + \frac{\sin\left(x\right)^{7}}{{\left(\cos\left(x\right) + 1\right)}^{7}} + 1\right)}} - \frac{2 \, A {\left(\frac{49 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{147 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{210 \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{210 \, \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{105 \, \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} + \frac{35 \, \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} + 12\right)}}{35 \, {\left(\frac{7 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{21 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{35 \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{35 \, \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{21 \, \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} + \frac{7 \, \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} + \frac{\sin\left(x\right)^{7}}{{\left(\cos\left(x\right) + 1\right)}^{7}} + 1\right)}}"," ",0,"-2/105*B*(91*sin(x)/(cos(x) + 1) + 168*sin(x)^2/(cos(x) + 1)^2 + 280*sin(x)^3/(cos(x) + 1)^3 + 175*sin(x)^4/(cos(x) + 1)^4 + 105*sin(x)^5/(cos(x) + 1)^5 + 13)/(7*sin(x)/(cos(x) + 1) + 21*sin(x)^2/(cos(x) + 1)^2 + 35*sin(x)^3/(cos(x) + 1)^3 + 35*sin(x)^4/(cos(x) + 1)^4 + 21*sin(x)^5/(cos(x) + 1)^5 + 7*sin(x)^6/(cos(x) + 1)^6 + sin(x)^7/(cos(x) + 1)^7 + 1) - 2/35*A*(49*sin(x)/(cos(x) + 1) + 147*sin(x)^2/(cos(x) + 1)^2 + 210*sin(x)^3/(cos(x) + 1)^3 + 210*sin(x)^4/(cos(x) + 1)^4 + 105*sin(x)^5/(cos(x) + 1)^5 + 35*sin(x)^6/(cos(x) + 1)^6 + 12)/(7*sin(x)/(cos(x) + 1) + 21*sin(x)^2/(cos(x) + 1)^2 + 35*sin(x)^3/(cos(x) + 1)^3 + 35*sin(x)^4/(cos(x) + 1)^4 + 21*sin(x)^5/(cos(x) + 1)^5 + 7*sin(x)^6/(cos(x) + 1)^6 + sin(x)^7/(cos(x) + 1)^7 + 1)","B",0
481,1,309,0,0.326823," ","integrate((A+B*sin(x))/(1-sin(x))^4,x, algorithm=""maxima"")","-\frac{2 \, B {\left(\frac{91 \, \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{168 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{280 \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} - \frac{175 \, \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{105 \, \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} - 13\right)}}{105 \, {\left(\frac{7 \, \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{21 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{35 \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} - \frac{35 \, \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{21 \, \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} - \frac{7 \, \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} + \frac{\sin\left(x\right)^{7}}{{\left(\cos\left(x\right) + 1\right)}^{7}} - 1\right)}} + \frac{2 \, A {\left(\frac{49 \, \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{147 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{210 \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} - \frac{210 \, \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{105 \, \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} - \frac{35 \, \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} - 12\right)}}{35 \, {\left(\frac{7 \, \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{21 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{35 \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} - \frac{35 \, \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{21 \, \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} - \frac{7 \, \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} + \frac{\sin\left(x\right)^{7}}{{\left(\cos\left(x\right) + 1\right)}^{7}} - 1\right)}}"," ",0,"-2/105*B*(91*sin(x)/(cos(x) + 1) - 168*sin(x)^2/(cos(x) + 1)^2 + 280*sin(x)^3/(cos(x) + 1)^3 - 175*sin(x)^4/(cos(x) + 1)^4 + 105*sin(x)^5/(cos(x) + 1)^5 - 13)/(7*sin(x)/(cos(x) + 1) - 21*sin(x)^2/(cos(x) + 1)^2 + 35*sin(x)^3/(cos(x) + 1)^3 - 35*sin(x)^4/(cos(x) + 1)^4 + 21*sin(x)^5/(cos(x) + 1)^5 - 7*sin(x)^6/(cos(x) + 1)^6 + sin(x)^7/(cos(x) + 1)^7 - 1) + 2/35*A*(49*sin(x)/(cos(x) + 1) - 147*sin(x)^2/(cos(x) + 1)^2 + 210*sin(x)^3/(cos(x) + 1)^3 - 210*sin(x)^4/(cos(x) + 1)^4 + 105*sin(x)^5/(cos(x) + 1)^5 - 35*sin(x)^6/(cos(x) + 1)^6 - 12)/(7*sin(x)/(cos(x) + 1) - 21*sin(x)^2/(cos(x) + 1)^2 + 35*sin(x)^3/(cos(x) + 1)^3 - 35*sin(x)^4/(cos(x) + 1)^4 + 21*sin(x)^5/(cos(x) + 1)^5 - 7*sin(x)^6/(cos(x) + 1)^6 + sin(x)^7/(cos(x) + 1)^7 - 1)","B",0
482,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(c+d*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^(5/2), x)","F",0
483,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(c+d*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^(3/2), x)","F",0
484,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)} \sqrt{d \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c), x)","F",0
485,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))/(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{a \sin\left(f x + e\right) + a}{\sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)/sqrt(d*sin(f*x + e) + c), x)","F",0
486,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))/(c+d*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{a \sin\left(f x + e\right) + a}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)/(d*sin(f*x + e) + c)^(3/2), x)","F",0
487,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))/(c+d*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{a \sin\left(f x + e\right) + a}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)/(d*sin(f*x + e) + c)^(5/2), x)","F",0
488,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))/(c+d*sin(f*x+e))^(7/2),x, algorithm=""maxima"")","\int \frac{a \sin\left(f x + e\right) + a}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)/(d*sin(f*x + e) + c)^(7/2), x)","F",0
489,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^2*(d*sin(f*x + e) + c)^(5/2), x)","F",0
490,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^2*(d*sin(f*x + e) + c)^(3/2), x)","F",0
491,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{2} \sqrt{d \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^2*sqrt(d*sin(f*x + e) + c), x)","F",0
492,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2/(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{2}}{\sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^2/sqrt(d*sin(f*x + e) + c), x)","F",0
493,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2/(c+d*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{2}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^2/(d*sin(f*x + e) + c)^(3/2), x)","F",0
494,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2/(c+d*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{2}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^2/(d*sin(f*x + e) + c)^(5/2), x)","F",0
495,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2/(c+d*sin(f*x+e))^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{2}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^2/(d*sin(f*x + e) + c)^(7/2), x)","F",0
496,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3*(c+d*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^3*(d*sin(f*x + e) + c)^(5/2), x)","F",0
497,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3*(c+d*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^3*(d*sin(f*x + e) + c)^(3/2), x)","F",0
498,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3*(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{3} \sqrt{d \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^3*sqrt(d*sin(f*x + e) + c), x)","F",0
499,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{3}}{\sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^3/sqrt(d*sin(f*x + e) + c), x)","F",0
500,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{3}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^3/(d*sin(f*x + e) + c)^(3/2), x)","F",0
501,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{3}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^3/(d*sin(f*x + e) + c)^(5/2), x)","F",0
502,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{3}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^3/(d*sin(f*x + e) + c)^(7/2), x)","F",0
503,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{3}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^3/(d*sin(f*x + e) + c)^(9/2), x)","F",0
504,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}{a \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(5/2)/(a*sin(f*x + e) + a), x)","F",0
505,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{a \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(3/2)/(a*sin(f*x + e) + a), x)","F",0
506,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sqrt{d \sin\left(f x + e\right) + c}}{a \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(sqrt(d*sin(f*x + e) + c)/(a*sin(f*x + e) + a), x)","F",0
507,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))/(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sin\left(f x + e\right) + a\right)} \sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(1/((a*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c)), x)","F",0
508,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))/(c+d*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sin\left(f x + e\right) + a\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((a*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^(3/2)), x)","F",0
509,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))/(c+d*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sin\left(f x + e\right) + a\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((a*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^(5/2)), x)","F",0
510,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(5/2)/(a*sin(f*x + e) + a)^2, x)","F",0
511,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(3/2)/(a*sin(f*x + e) + a)^2, x)","F",0
512,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{\sqrt{d \sin\left(f x + e\right) + c}}{{\left(a \sin\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(d*sin(f*x + e) + c)/(a*sin(f*x + e) + a)^2, x)","F",0
513,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^2/(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sin\left(f x + e\right) + a\right)}^{2} \sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(1/((a*sin(f*x + e) + a)^2*sqrt(d*sin(f*x + e) + c)), x)","F",0
514,-1,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^2/(c+d*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
515,-1,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^2/(c+d*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
516,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(5/2)/(a*sin(f*x + e) + a)^3, x)","F",0
517,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(3/2)/(a*sin(f*x + e) + a)^3, x)","F",0
518,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","\int \frac{\sqrt{d \sin\left(f x + e\right) + c}}{{\left(a \sin\left(f x + e\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(d*sin(f*x + e) + c)/(a*sin(f*x + e) + a)^3, x)","F",0
519,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sin\left(f x + e\right) + a\right)}^{3} \sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(1/((a*sin(f*x + e) + a)^3*sqrt(d*sin(f*x + e) + c)), x)","F",0
520,-1,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
521,-1,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
522,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)*(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\int \sqrt{a \sin\left(f x + e\right) + a} {\left(d \sin\left(f x + e\right) + c\right)}^{3}\,{d x}"," ",0,"integrate(sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^3, x)","F",0
523,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)*(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\int \sqrt{a \sin\left(f x + e\right) + a} {\left(d \sin\left(f x + e\right) + c\right)}^{2}\,{d x}"," ",0,"integrate(sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^2, x)","F",0
524,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)*(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(f x + e\right) + a} {\left(d \sin\left(f x + e\right) + c\right)}\,{d x}"," ",0,"integrate(sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e) + c), x)","F",0
525,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(sqrt(a*sin(f*x + e) + a), x)","F",0
526,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sqrt{a \sin\left(f x + e\right) + a}}{d \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate(sqrt(a*sin(f*x + e) + a)/(d*sin(f*x + e) + c), x)","F",0
527,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{\sqrt{a \sin\left(f x + e\right) + a}}{{\left(d \sin\left(f x + e\right) + c\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(a*sin(f*x + e) + a)/(d*sin(f*x + e) + c)^2, x)","F",0
528,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\int \frac{\sqrt{a \sin\left(f x + e\right) + a}}{{\left(d \sin\left(f x + e\right) + c\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(a*sin(f*x + e) + a)/(d*sin(f*x + e) + c)^3, x)","F",0
