1,0,0,0,0.000000," ","integrate((a*sin(x)^2)^(5/2),x, algorithm=""maxima"")","\int \left(a \sin\left(x\right)^{2}\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a*sin(x)^2)^(5/2), x)","F",0
2,0,0,0,0.000000," ","integrate((a*sin(x)^2)^(3/2),x, algorithm=""maxima"")","\int \left(a \sin\left(x\right)^{2}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*sin(x)^2)^(3/2), x)","F",0
3,1,13,0,0.705075," ","integrate((a*sin(x)^2)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{a}}{\sqrt{\tan\left(x\right)^{2} + 1}}"," ",0,"-sqrt(a)/sqrt(tan(x)^2 + 1)","A",0
4,1,26,0,0.634225," ","integrate(1/(a*sin(x)^2)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{-a} {\left(\arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right) - \arctan\left(\sin\left(x\right), \cos\left(x\right) - 1\right)\right)}}{a}"," ",0,"sqrt(-a)*(arctan2(sin(x), cos(x) + 1) - arctan2(sin(x), cos(x) - 1))/a","A",0
5,1,314,0,0.689692," ","integrate(1/(a*sin(x)^2)^(3/2),x, algorithm=""maxima"")","-\frac{{\left({\left(2 \, {\left(2 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) - \cos\left(4 \, x\right)^{2} - 4 \, \cos\left(2 \, x\right)^{2} - \sin\left(4 \, x\right)^{2} + 4 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) - 4 \, \sin\left(2 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right) - 1\right)} \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right) - {\left(2 \, {\left(2 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) - \cos\left(4 \, x\right)^{2} - 4 \, \cos\left(2 \, x\right)^{2} - \sin\left(4 \, x\right)^{2} + 4 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) - 4 \, \sin\left(2 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right) - 1\right)} \arctan\left(\sin\left(x\right), \cos\left(x\right) - 1\right) + 2 \, {\left(\sin\left(3 \, x\right) + \sin\left(x\right)\right)} \cos\left(4 \, x\right) - 2 \, {\left(\cos\left(3 \, x\right) + \cos\left(x\right)\right)} \sin\left(4 \, x\right) - 2 \, {\left(2 \, \cos\left(2 \, x\right) - 1\right)} \sin\left(3 \, x\right) + 4 \, \cos\left(3 \, x\right) \sin\left(2 \, x\right) + 4 \, \cos\left(x\right) \sin\left(2 \, x\right) - 4 \, \cos\left(2 \, x\right) \sin\left(x\right) + 2 \, \sin\left(x\right)\right)} \sqrt{-a}}{2 \, {\left(a^{2} \cos\left(4 \, x\right)^{2} + 4 \, a^{2} \cos\left(2 \, x\right)^{2} + a^{2} \sin\left(4 \, x\right)^{2} - 4 \, a^{2} \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 4 \, a^{2} \sin\left(2 \, x\right)^{2} - 4 \, a^{2} \cos\left(2 \, x\right) + a^{2} - 2 \, {\left(2 \, a^{2} \cos\left(2 \, x\right) - a^{2}\right)} \cos\left(4 \, x\right)\right)}}"," ",0,"-1/2*((2*(2*cos(2*x) - 1)*cos(4*x) - cos(4*x)^2 - 4*cos(2*x)^2 - sin(4*x)^2 + 4*sin(4*x)*sin(2*x) - 4*sin(2*x)^2 + 4*cos(2*x) - 1)*arctan2(sin(x), cos(x) + 1) - (2*(2*cos(2*x) - 1)*cos(4*x) - cos(4*x)^2 - 4*cos(2*x)^2 - sin(4*x)^2 + 4*sin(4*x)*sin(2*x) - 4*sin(2*x)^2 + 4*cos(2*x) - 1)*arctan2(sin(x), cos(x) - 1) + 2*(sin(3*x) + sin(x))*cos(4*x) - 2*(cos(3*x) + cos(x))*sin(4*x) - 2*(2*cos(2*x) - 1)*sin(3*x) + 4*cos(3*x)*sin(2*x) + 4*cos(x)*sin(2*x) - 4*cos(2*x)*sin(x) + 2*sin(x))*sqrt(-a)/(a^2*cos(4*x)^2 + 4*a^2*cos(2*x)^2 + a^2*sin(4*x)^2 - 4*a^2*sin(4*x)*sin(2*x) + 4*a^2*sin(2*x)^2 - 4*a^2*cos(2*x) + a^2 - 2*(2*a^2*cos(2*x) - a^2)*cos(4*x))","B",0
6,1,931,0,0.868416," ","integrate(1/(a*sin(x)^2)^(5/2),x, algorithm=""maxima"")","-\frac{{\left(3 \, {\left(2 \, {\left(4 \, \cos\left(6 \, x\right) - 6 \, \cos\left(4 \, x\right) + 4 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(8 \, x\right) - \cos\left(8 \, x\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, x\right) - 4 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(6 \, x\right) - 16 \, \cos\left(6 \, x\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) - 36 \, \cos\left(4 \, x\right)^{2} - 16 \, \cos\left(2 \, x\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, x\right) - 3 \, \sin\left(4 \, x\right) + 2 \, \sin\left(2 \, x\right)\right)} \sin\left(8 \, x\right) - \sin\left(8 \, x\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, x\right) - 2 \, \sin\left(2 \, x\right)\right)} \sin\left(6 \, x\right) - 16 \, \sin\left(6 \, x\right)^{2} - 36 \, \sin\left(4 \, x\right)^{2} + 48 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) - 16 \, \sin\left(2 \, x\right)^{2} + 8 \, \cos\left(2 \, x\right) - 1\right)} \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right) - 3 \, {\left(2 \, {\left(4 \, \cos\left(6 \, x\right) - 6 \, \cos\left(4 \, x\right) + 4 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(8 \, x\right) - \cos\left(8 \, x\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, x\right) - 4 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(6 \, x\right) - 16 \, \cos\left(6 \, x\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) - 36 \, \cos\left(4 \, x\right)^{2} - 16 \, \cos\left(2 \, x\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, x\right) - 3 \, \sin\left(4 \, x\right) + 2 \, \sin\left(2 \, x\right)\right)} \sin\left(8 \, x\right) - \sin\left(8 \, x\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, x\right) - 2 \, \sin\left(2 \, x\right)\right)} \sin\left(6 \, x\right) - 16 \, \sin\left(6 \, x\right)^{2} - 36 \, \sin\left(4 \, x\right)^{2} + 48 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) - 16 \, \sin\left(2 \, x\right)^{2} + 8 \, \cos\left(2 \, x\right) - 1\right)} \arctan\left(\sin\left(x\right), \cos\left(x\right) - 1\right) + 2 \, {\left(3 \, \sin\left(7 \, x\right) - 11 \, \sin\left(5 \, x\right) - 11 \, \sin\left(3 \, x\right) + 3 \, \sin\left(x\right)\right)} \cos\left(8 \, x\right) + 12 \, {\left(2 \, \sin\left(6 \, x\right) - 3 \, \sin\left(4 \, x\right) + 2 \, \sin\left(2 \, x\right)\right)} \cos\left(7 \, x\right) + 8 \, {\left(11 \, \sin\left(5 \, x\right) + 11 \, \sin\left(3 \, x\right) - 3 \, \sin\left(x\right)\right)} \cos\left(6 \, x\right) + 44 \, {\left(3 \, \sin\left(4 \, x\right) - 2 \, \sin\left(2 \, x\right)\right)} \cos\left(5 \, x\right) - 12 \, {\left(11 \, \sin\left(3 \, x\right) - 3 \, \sin\left(x\right)\right)} \cos\left(4 \, x\right) - 2 \, {\left(3 \, \cos\left(7 \, x\right) - 11 \, \cos\left(5 \, x\right) - 11 \, \cos\left(3 \, x\right) + 3 \, \cos\left(x\right)\right)} \sin\left(8 \, x\right) - 6 \, {\left(4 \, \cos\left(6 \, x\right) - 6 \, \cos\left(4 \, x\right) + 4 \, \cos\left(2 \, x\right) - 1\right)} \sin\left(7 \, x\right) - 8 \, {\left(11 \, \cos\left(5 \, x\right) + 11 \, \cos\left(3 \, x\right) - 3 \, \cos\left(x\right)\right)} \sin\left(6 \, x\right) - 22 \, {\left(6 \, \cos\left(4 \, x\right) - 4 \, \cos\left(2 \, x\right) + 1\right)} \sin\left(5 \, x\right) + 12 \, {\left(11 \, \cos\left(3 \, x\right) - 3 \, \cos\left(x\right)\right)} \sin\left(4 \, x\right) + 22 \, {\left(4 \, \cos\left(2 \, x\right) - 1\right)} \sin\left(3 \, x\right) - 88 \, \cos\left(3 \, x\right) \sin\left(2 \, x\right) + 24 \, \cos\left(x\right) \sin\left(2 \, x\right) - 24 \, \cos\left(2 \, x\right) \sin\left(x\right) + 6 \, \sin\left(x\right)\right)} \sqrt{-a}}{8 \, {\left(a^{3} \cos\left(8 \, x\right)^{2} + 16 \, a^{3} \cos\left(6 \, x\right)^{2} + 36 \, a^{3} \cos\left(4 \, x\right)^{2} + 16 \, a^{3} \cos\left(2 \, x\right)^{2} + a^{3} \sin\left(8 \, x\right)^{2} + 16 \, a^{3} \sin\left(6 \, x\right)^{2} + 36 \, a^{3} \sin\left(4 \, x\right)^{2} - 48 \, a^{3} \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 16 \, a^{3} \sin\left(2 \, x\right)^{2} - 8 \, a^{3} \cos\left(2 \, x\right) + a^{3} - 2 \, {\left(4 \, a^{3} \cos\left(6 \, x\right) - 6 \, a^{3} \cos\left(4 \, x\right) + 4 \, a^{3} \cos\left(2 \, x\right) - a^{3}\right)} \cos\left(8 \, x\right) - 8 \, {\left(6 \, a^{3} \cos\left(4 \, x\right) - 4 \, a^{3} \cos\left(2 \, x\right) + a^{3}\right)} \cos\left(6 \, x\right) - 12 \, {\left(4 \, a^{3} \cos\left(2 \, x\right) - a^{3}\right)} \cos\left(4 \, x\right) - 4 \, {\left(2 \, a^{3} \sin\left(6 \, x\right) - 3 \, a^{3} \sin\left(4 \, x\right) + 2 \, a^{3} \sin\left(2 \, x\right)\right)} \sin\left(8 \, x\right) - 16 \, {\left(3 \, a^{3} \sin\left(4 \, x\right) - 2 \, a^{3} \sin\left(2 \, x\right)\right)} \sin\left(6 \, x\right)\right)}}"," ",0,"-1/8*(3*(2*(4*cos(6*x) - 6*cos(4*x) + 4*cos(2*x) - 1)*cos(8*x) - cos(8*x)^2 + 8*(6*cos(4*x) - 4*cos(2*x) + 1)*cos(6*x) - 16*cos(6*x)^2 + 12*(4*cos(2*x) - 1)*cos(4*x) - 36*cos(4*x)^2 - 16*cos(2*x)^2 + 4*(2*sin(6*x) - 3*sin(4*x) + 2*sin(2*x))*sin(8*x) - sin(8*x)^2 + 16*(3*sin(4*x) - 2*sin(2*x))*sin(6*x) - 16*sin(6*x)^2 - 36*sin(4*x)^2 + 48*sin(4*x)*sin(2*x) - 16*sin(2*x)^2 + 8*cos(2*x) - 1)*arctan2(sin(x), cos(x) + 1) - 3*(2*(4*cos(6*x) - 6*cos(4*x) + 4*cos(2*x) - 1)*cos(8*x) - cos(8*x)^2 + 8*(6*cos(4*x) - 4*cos(2*x) + 1)*cos(6*x) - 16*cos(6*x)^2 + 12*(4*cos(2*x) - 1)*cos(4*x) - 36*cos(4*x)^2 - 16*cos(2*x)^2 + 4*(2*sin(6*x) - 3*sin(4*x) + 2*sin(2*x))*sin(8*x) - sin(8*x)^2 + 16*(3*sin(4*x) - 2*sin(2*x))*sin(6*x) - 16*sin(6*x)^2 - 36*sin(4*x)^2 + 48*sin(4*x)*sin(2*x) - 16*sin(2*x)^2 + 8*cos(2*x) - 1)*arctan2(sin(x), cos(x) - 1) + 2*(3*sin(7*x) - 11*sin(5*x) - 11*sin(3*x) + 3*sin(x))*cos(8*x) + 12*(2*sin(6*x) - 3*sin(4*x) + 2*sin(2*x))*cos(7*x) + 8*(11*sin(5*x) + 11*sin(3*x) - 3*sin(x))*cos(6*x) + 44*(3*sin(4*x) - 2*sin(2*x))*cos(5*x) - 12*(11*sin(3*x) - 3*sin(x))*cos(4*x) - 2*(3*cos(7*x) - 11*cos(5*x) - 11*cos(3*x) + 3*cos(x))*sin(8*x) - 6*(4*cos(6*x) - 6*cos(4*x) + 4*cos(2*x) - 1)*sin(7*x) - 8*(11*cos(5*x) + 11*cos(3*x) - 3*cos(x))*sin(6*x) - 22*(6*cos(4*x) - 4*cos(2*x) + 1)*sin(5*x) + 12*(11*cos(3*x) - 3*cos(x))*sin(4*x) + 22*(4*cos(2*x) - 1)*sin(3*x) - 88*cos(3*x)*sin(2*x) + 24*cos(x)*sin(2*x) - 24*cos(2*x)*sin(x) + 6*sin(x))*sqrt(-a)/(a^3*cos(8*x)^2 + 16*a^3*cos(6*x)^2 + 36*a^3*cos(4*x)^2 + 16*a^3*cos(2*x)^2 + a^3*sin(8*x)^2 + 16*a^3*sin(6*x)^2 + 36*a^3*sin(4*x)^2 - 48*a^3*sin(4*x)*sin(2*x) + 16*a^3*sin(2*x)^2 - 8*a^3*cos(2*x) + a^3 - 2*(4*a^3*cos(6*x) - 6*a^3*cos(4*x) + 4*a^3*cos(2*x) - a^3)*cos(8*x) - 8*(6*a^3*cos(4*x) - 4*a^3*cos(2*x) + a^3)*cos(6*x) - 12*(4*a^3*cos(2*x) - a^3)*cos(4*x) - 4*(2*a^3*sin(6*x) - 3*a^3*sin(4*x) + 2*a^3*sin(2*x))*sin(8*x) - 16*(3*a^3*sin(4*x) - 2*a^3*sin(2*x))*sin(6*x))","B",0