529,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)*(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(d \sin\left(f x + e\right) + c\right)}^{3}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(3/2)*(d*sin(f*x + e) + c)^3, x)","F",0
530,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)*(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(d \sin\left(f x + e\right) + c\right)}^{2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(3/2)*(d*sin(f*x + e) + c)^2, x)","F",0
531,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)*(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(d \sin\left(f x + e\right) + c\right)}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(3/2)*(d*sin(f*x + e) + c), x)","F",0
532,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(3/2), x)","F",0
533,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}{d \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(3/2)/(d*sin(f*x + e) + c), x)","F",0
534,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}{{\left(d \sin\left(f x + e\right) + c\right)}^{2}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(3/2)/(d*sin(f*x + e) + c)^2, x)","F",0
535,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}{{\left(d \sin\left(f x + e\right) + c\right)}^{3}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(3/2)/(d*sin(f*x + e) + c)^3, x)","F",0
536,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)*(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(d \sin\left(f x + e\right) + c\right)}^{3}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(5/2)*(d*sin(f*x + e) + c)^3, x)","F",0
537,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)*(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(d \sin\left(f x + e\right) + c\right)}^{2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(5/2)*(d*sin(f*x + e) + c)^2, x)","F",0
538,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)*(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(d \sin\left(f x + e\right) + c\right)}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(5/2)*(d*sin(f*x + e) + c), x)","F",0
539,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(5/2), x)","F",0
540,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}{d \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(5/2)/(d*sin(f*x + e) + c), x)","F",0
541,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}{{\left(d \sin\left(f x + e\right) + c\right)}^{2}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(5/2)/(d*sin(f*x + e) + c)^2, x)","F",0
542,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
543,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^3/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{3}}{\sqrt{a \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^3/sqrt(a*sin(f*x + e) + a), x)","F",0
544,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^2/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{2}}{\sqrt{a \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^2/sqrt(a*sin(f*x + e) + a), x)","F",0
545,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{d \sin\left(f x + e\right) + c}{\sqrt{a \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)/sqrt(a*sin(f*x + e) + a), x)","F",0
546,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{a \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate(1/sqrt(a*sin(f*x + e) + a), x)","F",0
547,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{a \sin\left(f x + e\right) + a} {\left(d \sin\left(f x + e\right) + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e) + c)), x)","F",0
548,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{1}{\sqrt{a \sin\left(f x + e\right) + a} {\left(d \sin\left(f x + e\right) + c\right)}^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^2), x)","F",0
549,-1,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
550,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^3/(a+a*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{3}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^3/(a*sin(f*x + e) + a)^(3/2), x)","F",0
551,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^2/(a+a*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{2}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^2/(a*sin(f*x + e) + a)^(3/2), x)","F",0
552,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))/(a+a*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{d \sin\left(f x + e\right) + c}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)/(a*sin(f*x + e) + a)^(3/2), x)","F",0
553,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(-3/2), x)","F",0
554,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(d \sin\left(f x + e\right) + c\right)}}\,{d x}"," ",0,"integrate(1/((a*sin(f*x + e) + a)^(3/2)*(d*sin(f*x + e) + c)), x)","F",0
555,-1,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
556,-1,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
557,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^3/(a+a*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{3}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^3/(a*sin(f*x + e) + a)^(5/2), x)","F",0
558,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^2/(a+a*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{2}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^2/(a*sin(f*x + e) + a)^(5/2), x)","F",0
559,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))/(a+a*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{d \sin\left(f x + e\right) + c}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)/(a*sin(f*x + e) + a)^(5/2), x)","F",0
560,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(-5/2), x)","F",0
561,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(d \sin\left(f x + e\right) + c\right)}}\,{d x}"," ",0,"integrate(1/((a*sin(f*x + e) + a)^(5/2)*(d*sin(f*x + e) + c)), x)","F",0
562,-1,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
563,-1,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
564,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)*(c+d*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(f x + e\right) + a} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate(sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^(5/2), x)","F",0
565,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)*(c+d*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(f x + e\right) + a} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^(3/2), x)","F",0
566,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)*(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate(sqrt(a*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c), x)","F",0
567,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{a \sin\left(f x + e\right) + a}}{\sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(sqrt(a*sin(f*x + e) + a)/sqrt(d*sin(f*x + e) + c), x)","F",0
568,1,179,0,1.030447," ","integrate((a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(\sqrt{a} c - \frac{\sqrt{a} {\left(c - 2 \, d\right)} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sqrt{a} {\left(c - 2 \, d\right)} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{\sqrt{a} c \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}}{{\left(c + d + \frac{{\left(c + d\right)} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)} {\left(c + \frac{2 \, d \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{c \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)}^{\frac{3}{2}} f}"," ",0,"-2*(sqrt(a)*c - sqrt(a)*(c - 2*d)*sin(f*x + e)/(cos(f*x + e) + 1) + sqrt(a)*(c - 2*d)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - sqrt(a)*c*sin(f*x + e)^3/(cos(f*x + e) + 1)^3)*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/((c + d + (c + d)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)*(c + 2*d*sin(f*x + e)/(cos(f*x + e) + 1) + c*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)^(3/2)*f)","B",0
569,1,340,0,1.052643," ","integrate((a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","-\frac{2 \, {\left({\left(3 \, c^{2} + c d\right)} \sqrt{a} - \frac{{\left(3 \, c^{2} - 9 \, c d - 2 \, d^{2}\right)} \sqrt{a} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{2 \, {\left(3 \, c^{2} - 4 \, c d + 3 \, d^{2}\right)} \sqrt{a} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{2 \, {\left(3 \, c^{2} - 4 \, c d + 3 \, d^{2}\right)} \sqrt{a} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{{\left(3 \, c^{2} - 9 \, c d - 2 \, d^{2}\right)} \sqrt{a} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{{\left(3 \, c^{2} + c d\right)} \sqrt{a} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{2}}{3 \, {\left(c^{2} + 2 \, c d + d^{2} + \frac{2 \, {\left(c^{2} + 2 \, c d + d^{2}\right)} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{{\left(c^{2} + 2 \, c d + d^{2}\right)} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}}\right)} {\left(c + \frac{2 \, d \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{c \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)}^{\frac{5}{2}} f}"," ",0,"-2/3*((3*c^2 + c*d)*sqrt(a) - (3*c^2 - 9*c*d - 2*d^2)*sqrt(a)*sin(f*x + e)/(cos(f*x + e) + 1) + 2*(3*c^2 - 4*c*d + 3*d^2)*sqrt(a)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 2*(3*c^2 - 4*c*d + 3*d^2)*sqrt(a)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + (3*c^2 - 9*c*d - 2*d^2)*sqrt(a)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - (3*c^2 + c*d)*sqrt(a)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^2/((c^2 + 2*c*d + d^2 + 2*(c^2 + 2*c*d + d^2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + (c^2 + 2*c*d + d^2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4)*(c + 2*d*sin(f*x + e)/(cos(f*x + e) + 1) + c*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)^(5/2)*f)","B",0
570,1,544,0,1.335204," ","integrate((a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^(7/2),x, algorithm=""maxima"")","-\frac{2 \, {\left({\left(15 \, c^{3} + 10 \, c^{2} d + 3 \, c d^{2}\right)} \sqrt{a} - \frac{{\left(15 \, c^{3} - 60 \, c^{2} d - 25 \, c d^{2} - 6 \, d^{3}\right)} \sqrt{a} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{{\left(45 \, c^{3} - 40 \, c^{2} d + 93 \, c d^{2} + 10 \, d^{3}\right)} \sqrt{a} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{5 \, {\left(9 \, c^{3} - 22 \, c^{2} d + 13 \, c d^{2} - 12 \, d^{3}\right)} \sqrt{a} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, {\left(9 \, c^{3} - 22 \, c^{2} d + 13 \, c d^{2} - 12 \, d^{3}\right)} \sqrt{a} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{{\left(45 \, c^{3} - 40 \, c^{2} d + 93 \, c d^{2} + 10 \, d^{3}\right)} \sqrt{a} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{{\left(15 \, c^{3} - 60 \, c^{2} d - 25 \, c d^{2} - 6 \, d^{3}\right)} \sqrt{a} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{{\left(15 \, c^{3} + 10 \, c^{2} d + 3 \, c d^{2}\right)} \sqrt{a} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{3}}{15 \, {\left(c^{3} + 3 \, c^{2} d + 3 \, c d^{2} + d^{3} + \frac{3 \, {\left(c^{3} + 3 \, c^{2} d + 3 \, c d^{2} + d^{3}\right)} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3 \, {\left(c^{3} + 3 \, c^{2} d + 3 \, c d^{2} + d^{3}\right)} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{{\left(c^{3} + 3 \, c^{2} d + 3 \, c d^{2} + d^{3}\right)} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}}\right)} {\left(c + \frac{2 \, d \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{c \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)}^{\frac{7}{2}} f}"," ",0,"-2/15*((15*c^3 + 10*c^2*d + 3*c*d^2)*sqrt(a) - (15*c^3 - 60*c^2*d - 25*c*d^2 - 6*d^3)*sqrt(a)*sin(f*x + e)/(cos(f*x + e) + 1) + (45*c^3 - 40*c^2*d + 93*c*d^2 + 10*d^3)*sqrt(a)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 5*(9*c^3 - 22*c^2*d + 13*c*d^2 - 12*d^3)*sqrt(a)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*(9*c^3 - 22*c^2*d + 13*c*d^2 - 12*d^3)*sqrt(a)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - (45*c^3 - 40*c^2*d + 93*c*d^2 + 10*d^3)*sqrt(a)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + (15*c^3 - 60*c^2*d - 25*c*d^2 - 6*d^3)*sqrt(a)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - (15*c^3 + 10*c^2*d + 3*c*d^2)*sqrt(a)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7)*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^3/((c^3 + 3*c^2*d + 3*c*d^2 + d^3 + 3*(c^3 + 3*c^2*d + 3*c*d^2 + d^3)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3*(c^3 + 3*c^2*d + 3*c*d^2 + d^3)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + (c^3 + 3*c^2*d + 3*c*d^2 + d^3)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6)*(c + 2*d*sin(f*x + e)/(cos(f*x + e) + 1) + c*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)^(7/2)*f)","B",0
571,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)*(c+d*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(3/2)*(d*sin(f*x + e) + c)^(5/2), x)","F",0
572,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)*(c+d*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(3/2)*(d*sin(f*x + e) + c)^(3/2), x)","F",0
573,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)*(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int {\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((a*sin(f*x + e) + a)^(3/2)*sqrt(d*sin(f*x + e) + c), x)","F",0