7,0,0,0,0.000000," ","integrate((a*sin(x)^3)^(5/2),x, algorithm=""maxima"")","\int \left(a \sin\left(x\right)^{3}\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a*sin(x)^3)^(5/2), x)","F",0
8,0,0,0,0.000000," ","integrate((a*sin(x)^3)^(3/2),x, algorithm=""maxima"")","\int \left(a \sin\left(x\right)^{3}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*sin(x)^3)^(3/2), x)","F",0
9,0,0,0,0.000000," ","integrate((a*sin(x)^3)^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(x\right)^{3}}\,{d x}"," ",0,"integrate(sqrt(a*sin(x)^3), x)","F",0
10,0,0,0,0.000000," ","integrate(1/(a*sin(x)^3)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{a \sin\left(x\right)^{3}}}\,{d x}"," ",0,"integrate(1/sqrt(a*sin(x)^3), x)","F",0
11,0,0,0,0.000000," ","integrate(1/(a*sin(x)^3)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{\left(a \sin\left(x\right)^{3}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sin(x)^3)^(-3/2), x)","F",0
12,0,0,0,0.000000," ","integrate(1/(a*sin(x)^3)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{\left(a \sin\left(x\right)^{3}\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sin(x)^3)^(-5/2), x)","F",0
13,1,85,0,0.543974," ","integrate((a*sin(x)^4)^(5/2),x, algorithm=""maxima"")","\frac{63}{256} \, a^{\frac{5}{2}} x - \frac{965 \, a^{\frac{5}{2}} \tan\left(x\right)^{9} + 2370 \, a^{\frac{5}{2}} \tan\left(x\right)^{7} + 2688 \, a^{\frac{5}{2}} \tan\left(x\right)^{5} + 1470 \, a^{\frac{5}{2}} \tan\left(x\right)^{3} + 315 \, a^{\frac{5}{2}} \tan\left(x\right)}{1280 \, {\left(\tan\left(x\right)^{10} + 5 \, \tan\left(x\right)^{8} + 10 \, \tan\left(x\right)^{6} + 10 \, \tan\left(x\right)^{4} + 5 \, \tan\left(x\right)^{2} + 1\right)}}"," ",0,"63/256*a^(5/2)*x - 1/1280*(965*a^(5/2)*tan(x)^9 + 2370*a^(5/2)*tan(x)^7 + 2688*a^(5/2)*tan(x)^5 + 1470*a^(5/2)*tan(x)^3 + 315*a^(5/2)*tan(x))/(tan(x)^10 + 5*tan(x)^8 + 10*tan(x)^6 + 10*tan(x)^4 + 5*tan(x)^2 + 1)","A",0
14,1,55,0,0.609653," ","integrate((a*sin(x)^4)^(3/2),x, algorithm=""maxima"")","\frac{5}{16} \, a^{\frac{3}{2}} x - \frac{33 \, a^{\frac{3}{2}} \tan\left(x\right)^{5} + 40 \, a^{\frac{3}{2}} \tan\left(x\right)^{3} + 15 \, a^{\frac{3}{2}} \tan\left(x\right)}{48 \, {\left(\tan\left(x\right)^{6} + 3 \, \tan\left(x\right)^{4} + 3 \, \tan\left(x\right)^{2} + 1\right)}}"," ",0,"5/16*a^(3/2)*x - 1/48*(33*a^(3/2)*tan(x)^5 + 40*a^(3/2)*tan(x)^3 + 15*a^(3/2)*tan(x))/(tan(x)^6 + 3*tan(x)^4 + 3*tan(x)^2 + 1)","A",0
15,1,22,0,0.476525," ","integrate((a*sin(x)^4)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, \sqrt{a} x - \frac{\sqrt{a} \tan\left(x\right)}{2 \, {\left(\tan\left(x\right)^{2} + 1\right)}}"," ",0,"1/2*sqrt(a)*x - 1/2*sqrt(a)*tan(x)/(tan(x)^2 + 1)","A",0
16,1,9,0,0.516970," ","integrate(1/(a*sin(x)^4)^(1/2),x, algorithm=""maxima"")","-\frac{1}{\sqrt{a} \tan\left(x\right)}"," ",0,"-1/(sqrt(a)*tan(x))","A",0
17,1,23,0,0.720583," ","integrate(1/(a*sin(x)^4)^(3/2),x, algorithm=""maxima"")","-\frac{15 \, \tan\left(x\right)^{4} + 10 \, \tan\left(x\right)^{2} + 3}{15 \, a^{\frac{3}{2}} \tan\left(x\right)^{5}}"," ",0,"-1/15*(15*tan(x)^4 + 10*tan(x)^2 + 3)/(a^(3/2)*tan(x)^5)","A",0
18,1,35,0,0.588757," ","integrate(1/(a*sin(x)^4)^(5/2),x, algorithm=""maxima"")","-\frac{315 \, \tan\left(x\right)^{8} + 420 \, \tan\left(x\right)^{6} + 378 \, \tan\left(x\right)^{4} + 180 \, \tan\left(x\right)^{2} + 35}{315 \, a^{\frac{5}{2}} \tan\left(x\right)^{9}}"," ",0,"-1/315*(315*tan(x)^8 + 420*tan(x)^6 + 378*tan(x)^4 + 180*tan(x)^2 + 35)/(a^(5/2)*tan(x)^9)","A",0
19,0,0,0,0.000000," ","integrate((c*sin(b*x+a)^m)^(5/2),x, algorithm=""maxima"")","\int \left(c \sin\left(b x + a\right)^{m}\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((c*sin(b*x + a)^m)^(5/2), x)","F",0
20,0,0,0,0.000000," ","integrate((c*sin(b*x+a)^m)^(3/2),x, algorithm=""maxima"")","\int \left(c \sin\left(b x + a\right)^{m}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((c*sin(b*x + a)^m)^(3/2), x)","F",0
21,0,0,0,0.000000," ","integrate((c*sin(b*x+a)^m)^(1/2),x, algorithm=""maxima"")","\int \sqrt{c \sin\left(b x + a\right)^{m}}\,{d x}"," ",0,"integrate(sqrt(c*sin(b*x + a)^m), x)","F",0
22,0,0,0,0.000000," ","integrate(1/(c*sin(b*x+a)^m)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{c \sin\left(b x + a\right)^{m}}}\,{d x}"," ",0,"integrate(1/sqrt(c*sin(b*x + a)^m), x)","F",0
23,0,0,0,0.000000," ","integrate(1/(c*sin(b*x+a)^m)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{\left(c \sin\left(b x + a\right)^{m}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c*sin(b*x + a)^m)^(-3/2), x)","F",0
24,0,0,0,0.000000," ","integrate(1/(c*sin(b*x+a)^m)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{\left(c \sin\left(b x + a\right)^{m}\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((c*sin(b*x + a)^m)^(-5/2), x)","F",0
25,0,0,0,0.000000," ","integrate((b*sin(d*x+c)^n)^p,x, algorithm=""maxima"")","\int \left(b \sin\left(d x + c\right)^{n}\right)^{p}\,{d x}"," ",0,"integrate((b*sin(d*x + c)^n)^p, x)","F",0
26,0,0,0,0.000000," ","integrate((c*sin(b*x+a)^2)^p,x, algorithm=""maxima"")","\int \left(c \sin\left(b x + a\right)^{2}\right)^{p}\,{d x}"," ",0,"integrate((c*sin(b*x + a)^2)^p, x)","F",0
27,0,0,0,0.000000," ","integrate((c*sin(b*x+a)^3)^p,x, algorithm=""maxima"")","\int \left(c \sin\left(b x + a\right)^{3}\right)^{p}\,{d x}"," ",0,"integrate((c*sin(b*x + a)^3)^p, x)","F",0
28,0,0,0,0.000000," ","integrate((c*sin(b*x+a)^4)^p,x, algorithm=""maxima"")","\int \left(c \sin\left(b x + a\right)^{4}\right)^{p}\,{d x}"," ",0,"integrate((c*sin(b*x + a)^4)^p, x)","F",0
29,0,0,0,0.000000," ","integrate((c*sin(b*x+a)^n)^(1/n),x, algorithm=""maxima"")","\int \left(c \sin\left(b x + a\right)^{n}\right)^{\left(\frac{1}{n}\right)}\,{d x}"," ",0,"integrate((c*sin(b*x + a)^n)^(1/n), x)","F",0
30,0,0,0,0.000000," ","integrate((a*(b*sin(d*x+c))^p)^n,x, algorithm=""maxima"")","\int \left(\left(b \sin\left(d x + c\right)\right)^{p} a\right)^{n}\,{d x}"," ",0,"integrate(((b*sin(d*x + c))^p*a)^n, x)","F",0
31,1,17,0,0.322501," ","integrate(a-a*sin(x)^2,x, algorithm=""maxima"")","-\frac{1}{4} \, a {\left(2 \, x - \sin\left(2 \, x\right)\right)} + a x"," ",0,"-1/4*a*(2*x - sin(2*x)) + a*x","A",0
32,1,40,0,0.349178," ","integrate((a-a*sin(x)^2)^2,x, algorithm=""maxima"")","\frac{1}{32} \, a^{2} {\left(12 \, x + \sin\left(4 \, x\right) - 8 \, \sin\left(2 \, x\right)\right)} - \frac{1}{2} \, a^{2} {\left(2 \, x - \sin\left(2 \, x\right)\right)} + a^{2} x"," ",0,"1/32*a^2*(12*x + sin(4*x) - 8*sin(2*x)) - 1/2*a^2*(2*x - sin(2*x)) + a^2*x","A",0
33,1,69,0,0.318686," ","integrate((a-a*sin(x)^2)^3,x, algorithm=""maxima"")","-\frac{1}{192} \, {\left(4 \, \sin\left(2 \, x\right)^{3} + 60 \, x + 9 \, \sin\left(4 \, x\right) - 48 \, \sin\left(2 \, x\right)\right)} a^{3} + \frac{3}{32} \, a^{3} {\left(12 \, x + \sin\left(4 \, x\right) - 8 \, \sin\left(2 \, x\right)\right)} - \frac{3}{4} \, a^{3} {\left(2 \, x - \sin\left(2 \, x\right)\right)} + a^{3} x"," ",0,"-1/192*(4*sin(2*x)^3 + 60*x + 9*sin(4*x) - 48*sin(2*x))*a^3 + 3/32*a^3*(12*x + sin(4*x) - 8*sin(2*x)) - 3/4*a^3*(2*x - sin(2*x)) + a^3*x","A",0
34,1,104,0,0.322829," ","integrate((a-a*sin(x)^2)^4,x, algorithm=""maxima"")","\frac{1}{3072} \, {\left(128 \, \sin\left(2 \, x\right)^{3} + 840 \, x + 3 \, \sin\left(8 \, x\right) + 168 \, \sin\left(4 \, x\right) - 768 \, \sin\left(2 \, x\right)\right)} a^{4} - \frac{1}{48} \, {\left(4 \, \sin\left(2 \, x\right)^{3} + 60 \, x + 9 \, \sin\left(4 \, x\right) - 48 \, \sin\left(2 \, x\right)\right)} a^{4} + \frac{3}{16} \, a^{4} {\left(12 \, x + \sin\left(4 \, x\right) - 8 \, \sin\left(2 \, x\right)\right)} - a^{4} {\left(2 \, x - \sin\left(2 \, x\right)\right)} + a^{4} x"," ",0,"1/3072*(128*sin(2*x)^3 + 840*x + 3*sin(8*x) + 168*sin(4*x) - 768*sin(2*x))*a^4 - 1/48*(4*sin(2*x)^3 + 60*x + 9*sin(4*x) - 48*sin(2*x))*a^4 + 3/16*a^4*(12*x + sin(4*x) - 8*sin(2*x)) - a^4*(2*x - sin(2*x)) + a^4*x","B",0
35,1,50,0,0.362374," ","integrate(sin(d*x+c)^7/(a-a*sin(d*x+c)^2),x, algorithm=""maxima"")","\frac{\frac{\cos\left(d x + c\right)^{5} - 5 \, \cos\left(d x + c\right)^{3} + 15 \, \cos\left(d x + c\right)}{a} + \frac{5}{a \cos\left(d x + c\right)}}{5 \, d}"," ",0,"1/5*((cos(d*x + c)^5 - 5*cos(d*x + c)^3 + 15*cos(d*x + c))/a + 5/(a*cos(d*x + c)))/d","A",0
36,1,40,0,0.362064," ","integrate(sin(d*x+c)^5/(a-a*sin(d*x+c)^2),x, algorithm=""maxima"")","-\frac{\frac{\cos\left(d x + c\right)^{3} - 6 \, \cos\left(d x + c\right)}{a} - \frac{3}{a \cos\left(d x + c\right)}}{3 \, d}"," ",0,"-1/3*((cos(d*x + c)^3 - 6*cos(d*x + c))/a - 3/(a*cos(d*x + c)))/d","A",0
37,1,27,0,0.343770," ","integrate(sin(d*x+c)^3/(a-a*sin(d*x+c)^2),x, algorithm=""maxima"")","\frac{\frac{\cos\left(d x + c\right)}{a} + \frac{1}{a \cos\left(d x + c\right)}}{d}"," ",0,"(cos(d*x + c)/a + 1/(a*cos(d*x + c)))/d","A",0
38,1,15,0,0.361319," ","integrate(sin(d*x+c)/(a-a*sin(d*x+c)^2),x, algorithm=""maxima"")","\frac{1}{a d \cos\left(d x + c\right)}"," ",0,"1/(a*d*cos(d*x + c))","A",0
39,1,46,0,0.349244," ","integrate(csc(d*x+c)/(a-a*sin(d*x+c)^2),x, algorithm=""maxima"")","-\frac{\frac{\log\left(\cos\left(d x + c\right) + 1\right)}{a} - \frac{\log\left(\cos\left(d x + c\right) - 1\right)}{a} - \frac{2}{a \cos\left(d x + c\right)}}{2 \, d}"," ",0,"-1/2*(log(cos(d*x + c) + 1)/a - log(cos(d*x + c) - 1)/a - 2/(a*cos(d*x + c)))/d","A",0
40,1,70,0,0.363175," ","integrate(csc(d*x+c)^3/(a-a*sin(d*x+c)^2),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{2} - 2\right)}}{a \cos\left(d x + c\right)^{3} - a \cos\left(d x + c\right)} - \frac{3 \, \log\left(\cos\left(d x + c\right) + 1\right)}{a} + \frac{3 \, \log\left(\cos\left(d x + c\right) - 1\right)}{a}}{4 \, d}"," ",0,"1/4*(2*(3*cos(d*x + c)^2 - 2)/(a*cos(d*x + c)^3 - a*cos(d*x + c)) - 3*log(cos(d*x + c) + 1)/a + 3*log(cos(d*x + c) - 1)/a)/d","A",0
41,1,90,0,0.343757," ","integrate(csc(d*x+c)^5/(a-a*sin(d*x+c)^2),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(15 \, \cos\left(d x + c\right)^{4} - 25 \, \cos\left(d x + c\right)^{2} + 8\right)}}{a \cos\left(d x + c\right)^{5} - 2 \, a \cos\left(d x + c\right)^{3} + a \cos\left(d x + c\right)} - \frac{15 \, \log\left(\cos\left(d x + c\right) + 1\right)}{a} + \frac{15 \, \log\left(\cos\left(d x + c\right) - 1\right)}{a}}{16 \, d}"," ",0,"1/16*(2*(15*cos(d*x + c)^4 - 25*cos(d*x + c)^2 + 8)/(a*cos(d*x + c)^5 - 2*a*cos(d*x + c)^3 + a*cos(d*x + c)) - 15*log(cos(d*x + c) + 1)/a + 15*log(cos(d*x + c) - 1)/a)/d","A",0
42,1,72,0,0.425893," ","integrate(sin(d*x+c)^6/(a-a*sin(d*x+c)^2),x, algorithm=""maxima"")","\frac{\frac{9 \, \tan\left(d x + c\right)^{3} + 7 \, \tan\left(d x + c\right)}{a \tan\left(d x + c\right)^{4} + 2 \, a \tan\left(d x + c\right)^{2} + a} - \frac{15 \, {\left(d x + c\right)}}{a} + \frac{8 \, \tan\left(d x + c\right)}{a}}{8 \, d}"," ",0,"1/8*((9*tan(d*x + c)^3 + 7*tan(d*x + c))/(a*tan(d*x + c)^4 + 2*a*tan(d*x + c)^2 + a) - 15*(d*x + c)/a + 8*tan(d*x + c)/a)/d","A",0
43,1,49,0,0.442202," ","integrate(sin(d*x+c)^4/(a-a*sin(d*x+c)^2),x, algorithm=""maxima"")","-\frac{\frac{3 \, {\left(d x + c\right)}}{a} - \frac{\tan\left(d x + c\right)}{a \tan\left(d x + c\right)^{2} + a} - \frac{2 \, \tan\left(d x + c\right)}{a}}{2 \, d}"," ",0,"-1/2*(3*(d*x + c)/a - tan(d*x + c)/(a*tan(d*x + c)^2 + a) - 2*tan(d*x + c)/a)/d","A",0
44,1,26,0,0.452113," ","integrate(sin(d*x+c)^2/(a-a*sin(d*x+c)^2),x, algorithm=""maxima"")","-\frac{\frac{d x + c}{a} - \frac{\tan\left(d x + c\right)}{a}}{d}"," ",0,"-((d*x + c)/a - tan(d*x + c)/a)/d","A",0
45,1,13,0,0.359408," ","integrate(1/(a-a*sin(d*x+c)^2),x, algorithm=""maxima"")","\frac{\tan\left(d x + c\right)}{a d}"," ",0,"tan(d*x + c)/(a*d)","A",0
46,1,28,0,0.347569," ","integrate(csc(d*x+c)^2/(a-a*sin(d*x+c)^2),x, algorithm=""maxima"")","\frac{\frac{\tan\left(d x + c\right)}{a} - \frac{1}{a \tan\left(d x + c\right)}}{d}"," ",0,"(tan(d*x + c)/a - 1/(a*tan(d*x + c)))/d","A",0
47,1,42,0,0.325613," ","integrate(csc(d*x+c)^4/(a-a*sin(d*x+c)^2),x, algorithm=""maxima"")","\frac{\frac{3 \, \tan\left(d x + c\right)}{a} - \frac{6 \, \tan\left(d x + c\right)^{2} + 1}{a \tan\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"1/3*(3*tan(d*x + c)/a - (6*tan(d*x + c)^2 + 1)/(a*tan(d*x + c)^3))/d","A",0
48,1,52,0,0.326343," ","integrate(csc(d*x+c)^6/(a-a*sin(d*x+c)^2),x, algorithm=""maxima"")","\frac{\frac{5 \, \tan\left(d x + c\right)}{a} - \frac{15 \, \tan\left(d x + c\right)^{4} + 5 \, \tan\left(d x + c\right)^{2} + 1}{a \tan\left(d x + c\right)^{5}}}{5 \, d}"," ",0,"1/5*(5*tan(d*x + c)/a - (15*tan(d*x + c)^4 + 5*tan(d*x + c)^2 + 1)/(a*tan(d*x + c)^5))/d","A",0
49,1,52,0,0.344666," ","integrate(sin(d*x+c)^7/(a-a*sin(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{\frac{\cos\left(d x + c\right)^{3} - 9 \, \cos\left(d x + c\right)}{a^{2}} - \frac{9 \, \cos\left(d x + c\right)^{2} - 1}{a^{2} \cos\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"1/3*((cos(d*x + c)^3 - 9*cos(d*x + c))/a^2 - (9*cos(d*x + c)^2 - 1)/(a^2*cos(d*x + c)^3))/d","A",0
50,1,41,0,0.343327," ","integrate(sin(d*x+c)^5/(a-a*sin(d*x+c)^2)^2,x, algorithm=""maxima"")","-\frac{\frac{3 \, \cos\left(d x + c\right)}{a^{2}} + \frac{6 \, \cos\left(d x + c\right)^{2} - 1}{a^{2} \cos\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"-1/3*(3*cos(d*x + c)/a^2 + (6*cos(d*x + c)^2 - 1)/(a^2*cos(d*x + c)^3))/d","A",0
51,1,28,0,0.334260," ","integrate(sin(d*x+c)^3/(a-a*sin(d*x+c)^2)^2,x, algorithm=""maxima"")","-\frac{3 \, \cos\left(d x + c\right)^{2} - 1}{3 \, a^{2} d \cos\left(d x + c\right)^{3}}"," ",0,"-1/3*(3*cos(d*x + c)^2 - 1)/(a^2*d*cos(d*x + c)^3)","A",0
52,1,16,0,0.344640," ","integrate(sin(d*x+c)/(a-a*sin(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{1}{3 \, a^{2} d \cos\left(d x + c\right)^{3}}"," ",0,"1/3/(a^2*d*cos(d*x + c)^3)","A",0
53,1,59,0,0.327220," ","integrate(csc(d*x+c)/(a-a*sin(d*x+c)^2)^2,x, algorithm=""maxima"")","-\frac{\frac{3 \, \log\left(\cos\left(d x + c\right) + 1\right)}{a^{2}} - \frac{3 \, \log\left(\cos\left(d x + c\right) - 1\right)}{a^{2}} - \frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{2} + 1\right)}}{a^{2} \cos\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"-1/6*(3*log(cos(d*x + c) + 1)/a^2 - 3*log(cos(d*x + c) - 1)/a^2 - 2*(3*cos(d*x + c)^2 + 1)/(a^2*cos(d*x + c)^3))/d","A",0
54,1,86,0,0.335064," ","integrate(csc(d*x+c)^3/(a-a*sin(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(15 \, \cos\left(d x + c\right)^{4} - 10 \, \cos\left(d x + c\right)^{2} - 2\right)}}{a^{2} \cos\left(d x + c\right)^{5} - a^{2} \cos\left(d x + c\right)^{3}} - \frac{15 \, \log\left(\cos\left(d x + c\right) + 1\right)}{a^{2}} + \frac{15 \, \log\left(\cos\left(d x + c\right) - 1\right)}{a^{2}}}{12 \, d}"," ",0,"1/12*(2*(15*cos(d*x + c)^4 - 10*cos(d*x + c)^2 - 2)/(a^2*cos(d*x + c)^5 - a^2*cos(d*x + c)^3) - 15*log(cos(d*x + c) + 1)/a^2 + 15*log(cos(d*x + c) - 1)/a^2)/d","A",0
55,1,64,0,0.449644," ","integrate(sin(d*x+c)^6/(a-a*sin(d*x+c)^2)^2,x, algorithm=""maxima"")","-\frac{\frac{3 \, \tan\left(d x + c\right)}{a^{2} \tan\left(d x + c\right)^{2} + a^{2}} - \frac{2 \, {\left(\tan\left(d x + c\right)^{3} - 6 \, \tan\left(d x + c\right)\right)}}{a^{2}} - \frac{15 \, {\left(d x + c\right)}}{a^{2}}}{6 \, d}"," ",0,"-1/6*(3*tan(d*x + c)/(a^2*tan(d*x + c)^2 + a^2) - 2*(tan(d*x + c)^3 - 6*tan(d*x + c))/a^2 - 15*(d*x + c)/a^2)/d","A",0
56,1,37,0,0.426560," ","integrate(sin(d*x+c)^4/(a-a*sin(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{\frac{\tan\left(d x + c\right)^{3} - 3 \, \tan\left(d x + c\right)}{a^{2}} + \frac{3 \, {\left(d x + c\right)}}{a^{2}}}{3 \, d}"," ",0,"1/3*((tan(d*x + c)^3 - 3*tan(d*x + c))/a^2 + 3*(d*x + c)/a^2)/d","A",0
57,1,16,0,0.326898," ","integrate(sin(d*x+c)^2/(a-a*sin(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{\tan\left(d x + c\right)^{3}}{3 \, a^{2} d}"," ",0,"1/3*tan(d*x + c)^3/(a^2*d)","A",0
58,1,25,0,0.352741," ","integrate(1/(a-a*sin(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)}{3 \, a^{2} d}"," ",0,"1/3*(tan(d*x + c)^3 + 3*tan(d*x + c))/(a^2*d)","A",0
59,1,40,0,0.337390," ","integrate(csc(d*x+c)^2/(a-a*sin(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{\frac{\tan\left(d x + c\right)^{3} + 6 \, \tan\left(d x + c\right)}{a^{2}} - \frac{3}{a^{2} \tan\left(d x + c\right)}}{3 \, d}"," ",0,"1/3*((tan(d*x + c)^3 + 6*tan(d*x + c))/a^2 - 3/(a^2*tan(d*x + c)))/d","A",0
60,1,52,0,0.339878," ","integrate(csc(d*x+c)^4/(a-a*sin(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{\frac{\tan\left(d x + c\right)^{3} + 9 \, \tan\left(d x + c\right)}{a^{2}} - \frac{9 \, \tan\left(d x + c\right)^{2} + 1}{a^{2} \tan\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"1/3*((tan(d*x + c)^3 + 9*tan(d*x + c))/a^2 - (9*tan(d*x + c)^2 + 1)/(a^2*tan(d*x + c)^3))/d","A",0
61,1,22,0,0.367012," ","integrate(1/(a-a*sin(x)^2)^3,x, algorithm=""maxima"")","\frac{3 \, \tan\left(x\right)^{5} + 10 \, \tan\left(x\right)^{3} + 15 \, \tan\left(x\right)}{15 \, a^{3}}"," ",0,"1/15*(3*tan(x)^5 + 10*tan(x)^3 + 15*tan(x))/a^3","A",0
62,1,28,0,0.340778," ","integrate(1/(a-a*sin(x)^2)^4,x, algorithm=""maxima"")","\frac{5 \, \tan\left(x\right)^{7} + 21 \, \tan\left(x\right)^{5} + 35 \, \tan\left(x\right)^{3} + 35 \, \tan\left(x\right)}{35 \, a^{4}}"," ",0,"1/35*(5*tan(x)^7 + 21*tan(x)^5 + 35*tan(x)^3 + 35*tan(x))/a^4","A",0
63,1,34,0,0.340270," ","integrate(1/(a-a*sin(x)^2)^5,x, algorithm=""maxima"")","\frac{35 \, \tan\left(x\right)^{9} + 180 \, \tan\left(x\right)^{7} + 378 \, \tan\left(x\right)^{5} + 420 \, \tan\left(x\right)^{3} + 315 \, \tan\left(x\right)}{315 \, a^{5}}"," ",0,"1/315*(35*tan(x)^9 + 180*tan(x)^7 + 378*tan(x)^5 + 420*tan(x)^3 + 315*tan(x))/a^5","A",0
64,1,43,0,0.338532," ","integrate(sin(d*x+c)^3*(a+b*sin(d*x+c)^2),x, algorithm=""maxima"")","-\frac{3 \, b \cos\left(d x + c\right)^{5} - 5 \, {\left(a + 2 \, b\right)} \cos\left(d x + c\right)^{3} + 15 \, {\left(a + b\right)} \cos\left(d x + c\right)}{15 \, d}"," ",0,"-1/15*(3*b*cos(d*x + c)^5 - 5*(a + 2*b)*cos(d*x + c)^3 + 15*(a + b)*cos(d*x + c))/d","A",0
65,1,34,0,0.333642," ","integrate(sin(d*x+c)*(a+b*sin(d*x+c)^2),x, algorithm=""maxima"")","\frac{{\left(\cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)} b - 3 \, a \cos\left(d x + c\right)}{3 \, d}"," ",0,"1/3*((cos(d*x + c)^3 - 3*cos(d*x + c))*b - 3*a*cos(d*x + c))/d","A",0
66,1,38,0,0.335081," ","integrate(csc(d*x+c)*(a+b*sin(d*x+c)^2),x, algorithm=""maxima"")","-\frac{2 \, b \cos\left(d x + c\right) + a \log\left(\cos\left(d x + c\right) + 1\right) - a \log\left(\cos\left(d x + c\right) - 1\right)}{2 \, d}"," ",0,"-1/2*(2*b*cos(d*x + c) + a*log(cos(d*x + c) + 1) - a*log(cos(d*x + c) - 1))/d","A",0
67,1,58,0,0.331639," ","integrate(csc(d*x+c)^3*(a+b*sin(d*x+c)^2),x, algorithm=""maxima"")","-\frac{{\left(a + 2 \, b\right)} \log\left(\cos\left(d x + c\right) + 1\right) - {\left(a + 2 \, b\right)} \log\left(\cos\left(d x + c\right) - 1\right) - \frac{2 \, a \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1}}{4 \, d}"," ",0,"-1/4*((a + 2*b)*log(cos(d*x + c) + 1) - (a + 2*b)*log(cos(d*x + c) - 1) - 2*a*cos(d*x + c)/(cos(d*x + c)^2 - 1))/d","A",0
68,1,104,0,0.439130," ","integrate(sin(d*x+c)^4*(a+b*sin(d*x+c)^2),x, algorithm=""maxima"")","\frac{3 \, {\left(d x + c\right)} {\left(6 \, a + 5 \, b\right)} - \frac{3 \, {\left(10 \, a + 11 \, b\right)} \tan\left(d x + c\right)^{5} + 8 \, {\left(6 \, a + 5 \, b\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(6 \, a + 5 \, b\right)} \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{6} + 3 \, \tan\left(d x + c\right)^{4} + 3 \, \tan\left(d x + c\right)^{2} + 1}}{48 \, d}"," ",0,"1/48*(3*(d*x + c)*(6*a + 5*b) - (3*(10*a + 11*b)*tan(d*x + c)^5 + 8*(6*a + 5*b)*tan(d*x + c)^3 + 3*(6*a + 5*b)*tan(d*x + c))/(tan(d*x + c)^6 + 3*tan(d*x + c)^4 + 3*tan(d*x + c)^2 + 1))/d","A",0
69,1,74,0,0.455060," ","integrate(sin(d*x+c)^2*(a+b*sin(d*x+c)^2),x, algorithm=""maxima"")","\frac{{\left(d x + c\right)} {\left(4 \, a + 3 \, b\right)} - \frac{{\left(4 \, a + 5 \, b\right)} \tan\left(d x + c\right)^{3} + {\left(4 \, a + 3 \, b\right)} \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{4} + 2 \, \tan\left(d x + c\right)^{2} + 1}}{8 \, d}"," ",0,"1/8*((d*x + c)*(4*a + 3*b) - ((4*a + 5*b)*tan(d*x + c)^3 + (4*a + 3*b)*tan(d*x + c))/(tan(d*x + c)^4 + 2*tan(d*x + c)^2 + 1))/d","A",0