574,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\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((a*sin(f*x + e) + a)^(3/2)/sqrt(d*sin(f*x + e) + c), x)","F",0
575,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(3/2)/(d*sin(f*x + e) + c)^(3/2), x)","F",0
576,1,307,0,1.269407," ","integrate((a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","-\frac{2 \, {\left({\left(5 \, c^{2} + c d\right)} a^{\frac{3}{2}} - \frac{{\left(3 \, c^{2} - 19 \, c d - 2 \, d^{2}\right)} a^{\frac{3}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{2 \, {\left(4 \, c^{2} - 7 \, c d + 9 \, d^{2}\right)} a^{\frac{3}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{2 \, {\left(4 \, c^{2} - 7 \, c d + 9 \, d^{2}\right)} a^{\frac{3}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{{\left(3 \, c^{2} - 19 \, c d - 2 \, d^{2}\right)} a^{\frac{3}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{{\left(5 \, c^{2} + c d\right)} a^{\frac{3}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}}{3 \, {\left(c^{2} + 2 \, c d + d^{2} + \frac{{\left(c^{2} + 2 \, c d + d^{2}\right)} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)} {\left(c + \frac{2 \, d \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{c \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)}^{\frac{5}{2}} f}"," ",0,"-2/3*((5*c^2 + c*d)*a^(3/2) - (3*c^2 - 19*c*d - 2*d^2)*a^(3/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 2*(4*c^2 - 7*c*d + 9*d^2)*a^(3/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 2*(4*c^2 - 7*c*d + 9*d^2)*a^(3/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + (3*c^2 - 19*c*d - 2*d^2)*a^(3/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - (5*c^2 + c*d)*a^(3/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/((c^2 + 2*c*d + d^2 + (c^2 + 2*c*d + d^2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)*(c + 2*d*sin(f*x + e)/(cos(f*x + e) + 1) + c*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)^(5/2)*f)","B",0
577,1,505,0,1.222593," ","integrate((a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^(7/2),x, algorithm=""maxima"")","-\frac{2 \, {\left({\left(25 \, c^{3} + 12 \, c^{2} d + 3 \, c d^{2}\right)} a^{\frac{3}{2}} - \frac{{\left(15 \, c^{3} - 130 \, c^{2} d - 39 \, c d^{2} - 6 \, d^{3}\right)} a^{\frac{3}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{{\left(65 \, c^{3} - 78 \, c^{2} d + 223 \, c d^{2} + 30 \, d^{3}\right)} a^{\frac{3}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{5 \, {\left(11 \, c^{3} - 44 \, c^{2} d + 33 \, c d^{2} - 24 \, d^{3}\right)} a^{\frac{3}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, {\left(11 \, c^{3} - 44 \, c^{2} d + 33 \, c d^{2} - 24 \, d^{3}\right)} a^{\frac{3}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{{\left(65 \, c^{3} - 78 \, c^{2} d + 223 \, c d^{2} + 30 \, d^{3}\right)} a^{\frac{3}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{{\left(15 \, c^{3} - 130 \, c^{2} d - 39 \, c d^{2} - 6 \, d^{3}\right)} a^{\frac{3}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{{\left(25 \, c^{3} + 12 \, c^{2} d + 3 \, c d^{2}\right)} a^{\frac{3}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{2}}{15 \, {\left(c^{3} + 3 \, c^{2} d + 3 \, c d^{2} + d^{3} + \frac{2 \, {\left(c^{3} + 3 \, c^{2} d + 3 \, c d^{2} + d^{3}\right)} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{{\left(c^{3} + 3 \, c^{2} d + 3 \, c d^{2} + d^{3}\right)} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}}\right)} {\left(c + \frac{2 \, d \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{c \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)}^{\frac{7}{2}} f}"," ",0,"-2/15*((25*c^3 + 12*c^2*d + 3*c*d^2)*a^(3/2) - (15*c^3 - 130*c^2*d - 39*c*d^2 - 6*d^3)*a^(3/2)*sin(f*x + e)/(cos(f*x + e) + 1) + (65*c^3 - 78*c^2*d + 223*c*d^2 + 30*d^3)*a^(3/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 5*(11*c^3 - 44*c^2*d + 33*c*d^2 - 24*d^3)*a^(3/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*(11*c^3 - 44*c^2*d + 33*c*d^2 - 24*d^3)*a^(3/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - (65*c^3 - 78*c^2*d + 223*c*d^2 + 30*d^3)*a^(3/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + (15*c^3 - 130*c^2*d - 39*c*d^2 - 6*d^3)*a^(3/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - (25*c^3 + 12*c^2*d + 3*c*d^2)*a^(3/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7)*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^2/((c^3 + 3*c^2*d + 3*c*d^2 + d^3 + 2*(c^3 + 3*c^2*d + 3*c*d^2 + d^3)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + (c^3 + 3*c^2*d + 3*c*d^2 + d^3)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4)*(c + 2*d*sin(f*x + e)/(cos(f*x + e) + 1) + c*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)^(7/2)*f)","B",0
578,1,750,0,1.327454," ","integrate((a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^(9/2),x, algorithm=""maxima"")","-\frac{2 \, {\left({\left(175 \, c^{4} + 133 \, c^{3} d + 69 \, c^{2} d^{2} + 15 \, c d^{3}\right)} a^{\frac{3}{2}} - \frac{3 \, {\left(35 \, c^{4} - 385 \, c^{3} d - 189 \, c^{2} d^{2} - 67 \, c d^{3} - 10 \, d^{4}\right)} a^{\frac{3}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{18 \, {\left(35 \, c^{4} - 28 \, c^{3} d + 166 \, c^{2} d^{2} + 44 \, c d^{3} + 7 \, d^{4}\right)} a^{\frac{3}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{14 \, {\left(35 \, c^{4} - 220 \, c^{3} d + 102 \, c^{2} d^{2} - 244 \, c d^{3} - 25 \, d^{4}\right)} a^{\frac{3}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{42 \, {\left(20 \, c^{4} - 61 \, c^{3} d + 117 \, c^{2} d^{2} - 55 \, c d^{3} + 35 \, d^{4}\right)} a^{\frac{3}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{42 \, {\left(20 \, c^{4} - 61 \, c^{3} d + 117 \, c^{2} d^{2} - 55 \, c d^{3} + 35 \, d^{4}\right)} a^{\frac{3}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{14 \, {\left(35 \, c^{4} - 220 \, c^{3} d + 102 \, c^{2} d^{2} - 244 \, c d^{3} - 25 \, d^{4}\right)} a^{\frac{3}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{18 \, {\left(35 \, c^{4} - 28 \, c^{3} d + 166 \, c^{2} d^{2} + 44 \, c d^{3} + 7 \, d^{4}\right)} a^{\frac{3}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{3 \, {\left(35 \, c^{4} - 385 \, c^{3} d - 189 \, c^{2} d^{2} - 67 \, c d^{3} - 10 \, d^{4}\right)} a^{\frac{3}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{{\left(175 \, c^{4} + 133 \, c^{3} d + 69 \, c^{2} d^{2} + 15 \, c d^{3}\right)} a^{\frac{3}{2}} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{3}}{105 \, {\left(c^{4} + 4 \, c^{3} d + 6 \, c^{2} d^{2} + 4 \, c d^{3} + d^{4} + \frac{3 \, {\left(c^{4} + 4 \, c^{3} d + 6 \, c^{2} d^{2} + 4 \, c d^{3} + d^{4}\right)} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3 \, {\left(c^{4} + 4 \, c^{3} d + 6 \, c^{2} d^{2} + 4 \, c d^{3} + d^{4}\right)} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{{\left(c^{4} + 4 \, c^{3} d + 6 \, c^{2} d^{2} + 4 \, c d^{3} + d^{4}\right)} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}}\right)} {\left(c + \frac{2 \, d \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{c \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)}^{\frac{9}{2}} f}"," ",0,"-2/105*((175*c^4 + 133*c^3*d + 69*c^2*d^2 + 15*c*d^3)*a^(3/2) - 3*(35*c^4 - 385*c^3*d - 189*c^2*d^2 - 67*c*d^3 - 10*d^4)*a^(3/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 18*(35*c^4 - 28*c^3*d + 166*c^2*d^2 + 44*c*d^3 + 7*d^4)*a^(3/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 14*(35*c^4 - 220*c^3*d + 102*c^2*d^2 - 244*c*d^3 - 25*d^4)*a^(3/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 42*(20*c^4 - 61*c^3*d + 117*c^2*d^2 - 55*c*d^3 + 35*d^4)*a^(3/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 42*(20*c^4 - 61*c^3*d + 117*c^2*d^2 - 55*c*d^3 + 35*d^4)*a^(3/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 14*(35*c^4 - 220*c^3*d + 102*c^2*d^2 - 244*c*d^3 - 25*d^4)*a^(3/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 18*(35*c^4 - 28*c^3*d + 166*c^2*d^2 + 44*c*d^3 + 7*d^4)*a^(3/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 3*(35*c^4 - 385*c^3*d - 189*c^2*d^2 - 67*c*d^3 - 10*d^4)*a^(3/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - (175*c^4 + 133*c^3*d + 69*c^2*d^2 + 15*c*d^3)*a^(3/2)*sin(f*x + e)^9/(cos(f*x + e) + 1)^9)*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^3/((c^4 + 4*c^3*d + 6*c^2*d^2 + 4*c*d^3 + d^4 + 3*(c^4 + 4*c^3*d + 6*c^2*d^2 + 4*c*d^3 + d^4)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3*(c^4 + 4*c^3*d + 6*c^2*d^2 + 4*c*d^3 + d^4)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + (c^4 + 4*c^3*d + 6*c^2*d^2 + 4*c*d^3 + d^4)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6)*(c + 2*d*sin(f*x + e)/(cos(f*x + e) + 1) + c*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)^(9/2)*f)","B",0
579,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)*(c+d*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(5/2)*(d*sin(f*x + e) + c)^(5/2), x)","F",0
580,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)*(c+d*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(5/2)*(d*sin(f*x + e) + c)^(3/2), x)","F",0
581,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)*(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} \sqrt{d \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(5/2)*sqrt(d*sin(f*x + e) + c), x)","F",0
582,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}{\sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(5/2)/sqrt(d*sin(f*x + e) + c), x)","F",0
583,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(5/2)/(d*sin(f*x + e) + c)^(3/2), x)","F",0
584,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(5/2)/(d*sin(f*x + e) + c)^(5/2), x)","F",0
585,1,464,0,1.140337," ","integrate((a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(7/2),x, algorithm=""maxima"")","-\frac{2 \, {\left({\left(43 \, c^{3} + 14 \, c^{2} d + 3 \, c d^{2}\right)} a^{\frac{5}{2}} - \frac{{\left(15 \, c^{3} - 256 \, c^{2} d - 53 \, c d^{2} - 6 \, d^{3}\right)} a^{\frac{5}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{{\left(113 \, c^{3} - 116 \, c^{2} d + 493 \, c d^{2} + 50 \, d^{3}\right)} a^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{5 \, {\left(17 \, c^{3} - 82 \, c^{2} d + 65 \, c d^{2} - 60 \, d^{3}\right)} a^{\frac{5}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, {\left(17 \, c^{3} - 82 \, c^{2} d + 65 \, c d^{2} - 60 \, d^{3}\right)} a^{\frac{5}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{{\left(113 \, c^{3} - 116 \, c^{2} d + 493 \, c d^{2} + 50 \, d^{3}\right)} a^{\frac{5}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{{\left(15 \, c^{3} - 256 \, c^{2} d - 53 \, c d^{2} - 6 \, d^{3}\right)} a^{\frac{5}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{{\left(43 \, c^{3} + 14 \, c^{2} d + 3 \, c d^{2}\right)} a^{\frac{5}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}}{15 \, {\left(c^{3} + 3 \, c^{2} d + 3 \, c d^{2} + d^{3} + \frac{{\left(c^{3} + 3 \, c^{2} d + 3 \, c d^{2} + d^{3}\right)} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)} {\left(c + \frac{2 \, d \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{c \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)}^{\frac{7}{2}} f}"," ",0,"-2/15*((43*c^3 + 14*c^2*d + 3*c*d^2)*a^(5/2) - (15*c^3 - 256*c^2*d - 53*c*d^2 - 6*d^3)*a^(5/2)*sin(f*x + e)/(cos(f*x + e) + 1) + (113*c^3 - 116*c^2*d + 493*c*d^2 + 50*d^3)*a^(5/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 5*(17*c^3 - 82*c^2*d + 65*c*d^2 - 60*d^3)*a^(5/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*(17*c^3 - 82*c^2*d + 65*c*d^2 - 60*d^3)*a^(5/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - (113*c^3 - 116*c^2*d + 493*c*d^2 + 50*d^3)*a^(5/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + (15*c^3 - 256*c^2*d - 53*c*d^2 - 6*d^3)*a^(5/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - (43*c^3 + 14*c^2*d + 3*c*d^2)*a^(5/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7)*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/((c^3 + 3*c^2*d + 3*c*d^2 + d^3 + (c^3 + 3*c^2*d + 3*c*d^2 + d^3)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)*(c + 2*d*sin(f*x + e)/(cos(f*x + e) + 1) + c*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)^(7/2)*f)","B",0