70,1,29,0,0.326177," ","integrate(a+b*sin(d*x+c)^2,x, algorithm=""maxima"")","a x + \frac{{\left(2 \, d x + 2 \, c - \sin\left(2 \, d x + 2 \, c\right)\right)} b}{4 \, d}"," ",0,"a*x + 1/4*(2*d*x + 2*c - sin(2*d*x + 2*c))*b/d","A",0
71,1,23,0,0.456503," ","integrate(csc(d*x+c)^2*(a+b*sin(d*x+c)^2),x, algorithm=""maxima"")","\frac{{\left(d x + c\right)} b - \frac{a}{\tan\left(d x + c\right)}}{d}"," ",0,"((d*x + c)*b - a/tan(d*x + c))/d","A",0
72,1,28,0,0.330526," ","integrate(csc(d*x+c)^4*(a+b*sin(d*x+c)^2),x, algorithm=""maxima"")","-\frac{3 \, {\left(a + b\right)} \tan\left(d x + c\right)^{2} + a}{3 \, d \tan\left(d x + c\right)^{3}}"," ",0,"-1/3*(3*(a + b)*tan(d*x + c)^2 + a)/(d*tan(d*x + c)^3)","A",0
73,1,45,0,0.381962," ","integrate(csc(d*x+c)^6*(a+b*sin(d*x+c)^2),x, algorithm=""maxima"")","-\frac{15 \, {\left(a + b\right)} \tan\left(d x + c\right)^{4} + 5 \, {\left(2 \, a + b\right)} \tan\left(d x + c\right)^{2} + 3 \, a}{15 \, d \tan\left(d x + c\right)^{5}}"," ",0,"-1/15*(15*(a + b)*tan(d*x + c)^4 + 5*(2*a + b)*tan(d*x + c)^2 + 3*a)/(d*tan(d*x + c)^5)","A",0
74,1,17,0,0.336669," ","integrate(a+b*sin(x)^2,x, algorithm=""maxima"")","\frac{1}{4} \, b {\left(2 \, x - \sin\left(2 \, x\right)\right)} + a x"," ",0,"1/4*b*(2*x - sin(2*x)) + a*x","A",0
75,1,39,0,0.332057," ","integrate((a+b*sin(x)^2)^2,x, algorithm=""maxima"")","\frac{1}{32} \, b^{2} {\left(12 \, x + \sin\left(4 \, x\right) - 8 \, \sin\left(2 \, x\right)\right)} + \frac{1}{2} \, a b {\left(2 \, x - \sin\left(2 \, x\right)\right)} + a^{2} x"," ",0,"1/32*b^2*(12*x + sin(4*x) - 8*sin(2*x)) + 1/2*a*b*(2*x - sin(2*x)) + a^2*x","A",0
76,1,71,0,0.346728," ","integrate((a+b*sin(x)^2)^3,x, algorithm=""maxima"")","\frac{1}{192} \, {\left(4 \, \sin\left(2 \, x\right)^{3} + 60 \, x + 9 \, \sin\left(4 \, x\right) - 48 \, \sin\left(2 \, x\right)\right)} b^{3} + \frac{3}{32} \, a b^{2} {\left(12 \, x + \sin\left(4 \, x\right) - 8 \, \sin\left(2 \, x\right)\right)} + \frac{3}{4} \, a^{2} b {\left(2 \, x - \sin\left(2 \, x\right)\right)} + a^{3} x"," ",0,"1/192*(4*sin(2*x)^3 + 60*x + 9*sin(4*x) - 48*sin(2*x))*b^3 + 3/32*a*b^2*(12*x + sin(4*x) - 8*sin(2*x)) + 3/4*a^2*b*(2*x - sin(2*x)) + a^3*x","A",0
77,1,108,0,0.340670," ","integrate((a+b*sin(x)^2)^4,x, algorithm=""maxima"")","\frac{1}{48} \, {\left(4 \, \sin\left(2 \, x\right)^{3} + 60 \, x + 9 \, \sin\left(4 \, x\right) - 48 \, \sin\left(2 \, x\right)\right)} a b^{3} + \frac{1}{3072} \, {\left(128 \, \sin\left(2 \, x\right)^{3} + 840 \, x + 3 \, \sin\left(8 \, x\right) + 168 \, \sin\left(4 \, x\right) - 768 \, \sin\left(2 \, x\right)\right)} b^{4} + \frac{3}{16} \, a^{2} b^{2} {\left(12 \, x + \sin\left(4 \, x\right) - 8 \, \sin\left(2 \, x\right)\right)} + a^{3} b {\left(2 \, x - \sin\left(2 \, x\right)\right)} + a^{4} x"," ",0,"1/48*(4*sin(2*x)^3 + 60*x + 9*sin(4*x) - 48*sin(2*x))*a*b^3 + 1/3072*(128*sin(2*x)^3 + 840*x + 3*sin(8*x) + 168*sin(4*x) - 768*sin(2*x))*b^4 + 3/16*a^2*b^2*(12*x + sin(4*x) - 8*sin(2*x)) + a^3*b*(2*x - sin(2*x)) + a^4*x","A",0
78,1,116,0,0.451729," ","integrate(sin(d*x+c)^7/(a+b*sin(d*x+c)^2),x, algorithm=""maxima"")","-\frac{\frac{15 \, a^{3} \log\left(\frac{b \cos\left(d x + c\right) - \sqrt{{\left(a + b\right)} b}}{b \cos\left(d x + c\right) + \sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{{\left(a + b\right)} b} b^{3}} + \frac{2 \, {\left(3 \, b^{2} \cos\left(d x + c\right)^{5} + 5 \, {\left(a b - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{3} + 15 \, {\left(a^{2} - a b + b^{2}\right)} \cos\left(d x + c\right)\right)}}{b^{3}}}{30 \, d}"," ",0,"-1/30*(15*a^3*log((b*cos(d*x + c) - sqrt((a + b)*b))/(b*cos(d*x + c) + sqrt((a + b)*b)))/(sqrt((a + b)*b)*b^3) + 2*(3*b^2*cos(d*x + c)^5 + 5*(a*b - 2*b^2)*cos(d*x + c)^3 + 15*(a^2 - a*b + b^2)*cos(d*x + c))/b^3)/d","A",0
79,1,88,0,0.441904," ","integrate(sin(d*x+c)^5/(a+b*sin(d*x+c)^2),x, algorithm=""maxima"")","\frac{\frac{3 \, a^{2} \log\left(\frac{b \cos\left(d x + c\right) - \sqrt{{\left(a + b\right)} b}}{b \cos\left(d x + c\right) + \sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{{\left(a + b\right)} b} b^{2}} + \frac{2 \, {\left(b \cos\left(d x + c\right)^{3} + 3 \, {\left(a - b\right)} \cos\left(d x + c\right)\right)}}{b^{2}}}{6 \, d}"," ",0,"1/6*(3*a^2*log((b*cos(d*x + c) - sqrt((a + b)*b))/(b*cos(d*x + c) + sqrt((a + b)*b)))/(sqrt((a + b)*b)*b^2) + 2*(b*cos(d*x + c)^3 + 3*(a - b)*cos(d*x + c))/b^2)/d","A",0
80,1,67,0,0.425152," ","integrate(sin(d*x+c)^3/(a+b*sin(d*x+c)^2),x, algorithm=""maxima"")","-\frac{\frac{a \log\left(\frac{b \cos\left(d x + c\right) - \sqrt{{\left(a + b\right)} b}}{b \cos\left(d x + c\right) + \sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{{\left(a + b\right)} b} b} + \frac{2 \, \cos\left(d x + c\right)}{b}}{2 \, d}"," ",0,"-1/2*(a*log((b*cos(d*x + c) - sqrt((a + b)*b))/(b*cos(d*x + c) + sqrt((a + b)*b)))/(sqrt((a + b)*b)*b) + 2*cos(d*x + c)/b)/d","A",0
81,1,50,0,0.431758," ","integrate(sin(d*x+c)/(a+b*sin(d*x+c)^2),x, algorithm=""maxima"")","\frac{\log\left(\frac{b \cos\left(d x + c\right) - \sqrt{{\left(a + b\right)} b}}{b \cos\left(d x + c\right) + \sqrt{{\left(a + b\right)} b}}\right)}{2 \, \sqrt{{\left(a + b\right)} b} d}"," ",0,"1/2*log((b*cos(d*x + c) - sqrt((a + b)*b))/(b*cos(d*x + c) + sqrt((a + b)*b)))/(sqrt((a + b)*b)*d)","A",0
82,1,83,0,0.433084," ","integrate(csc(d*x+c)/(a+b*sin(d*x+c)^2),x, algorithm=""maxima"")","-\frac{\frac{b \log\left(\frac{b \cos\left(d x + c\right) - \sqrt{{\left(a + b\right)} b}}{b \cos\left(d x + c\right) + \sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{{\left(a + b\right)} b} a} + \frac{\log\left(\cos\left(d x + c\right) + 1\right)}{a} - \frac{\log\left(\cos\left(d x + c\right) - 1\right)}{a}}{2 \, d}"," ",0,"-1/2*(b*log((b*cos(d*x + c) - sqrt((a + b)*b))/(b*cos(d*x + c) + sqrt((a + b)*b)))/(sqrt((a + b)*b)*a) + log(cos(d*x + c) + 1)/a - log(cos(d*x + c) - 1)/a)/d","A",0
83,1,120,0,0.428556," ","integrate(csc(d*x+c)^3/(a+b*sin(d*x+c)^2),x, algorithm=""maxima"")","\frac{\frac{2 \, b^{2} \log\left(\frac{b \cos\left(d x + c\right) - \sqrt{{\left(a + b\right)} b}}{b \cos\left(d x + c\right) + \sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{{\left(a + b\right)} b} a^{2}} + \frac{2 \, \cos\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a} - \frac{{\left(a - 2 \, b\right)} \log\left(\cos\left(d x + c\right) + 1\right)}{a^{2}} + \frac{{\left(a - 2 \, b\right)} \log\left(\cos\left(d x + c\right) - 1\right)}{a^{2}}}{4 \, d}"," ",0,"1/4*(2*b^2*log((b*cos(d*x + c) - sqrt((a + b)*b))/(b*cos(d*x + c) + sqrt((a + b)*b)))/(sqrt((a + b)*b)*a^2) + 2*cos(d*x + c)/(a*cos(d*x + c)^2 - a) - (a - 2*b)*log(cos(d*x + c) + 1)/a^2 + (a - 2*b)*log(cos(d*x + c) - 1)/a^2)/d","A",0
84,1,181,0,0.432789," ","integrate(csc(d*x+c)^5/(a+b*sin(d*x+c)^2),x, algorithm=""maxima"")","-\frac{\frac{8 \, b^{3} \log\left(\frac{b \cos\left(d x + c\right) - \sqrt{{\left(a + b\right)} b}}{b \cos\left(d x + c\right) + \sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{{\left(a + b\right)} b} a^{3}} - \frac{2 \, {\left({\left(3 \, a - 4 \, b\right)} \cos\left(d x + c\right)^{3} - {\left(5 \, a - 4 \, b\right)} \cos\left(d x + c\right)\right)}}{a^{2} \cos\left(d x + c\right)^{4} - 2 \, a^{2} \cos\left(d x + c\right)^{2} + a^{2}} + \frac{{\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \log\left(\cos\left(d x + c\right) + 1\right)}{a^{3}} - \frac{{\left(3 \, a^{2} - 4 \, a b + 8 \, b^{2}\right)} \log\left(\cos\left(d x + c\right) - 1\right)}{a^{3}}}{16 \, d}"," ",0,"-1/16*(8*b^3*log((b*cos(d*x + c) - sqrt((a + b)*b))/(b*cos(d*x + c) + sqrt((a + b)*b)))/(sqrt((a + b)*b)*a^3) - 2*((3*a - 4*b)*cos(d*x + c)^3 - (5*a - 4*b)*cos(d*x + c))/(a^2*cos(d*x + c)^4 - 2*a^2*cos(d*x + c)^2 + a^2) + (3*a^2 - 4*a*b + 8*b^2)*log(cos(d*x + c) + 1)/a^3 - (3*a^2 - 4*a*b + 8*b^2)*log(cos(d*x + c) - 1)/a^3)/d","A",0
85,1,192,0,0.444912," ","integrate(sin(d*x+c)^8/(a+b*sin(d*x+c)^2),x, algorithm=""maxima"")","\frac{\frac{48 \, a^{4} \arctan\left(\frac{{\left(a + b\right)} \tan\left(d x + c\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{\sqrt{{\left(a + b\right)} a} b^{4}} - \frac{3 \, {\left(8 \, a^{2} - 10 \, a b + 11 \, b^{2}\right)} \tan\left(d x + c\right)^{5} + 8 \, {\left(6 \, a^{2} - 6 \, a b + 5 \, b^{2}\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{2} - 6 \, a b + 5 \, b^{2}\right)} \tan\left(d x + c\right)}{b^{3} \tan\left(d x + c\right)^{6} + 3 \, b^{3} \tan\left(d x + c\right)^{4} + 3 \, b^{3} \tan\left(d x + c\right)^{2} + b^{3}} - \frac{3 \, {\left(16 \, a^{3} - 8 \, a^{2} b + 6 \, a b^{2} - 5 \, b^{3}\right)} {\left(d x + c\right)}}{b^{4}}}{48 \, d}"," ",0,"1/48*(48*a^4*arctan((a + b)*tan(d*x + c)/sqrt((a + b)*a))/(sqrt((a + b)*a)*b^4) - (3*(8*a^2 - 10*a*b + 11*b^2)*tan(d*x + c)^5 + 8*(6*a^2 - 6*a*b + 5*b^2)*tan(d*x + c)^3 + 3*(8*a^2 - 6*a*b + 5*b^2)*tan(d*x + c))/(b^3*tan(d*x + c)^6 + 3*b^3*tan(d*x + c)^4 + 3*b^3*tan(d*x + c)^2 + b^3) - 3*(16*a^3 - 8*a^2*b + 6*a*b^2 - 5*b^3)*(d*x + c)/b^4)/d","A",0
86,1,128,0,0.449168," ","integrate(sin(d*x+c)^6/(a+b*sin(d*x+c)^2),x, algorithm=""maxima"")","-\frac{\frac{8 \, a^{3} \arctan\left(\frac{{\left(a + b\right)} \tan\left(d x + c\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{\sqrt{{\left(a + b\right)} a} b^{3}} - \frac{{\left(4 \, a - 5 \, b\right)} \tan\left(d x + c\right)^{3} + {\left(4 \, a - 3 \, b\right)} \tan\left(d x + c\right)}{b^{2} \tan\left(d x + c\right)^{4} + 2 \, b^{2} \tan\left(d x + c\right)^{2} + b^{2}} - \frac{{\left(8 \, a^{2} - 4 \, a b + 3 \, b^{2}\right)} {\left(d x + c\right)}}{b^{3}}}{8 \, d}"," ",0,"-1/8*(8*a^3*arctan((a + b)*tan(d*x + c)/sqrt((a + b)*a))/(sqrt((a + b)*a)*b^3) - ((4*a - 5*b)*tan(d*x + c)^3 + (4*a - 3*b)*tan(d*x + c))/(b^2*tan(d*x + c)^4 + 2*b^2*tan(d*x + c)^2 + b^2) - (8*a^2 - 4*a*b + 3*b^2)*(d*x + c)/b^3)/d","A",0