586,1,703,0,1.210661," ","integrate((a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(9/2),x, algorithm=""maxima"")","-\frac{2 \, {\left({\left(301 \, c^{4} + 169 \, c^{3} d + 75 \, c^{2} d^{2} + 15 \, c d^{3}\right)} a^{\frac{5}{2}} - \frac{3 \, {\left(35 \, c^{4} - 763 \, c^{3} d - 297 \, c^{2} d^{2} - 85 \, c d^{3} - 10 \, d^{4}\right)} a^{\frac{5}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{6 \, {\left(182 \, c^{4} - 127 \, c^{3} d + 1059 \, c^{2} d^{2} + 251 \, c d^{3} + 35 \, d^{4}\right)} a^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{14 \, {\left(50 \, c^{4} - 421 \, c^{3} d + 201 \, c^{2} d^{2} - 535 \, c d^{3} - 55 \, d^{4}\right)} a^{\frac{5}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{126 \, {\left(11 \, c^{4} - 36 \, c^{3} d + 80 \, c^{2} d^{2} - 40 \, c d^{3} + 25 \, d^{4}\right)} a^{\frac{5}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{126 \, {\left(11 \, c^{4} - 36 \, c^{3} d + 80 \, c^{2} d^{2} - 40 \, c d^{3} + 25 \, d^{4}\right)} a^{\frac{5}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{14 \, {\left(50 \, c^{4} - 421 \, c^{3} d + 201 \, c^{2} d^{2} - 535 \, c d^{3} - 55 \, d^{4}\right)} a^{\frac{5}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{6 \, {\left(182 \, c^{4} - 127 \, c^{3} d + 1059 \, c^{2} d^{2} + 251 \, c d^{3} + 35 \, d^{4}\right)} a^{\frac{5}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{3 \, {\left(35 \, c^{4} - 763 \, c^{3} d - 297 \, c^{2} d^{2} - 85 \, c d^{3} - 10 \, d^{4}\right)} a^{\frac{5}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{{\left(301 \, c^{4} + 169 \, c^{3} d + 75 \, c^{2} d^{2} + 15 \, c d^{3}\right)} a^{\frac{5}{2}} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{2}}{105 \, {\left(c^{4} + 4 \, c^{3} d + 6 \, c^{2} d^{2} + 4 \, c d^{3} + d^{4} + \frac{2 \, {\left(c^{4} + 4 \, c^{3} d + 6 \, c^{2} d^{2} + 4 \, c d^{3} + d^{4}\right)} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{{\left(c^{4} + 4 \, c^{3} d + 6 \, c^{2} d^{2} + 4 \, c d^{3} + d^{4}\right)} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}}\right)} {\left(c + \frac{2 \, d \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{c \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)}^{\frac{9}{2}} f}"," ",0,"-2/105*((301*c^4 + 169*c^3*d + 75*c^2*d^2 + 15*c*d^3)*a^(5/2) - 3*(35*c^4 - 763*c^3*d - 297*c^2*d^2 - 85*c*d^3 - 10*d^4)*a^(5/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 6*(182*c^4 - 127*c^3*d + 1059*c^2*d^2 + 251*c*d^3 + 35*d^4)*a^(5/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 14*(50*c^4 - 421*c^3*d + 201*c^2*d^2 - 535*c*d^3 - 55*d^4)*a^(5/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 126*(11*c^4 - 36*c^3*d + 80*c^2*d^2 - 40*c*d^3 + 25*d^4)*a^(5/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 126*(11*c^4 - 36*c^3*d + 80*c^2*d^2 - 40*c*d^3 + 25*d^4)*a^(5/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 14*(50*c^4 - 421*c^3*d + 201*c^2*d^2 - 535*c*d^3 - 55*d^4)*a^(5/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 6*(182*c^4 - 127*c^3*d + 1059*c^2*d^2 + 251*c*d^3 + 35*d^4)*a^(5/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 3*(35*c^4 - 763*c^3*d - 297*c^2*d^2 - 85*c*d^3 - 10*d^4)*a^(5/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - (301*c^4 + 169*c^3*d + 75*c^2*d^2 + 15*c*d^3)*a^(5/2)*sin(f*x + e)^9/(cos(f*x + e) + 1)^9)*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^2/((c^4 + 4*c^3*d + 6*c^2*d^2 + 4*c*d^3 + d^4 + 2*(c^4 + 4*c^3*d + 6*c^2*d^2 + 4*c*d^3 + d^4)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + (c^4 + 4*c^3*d + 6*c^2*d^2 + 4*c*d^3 + d^4)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4)*(c + 2*d*sin(f*x + e)/(cos(f*x + e) + 1) + c*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)^(9/2)*f)","B",0
587,1,984,0,1.945828," ","integrate((a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(11/2),x, algorithm=""maxima"")","-\frac{2 \, {\left({\left(903 \, c^{5} + 720 \, c^{4} d + 494 \, c^{3} d^{2} + 200 \, c^{2} d^{3} + 35 \, c d^{4}\right)} a^{\frac{5}{2}} - \frac{{\left(315 \, c^{5} - 8358 \, c^{4} d - 4770 \, c^{3} d^{2} - 2284 \, c^{2} d^{3} - 625 \, c d^{4} - 70 \, d^{5}\right)} a^{\frac{5}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{{\left(4179 \, c^{5} - 1710 \, c^{4} d + 30878 \, c^{3} d^{2} + 11540 \, c^{2} d^{3} + 3383 \, c d^{4} + 450 \, d^{5}\right)} a^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{3 \, {\left(805 \, c^{5} - 9912 \, c^{4} d + 2330 \, c^{3} d^{2} - 18504 \, c^{2} d^{3} - 3895 \, c d^{4} - 504 \, d^{5}\right)} a^{\frac{5}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{6 \, {\left(1239 \, c^{5} - 3100 \, c^{4} d + 12918 \, c^{3} d^{2} - 3560 \, c^{2} d^{3} + 8043 \, c d^{4} + 700 \, d^{5}\right)} a^{\frac{5}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{42 \, {\left(149 \, c^{5} - 894 \, c^{4} d + 1402 \, c^{3} d^{2} - 2052 \, c^{2} d^{3} + 745 \, c d^{4} - 390 \, d^{5}\right)} a^{\frac{5}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{42 \, {\left(149 \, c^{5} - 894 \, c^{4} d + 1402 \, c^{3} d^{2} - 2052 \, c^{2} d^{3} + 745 \, c d^{4} - 390 \, d^{5}\right)} a^{\frac{5}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{6 \, {\left(1239 \, c^{5} - 3100 \, c^{4} d + 12918 \, c^{3} d^{2} - 3560 \, c^{2} d^{3} + 8043 \, c d^{4} + 700 \, d^{5}\right)} a^{\frac{5}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{3 \, {\left(805 \, c^{5} - 9912 \, c^{4} d + 2330 \, c^{3} d^{2} - 18504 \, c^{2} d^{3} - 3895 \, c d^{4} - 504 \, d^{5}\right)} a^{\frac{5}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{{\left(4179 \, c^{5} - 1710 \, c^{4} d + 30878 \, c^{3} d^{2} + 11540 \, c^{2} d^{3} + 3383 \, c d^{4} + 450 \, d^{5}\right)} a^{\frac{5}{2}} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{{\left(315 \, c^{5} - 8358 \, c^{4} d - 4770 \, c^{3} d^{2} - 2284 \, c^{2} d^{3} - 625 \, c d^{4} - 70 \, d^{5}\right)} a^{\frac{5}{2}} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{{\left(903 \, c^{5} + 720 \, c^{4} d + 494 \, c^{3} d^{2} + 200 \, c^{2} d^{3} + 35 \, c d^{4}\right)} a^{\frac{5}{2}} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}}\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{3}}{315 \, {\left(c^{5} + 5 \, c^{4} d + 10 \, c^{3} d^{2} + 10 \, c^{2} d^{3} + 5 \, c d^{4} + d^{5} + \frac{3 \, {\left(c^{5} + 5 \, c^{4} d + 10 \, c^{3} d^{2} + 10 \, c^{2} d^{3} + 5 \, c d^{4} + d^{5}\right)} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3 \, {\left(c^{5} + 5 \, c^{4} d + 10 \, c^{3} d^{2} + 10 \, c^{2} d^{3} + 5 \, c d^{4} + d^{5}\right)} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{{\left(c^{5} + 5 \, c^{4} d + 10 \, c^{3} d^{2} + 10 \, c^{2} d^{3} + 5 \, c d^{4} + d^{5}\right)} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}}\right)} {\left(c + \frac{2 \, d \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{c \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)}^{\frac{11}{2}} f}"," ",0,"-2/315*((903*c^5 + 720*c^4*d + 494*c^3*d^2 + 200*c^2*d^3 + 35*c*d^4)*a^(5/2) - (315*c^5 - 8358*c^4*d - 4770*c^3*d^2 - 2284*c^2*d^3 - 625*c*d^4 - 70*d^5)*a^(5/2)*sin(f*x + e)/(cos(f*x + e) + 1) + (4179*c^5 - 1710*c^4*d + 30878*c^3*d^2 + 11540*c^2*d^3 + 3383*c*d^4 + 450*d^5)*a^(5/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 3*(805*c^5 - 9912*c^4*d + 2330*c^3*d^2 - 18504*c^2*d^3 - 3895*c*d^4 - 504*d^5)*a^(5/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 6*(1239*c^5 - 3100*c^4*d + 12918*c^3*d^2 - 3560*c^2*d^3 + 8043*c*d^4 + 700*d^5)*a^(5/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 42*(149*c^5 - 894*c^4*d + 1402*c^3*d^2 - 2052*c^2*d^3 + 745*c*d^4 - 390*d^5)*a^(5/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 42*(149*c^5 - 894*c^4*d + 1402*c^3*d^2 - 2052*c^2*d^3 + 745*c*d^4 - 390*d^5)*a^(5/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 6*(1239*c^5 - 3100*c^4*d + 12918*c^3*d^2 - 3560*c^2*d^3 + 8043*c*d^4 + 700*d^5)*a^(5/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 3*(805*c^5 - 9912*c^4*d + 2330*c^3*d^2 - 18504*c^2*d^3 - 3895*c*d^4 - 504*d^5)*a^(5/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - (4179*c^5 - 1710*c^4*d + 30878*c^3*d^2 + 11540*c^2*d^3 + 3383*c*d^4 + 450*d^5)*a^(5/2)*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + (315*c^5 - 8358*c^4*d - 4770*c^3*d^2 - 2284*c^2*d^3 - 625*c*d^4 - 70*d^5)*a^(5/2)*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - (903*c^5 + 720*c^4*d + 494*c^3*d^2 + 200*c^2*d^3 + 35*c*d^4)*a^(5/2)*sin(f*x + e)^11/(cos(f*x + e) + 1)^11)*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^3/((c^5 + 5*c^4*d + 10*c^3*d^2 + 10*c^2*d^3 + 5*c*d^4 + d^5 + 3*(c^5 + 5*c^4*d + 10*c^3*d^2 + 10*c^2*d^3 + 5*c*d^4 + d^5)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3*(c^5 + 5*c^4*d + 10*c^3*d^2 + 10*c^2*d^3 + 5*c*d^4 + d^5)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + (c^5 + 5*c^4*d + 10*c^3*d^2 + 10*c^2*d^3 + 5*c*d^4 + d^5)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6)*(c + 2*d*sin(f*x + e)/(cos(f*x + e) + 1) + c*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)^(11/2)*f)","B",0
588,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}{\sqrt{a \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(5/2)/sqrt(a*sin(f*x + e) + a), x)","F",0
589,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{\sqrt{a \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(3/2)/sqrt(a*sin(f*x + e) + a), x)","F",0
590,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{d \sin\left(f x + e\right) + c}}{\sqrt{a \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate(sqrt(d*sin(f*x + e) + c)/sqrt(a*sin(f*x + e) + a), x)","F",0
591,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{a \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(1/(sqrt(a*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c)), x)","F",0
592,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{a \sin\left(f x + e\right) + a} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^(3/2)), x)","F",0
593,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{a \sin\left(f x + e\right) + a} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^(5/2)), x)","F",0
594,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(5/2)/(a*sin(f*x + e) + a)^(3/2), x)","F",0
595,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(3/2)/(a*sin(f*x + e) + a)^(3/2), x)","F",0
596,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{d \sin\left(f x + e\right) + c}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(d*sin(f*x + e) + c)/(a*sin(f*x + e) + a)^(3/2), x)","F",0
597,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\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(1/((a*sin(f*x + e) + a)^(3/2)*sqrt(d*sin(f*x + e) + c)), x)","F",0
598,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((a*sin(f*x + e) + a)^(3/2)*(d*sin(f*x + e) + c)^(3/2)), x)","F",0
599,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((a*sin(f*x + e) + a)^(3/2)*(d*sin(f*x + e) + c)^(5/2)), x)","F",0
600,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(5/2)/(a*sin(f*x + e) + a)^(5/2), x)","F",0
601,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(3/2)/(a*sin(f*x + e) + a)^(5/2), x)","F",0
602,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{\sqrt{d \sin\left(f x + e\right) + c}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(d*sin(f*x + e) + c)/(a*sin(f*x + e) + a)^(5/2), x)","F",0
603,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} \sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(1/((a*sin(f*x + e) + a)^(5/2)*sqrt(d*sin(f*x + e) + c)), x)","F",0
604,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((a*sin(f*x + e) + a)^(5/2)*(d*sin(f*x + e) + c)^(3/2)), x)","F",0
605,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((a*sin(f*x + e) + a)^(5/2)*(d*sin(f*x + e) + c)^(5/2)), x)","F",0
606,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x, algorithm=""maxima"")","\int {\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((a*sin(f*x + e) + a)^m*(d*sin(f*x + e) + c)^n, x)","F",0
607,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\int {\left(d \sin\left(f x + e\right) + c\right)}^{3} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^3*(a*sin(f*x + e) + a)^m, x)","F",0
608,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\int {\left(d \sin\left(f x + e\right) + c\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^2*(a*sin(f*x + e) + a)^m, x)","F",0
609,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\int {\left(d \sin\left(f x + e\right) + c\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m, x)","F",0
610,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m, x)","F",0
611,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m/(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m}}{d \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m/(d*sin(f*x + e) + c), x)","F",0
612,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m/(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m}}{{\left(d \sin\left(f x + e\right) + c\right)}^{2}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m/(d*sin(f*x + e) + c)^2, x)","F",0
613,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m/(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m}}{{\left(d \sin\left(f x + e\right) + c\right)}^{3}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m/(d*sin(f*x + e) + c)^3, x)","F",0
614,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int {\left(d \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((d*sin(f*x + e) + c)^(5/2)*(a*sin(f*x + e) + a)^m, x)","F",0
615,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(d \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((d*sin(f*x + e) + c)^(3/2)*(a*sin(f*x + e) + a)^m, x)","F",0
616,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sqrt{d \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate(sqrt(d*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m, x)","F",0
617,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m/(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m}}{\sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m/sqrt(d*sin(f*x + e) + c), x)","F",0
618,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m/(c+d*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m/(d*sin(f*x + e) + c)^(3/2), x)","F",0
619,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m/(c+d*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m/(d*sin(f*x + e) + c)^(5/2), x)","F",0
620,0,0,0,0.000000," ","integrate((1+sin(f*x+e))^m*(3+5*sin(f*x+e))^(-1-m),x, algorithm=""maxima"")","\int {\left(5 \, \sin\left(f x + e\right) + 3\right)}^{-m - 1} {\left(\sin\left(f x + e\right) + 1\right)}^{m}\,{d x}"," ",0,"integrate((5*sin(f*x + e) + 3)^(-m - 1)*(sin(f*x + e) + 1)^m, x)","F",0
621,0,0,0,0.000000," ","integrate((1+sin(f*x+e))^m*(3+4*sin(f*x+e))^(-1-m),x, algorithm=""maxima"")","\int {\left(4 \, \sin\left(f x + e\right) + 3\right)}^{-m - 1} {\left(\sin\left(f x + e\right) + 1\right)}^{m}\,{d x}"," ",0,"integrate((4*sin(f*x + e) + 3)^(-m - 1)*(sin(f*x + e) + 1)^m, x)","F",0
622,1,35,0,0.835267," ","integrate((1+sin(f*x+e))^m*(3+3*sin(f*x+e))^(-1-m),x, algorithm=""maxima"")","-\frac{2}{{\left(3^{m + 1} + \frac{3^{m + 1} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)} f}"," ",0,"-2/((3^(m + 1) + 3^(m + 1)*sin(f*x + e)/(cos(f*x + e) + 1))*f)","A",0
623,0,0,0,0.000000," ","integrate((1+sin(f*x+e))^m*(3+2*sin(f*x+e))^(-1-m),x, algorithm=""maxima"")","\int {\left(2 \, \sin\left(f x + e\right) + 3\right)}^{-m - 1} {\left(\sin\left(f x + e\right) + 1\right)}^{m}\,{d x}"," ",0,"integrate((2*sin(f*x + e) + 3)^(-m - 1)*(sin(f*x + e) + 1)^m, x)","F",0
624,0,0,0,0.000000," ","integrate((1+sin(f*x+e))^m*(3+sin(f*x+e))^(-1-m),x, algorithm=""maxima"")","\int {\left(\sin\left(f x + e\right) + 3\right)}^{-m - 1} {\left(\sin\left(f x + e\right) + 1\right)}^{m}\,{d x}"," ",0,"integrate((sin(f*x + e) + 3)^(-m - 1)*(sin(f*x + e) + 1)^m, x)","F",0
625,0,0,0,0.000000," ","integrate(3^(-1-m)*(1+sin(f*x+e))^m,x, algorithm=""maxima"")","3^{-m - 1} \int {\left(\sin\left(f x + e\right) + 1\right)}^{m}\,{d x}"," ",0,"3^(-m - 1)*integrate((sin(f*x + e) + 1)^m, x)","F",0
626,0,0,0,0.000000," ","integrate((3-sin(f*x+e))^(-1-m)*(1+sin(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(\sin\left(f x + e\right) + 1\right)}^{m} {\left(-\sin\left(f x + e\right) + 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((sin(f*x + e) + 1)^m*(-sin(f*x + e) + 3)^(-m - 1), x)","F",0
627,0,0,0,0.000000," ","integrate((3-2*sin(f*x+e))^(-1-m)*(1+sin(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(\sin\left(f x + e\right) + 1\right)}^{m} {\left(-2 \, \sin\left(f x + e\right) + 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((sin(f*x + e) + 1)^m*(-2*sin(f*x + e) + 3)^(-m - 1), x)","F",0
628,0,0,0,0.000000," ","integrate((3-3*sin(f*x+e))^(-1-m)*(1+sin(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(\sin\left(f x + e\right) + 1\right)}^{m} {\left(-3 \, \sin\left(f x + e\right) + 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((sin(f*x + e) + 1)^m*(-3*sin(f*x + e) + 3)^(-m - 1), x)","F",0
629,0,0,0,0.000000," ","integrate((3-4*sin(f*x+e))^(-1-m)*(1+sin(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(\sin\left(f x + e\right) + 1\right)}^{m} {\left(-4 \, \sin\left(f x + e\right) + 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((sin(f*x + e) + 1)^m*(-4*sin(f*x + e) + 3)^(-m - 1), x)","F",0
630,0,0,0,0.000000," ","integrate((3-5*sin(f*x+e))^(-1-m)*(1+sin(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(\sin\left(f x + e\right) + 1\right)}^{m} {\left(-5 \, \sin\left(f x + e\right) + 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((sin(f*x + e) + 1)^m*(-5*sin(f*x + e) + 3)^(-m - 1), x)","F",0
631,0,0,0,0.000000," ","integrate((3+5*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(5 \, \sin\left(f x + e\right) + 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(5*sin(f*x + e) + 3)^(-m - 1), x)","F",0
632,0,0,0,0.000000," ","integrate((3+4*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(4 \, \sin\left(f x + e\right) + 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(4*sin(f*x + e) + 3)^(-m - 1), x)","F",0
633,1,38,0,0.884460," ","integrate((3+3*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""maxima"")","-\frac{2 \, a^{m}}{{\left(3^{m + 1} + \frac{3^{m + 1} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)} f}"," ",0,"-2*a^m/((3^(m + 1) + 3^(m + 1)*sin(f*x + e)/(cos(f*x + e) + 1))*f)","A",0
634,0,0,0,0.000000," ","integrate((3+2*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(2 \, \sin\left(f x + e\right) + 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(2*sin(f*x + e) + 3)^(-m - 1), x)","F",0
635,0,0,0,0.000000," ","integrate((3+sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(\sin\left(f x + e\right) + 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(sin(f*x + e) + 3)^(-m - 1), x)","F",0
636,0,0,0,0.000000," ","integrate(3^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""maxima"")","3^{-m - 1} \int {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"3^(-m - 1)*integrate((a*sin(f*x + e) + a)^m, x)","F",0
637,0,0,0,0.000000," ","integrate((3-sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-\sin\left(f x + e\right) + 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(-sin(f*x + e) + 3)^(-m - 1), x)","F",0
638,0,0,0,0.000000," ","integrate((3-2*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-2 \, \sin\left(f x + e\right) + 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(-2*sin(f*x + e) + 3)^(-m - 1), x)","F",0
639,0,0,0,0.000000," ","integrate((3-3*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-3 \, \sin\left(f x + e\right) + 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(-3*sin(f*x + e) + 3)^(-m - 1), x)","F",0
640,0,0,0,0.000000," ","integrate((3-4*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-4 \, \sin\left(f x + e\right) + 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(-4*sin(f*x + e) + 3)^(-m - 1), x)","F",0
641,0,0,0,0.000000," ","integrate((3-5*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-5 \, \sin\left(f x + e\right) + 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(-5*sin(f*x + e) + 3)^(-m - 1), x)","F",0
642,0,0,0,0.000000," ","integrate((-3+5*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(5 \, \sin\left(f x + e\right) - 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(5*sin(f*x + e) - 3)^(-m - 1), x)","F",0
643,0,0,0,0.000000," ","integrate((-3+4*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(4 \, \sin\left(f x + e\right) - 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(4*sin(f*x + e) - 3)^(-m - 1), x)","F",0
644,0,0,0,0.000000," ","integrate((-3+3*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(3 \, \sin\left(f x + e\right) - 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(3*sin(f*x + e) - 3)^(-m - 1), x)","F",0
645,0,0,0,0.000000," ","integrate((-3+2*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(2 \, \sin\left(f x + e\right) - 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(2*sin(f*x + e) - 3)^(-m - 1), x)","F",0
646,0,0,0,0.000000," ","integrate((-3+sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(\sin\left(f x + e\right) - 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(sin(f*x + e) - 3)^(-m - 1), x)","F",0
647,0,0,0,0.000000," ","integrate((-3)^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""maxima"")","\left(-3\right)^{-m - 1} \int {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"(-3)^(-m - 1)*integrate((a*sin(f*x + e) + a)^m, x)","F",0
648,0,0,0,0.000000," ","integrate((-3-sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-\sin\left(f x + e\right) - 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(-sin(f*x + e) - 3)^(-m - 1), x)","F",0
649,0,0,0,0.000000," ","integrate((-3-2*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-2 \, \sin\left(f x + e\right) - 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(-2*sin(f*x + e) - 3)^(-m - 1), x)","F",0
650,1,45,0,1.234272," ","integrate((-3-3*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""maxima"")","\frac{2 \, a^{m}}{{\left(3^{m + 1} \left(-1\right)^{m} + \frac{3^{m + 1} \left(-1\right)^{m} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)} f}"," ",0,"2*a^m/((3^(m + 1)*(-1)^m + 3^(m + 1)*(-1)^m*sin(f*x + e)/(cos(f*x + e) + 1))*f)","A",0
651,0,0,0,0.000000," ","integrate((-3-4*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-4 \, \sin\left(f x + e\right) - 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(-4*sin(f*x + e) - 3)^(-m - 1), x)","F",0
652,0,0,0,0.000000," ","integrate((-3-5*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-5 \, \sin\left(f x + e\right) - 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(-5*sin(f*x + e) - 3)^(-m - 1), x)","F",0
653,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} \left(d \sin\left(f x + e\right)\right)^{-m - 1}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(d*sin(f*x + e))^(-m - 1), x)","F",0
654,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^(-1-m),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(d \sin\left(f x + e\right) + c\right)}^{-m - 1}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(d*sin(f*x + e) + c)^(-m - 1), x)","F",0
655,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3*(c+d*sin(f*x+e))^n,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(d \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^3*(d*sin(f*x + e) + c)^n, x)","F",0
656,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^n,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^2*(d*sin(f*x + e) + c)^n, x)","F",0
657,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(c+d*sin(f*x+e))^n,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^n, x)","F",0
658,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^n,x, algorithm=""maxima"")","\int {\left(d \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^n, x)","F",0
659,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^n/(a+a*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n}}{a \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^n/(a*sin(f*x + e) + a), x)","F",0
660,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{{\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((d*sin(f*x + e) + c)^n/(a*sin(f*x + e) + a)^2, x)","F",0
661,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","\int \frac{{\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((d*sin(f*x + e) + c)^n/(a*sin(f*x + e) + a)^3, x)","F",0
662,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)*(c+d*sin(f*x+e))^n,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(d \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(5/2)*(d*sin(f*x + e) + c)^n, x)","F",0
663,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)*(c+d*sin(f*x+e))^n,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(d \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(3/2)*(d*sin(f*x + e) + c)^n, x)","F",0
664,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)*(c+d*sin(f*x+e))^n,x, algorithm=""maxima"")","\int \sqrt{a \sin\left(f x + e\right) + a} {\left(d \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate(sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^n, x)","F",0
665,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n}}{\sqrt{a \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^n/sqrt(a*sin(f*x + e) + a), x)","F",0
666,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^n/(a*sin(f*x + e) + a)^(3/2), x)","F",0
667,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^n/(a*sin(f*x + e) + a)^(5/2), x)","F",0
668,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(c+d*sin(f*x+e))^(1/3),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{1}{3}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^(1/3), x)","F",0
669,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))/(c+d*sin(f*x+e))^(1/3),x, algorithm=""maxima"")","\int \frac{a \sin\left(f x + e\right) + a}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)/(d*sin(f*x + e) + c)^(1/3), x)","F",0
670,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))/(c+d*sin(f*x+e))^(4/3),x, algorithm=""maxima"")","\int \frac{a \sin\left(f x + e\right) + a}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)/(d*sin(f*x + e) + c)^(4/3), x)","F",0
671,1,175,0,1.172250," ","integrate((a+b*sin(f*x+e))*(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\frac{96 \, {\left(f x + e\right)} a c^{3} + 72 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} b c^{2} d + 72 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a c d^{2} + 96 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} b c d^{2} + 32 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a d^{3} + 3 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} b d^{3} - 96 \, b c^{3} \cos\left(f x + e\right) - 288 \, a c^{2} d \cos\left(f x + e\right)}{96 \, f}"," ",0,"1/96*(96*(f*x + e)*a*c^3 + 72*(2*f*x + 2*e - sin(2*f*x + 2*e))*b*c^2*d + 72*(2*f*x + 2*e - sin(2*f*x + 2*e))*a*c*d^2 + 96*(cos(f*x + e)^3 - 3*cos(f*x + e))*b*c*d^2 + 32*(cos(f*x + e)^3 - 3*cos(f*x + e))*a*d^3 + 3*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*b*d^3 - 96*b*c^3*cos(f*x + e) - 288*a*c^2*d*cos(f*x + e))/f","A",0