87,1,78,0,0.435726," ","integrate(sin(d*x+c)^4/(a+b*sin(d*x+c)^2),x, algorithm=""maxima"")","\frac{\frac{2 \, a^{2} \arctan\left(\frac{{\left(a + b\right)} \tan\left(d x + c\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{\sqrt{{\left(a + b\right)} a} b^{2}} - \frac{{\left(d x + c\right)} {\left(2 \, a - b\right)}}{b^{2}} - \frac{\tan\left(d x + c\right)}{b \tan\left(d x + c\right)^{2} + b}}{2 \, d}"," ",0,"1/2*(2*a^2*arctan((a + b)*tan(d*x + c)/sqrt((a + b)*a))/(sqrt((a + b)*a)*b^2) - (d*x + c)*(2*a - b)/b^2 - tan(d*x + c)/(b*tan(d*x + c)^2 + b))/d","A",0
88,1,46,0,0.450767," ","integrate(sin(d*x+c)^2/(a+b*sin(d*x+c)^2),x, algorithm=""maxima"")","-\frac{\frac{a \arctan\left(\frac{{\left(a + b\right)} \tan\left(d x + c\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{\sqrt{{\left(a + b\right)} a} b} - \frac{d x + c}{b}}{d}"," ",0,"-(a*arctan((a + b)*tan(d*x + c)/sqrt((a + b)*a))/(sqrt((a + b)*a)*b) - (d*x + c)/b)/d","A",0
89,1,29,0,0.428941," ","integrate(1/(a+b*sin(d*x+c)^2),x, algorithm=""maxima"")","\frac{\arctan\left(\frac{{\left(a + b\right)} \tan\left(d x + c\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{\sqrt{{\left(a + b\right)} a} d}"," ",0,"arctan((a + b)*tan(d*x + c)/sqrt((a + b)*a))/(sqrt((a + b)*a)*d)","A",0
90,1,48,0,1.337187," ","integrate(csc(d*x+c)^2/(a+b*sin(d*x+c)^2),x, algorithm=""maxima"")","-\frac{\frac{b \arctan\left(\frac{{\left(a + b\right)} \tan\left(d x + c\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{\sqrt{{\left(a + b\right)} a} a} + \frac{1}{a \tan\left(d x + c\right)}}{d}"," ",0,"-(b*arctan((a + b)*tan(d*x + c)/sqrt((a + b)*a))/(sqrt((a + b)*a)*a) + 1/(a*tan(d*x + c)))/d","A",0
91,1,69,0,0.427947," ","integrate(csc(d*x+c)^4/(a+b*sin(d*x+c)^2),x, algorithm=""maxima"")","\frac{\frac{3 \, b^{2} \arctan\left(\frac{{\left(a + b\right)} \tan\left(d x + c\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{\sqrt{{\left(a + b\right)} a} a^{2}} - \frac{3 \, {\left(a - b\right)} \tan\left(d x + c\right)^{2} + a}{a^{2} \tan\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"1/3*(3*b^2*arctan((a + b)*tan(d*x + c)/sqrt((a + b)*a))/(sqrt((a + b)*a)*a^2) - (3*(a - b)*tan(d*x + c)^2 + a)/(a^2*tan(d*x + c)^3))/d","A",0
92,1,98,0,0.456851," ","integrate(csc(d*x+c)^6/(a+b*sin(d*x+c)^2),x, algorithm=""maxima"")","-\frac{\frac{15 \, b^{3} \arctan\left(\frac{{\left(a + b\right)} \tan\left(d x + c\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{\sqrt{{\left(a + b\right)} a} a^{3}} + \frac{15 \, {\left(a^{2} - a b + b^{2}\right)} \tan\left(d x + c\right)^{4} + 5 \, {\left(2 \, a^{2} - a b\right)} \tan\left(d x + c\right)^{2} + 3 \, a^{2}}{a^{3} \tan\left(d x + c\right)^{5}}}{15 \, d}"," ",0,"-1/15*(15*b^3*arctan((a + b)*tan(d*x + c)/sqrt((a + b)*a))/(sqrt((a + b)*a)*a^3) + (15*(a^2 - a*b + b^2)*tan(d*x + c)^4 + 5*(2*a^2 - a*b)*tan(d*x + c)^2 + 3*a^2)/(a^3*tan(d*x + c)^5))/d","A",0
93,1,137,0,0.562251," ","integrate(csc(d*x+c)^8/(a+b*sin(d*x+c)^2),x, algorithm=""maxima"")","\frac{\frac{105 \, b^{4} \arctan\left(\frac{{\left(a + b\right)} \tan\left(d x + c\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{\sqrt{{\left(a + b\right)} a} a^{4}} - \frac{105 \, {\left(a^{3} - a^{2} b + a b^{2} - b^{3}\right)} \tan\left(d x + c\right)^{6} + 35 \, {\left(3 \, a^{3} - 2 \, a^{2} b + a b^{2}\right)} \tan\left(d x + c\right)^{4} + 15 \, a^{3} + 21 \, {\left(3 \, a^{3} - a^{2} b\right)} \tan\left(d x + c\right)^{2}}{a^{4} \tan\left(d x + c\right)^{7}}}{105 \, d}"," ",0,"1/105*(105*b^4*arctan((a + b)*tan(d*x + c)/sqrt((a + b)*a))/(sqrt((a + b)*a)*a^4) - (105*(a^3 - a^2*b + a*b^2 - b^3)*tan(d*x + c)^6 + 35*(3*a^3 - 2*a^2*b + a*b^2)*tan(d*x + c)^4 + 15*a^3 + 21*(3*a^3 - a^2*b)*tan(d*x + c)^2)/(a^4*tan(d*x + c)^7))/d","A",0
94,1,154,0,0.718554," ","integrate(sin(d*x+c)^7/(a+b*sin(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{\frac{6 \, a^{3} \cos\left(d x + c\right)}{a^{2} b^{3} + 2 \, a b^{4} + b^{5} - {\left(a b^{4} + b^{5}\right)} \cos\left(d x + c\right)^{2}} + \frac{3 \, {\left(5 \, a + 6 \, b\right)} a^{2} \log\left(\frac{b \cos\left(d x + c\right) - \sqrt{{\left(a + b\right)} b}}{b \cos\left(d x + c\right) + \sqrt{{\left(a + b\right)} b}}\right)}{{\left(a b^{3} + b^{4}\right)} \sqrt{{\left(a + b\right)} b}} + \frac{4 \, {\left(b \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, a - b\right)} \cos\left(d x + c\right)\right)}}{b^{3}}}{12 \, d}"," ",0,"1/12*(6*a^3*cos(d*x + c)/(a^2*b^3 + 2*a*b^4 + b^5 - (a*b^4 + b^5)*cos(d*x + c)^2) + 3*(5*a + 6*b)*a^2*log((b*cos(d*x + c) - sqrt((a + b)*b))/(b*cos(d*x + c) + sqrt((a + b)*b)))/((a*b^3 + b^4)*sqrt((a + b)*b)) + 4*(b*cos(d*x + c)^3 + 3*(2*a - b)*cos(d*x + c))/b^3)/d","A",0
95,1,131,0,0.900405," ","integrate(sin(d*x+c)^5/(a+b*sin(d*x+c)^2)^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, a^{2} \cos\left(d x + c\right)}{a^{2} b^{2} + 2 \, a b^{3} + b^{4} - {\left(a b^{3} + b^{4}\right)} \cos\left(d x + c\right)^{2}} + \frac{{\left(3 \, a + 4 \, b\right)} a \log\left(\frac{b \cos\left(d x + c\right) - \sqrt{{\left(a + b\right)} b}}{b \cos\left(d x + c\right) + \sqrt{{\left(a + b\right)} b}}\right)}{{\left(a b^{2} + b^{3}\right)} \sqrt{{\left(a + b\right)} b}} + \frac{4 \, \cos\left(d x + c\right)}{b^{2}}}{4 \, d}"," ",0,"-1/4*(2*a^2*cos(d*x + c)/(a^2*b^2 + 2*a*b^3 + b^4 - (a*b^3 + b^4)*cos(d*x + c)^2) + (3*a + 4*b)*a*log((b*cos(d*x + c) - sqrt((a + b)*b))/(b*cos(d*x + c) + sqrt((a + b)*b)))/((a*b^2 + b^3)*sqrt((a + b)*b)) + 4*cos(d*x + c)/b^2)/d","A",0
96,1,111,0,0.422634," ","integrate(sin(d*x+c)^3/(a+b*sin(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{\frac{2 \, a \cos\left(d x + c\right)}{a^{2} b + 2 \, a b^{2} + b^{3} - {\left(a b^{2} + b^{3}\right)} \cos\left(d x + c\right)^{2}} + \frac{{\left(a + 2 \, b\right)} \log\left(\frac{b \cos\left(d x + c\right) - \sqrt{{\left(a + b\right)} b}}{b \cos\left(d x + c\right) + \sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{{\left(a + b\right)} b} {\left(a b + b^{2}\right)}}}{4 \, d}"," ",0,"1/4*(2*a*cos(d*x + c)/(a^2*b + 2*a*b^2 + b^3 - (a*b^2 + b^3)*cos(d*x + c)^2) + (a + 2*b)*log((b*cos(d*x + c) - sqrt((a + b)*b))/(b*cos(d*x + c) + sqrt((a + b)*b)))/(sqrt((a + b)*b)*(a*b + b^2)))/d","A",0
97,1,98,0,0.460596," ","integrate(sin(d*x+c)/(a+b*sin(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{\frac{2 \, \cos\left(d x + c\right)}{{\left(a b + b^{2}\right)} \cos\left(d x + c\right)^{2} - a^{2} - 2 \, a b - b^{2}} + \frac{\log\left(\frac{b \cos\left(d x + c\right) - \sqrt{{\left(a + b\right)} b}}{b \cos\left(d x + c\right) + \sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{{\left(a + b\right)} b} {\left(a + b\right)}}}{4 \, d}"," ",0,"1/4*(2*cos(d*x + c)/((a*b + b^2)*cos(d*x + c)^2 - a^2 - 2*a*b - b^2) + log((b*cos(d*x + c) - sqrt((a + b)*b))/(b*cos(d*x + c) + sqrt((a + b)*b)))/(sqrt((a + b)*b)*(a + b)))/d","A",0
98,1,149,0,0.571054," ","integrate(csc(d*x+c)/(a+b*sin(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{\frac{2 \, b \cos\left(d x + c\right)}{a^{3} + 2 \, a^{2} b + a b^{2} - {\left(a^{2} b + a b^{2}\right)} \cos\left(d x + c\right)^{2}} - \frac{{\left(3 \, a b + 2 \, b^{2}\right)} \log\left(\frac{b \cos\left(d x + c\right) - \sqrt{{\left(a + b\right)} b}}{b \cos\left(d x + c\right) + \sqrt{{\left(a + b\right)} b}}\right)}{{\left(a^{3} + a^{2} b\right)} \sqrt{{\left(a + b\right)} b}} - \frac{2 \, \log\left(\cos\left(d x + c\right) + 1\right)}{a^{2}} + \frac{2 \, \log\left(\cos\left(d x + c\right) - 1\right)}{a^{2}}}{4 \, d}"," ",0,"1/4*(2*b*cos(d*x + c)/(a^3 + 2*a^2*b + a*b^2 - (a^2*b + a*b^2)*cos(d*x + c)^2) - (3*a*b + 2*b^2)*log((b*cos(d*x + c) - sqrt((a + b)*b))/(b*cos(d*x + c) + sqrt((a + b)*b)))/((a^3 + a^2*b)*sqrt((a + b)*b)) - 2*log(cos(d*x + c) + 1)/a^2 + 2*log(cos(d*x + c) - 1)/a^2)/d","A",0
99,1,223,0,0.476607," ","integrate(csc(d*x+c)^3/(a+b*sin(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{\frac{{\left(5 \, a b^{2} + 4 \, b^{3}\right)} \log\left(\frac{b \cos\left(d x + c\right) - \sqrt{{\left(a + b\right)} b}}{b \cos\left(d x + c\right) + \sqrt{{\left(a + b\right)} b}}\right)}{{\left(a^{4} + a^{3} b\right)} \sqrt{{\left(a + b\right)} b}} + \frac{2 \, {\left({\left(a b + 2 \, b^{2}\right)} \cos\left(d x + c\right)^{3} - {\left(a^{2} + 2 \, a b + 2 \, b^{2}\right)} \cos\left(d x + c\right)\right)}}{{\left(a^{3} b + a^{2} b^{2}\right)} \cos\left(d x + c\right)^{4} + a^{4} + 2 \, a^{3} b + a^{2} b^{2} - {\left(a^{4} + 3 \, a^{3} b + 2 \, a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2}} - \frac{{\left(a - 4 \, b\right)} \log\left(\cos\left(d x + c\right) + 1\right)}{a^{3}} + \frac{{\left(a - 4 \, b\right)} \log\left(\cos\left(d x + c\right) - 1\right)}{a^{3}}}{4 \, d}"," ",0,"1/4*((5*a*b^2 + 4*b^3)*log((b*cos(d*x + c) - sqrt((a + b)*b))/(b*cos(d*x + c) + sqrt((a + b)*b)))/((a^4 + a^3*b)*sqrt((a + b)*b)) + 2*((a*b + 2*b^2)*cos(d*x + c)^3 - (a^2 + 2*a*b + 2*b^2)*cos(d*x + c))/((a^3*b + a^2*b^2)*cos(d*x + c)^4 + a^4 + 2*a^3*b + a^2*b^2 - (a^4 + 3*a^3*b + 2*a^2*b^2)*cos(d*x + c)^2) - (a - 4*b)*log(cos(d*x + c) + 1)/a^3 + (a - 4*b)*log(cos(d*x + c) - 1)/a^3)/d","A",0
100,1,181,0,0.454095," ","integrate(sin(d*x+c)^6/(a+b*sin(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{\frac{{\left(4 \, a^{3} + 5 \, a^{2} b\right)} \arctan\left(\frac{{\left(a + b\right)} \tan\left(d x + c\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{{\left(a b^{3} + b^{4}\right)} \sqrt{{\left(a + b\right)} a}} - \frac{{\left(2 \, a^{2} + 2 \, a b + b^{2}\right)} \tan\left(d x + c\right)^{3} + {\left(2 \, a^{2} + a b\right)} \tan\left(d x + c\right)}{{\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} \tan\left(d x + c\right)^{4} + a^{2} b^{2} + a b^{3} + {\left(2 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} \tan\left(d x + c\right)^{2}} - \frac{{\left(d x + c\right)} {\left(4 \, a - b\right)}}{b^{3}}}{2 \, d}"," ",0,"1/2*((4*a^3 + 5*a^2*b)*arctan((a + b)*tan(d*x + c)/sqrt((a + b)*a))/((a*b^3 + b^4)*sqrt((a + b)*a)) - ((2*a^2 + 2*a*b + b^2)*tan(d*x + c)^3 + (2*a^2 + a*b)*tan(d*x + c))/((a^2*b^2 + 2*a*b^3 + b^4)*tan(d*x + c)^4 + a^2*b^2 + a*b^3 + (2*a^2*b^2 + 3*a*b^3 + b^4)*tan(d*x + c)^2) - (d*x + c)*(4*a - b)/b^3)/d","A",0
101,1,109,0,0.482935," ","integrate(sin(d*x+c)^4/(a+b*sin(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{\frac{a \tan\left(d x + c\right)}{a^{2} b + a b^{2} + {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \tan\left(d x + c\right)^{2}} - \frac{{\left(2 \, a^{2} + 3 \, a b\right)} \arctan\left(\frac{{\left(a + b\right)} \tan\left(d x + c\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{{\left(a b^{2} + b^{3}\right)} \sqrt{{\left(a + b\right)} a}} + \frac{2 \, {\left(d x + c\right)}}{b^{2}}}{2 \, d}"," ",0,"1/2*(a*tan(d*x + c)/(a^2*b + a*b^2 + (a^2*b + 2*a*b^2 + b^3)*tan(d*x + c)^2) - (2*a^2 + 3*a*b)*arctan((a + b)*tan(d*x + c)/sqrt((a + b)*a))/((a*b^2 + b^3)*sqrt((a + b)*a)) + 2*(d*x + c)/b^2)/d","A",0
102,1,74,0,0.467527," ","integrate(sin(d*x+c)^2/(a+b*sin(d*x+c)^2)^2,x, algorithm=""maxima"")","-\frac{\frac{\tan\left(d x + c\right)}{{\left(a^{2} + 2 \, a b + b^{2}\right)} \tan\left(d x + c\right)^{2} + a^{2} + a b} - \frac{\arctan\left(\frac{{\left(a + b\right)} \tan\left(d x + c\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{\sqrt{{\left(a + b\right)} a} {\left(a + b\right)}}}{2 \, d}"," ",0,"-1/2*(tan(d*x + c)/((a^2 + 2*a*b + b^2)*tan(d*x + c)^2 + a^2 + a*b) - arctan((a + b)*tan(d*x + c)/sqrt((a + b)*a))/(sqrt((a + b)*a)*(a + b)))/d","A",0
103,1,89,0,0.482699," ","integrate(1/(a+b*sin(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{\frac{b \tan\left(d x + c\right)}{a^{3} + a^{2} b + {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \tan\left(d x + c\right)^{2}} + \frac{{\left(2 \, a + b\right)} \arctan\left(\frac{{\left(a + b\right)} \tan\left(d x + c\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{\sqrt{{\left(a + b\right)} a} {\left(a^{2} + a b\right)}}}{2 \, d}"," ",0,"1/2*(b*tan(d*x + c)/(a^3 + a^2*b + (a^3 + 2*a^2*b + a*b^2)*tan(d*x + c)^2) + (2*a + b)*arctan((a + b)*tan(d*x + c)/sqrt((a + b)*a))/(sqrt((a + b)*a)*(a^2 + a*b)))/d","A",0
104,1,133,0,0.468406," ","integrate(csc(d*x+c)^2/(a+b*sin(d*x+c)^2)^2,x, algorithm=""maxima"")","-\frac{\frac{{\left(4 \, a b + 3 \, b^{2}\right)} \arctan\left(\frac{{\left(a + b\right)} \tan\left(d x + c\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{{\left(a^{3} + a^{2} b\right)} \sqrt{{\left(a + b\right)} a}} + \frac{{\left(2 \, a^{2} + 4 \, a b + 3 \, b^{2}\right)} \tan\left(d x + c\right)^{2} + 2 \, a^{2} + 2 \, a b}{{\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \tan\left(d x + c\right)^{3} + {\left(a^{4} + a^{3} b\right)} \tan\left(d x + c\right)}}{2 \, d}"," ",0,"-1/2*((4*a*b + 3*b^2)*arctan((a + b)*tan(d*x + c)/sqrt((a + b)*a))/((a^3 + a^2*b)*sqrt((a + b)*a)) + ((2*a^2 + 4*a*b + 3*b^2)*tan(d*x + c)^2 + 2*a^2 + 2*a*b)/((a^4 + 2*a^3*b + a^2*b^2)*tan(d*x + c)^3 + (a^4 + a^3*b)*tan(d*x + c)))/d","A",0
105,1,172,0,0.561506," ","integrate(csc(d*x+c)^4/(a+b*sin(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{\frac{3 \, {\left(6 \, a b^{2} + 5 \, b^{3}\right)} \arctan\left(\frac{{\left(a + b\right)} \tan\left(d x + c\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{{\left(a^{4} + a^{3} b\right)} \sqrt{{\left(a + b\right)} a}} - \frac{3 \, {\left(2 \, a^{3} - 6 \, a b^{2} - 5 \, b^{3}\right)} \tan\left(d x + c\right)^{4} + 2 \, a^{3} + 2 \, a^{2} b + 2 \, {\left(4 \, a^{3} - a^{2} b - 5 \, a b^{2}\right)} \tan\left(d x + c\right)^{2}}{{\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \tan\left(d x + c\right)^{5} + {\left(a^{5} + a^{4} b\right)} \tan\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(3*(6*a*b^2 + 5*b^3)*arctan((a + b)*tan(d*x + c)/sqrt((a + b)*a))/((a^4 + a^3*b)*sqrt((a + b)*a)) - (3*(2*a^3 - 6*a*b^2 - 5*b^3)*tan(d*x + c)^4 + 2*a^3 + 2*a^2*b + 2*(4*a^3 - a^2*b - 5*a*b^2)*tan(d*x + c)^2)/((a^5 + 2*a^4*b + a^3*b^2)*tan(d*x + c)^5 + (a^5 + a^4*b)*tan(d*x + c)^3))/d","A",0
106,1,234,0,0.516834," ","integrate(sin(d*x+c)^6/(a+b*sin(d*x+c)^2)^3,x, algorithm=""maxima"")","-\frac{\frac{{\left(8 \, a^{3} + 20 \, a^{2} b + 15 \, a b^{2}\right)} \arctan\left(\frac{{\left(a + b\right)} \tan\left(d x + c\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{{\left(a^{2} b^{3} + 2 \, a b^{4} + b^{5}\right)} \sqrt{{\left(a + b\right)} a}} - \frac{{\left(4 \, a^{3} + 13 \, a^{2} b + 9 \, a b^{2}\right)} \tan\left(d x + c\right)^{3} + {\left(4 \, a^{3} + 7 \, a^{2} b\right)} \tan\left(d x + c\right)}{a^{4} b^{2} + 2 \, a^{3} b^{3} + a^{2} b^{4} + {\left(a^{4} b^{2} + 4 \, a^{3} b^{3} + 6 \, a^{2} b^{4} + 4 \, a b^{5} + b^{6}\right)} \tan\left(d x + c\right)^{4} + 2 \, {\left(a^{4} b^{2} + 3 \, a^{3} b^{3} + 3 \, a^{2} b^{4} + a b^{5}\right)} \tan\left(d x + c\right)^{2}} - \frac{8 \, {\left(d x + c\right)}}{b^{3}}}{8 \, d}"," ",0,"-1/8*((8*a^3 + 20*a^2*b + 15*a*b^2)*arctan((a + b)*tan(d*x + c)/sqrt((a + b)*a))/((a^2*b^3 + 2*a*b^4 + b^5)*sqrt((a + b)*a)) - ((4*a^3 + 13*a^2*b + 9*a*b^2)*tan(d*x + c)^3 + (4*a^3 + 7*a^2*b)*tan(d*x + c))/(a^4*b^2 + 2*a^3*b^3 + a^2*b^4 + (a^4*b^2 + 4*a^3*b^3 + 6*a^2*b^4 + 4*a*b^5 + b^6)*tan(d*x + c)^4 + 2*(a^4*b^2 + 3*a^3*b^3 + 3*a^2*b^4 + a*b^5)*tan(d*x + c)^2) - 8*(d*x + c)/b^3)/d","A",0
107,1,158,0,0.514151," ","integrate(sin(d*x+c)^4/(a+b*sin(d*x+c)^2)^3,x, algorithm=""maxima"")","-\frac{\frac{5 \, {\left(a + b\right)} \tan\left(d x + c\right)^{3} + 3 \, a \tan\left(d x + c\right)}{{\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \tan\left(d x + c\right)^{4} + a^{4} + 2 \, a^{3} b + a^{2} b^{2} + 2 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \tan\left(d x + c\right)^{2}} - \frac{3 \, \arctan\left(\frac{{\left(a + b\right)} \tan\left(d x + c\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{\sqrt{{\left(a + b\right)} a} {\left(a^{2} + 2 \, a b + b^{2}\right)}}}{8 \, d}"," ",0,"-1/8*((5*(a + b)*tan(d*x + c)^3 + 3*a*tan(d*x + c))/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*tan(d*x + c)^4 + a^4 + 2*a^3*b + a^2*b^2 + 2*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*tan(d*x + c)^2) - 3*arctan((a + b)*tan(d*x + c)/sqrt((a + b)*a))/(sqrt((a + b)*a)*(a^2 + 2*a*b + b^2)))/d","A",0
108,1,191,0,0.948288," ","integrate(sin(d*x+c)^2/(a+b*sin(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{\frac{{\left(4 \, a + b\right)} \arctan\left(\frac{{\left(a + b\right)} \tan\left(d x + c\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{{\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sqrt{{\left(a + b\right)} a}} - \frac{{\left(4 \, a^{2} + 3 \, a b - b^{2}\right)} \tan\left(d x + c\right)^{3} + {\left(4 \, a^{2} + a b\right)} \tan\left(d x + c\right)}{a^{5} + 2 \, a^{4} b + a^{3} b^{2} + {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \tan\left(d x + c\right)^{4} + 2 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \tan\left(d x + c\right)^{2}}}{8 \, d}"," ",0,"1/8*((4*a + b)*arctan((a + b)*tan(d*x + c)/sqrt((a + b)*a))/((a^3 + 2*a^2*b + a*b^2)*sqrt((a + b)*a)) - ((4*a^2 + 3*a*b - b^2)*tan(d*x + c)^3 + (4*a^2 + a*b)*tan(d*x + c))/(a^5 + 2*a^4*b + a^3*b^2 + (a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*tan(d*x + c)^4 + 2*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*tan(d*x + c)^2))/d","A",0
109,1,211,0,0.550564," ","integrate(1/(a+b*sin(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{\frac{{\left(8 \, a^{2} + 8 \, a b + 3 \, b^{2}\right)} \arctan\left(\frac{{\left(a + b\right)} \tan\left(d x + c\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{{\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \sqrt{{\left(a + b\right)} a}} + \frac{{\left(8 \, a^{2} b + 11 \, a b^{2} + 3 \, b^{3}\right)} \tan\left(d x + c\right)^{3} + {\left(8 \, a^{2} b + 5 \, a b^{2}\right)} \tan\left(d x + c\right)}{a^{6} + 2 \, a^{5} b + a^{4} b^{2} + {\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} \tan\left(d x + c\right)^{4} + 2 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} \tan\left(d x + c\right)^{2}}}{8 \, d}"," ",0,"1/8*((8*a^2 + 8*a*b + 3*b^2)*arctan((a + b)*tan(d*x + c)/sqrt((a + b)*a))/((a^4 + 2*a^3*b + a^2*b^2)*sqrt((a + b)*a)) + ((8*a^2*b + 11*a*b^2 + 3*b^3)*tan(d*x + c)^3 + (8*a^2*b + 5*a*b^2)*tan(d*x + c))/(a^6 + 2*a^5*b + a^4*b^2 + (a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*tan(d*x + c)^4 + 2*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*tan(d*x + c)^2))/d","A",0
110,1,270,0,0.513281," ","integrate(csc(d*x+c)^2/(a+b*sin(d*x+c)^2)^3,x, algorithm=""maxima"")","-\frac{\frac{3 \, {\left(8 \, a^{2} b + 12 \, a b^{2} + 5 \, b^{3}\right)} \arctan\left(\frac{{\left(a + b\right)} \tan\left(d x + c\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{{\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \sqrt{{\left(a + b\right)} a}} + \frac{{\left(8 \, a^{4} + 32 \, a^{3} b + 60 \, a^{2} b^{2} + 51 \, a b^{3} + 15 \, b^{4}\right)} \tan\left(d x + c\right)^{4} + 8 \, a^{4} + 16 \, a^{3} b + 8 \, a^{2} b^{2} + {\left(16 \, a^{4} + 48 \, a^{3} b + 60 \, a^{2} b^{2} + 25 \, a b^{3}\right)} \tan\left(d x + c\right)^{2}}{{\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} \tan\left(d x + c\right)^{5} + 2 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} \tan\left(d x + c\right)^{3} + {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} \tan\left(d x + c\right)}}{8 \, d}"," ",0,"-1/8*(3*(8*a^2*b + 12*a*b^2 + 5*b^3)*arctan((a + b)*tan(d*x + c)/sqrt((a + b)*a))/((a^5 + 2*a^4*b + a^3*b^2)*sqrt((a + b)*a)) + ((8*a^4 + 32*a^3*b + 60*a^2*b^2 + 51*a*b^3 + 15*b^4)*tan(d*x + c)^4 + 8*a^4 + 16*a^3*b + 8*a^2*b^2 + (16*a^4 + 48*a^3*b + 60*a^2*b^2 + 25*a*b^3)*tan(d*x + c)^2)/((a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*tan(d*x + c)^5 + 2*(a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*tan(d*x + c)^3 + (a^7 + 2*a^6*b + a^5*b^2)*tan(d*x + c)))/d","A",0