672,1,112,0,0.403479," ","integrate((a+b*sin(f*x+e))*(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{12 \, {\left(f x + e\right)} a c^{2} + 6 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} b c d + 3 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a d^{2} + 4 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} b d^{2} - 12 \, b c^{2} \cos\left(f x + e\right) - 24 \, a c d \cos\left(f x + e\right)}{12 \, f}"," ",0,"1/12*(12*(f*x + e)*a*c^2 + 6*(2*f*x + 2*e - sin(2*f*x + 2*e))*b*c*d + 3*(2*f*x + 2*e - sin(2*f*x + 2*e))*a*d^2 + 4*(cos(f*x + e)^3 - 3*cos(f*x + e))*b*d^2 - 12*b*c^2*cos(f*x + e) - 24*a*c*d*cos(f*x + e))/f","A",0
673,1,57,0,0.666713," ","integrate((a+b*sin(f*x+e))*(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\frac{4 \, {\left(f x + e\right)} a c + {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} b d - 4 \, b c \cos\left(f x + e\right) - 4 \, a d \cos\left(f x + e\right)}{4 \, f}"," ",0,"1/4*(4*(f*x + e)*a*c + (2*f*x + 2*e - sin(2*f*x + 2*e))*b*d - 4*b*c*cos(f*x + e) - 4*a*d*cos(f*x + e))/f","A",0
674,1,16,0,0.627993," ","integrate(a+b*sin(f*x+e),x, algorithm=""maxima"")","a x - \frac{b \cos\left(f x + e\right)}{f}"," ",0,"a*x - b*cos(f*x + e)/f","A",0
675,-2,0,0,0.000000," ","integrate((a+b*sin(f*x+e))/(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
676,-2,0,0,0.000000," ","integrate((a+b*sin(f*x+e))/(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
677,-2,0,0,0.000000," ","integrate((a+b*sin(f*x+e))/(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
678,1,314,0,0.852867," ","integrate((a+b*sin(f*x+e))^2*(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\frac{480 \, {\left(f x + e\right)} a^{2} c^{3} + 120 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} b^{2} c^{3} + 720 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a b c^{2} d + 480 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} b^{2} c^{2} d + 360 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c d^{2} + 960 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a b c d^{2} + 45 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} b^{2} c d^{2} + 160 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a^{2} d^{3} + 30 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a b d^{3} - 32 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} b^{2} d^{3} - 960 \, a b c^{3} \cos\left(f x + e\right) - 1440 \, a^{2} c^{2} d \cos\left(f x + e\right)}{480 \, f}"," ",0,"1/480*(480*(f*x + e)*a^2*c^3 + 120*(2*f*x + 2*e - sin(2*f*x + 2*e))*b^2*c^3 + 720*(2*f*x + 2*e - sin(2*f*x + 2*e))*a*b*c^2*d + 480*(cos(f*x + e)^3 - 3*cos(f*x + e))*b^2*c^2*d + 360*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^2*c*d^2 + 960*(cos(f*x + e)^3 - 3*cos(f*x + e))*a*b*c*d^2 + 45*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*b^2*c*d^2 + 160*(cos(f*x + e)^3 - 3*cos(f*x + e))*a^2*d^3 + 30*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*a*b*d^3 - 32*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*b^2*d^3 - 960*a*b*c^3*cos(f*x + e) - 1440*a^2*c^2*d*cos(f*x + e))/f","A",0
679,1,208,0,0.747076," ","integrate((a+b*sin(f*x+e))^2*(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{96 \, {\left(f x + e\right)} a^{2} c^{2} + 24 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} b^{2} c^{2} + 96 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a b c d + 64 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} b^{2} c d + 24 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} d^{2} + 64 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a b d^{2} + 3 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} b^{2} d^{2} - 192 \, a b c^{2} \cos\left(f x + e\right) - 192 \, a^{2} c d \cos\left(f x + e\right)}{96 \, f}"," ",0,"1/96*(96*(f*x + e)*a^2*c^2 + 24*(2*f*x + 2*e - sin(2*f*x + 2*e))*b^2*c^2 + 96*(2*f*x + 2*e - sin(2*f*x + 2*e))*a*b*c*d + 64*(cos(f*x + e)^3 - 3*cos(f*x + e))*b^2*c*d + 24*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^2*d^2 + 64*(cos(f*x + e)^3 - 3*cos(f*x + e))*a*b*d^2 + 3*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*b^2*d^2 - 192*a*b*c^2*cos(f*x + e) - 192*a^2*c*d*cos(f*x + e))/f","A",0
680,1,112,0,0.444464," ","integrate((a+b*sin(f*x+e))^2*(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\frac{12 \, {\left(f x + e\right)} a^{2} c + 3 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} b^{2} c + 6 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a b d + 4 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} b^{2} d - 24 \, a b c \cos\left(f x + e\right) - 12 \, a^{2} d \cos\left(f x + e\right)}{12 \, f}"," ",0,"1/12*(12*(f*x + e)*a^2*c + 3*(2*f*x + 2*e - sin(2*f*x + 2*e))*b^2*c + 6*(2*f*x + 2*e - sin(2*f*x + 2*e))*a*b*d + 4*(cos(f*x + e)^3 - 3*cos(f*x + e))*b^2*d - 24*a*b*c*cos(f*x + e) - 12*a^2*d*cos(f*x + e))/f","A",0
681,1,46,0,0.626060," ","integrate((a+b*sin(f*x+e))^2,x, algorithm=""maxima"")","a^{2} x + \frac{{\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} b^{2}}{4 \, f} - \frac{2 \, a b \cos\left(f x + e\right)}{f}"," ",0,"a^2*x + 1/4*(2*f*x + 2*e - sin(2*f*x + 2*e))*b^2/f - 2*a*b*cos(f*x + e)/f","A",0
682,-2,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^2/(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
683,-2,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^2/(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
684,-2,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^2/(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
685,-2,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^2/(c+d*sin(f*x+e))^4,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
686,1,477,0,0.726175," ","integrate((a+b*sin(f*x+e))^3*(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\frac{960 \, {\left(f x + e\right)} a^{3} c^{3} + 720 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a b^{2} c^{3} + 320 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} b^{3} c^{3} + 2160 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} b c^{2} d + 2880 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a b^{2} c^{2} d + 90 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} b^{3} c^{2} d + 720 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{3} c d^{2} + 2880 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a^{2} b c d^{2} + 270 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a b^{2} c d^{2} - 192 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} b^{3} c d^{2} + 320 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a^{3} d^{3} + 90 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} b d^{3} - 192 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} a b^{2} d^{3} + 5 \, {\left(4 \, \sin\left(2 \, f x + 2 \, e\right)^{3} + 60 \, f x + 60 \, e + 9 \, \sin\left(4 \, f x + 4 \, e\right) - 48 \, \sin\left(2 \, f x + 2 \, e\right)\right)} b^{3} d^{3} - 2880 \, a^{2} b c^{3} \cos\left(f x + e\right) - 2880 \, a^{3} c^{2} d \cos\left(f x + e\right)}{960 \, f}"," ",0,"1/960*(960*(f*x + e)*a^3*c^3 + 720*(2*f*x + 2*e - sin(2*f*x + 2*e))*a*b^2*c^3 + 320*(cos(f*x + e)^3 - 3*cos(f*x + e))*b^3*c^3 + 2160*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^2*b*c^2*d + 2880*(cos(f*x + e)^3 - 3*cos(f*x + e))*a*b^2*c^2*d + 90*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*b^3*c^2*d + 720*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^3*c*d^2 + 2880*(cos(f*x + e)^3 - 3*cos(f*x + e))*a^2*b*c*d^2 + 270*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*a*b^2*c*d^2 - 192*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*b^3*c*d^2 + 320*(cos(f*x + e)^3 - 3*cos(f*x + e))*a^3*d^3 + 90*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*a^2*b*d^3 - 192*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*a*b^2*d^3 + 5*(4*sin(2*f*x + 2*e)^3 + 60*f*x + 60*e + 9*sin(4*f*x + 4*e) - 48*sin(2*f*x + 2*e))*b^3*d^3 - 2880*a^2*b*c^3*cos(f*x + e) - 2880*a^3*c^2*d*cos(f*x + e))/f","A",0
687,1,314,0,0.522753," ","integrate((a+b*sin(f*x+e))^3*(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{480 \, {\left(f x + e\right)} a^{3} c^{2} + 360 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a b^{2} c^{2} + 160 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} b^{3} c^{2} + 720 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} b c d + 960 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a b^{2} c d + 30 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} b^{3} c d + 120 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{3} d^{2} + 480 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a^{2} b d^{2} + 45 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a b^{2} d^{2} - 32 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} b^{3} d^{2} - 1440 \, a^{2} b c^{2} \cos\left(f x + e\right) - 960 \, a^{3} c d \cos\left(f x + e\right)}{480 \, f}"," ",0,"1/480*(480*(f*x + e)*a^3*c^2 + 360*(2*f*x + 2*e - sin(2*f*x + 2*e))*a*b^2*c^2 + 160*(cos(f*x + e)^3 - 3*cos(f*x + e))*b^3*c^2 + 720*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^2*b*c*d + 960*(cos(f*x + e)^3 - 3*cos(f*x + e))*a*b^2*c*d + 30*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*b^3*c*d + 120*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^3*d^2 + 480*(cos(f*x + e)^3 - 3*cos(f*x + e))*a^2*b*d^2 + 45*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*a*b^2*d^2 - 32*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*b^3*d^2 - 1440*a^2*b*c^2*cos(f*x + e) - 960*a^3*c*d*cos(f*x + e))/f","A",0
688,1,175,0,0.966994," ","integrate((a+b*sin(f*x+e))^3*(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\frac{96 \, {\left(f x + e\right)} a^{3} c + 72 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a b^{2} c + 32 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} b^{3} c + 72 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} b d + 96 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a b^{2} d + 3 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} b^{3} d - 288 \, a^{2} b c \cos\left(f x + e\right) - 96 \, a^{3} d \cos\left(f x + e\right)}{96 \, f}"," ",0,"1/96*(96*(f*x + e)*a^3*c + 72*(2*f*x + 2*e - sin(2*f*x + 2*e))*a*b^2*c + 32*(cos(f*x + e)^3 - 3*cos(f*x + e))*b^3*c + 72*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^2*b*d + 96*(cos(f*x + e)^3 - 3*cos(f*x + e))*a*b^2*d + 3*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*b^3*d - 288*a^2*b*c*cos(f*x + e) - 96*a^3*d*cos(f*x + e))/f","A",0
689,1,74,0,0.672199," ","integrate((a+b*sin(f*x+e))^3,x, algorithm=""maxima"")","a^{3} x + \frac{3 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a b^{2}}{4 \, f} + \frac{{\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} b^{3}}{3 \, f} - \frac{3 \, a^{2} b \cos\left(f x + e\right)}{f}"," ",0,"a^3*x + 3/4*(2*f*x + 2*e - sin(2*f*x + 2*e))*a*b^2/f + 1/3*(cos(f*x + e)^3 - 3*cos(f*x + e))*b^3/f - 3*a^2*b*cos(f*x + e)/f","A",0
690,-2,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^3/(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
691,-2,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^3/(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
692,-2,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^3/(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
693,-2,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^3/(c+d*sin(f*x+e))^4,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
694,-2,0,0,0.000000," ","integrate((b*B/a+B*sin(x))/(a+b*sin(x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
695,-2,0,0,0.000000," ","integrate((a*B/b+B*sin(x))/(a+b*sin(x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
696,-2,0,0,0.000000," ","integrate((a+b*sin(x))/(b+a*sin(x))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
697,1,36,0,1.224780," ","integrate((2-sin(x))/(2+sin(x)),x, algorithm=""maxima"")","\frac{8}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(\frac{2 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + 1\right)}\right) - 2 \, \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)"," ",0,"8/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*sin(x)/(cos(x) + 1) + 1)) - 2*arctan(sin(x)/(cos(x) + 1))","A",0
698,-2,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^4/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
699,-2,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^3/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
700,-2,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^2/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
701,-2,0,0,0.000000," ","integrate((c+d*sin(f*x+e))/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
702,-2,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
703,-2,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))/(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
704,-2,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))/(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
705,-2,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))/(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
706,-2,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^4/(a+b*sin(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
707,-2,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^3/(a+b*sin(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
708,-2,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^2/(a+b*sin(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
709,-2,0,0,0.000000," ","integrate((c+d*sin(f*x+e))/(a+b*sin(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
710,-2,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
711,-2,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))^2/(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
712,-2,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))^2/(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
713,-2,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))^2/(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
714,-2,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^5/(a+b*sin(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
715,-2,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^4/(a+b*sin(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
716,-2,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^3/(a+b*sin(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
717,-2,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^2/(a+b*sin(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
718,-2,0,0,0.000000," ","integrate((c+d*sin(f*x+e))/(a+b*sin(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
719,-2,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
720,-2,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))^3/(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
721,-2,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))^3/(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
722,-2,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))^3/(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
723,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))*(c+d*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right) + a\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^(5/2), x)","F",0
724,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))*(c+d*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right) + a\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^(3/2), x)","F",0
725,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))*(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right) + a\right)} \sqrt{d \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c), x)","F",0
726,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))/(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{b \sin\left(f x + e\right) + a}{\sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)/sqrt(d*sin(f*x + e) + c), x)","F",0
727,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))/(c+d*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{b \sin\left(f x + e\right) + a}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)/(d*sin(f*x + e) + c)^(3/2), x)","F",0
728,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))/(c+d*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{b \sin\left(f x + e\right) + a}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)/(d*sin(f*x + e) + c)^(5/2), x)","F",0
729,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))/(c+d*sin(f*x+e))^(7/2),x, algorithm=""maxima"")","\int \frac{b \sin\left(f x + e\right) + a}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)/(d*sin(f*x + e) + c)^(7/2), x)","F",0
730,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^2*(c+d*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right) + a\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^2*(d*sin(f*x + e) + c)^(5/2), x)","F",0
731,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^2*(c+d*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right) + a\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^2*(d*sin(f*x + e) + c)^(3/2), x)","F",0
732,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^2*(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right) + a\right)}^{2} \sqrt{d \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^2*sqrt(d*sin(f*x + e) + c), x)","F",0
733,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^2/(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{2}}{\sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^2/sqrt(d*sin(f*x + e) + c), x)","F",0
734,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^2/(c+d*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{2}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^2/(d*sin(f*x + e) + c)^(3/2), x)","F",0
735,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^2/(c+d*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{2}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^2/(d*sin(f*x + e) + c)^(5/2), x)","F",0
736,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^2/(c+d*sin(f*x+e))^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{2}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^2/(d*sin(f*x + e) + c)^(7/2), x)","F",0
737,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^3*(c+d*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right) + a\right)}^{3} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^3*(d*sin(f*x + e) + c)^(5/2), x)","F",0
738,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^3*(c+d*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right) + a\right)}^{3} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^3*(d*sin(f*x + e) + c)^(3/2), x)","F",0
739,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^3*(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right) + a\right)}^{3} \sqrt{d \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^3*sqrt(d*sin(f*x + e) + c), x)","F",0
740,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^3/(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{3}}{\sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^3/sqrt(d*sin(f*x + e) + c), x)","F",0
741,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^3/(c+d*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{3}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^3/(d*sin(f*x + e) + c)^(3/2), x)","F",0
742,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^3/(c+d*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{3}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^3/(d*sin(f*x + e) + c)^(5/2), x)","F",0
743,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^3/(c+d*sin(f*x+e))^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{3}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^3/(d*sin(f*x + e) + c)^(7/2), x)","F",0
744,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^3/(c+d*sin(f*x+e))^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{3}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^3/(d*sin(f*x + e) + c)^(9/2), x)","F",0
745,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(5/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(5/2)/(b*sin(f*x + e) + a), x)","F",0
746,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(3/2)/(b*sin(f*x + e) + a), x)","F",0
747,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sqrt{d \sin\left(f x + e\right) + c}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(sqrt(d*sin(f*x + e) + c)/(b*sin(f*x + e) + a), x)","F",0
748,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))/(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sin\left(f x + e\right) + a\right)} \sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(1/((b*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c)), x)","F",0
749,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))/(c+d*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sin\left(f x + e\right) + a\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^(3/2)), x)","F",0
750,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))/(c+d*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sin\left(f x + e\right) + a\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((b*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^(5/2)), x)","F",0
751,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(7/2)/(a+b*sin(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}}{{\left(b \sin\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(7/2)/(b*sin(f*x + e) + a)^2, x)","F",0
752,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(5/2)/(a+b*sin(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}{{\left(b \sin\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(5/2)/(b*sin(f*x + e) + a)^2, x)","F",0
753,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{{\left(b \sin\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(3/2)/(b*sin(f*x + e) + a)^2, x)","F",0
754,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{\sqrt{d \sin\left(f x + e\right) + c}}{{\left(b \sin\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(d*sin(f*x + e) + c)/(b*sin(f*x + e) + a)^2, x)","F",0
755,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))^2/(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sin\left(f x + e\right) + a\right)}^{2} \sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(1/((b*sin(f*x + e) + a)^2*sqrt(d*sin(f*x + e) + c)), x)","F",0
756,-1,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))^2/(c+d*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
757,-1,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))^2/(c+d*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
758,-1,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(9/2)/(a+b*sin(f*x+e))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
759,-1,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(7/2)/(a+b*sin(f*x+e))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
760,-1,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(5/2)/(a+b*sin(f*x+e))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
761,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e))^3,x, algorithm=""maxima"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{{\left(b \sin\left(f x + e\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(3/2)/(b*sin(f*x + e) + a)^3, x)","F",0
762,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e))^3,x, algorithm=""maxima"")","\int \frac{\sqrt{d \sin\left(f x + e\right) + c}}{{\left(b \sin\left(f x + e\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(d*sin(f*x + e) + c)/(b*sin(f*x + e) + a)^3, x)","F",0
763,-1,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))^3/(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
764,-1,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))^3/(c+d*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
765,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(1/2)*(c+d*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \sqrt{b \sin\left(f x + e\right) + a} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^(5/2), x)","F",0
766,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(1/2)*(c+d*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \sqrt{b \sin\left(f x + e\right) + a} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^(3/2), x)","F",0
767,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(1/2)*(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c), x)","F",0
768,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{b \sin\left(f x + e\right) + a}}{\sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e) + a)/sqrt(d*sin(f*x + e) + c), x)","F",0
769,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{b \sin\left(f x + e\right) + a}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e) + a)/(d*sin(f*x + e) + c)^(3/2), x)","F",0
770,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{\sqrt{b \sin\left(f x + e\right) + a}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e) + a)/(d*sin(f*x + e) + c)^(5/2), x)","F",0
771,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(3/2)*(c+d*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^(3/2)*(d*sin(f*x + e) + c)^(5/2), x)","F",0
772,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(3/2)*(c+d*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^(3/2)*(d*sin(f*x + e) + c)^(3/2), x)","F",0
773,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(3/2)*(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} \sqrt{d \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^(3/2)*sqrt(d*sin(f*x + e) + c), x)","F",0
774,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}{\sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^(3/2)/sqrt(d*sin(f*x + e) + c), x)","F",0
775,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^(3/2)/(d*sin(f*x + e) + c)^(3/2), x)","F",0
776,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^(3/2)/(d*sin(f*x + e) + c)^(5/2), x)","F",0