111,1,378,0,0.669998," ","integrate(1/(a+b*sin(d*x+c)^2)^4,x, algorithm=""maxima"")","\frac{\frac{3 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \arctan\left(\frac{{\left(a + b\right)} \tan\left(d x + c\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{{\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} \sqrt{{\left(a + b\right)} a}} + \frac{3 \, {\left(24 \, a^{4} b + 66 \, a^{3} b^{2} + 65 \, a^{2} b^{3} + 28 \, a b^{4} + 5 \, b^{5}\right)} \tan\left(d x + c\right)^{5} + 8 \, {\left(18 \, a^{4} b + 36 \, a^{3} b^{2} + 23 \, a^{2} b^{3} + 5 \, a b^{4}\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(24 \, a^{4} b + 30 \, a^{3} b^{2} + 11 \, a^{2} b^{3}\right)} \tan\left(d x + c\right)}{a^{9} + 3 \, a^{8} b + 3 \, a^{7} b^{2} + a^{6} b^{3} + {\left(a^{9} + 6 \, a^{8} b + 15 \, a^{7} b^{2} + 20 \, a^{6} b^{3} + 15 \, a^{5} b^{4} + 6 \, a^{4} b^{5} + a^{3} b^{6}\right)} \tan\left(d x + c\right)^{6} + 3 \, {\left(a^{9} + 5 \, a^{8} b + 10 \, a^{7} b^{2} + 10 \, a^{6} b^{3} + 5 \, a^{5} b^{4} + a^{4} b^{5}\right)} \tan\left(d x + c\right)^{4} + 3 \, {\left(a^{9} + 4 \, a^{8} b + 6 \, a^{7} b^{2} + 4 \, a^{6} b^{3} + a^{5} b^{4}\right)} \tan\left(d x + c\right)^{2}}}{48 \, d}"," ",0,"1/48*(3*(16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3)*arctan((a + b)*tan(d*x + c)/sqrt((a + b)*a))/((a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*sqrt((a + b)*a)) + (3*(24*a^4*b + 66*a^3*b^2 + 65*a^2*b^3 + 28*a*b^4 + 5*b^5)*tan(d*x + c)^5 + 8*(18*a^4*b + 36*a^3*b^2 + 23*a^2*b^3 + 5*a*b^4)*tan(d*x + c)^3 + 3*(24*a^4*b + 30*a^3*b^2 + 11*a^2*b^3)*tan(d*x + c))/(a^9 + 3*a^8*b + 3*a^7*b^2 + a^6*b^3 + (a^9 + 6*a^8*b + 15*a^7*b^2 + 20*a^6*b^3 + 15*a^5*b^4 + 6*a^4*b^5 + a^3*b^6)*tan(d*x + c)^6 + 3*(a^9 + 5*a^8*b + 10*a^7*b^2 + 10*a^6*b^3 + 5*a^5*b^4 + a^4*b^5)*tan(d*x + c)^4 + 3*(a^9 + 4*a^8*b + 6*a^7*b^2 + 4*a^6*b^3 + a^5*b^4)*tan(d*x + c)^2))/d","A",0
112,1,588,0,0.532689," ","integrate(1/(a+b*sin(d*x+c)^2)^5,x, algorithm=""maxima"")","\frac{\frac{3 \, {\left(128 \, a^{4} + 256 \, a^{3} b + 288 \, a^{2} b^{2} + 160 \, a b^{3} + 35 \, b^{4}\right)} \arctan\left(\frac{{\left(a + b\right)} \tan\left(d x + c\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{{\left(a^{8} + 4 \, a^{7} b + 6 \, a^{6} b^{2} + 4 \, a^{5} b^{3} + a^{4} b^{4}\right)} \sqrt{{\left(a + b\right)} a}} + \frac{3 \, {\left(256 \, a^{6} b + 1056 \, a^{5} b^{2} + 1792 \, a^{4} b^{3} + 1635 \, a^{3} b^{4} + 873 \, a^{2} b^{5} + 265 \, a b^{6} + 35 \, b^{7}\right)} \tan\left(d x + c\right)^{7} + {\left(2304 \, a^{6} b + 7776 \, a^{5} b^{2} + 10400 \, a^{4} b^{3} + 7073 \, a^{3} b^{4} + 2530 \, a^{2} b^{5} + 385 \, a b^{6}\right)} \tan\left(d x + c\right)^{5} + {\left(2304 \, a^{6} b + 6048 \, a^{5} b^{2} + 6080 \, a^{4} b^{3} + 2847 \, a^{3} b^{4} + 511 \, a^{2} b^{5}\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(256 \, a^{6} b + 480 \, a^{5} b^{2} + 352 \, a^{4} b^{3} + 93 \, a^{3} b^{4}\right)} \tan\left(d x + c\right)}{a^{12} + 4 \, a^{11} b + 6 \, a^{10} b^{2} + 4 \, a^{9} b^{3} + a^{8} b^{4} + {\left(a^{12} + 8 \, a^{11} b + 28 \, a^{10} b^{2} + 56 \, a^{9} b^{3} + 70 \, a^{8} b^{4} + 56 \, a^{7} b^{5} + 28 \, a^{6} b^{6} + 8 \, a^{5} b^{7} + a^{4} b^{8}\right)} \tan\left(d x + c\right)^{8} + 4 \, {\left(a^{12} + 7 \, a^{11} b + 21 \, a^{10} b^{2} + 35 \, a^{9} b^{3} + 35 \, a^{8} b^{4} + 21 \, a^{7} b^{5} + 7 \, a^{6} b^{6} + a^{5} b^{7}\right)} \tan\left(d x + c\right)^{6} + 6 \, {\left(a^{12} + 6 \, a^{11} b + 15 \, a^{10} b^{2} + 20 \, a^{9} b^{3} + 15 \, a^{8} b^{4} + 6 \, a^{7} b^{5} + a^{6} b^{6}\right)} \tan\left(d x + c\right)^{4} + 4 \, {\left(a^{12} + 5 \, a^{11} b + 10 \, a^{10} b^{2} + 10 \, a^{9} b^{3} + 5 \, a^{8} b^{4} + a^{7} b^{5}\right)} \tan\left(d x + c\right)^{2}}}{384 \, d}"," ",0,"1/384*(3*(128*a^4 + 256*a^3*b + 288*a^2*b^2 + 160*a*b^3 + 35*b^4)*arctan((a + b)*tan(d*x + c)/sqrt((a + b)*a))/((a^8 + 4*a^7*b + 6*a^6*b^2 + 4*a^5*b^3 + a^4*b^4)*sqrt((a + b)*a)) + (3*(256*a^6*b + 1056*a^5*b^2 + 1792*a^4*b^3 + 1635*a^3*b^4 + 873*a^2*b^5 + 265*a*b^6 + 35*b^7)*tan(d*x + c)^7 + (2304*a^6*b + 7776*a^5*b^2 + 10400*a^4*b^3 + 7073*a^3*b^4 + 2530*a^2*b^5 + 385*a*b^6)*tan(d*x + c)^5 + (2304*a^6*b + 6048*a^5*b^2 + 6080*a^4*b^3 + 2847*a^3*b^4 + 511*a^2*b^5)*tan(d*x + c)^3 + 3*(256*a^6*b + 480*a^5*b^2 + 352*a^4*b^3 + 93*a^3*b^4)*tan(d*x + c))/(a^12 + 4*a^11*b + 6*a^10*b^2 + 4*a^9*b^3 + a^8*b^4 + (a^12 + 8*a^11*b + 28*a^10*b^2 + 56*a^9*b^3 + 70*a^8*b^4 + 56*a^7*b^5 + 28*a^6*b^6 + 8*a^5*b^7 + a^4*b^8)*tan(d*x + c)^8 + 4*(a^12 + 7*a^11*b + 21*a^10*b^2 + 35*a^9*b^3 + 35*a^8*b^4 + 21*a^7*b^5 + 7*a^6*b^6 + a^5*b^7)*tan(d*x + c)^6 + 6*(a^12 + 6*a^11*b + 15*a^10*b^2 + 20*a^9*b^3 + 15*a^8*b^4 + 6*a^7*b^5 + a^6*b^6)*tan(d*x + c)^4 + 4*(a^12 + 5*a^11*b + 10*a^10*b^2 + 10*a^9*b^3 + 5*a^8*b^4 + a^7*b^5)*tan(d*x + c)^2))/d","B",0
113,1,10,0,0.513356," ","integrate(sin(x)/(1+sin(x)^2)^(1/2),x, algorithm=""maxima"")","-\arcsin\left(\frac{1}{2} \, \sqrt{2} \cos\left(x\right)\right)"," ",0,"-arcsin(1/2*sqrt(2)*cos(x))","A",0
114,1,25,0,0.543607," ","integrate(sin(x)*(1+sin(x)^2)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2} \, \sqrt{-\cos\left(x\right)^{2} + 2} \cos\left(x\right) - \arcsin\left(\frac{1}{2} \, \sqrt{2} \cos\left(x\right)\right)"," ",0,"-1/2*sqrt(-cos(x)^2 + 2)*cos(x) - arcsin(1/2*sqrt(2)*cos(x))","A",0
115,1,11,0,0.439878," ","integrate(sin(7+3*x)/(3+sin(7+3*x)^2)^(1/2),x, algorithm=""maxima"")","-\frac{1}{3} \, \arcsin\left(\frac{1}{2} \, \cos\left(3 \, x + 7\right)\right)"," ",0,"-1/3*arcsin(1/2*cos(3*x + 7))","A",0
116,1,31,0,0.522058," ","integrate((a-a*sin(x)^2)^(5/2),x, algorithm=""maxima"")","\frac{1}{240} \, {\left(3 \, a^{2} \sin\left(5 \, x\right) + 25 \, a^{2} \sin\left(3 \, x\right) + 150 \, a^{2} \sin\left(x\right)\right)} \sqrt{a}"," ",0,"1/240*(3*a^2*sin(5*x) + 25*a^2*sin(3*x) + 150*a^2*sin(x))*sqrt(a)","A",0
117,1,17,0,0.493627," ","integrate((a-a*sin(x)^2)^(3/2),x, algorithm=""maxima"")","\frac{1}{12} \, {\left(a \sin\left(3 \, x\right) + 9 \, a \sin\left(x\right)\right)} \sqrt{a}"," ",0,"1/12*(a*sin(3*x) + 9*a*sin(x))*sqrt(a)","A",0
118,1,6,0,0.477002," ","integrate((a-a*sin(x)^2)^(1/2),x, algorithm=""maxima"")","\sqrt{a} \sin\left(x\right)"," ",0,"sqrt(a)*sin(x)","A",0
119,1,38,0,0.508577," ","integrate(1/(a-a*sin(x)^2)^(1/2),x, algorithm=""maxima"")","\frac{\log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sin\left(x\right) + 1\right) - \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sin\left(x\right) + 1\right)}{2 \, \sqrt{a}}"," ",0,"1/2*(log(cos(x)^2 + sin(x)^2 + 2*sin(x) + 1) - log(cos(x)^2 + sin(x)^2 - 2*sin(x) + 1))/sqrt(a)","B",0
120,1,304,0,0.535105," ","integrate(1/(a-a*sin(x)^2)^(3/2),x, algorithm=""maxima"")","\frac{4 \, {\left(\sin\left(3 \, x\right) - \sin\left(x\right)\right)} \cos\left(4 \, x\right) + {\left(2 \, {\left(2 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(4 \, x\right) + \cos\left(4 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 4 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 4 \, \sin\left(2 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right) + 1\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sin\left(x\right) + 1\right) - {\left(2 \, {\left(2 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(4 \, x\right) + \cos\left(4 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 4 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 4 \, \sin\left(2 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right) + 1\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sin\left(x\right) + 1\right) - 4 \, {\left(\cos\left(3 \, x\right) - \cos\left(x\right)\right)} \sin\left(4 \, x\right) + 4 \, {\left(2 \, \cos\left(2 \, x\right) + 1\right)} \sin\left(3 \, x\right) - 8 \, \cos\left(3 \, x\right) \sin\left(2 \, x\right) + 8 \, \cos\left(x\right) \sin\left(2 \, x\right) - 8 \, \cos\left(2 \, x\right) \sin\left(x\right) - 4 \, \sin\left(x\right)}{4 \, {\left(a \cos\left(4 \, x\right)^{2} + 4 \, a \cos\left(2 \, x\right)^{2} + a \sin\left(4 \, x\right)^{2} + 4 \, a \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 4 \, a \sin\left(2 \, x\right)^{2} + 2 \, {\left(2 \, a \cos\left(2 \, x\right) + a\right)} \cos\left(4 \, x\right) + 4 \, a \cos\left(2 \, x\right) + a\right)} \sqrt{a}}"," ",0,"1/4*(4*(sin(3*x) - sin(x))*cos(4*x) + (2*(2*cos(2*x) + 1)*cos(4*x) + cos(4*x)^2 + 4*cos(2*x)^2 + sin(4*x)^2 + 4*sin(4*x)*sin(2*x) + 4*sin(2*x)^2 + 4*cos(2*x) + 1)*log(cos(x)^2 + sin(x)^2 + 2*sin(x) + 1) - (2*(2*cos(2*x) + 1)*cos(4*x) + cos(4*x)^2 + 4*cos(2*x)^2 + sin(4*x)^2 + 4*sin(4*x)*sin(2*x) + 4*sin(2*x)^2 + 4*cos(2*x) + 1)*log(cos(x)^2 + sin(x)^2 - 2*sin(x) + 1) - 4*(cos(3*x) - cos(x))*sin(4*x) + 4*(2*cos(2*x) + 1)*sin(3*x) - 8*cos(3*x)*sin(2*x) + 8*cos(x)*sin(2*x) - 8*cos(2*x)*sin(x) - 4*sin(x))/((a*cos(4*x)^2 + 4*a*cos(2*x)^2 + a*sin(4*x)^2 + 4*a*sin(4*x)*sin(2*x) + 4*a*sin(2*x)^2 + 2*(2*a*cos(2*x) + a)*cos(4*x) + 4*a*cos(2*x) + a)*sqrt(a))","B",0
121,1,933,0,0.714974," ","integrate(1/(a-a*sin(x)^2)^(5/2),x, algorithm=""maxima"")","\frac{4 \, {\left(3 \, \sin\left(7 \, x\right) + 11 \, \sin\left(5 \, x\right) - 11 \, \sin\left(3 \, x\right) - 3 \, \sin\left(x\right)\right)} \cos\left(8 \, x\right) - 24 \, {\left(2 \, \sin\left(6 \, x\right) + 3 \, \sin\left(4 \, x\right) + 2 \, \sin\left(2 \, x\right)\right)} \cos\left(7 \, x\right) + 16 \, {\left(11 \, \sin\left(5 \, x\right) - 11 \, \sin\left(3 \, x\right) - 3 \, \sin\left(x\right)\right)} \cos\left(6 \, x\right) - 88 \, {\left(3 \, \sin\left(4 \, x\right) + 2 \, \sin\left(2 \, x\right)\right)} \cos\left(5 \, x\right) - 24 \, {\left(11 \, \sin\left(3 \, x\right) + 3 \, \sin\left(x\right)\right)} \cos\left(4 \, x\right) + 3 \, {\left(2 \, {\left(4 \, \cos\left(6 \, x\right) + 6 \, \cos\left(4 \, x\right) + 4 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(8 \, x\right) + \cos\left(8 \, x\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, x\right) + 4 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(6 \, x\right) + 16 \, \cos\left(6 \, x\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(4 \, x\right) + 36 \, \cos\left(4 \, x\right)^{2} + 16 \, \cos\left(2 \, x\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, x\right) + 3 \, \sin\left(4 \, x\right) + 2 \, \sin\left(2 \, x\right)\right)} \sin\left(8 \, x\right) + \sin\left(8 \, x\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, x\right) + 2 \, \sin\left(2 \, x\right)\right)} \sin\left(6 \, x\right) + 16 \, \sin\left(6 \, x\right)^{2} + 36 \, \sin\left(4 \, x\right)^{2} + 48 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 16 \, \sin\left(2 \, x\right)^{2} + 8 \, \cos\left(2 \, x\right) + 1\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sin\left(x\right) + 