777,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(5/2)*(c+d*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^(5/2)*(d*sin(f*x + e) + c)^(5/2), x)","F",0
778,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(5/2)*(c+d*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^(5/2)*(d*sin(f*x + e) + c)^(3/2), x)","F",0
779,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(5/2)*(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} \sqrt{d \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^(5/2)*sqrt(d*sin(f*x + e) + c), x)","F",0
780,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}{\sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^(5/2)/sqrt(d*sin(f*x + e) + c), x)","F",0
781,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^(5/2)/(d*sin(f*x + e) + c)^(3/2), x)","F",0
782,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^(5/2)/(d*sin(f*x + e) + c)^(5/2), x)","F",0
783,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(5/2)/(a+b*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}{\sqrt{b \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(5/2)/sqrt(b*sin(f*x + e) + a), x)","F",0
784,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{\sqrt{b \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(3/2)/sqrt(b*sin(f*x + e) + a), x)","F",0
785,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{d \sin\left(f x + e\right) + c}}{\sqrt{b \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate(sqrt(d*sin(f*x + e) + c)/sqrt(b*sin(f*x + e) + a), x)","F",0
786,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(1/(sqrt(b*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c)), x)","F",0
787,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \sin\left(f x + e\right) + a} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(b*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^(3/2)), x)","F",0
788,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \sin\left(f x + e\right) + a} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(b*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^(5/2)), x)","F",0
789,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(5/2)/(a+b*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(5/2)/(b*sin(f*x + e) + a)^(3/2), x)","F",0
790,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(3/2)/(b*sin(f*x + e) + a)^(3/2), x)","F",0
791,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{d \sin\left(f x + e\right) + c}}{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(d*sin(f*x + e) + c)/(b*sin(f*x + e) + a)^(3/2), x)","F",0
792,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} \sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(1/((b*sin(f*x + e) + a)^(3/2)*sqrt(d*sin(f*x + e) + c)), x)","F",0
793,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*sin(f*x + e) + a)^(3/2)*(d*sin(f*x + e) + c)^(3/2)), x)","F",0
794,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((b*sin(f*x + e) + a)^(3/2)*(d*sin(f*x + e) + c)^(5/2)), x)","F",0
795,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(5/2)/(a+b*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(5/2)/(b*sin(f*x + e) + a)^(5/2), x)","F",0
796,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(3/2)/(b*sin(f*x + e) + a)^(5/2), x)","F",0
797,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{\sqrt{d \sin\left(f x + e\right) + c}}{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(d*sin(f*x + e) + c)/(b*sin(f*x + e) + a)^(5/2), x)","F",0
798,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} \sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(1/((b*sin(f*x + e) + a)^(5/2)*sqrt(d*sin(f*x + e) + c)), x)","F",0
799,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*sin(f*x + e) + a)^(5/2)*(d*sin(f*x + e) + c)^(3/2)), x)","F",0
800,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((b*sin(f*x + e) + a)^(5/2)*(d*sin(f*x + e) + c)^(5/2)), x)","F",0
801,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right) + a\right)}^{m} {\left(d \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^m*(d*sin(f*x + e) + c)^n, x)","F",0
802,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^m*(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\int {\left(d \sin\left(f x + e\right) + c\right)}^{2} {\left(b \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^2*(b*sin(f*x + e) + a)^m, x)","F",0
803,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^m*(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\int {\left(d \sin\left(f x + e\right) + c\right)} {\left(b \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)*(b*sin(f*x + e) + a)^m, x)","F",0
804,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^m, x)","F",0
805,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^m/(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{m}}{d \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^m/(d*sin(f*x + e) + c), x)","F",0
806,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^m/(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{m}}{{\left(d \sin\left(f x + e\right) + c\right)}^{2}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^m/(d*sin(f*x + e) + c)^2, x)","F",0
807,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^m/(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
808,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^m*(c+d*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}} {\left(b \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(5/2)*(b*sin(f*x + e) + a)^m, x)","F",0
809,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^m*(c+d*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}} {\left(b \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(3/2)*(b*sin(f*x + e) + a)^m, x)","F",0
810,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^m*(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sqrt{d \sin\left(f x + e\right) + c} {\left(b \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate(sqrt(d*sin(f*x + e) + c)*(b*sin(f*x + e) + a)^m, x)","F",0
811,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^m/(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{m}}{\sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^m/sqrt(d*sin(f*x + e) + c), x)","F",0
812,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^m/(c+d*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{m}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^m/(d*sin(f*x + e) + c)^(3/2), x)","F",0
813,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^m/(c+d*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{m}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^m/(d*sin(f*x + e) + c)^(5/2), x)","F",0
814,0,0,0,0.000000," ","integrate((d*csc(f*x+e))^n*(a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{3} \left(d \csc\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^3*(d*csc(f*x + e))^n, x)","F",0
815,0,0,0,0.000000," ","integrate((d*csc(f*x+e))^n*(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{2} \left(d \csc\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^2*(d*csc(f*x + e))^n, x)","F",0
816,0,0,0,0.000000," ","integrate((d*csc(f*x+e))^n*(a+a*sin(f*x+e)),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)} \left(d \csc\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)*(d*csc(f*x + e))^n, x)","F",0
817,0,0,0,0.000000," ","integrate((d*csc(f*x+e))^n/(a+a*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(d \csc\left(f x + e\right)\right)^{n}}{a \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*csc(f*x + e))^n/(a*sin(f*x + e) + a), x)","F",0
818,0,0,0,0.000000," ","integrate((d*csc(f*x+e))^n/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{\left(d \csc\left(f x + e\right)\right)^{n}}{{\left(a \sin\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*csc(f*x + e))^n/(a*sin(f*x + e) + a)^2, x)","F",0
819,0,0,0,0.000000," ","integrate((c*(d*sin(f*x+e))^p)^n*(a+a*sin(f*x+e))^m,x, algorithm=""maxima"")","\int \left(\left(d \sin\left(f x + e\right)\right)^{p} c\right)^{n} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate(((d*sin(f*x + e))^p*c)^n*(a*sin(f*x + e) + a)^m, x)","F",0
820,0,0,0,0.000000," ","integrate((c*(d*sin(f*x+e))^p)^n*(a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{3} \left(\left(d \sin\left(f x + e\right)\right)^{p} c\right)^{n}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^3*((d*sin(f*x + e))^p*c)^n, x)","F",0
821,0,0,0,0.000000," ","integrate((c*(d*sin(f*x+e))^p)^n*(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{2} \left(\left(d \sin\left(f x + e\right)\right)^{p} c\right)^{n}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^2*((d*sin(f*x + e))^p*c)^n, x)","F",0
822,0,0,0,0.000000," ","integrate((c*(d*sin(f*x+e))^p)^n*(a+a*sin(f*x+e)),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)} \left(\left(d \sin\left(f x + e\right)\right)^{p} c\right)^{n}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)*((d*sin(f*x + e))^p*c)^n, x)","F",0
823,0,0,0,0.000000," ","integrate((c*(d*sin(f*x+e))^p)^n/(a+a*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(\left(d \sin\left(f x + e\right)\right)^{p} c\right)^{n}}{a \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(((d*sin(f*x + e))^p*c)^n/(a*sin(f*x + e) + a), x)","F",0
824,0,0,0,0.000000," ","integrate((c*(d*sin(f*x+e))^p)^n/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{\left(\left(d \sin\left(f x + e\right)\right)^{p} c\right)^{n}}{{\left(a \sin\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(((d*sin(f*x + e))^p*c)^n/(a*sin(f*x + e) + a)^2, x)","F",0
825,0,0,0,0.000000," ","integrate((d*csc(f*x+e))^n*(a+b*sin(f*x+e))^3,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right) + a\right)}^{3} \left(d \csc\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^3*(d*csc(f*x + e))^n, x)","F",0
826,0,0,0,0.000000," ","integrate((d*csc(f*x+e))^n*(a+b*sin(f*x+e))^2,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right) + a\right)}^{2} \left(d \csc\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^2*(d*csc(f*x + e))^n, x)","F",0
827,0,0,0,0.000000," ","integrate((d*csc(f*x+e))^n*(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right) + a\right)} \left(d \csc\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)*(d*csc(f*x + e))^n, x)","F",0
828,0,0,0,0.000000," ","integrate((d*csc(f*x+e))^n/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(d \csc\left(f x + e\right)\right)^{n}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*csc(f*x + e))^n/(b*sin(f*x + e) + a), x)","F",0
829,0,0,0,0.000000," ","integrate((d*csc(f*x+e))^n/(a+b*sin(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{\left(d \csc\left(f x + e\right)\right)^{n}}{{\left(b \sin\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*csc(f*x + e))^n/(b*sin(f*x + e) + a)^2, x)","F",0
830,0,0,0,0.000000," ","integrate((d*csc(f*x+e))^n/(a+b*sin(f*x+e))^3,x, algorithm=""maxima"")","\int \frac{\left(d \csc\left(f x + e\right)\right)^{n}}{{\left(b \sin\left(f x + e\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((d*csc(f*x + e))^n/(b*sin(f*x + e) + a)^3, x)","F",0
831,0,0,0,0.000000," ","integrate((c*(d*sin(f*x+e))^p)^n*(a+b*sin(f*x+e))^m,x, algorithm=""maxima"")","\int \left(\left(d \sin\left(f x + e\right)\right)^{p} c\right)^{n} {\left(b \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate(((d*sin(f*x + e))^p*c)^n*(b*sin(f*x + e) + a)^m, x)","F",0
832,0,0,0,0.000000," ","integrate((c*(d*sin(f*x+e))^p)^n*(a+b*sin(f*x+e))^3,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right) + a\right)}^{3} \left(\left(d \sin\left(f x + e\right)\right)^{p} c\right)^{n}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^3*((d*sin(f*x + e))^p*c)^n, x)","F",0
833,0,0,0,0.000000," ","integrate((c*(d*sin(f*x+e))^p)^n*(a+b*sin(f*x+e))^2,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right) + a\right)}^{2} \left(\left(d \sin\left(f x + e\right)\right)^{p} c\right)^{n}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^2*((d*sin(f*x + e))^p*c)^n, x)","F",0
834,0,0,0,0.000000," ","integrate((c*(d*sin(f*x+e))^p)^n*(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right) + a\right)} \left(\left(d \sin\left(f x + e\right)\right)^{p} c\right)^{n}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)*((d*sin(f*x + e))^p*c)^n, x)","F",0
835,0,0,0,0.000000," ","integrate((c*(d*sin(f*x+e))^p)^n/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(\left(d \sin\left(f x + e\right)\right)^{p} c\right)^{n}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(((d*sin(f*x + e))^p*c)^n/(b*sin(f*x + e) + a), x)","F",0
836,0,0,0,0.000000," ","integrate((c*(d*sin(f*x+e))^p)^n/(a+b*sin(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{\left(\left(d \sin\left(f x + e\right)\right)^{p} c\right)^{n}}{{\left(b \sin\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(((d*sin(f*x + e))^p*c)^n/(b*sin(f*x + e) + a)^2, x)","F",0
837,0,0,0,0.000000," ","integrate((c*(d*sin(f*x+e))^p)^n/(a+b*sin(f*x+e))^3,x, algorithm=""maxima"")","\int \frac{\left(\left(d \sin\left(f x + e\right)\right)^{p} c\right)^{n}}{{\left(b \sin\left(f x + e\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(((d*sin(f*x + e))^p*c)^n/(b*sin(f*x + e) + a)^3, x)","F",0