1\right) - 3 \, {\left(2 \, {\left(4 \, \cos\left(6 \, x\right) + 6 \, \cos\left(4 \, x\right) + 4 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(8 \, x\right) + \cos\left(8 \, x\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, x\right) + 4 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(6 \, x\right) + 16 \, \cos\left(6 \, x\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(4 \, x\right) + 36 \, \cos\left(4 \, x\right)^{2} + 16 \, \cos\left(2 \, x\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, x\right) + 3 \, \sin\left(4 \, x\right) + 2 \, \sin\left(2 \, x\right)\right)} \sin\left(8 \, x\right) + \sin\left(8 \, x\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, x\right) + 2 \, \sin\left(2 \, x\right)\right)} \sin\left(6 \, x\right) + 16 \, \sin\left(6 \, x\right)^{2} + 36 \, \sin\left(4 \, x\right)^{2} + 48 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 16 \, \sin\left(2 \, x\right)^{2} + 8 \, \cos\left(2 \, x\right) + 1\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sin\left(x\right) + 1\right) - 4 \, {\left(3 \, \cos\left(7 \, x\right) + 11 \, \cos\left(5 \, x\right) - 11 \, \cos\left(3 \, x\right) - 3 \, \cos\left(x\right)\right)} \sin\left(8 \, x\right) + 12 \, {\left(4 \, \cos\left(6 \, x\right) + 6 \, \cos\left(4 \, x\right) + 4 \, \cos\left(2 \, x\right) + 1\right)} \sin\left(7 \, x\right) - 16 \, {\left(11 \, \cos\left(5 \, x\right) - 11 \, \cos\left(3 \, x\right) - 3 \, \cos\left(x\right)\right)} \sin\left(6 \, x\right) + 44 \, {\left(6 \, \cos\left(4 \, x\right) + 4 \, \cos\left(2 \, x\right) + 1\right)} \sin\left(5 \, x\right) + 24 \, {\left(11 \, \cos\left(3 \, x\right) + 3 \, \cos\left(x\right)\right)} \sin\left(4 \, x\right) - 44 \, {\left(4 \, \cos\left(2 \, x\right) + 1\right)} \sin\left(3 \, x\right) + 176 \, \cos\left(3 \, x\right) \sin\left(2 \, x\right) + 48 \, \cos\left(x\right) \sin\left(2 \, x\right) - 48 \, \cos\left(2 \, x\right) \sin\left(x\right) - 12 \, \sin\left(x\right)}{16 \, {\left(a^{2} \cos\left(8 \, x\right)^{2} + 16 \, a^{2} \cos\left(6 \, x\right)^{2} + 36 \, a^{2} \cos\left(4 \, x\right)^{2} + 16 \, a^{2} \cos\left(2 \, x\right)^{2} + a^{2} \sin\left(8 \, x\right)^{2} + 16 \, a^{2} \sin\left(6 \, x\right)^{2} + 36 \, a^{2} \sin\left(4 \, x\right)^{2} + 48 \, a^{2} \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 16 \, a^{2} \sin\left(2 \, x\right)^{2} + 8 \, a^{2} \cos\left(2 \, x\right) + a^{2} + 2 \, {\left(4 \, a^{2} \cos\left(6 \, x\right) + 6 \, a^{2} \cos\left(4 \, x\right) + 4 \, a^{2} \cos\left(2 \, x\right) + a^{2}\right)} \cos\left(8 \, x\right) + 8 \, {\left(6 \, a^{2} \cos\left(4 \, x\right) + 4 \, a^{2} \cos\left(2 \, x\right) + a^{2}\right)} \cos\left(6 \, x\right) + 12 \, {\left(4 \, a^{2} \cos\left(2 \, x\right) + a^{2}\right)} \cos\left(4 \, x\right) + 4 \, {\left(2 \, a^{2} \sin\left(6 \, x\right) + 3 \, a^{2} \sin\left(4 \, x\right) + 2 \, a^{2} \sin\left(2 \, x\right)\right)} \sin\left(8 \, x\right) + 16 \, {\left(3 \, a^{2} \sin\left(4 \, x\right) + 2 \, a^{2} \sin\left(2 \, x\right)\right)} \sin\left(6 \, x\right)\right)} \sqrt{a}}"," ",0,"1/16*(4*(3*sin(7*x) + 11*sin(5*x) - 11*sin(3*x) - 3*sin(x))*cos(8*x) - 24*(2*sin(6*x) + 3*sin(4*x) + 2*sin(2*x))*cos(7*x) + 16*(11*sin(5*x) - 11*sin(3*x) - 3*sin(x))*cos(6*x) - 88*(3*sin(4*x) + 2*sin(2*x))*cos(5*x) - 24*(11*sin(3*x) + 3*sin(x))*cos(4*x) + 3*(2*(4*cos(6*x) + 6*cos(4*x) + 4*cos(2*x) + 1)*cos(8*x) + cos(8*x)^2 + 8*(6*cos(4*x) + 4*cos(2*x) + 1)*cos(6*x) + 16*cos(6*x)^2 + 12*(4*cos(2*x) + 1)*cos(4*x) + 36*cos(4*x)^2 + 16*cos(2*x)^2 + 4*(2*sin(6*x) + 3*sin(4*x) + 2*sin(2*x))*sin(8*x) + sin(8*x)^2 + 16*(3*sin(4*x) + 2*sin(2*x))*sin(6*x) + 16*sin(6*x)^2 + 36*sin(4*x)^2 + 48*sin(4*x)*sin(2*x) + 16*sin(2*x)^2 + 8*cos(2*x) + 1)*log(cos(x)^2 + sin(x)^2 + 2*sin(x) + 1) - 3*(2*(4*cos(6*x) + 6*cos(4*x) + 4*cos(2*x) + 1)*cos(8*x) + cos(8*x)^2 + 8*(6*cos(4*x) + 4*cos(2*x) + 1)*cos(6*x) + 16*cos(6*x)^2 + 12*(4*cos(2*x) + 1)*cos(4*x) + 36*cos(4*x)^2 + 16*cos(2*x)^2 + 4*(2*sin(6*x) + 3*sin(4*x) + 2*sin(2*x))*sin(8*x) + sin(8*x)^2 + 16*(3*sin(4*x) + 2*sin(2*x))*sin(6*x) + 16*sin(6*x)^2 + 36*sin(4*x)^2 + 48*sin(4*x)*sin(2*x) + 16*sin(2*x)^2 + 8*cos(2*x) + 1)*log(cos(x)^2 + sin(x)^2 - 2*sin(x) + 1) - 4*(3*cos(7*x) + 11*cos(5*x) - 11*cos(3*x) - 3*cos(x))*sin(8*x) + 12*(4*cos(6*x) + 6*cos(4*x) + 4*cos(2*x) + 1)*sin(7*x) - 16*(11*cos(5*x) - 11*cos(3*x) - 3*cos(x))*sin(6*x) + 44*(6*cos(4*x) + 4*cos(2*x) + 1)*sin(5*x) + 24*(11*cos(3*x) + 3*cos(x))*sin(4*x) - 44*(4*cos(2*x) + 1)*sin(3*x) + 176*cos(3*x)*sin(2*x) + 48*cos(x)*sin(2*x) - 48*cos(2*x)*sin(x) - 12*sin(x))/((a^2*cos(8*x)^2 + 16*a^2*cos(6*x)^2 + 36*a^2*cos(4*x)^2 + 16*a^2*cos(2*x)^2 + a^2*sin(8*x)^2 + 16*a^2*sin(6*x)^2 + 36*a^2*sin(4*x)^2 + 48*a^2*sin(4*x)*sin(2*x) + 16*a^2*sin(2*x)^2 + 8*a^2*cos(2*x) + a^2 + 2*(4*a^2*cos(6*x) + 6*a^2*cos(4*x) + 4*a^2*cos(2*x) + a^2)*cos(8*x) + 8*(6*a^2*cos(4*x) + 4*a^2*cos(2*x) + a^2)*cos(6*x) + 12*(4*a^2*cos(2*x) + a^2)*cos(4*x) + 4*(2*a^2*sin(6*x) + 3*a^2*sin(4*x) + 2*a^2*sin(2*x))*sin(8*x) + 16*(3*a^2*sin(4*x) + 2*a^2*sin(2*x))*sin(6*x))*sqrt(a))","B",0
122,1,176,0,0.464489," ","integrate(sin(f*x+e)^3*(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\frac{\frac{{\left(a + b\right)} a \arcsin\left(\frac{b \cos\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{b^{\frac{3}{2}}} + \frac{{\left(a + b\right)} \arcsin\left(\frac{b \cos\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{b}} - \frac{4 \, a \arcsin\left(\frac{b \cos\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{b}} - 4 \, \sqrt{b} \arcsin\left(\frac{b \cos\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right) - 4 \, \sqrt{-b \cos\left(f x + e\right)^{2} + a + b} \cos\left(f x + e\right) - \frac{2 \, {\left(-b \cos\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} \cos\left(f x + e\right)}{b} + \frac{\sqrt{-b \cos\left(f x + e\right)^{2} + a + b} {\left(a + b\right)} \cos\left(f x + e\right)}{b}}{8 \, f}"," ",0,"1/8*((a + b)*a*arcsin(b*cos(f*x + e)/sqrt((a + b)*b))/b^(3/2) + (a + b)*arcsin(b*cos(f*x + e)/sqrt((a + b)*b))/sqrt(b) - 4*a*arcsin(b*cos(f*x + e)/sqrt((a + b)*b))/sqrt(b) - 4*sqrt(b)*arcsin(b*cos(f*x + e)/sqrt((a + b)*b)) - 4*sqrt(-b*cos(f*x + e)^2 + a + b)*cos(f*x + e) - 2*(-b*cos(f*x + e)^2 + a + b)^(3/2)*cos(f*x + e)/b + sqrt(-b*cos(f*x + e)^2 + a + b)*(a + b)*cos(f*x + e)/b)/f","A",0
123,1,70,0,0.443226," ","integrate(sin(f*x+e)*(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","-\frac{\frac{a \arcsin\left(\frac{b \cos\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{b}} + \sqrt{b} \arcsin\left(\frac{b \cos\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right) + \sqrt{-b \cos\left(f x + e\right)^{2} + a + b} \cos\left(f x + e\right)}{2 \, f}"," ",0,"-1/2*(a*arcsin(b*cos(f*x + e)/sqrt((a + b)*b))/sqrt(b) + sqrt(b)*arcsin(b*cos(f*x + e)/sqrt((a + b)*b)) + sqrt(-b*cos(f*x + e)^2 + a + b)*cos(f*x + e))/f","A",0
124,1,132,0,0.451426," ","integrate(csc(f*x+e)*(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{b} \arcsin\left(\frac{b \cos\left(f x + e\right)}{\sqrt{a b + b^{2}}}\right) + \sqrt{a} \log\left(b - \frac{\sqrt{-b \cos\left(f x + e\right)^{2} + a + b} \sqrt{a}}{\cos\left(f x + e\right) - 1} - \frac{a}{\cos\left(f x + e\right) - 1}\right) - \sqrt{a} \log\left(-b + \frac{\sqrt{-b \cos\left(f x + e\right)^{2} + a + b} \sqrt{a}}{\cos\left(f x + e\right) + 1} + \frac{a}{\cos\left(f x + e\right) + 1}\right)}{2 \, f}"," ",0,"-1/2*(2*sqrt(b)*arcsin(b*cos(f*x + e)/sqrt(a*b + b^2)) + sqrt(a)*log(b - sqrt(-b*cos(f*x + e)^2 + a + b)*sqrt(a)/(cos(f*x + e) - 1) - a/(cos(f*x + e) - 1)) - sqrt(a)*log(-b + sqrt(-b*cos(f*x + e)^2 + a + b)*sqrt(a)/(cos(f*x + e) + 1) + a/(cos(f*x + e) + 1)))/f","A",0
125,0,0,0,0.000000," ","integrate(csc(f*x+e)^3*(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sin\left(f x + e\right)^{2} + a} \csc\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e)^2 + a)*csc(f*x + e)^3, x)","F",0
126,0,0,0,0.000000," ","integrate(csc(f*x+e)^5*(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sin\left(f x + e\right)^{2} + a} \csc\left(f x + e\right)^{5}\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e)^2 + a)*csc(f*x + e)^5, x)","F",0
127,0,0,0,0.000000," ","integrate(sin(f*x+e)^4*(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sin\left(f x + e\right)^{2} + a} \sin\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e)^2 + a)*sin(f*x + e)^4, x)","F",0
128,0,0,0,0.000000," ","integrate(sin(f*x+e)^2*(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sin\left(f x + e\right)^{2} + a} \sin\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e)^2 + a)*sin(f*x + e)^2, x)","F",0
129,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sin\left(f x + e\right)^{2} + a}\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e)^2 + a), x)","F",0
130,0,0,0,0.000000," ","integrate(csc(f*x+e)^2*(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sin\left(f x + e\right)^{2} + a} \csc\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e)^2 + a)*csc(f*x + e)^2, x)","F",0
131,0,0,0,0.000000," ","integrate(csc(f*x+e)^4*(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sin\left(f x + e\right)^{2} + a} \csc\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e)^2 + a)*csc(f*x + e)^4, x)","F",0
132,1,248,0,0.452143," ","integrate(sin(f*x+e)^3*(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\frac{\frac{3 \, {\left(a + b\right)}^{2} a \arcsin\left(\frac{b \cos\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{b^{\frac{3}{2}}} + \frac{3 \, {\left(a + b\right)}^{2} \arcsin\left(\frac{b \cos\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{b}} - \frac{18 \, {\left(a + b\right)} a \arcsin\left(\frac{b \cos\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{b}} - 18 \, {\left(a + b\right)} \sqrt{b} \arcsin\left(\frac{b \cos\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right) - 12 \, {\left(-b \cos\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} \cos\left(f x + e\right) - 18 \, \sqrt{-b \cos\left(f x + e\right)^{2} + a + b} {\left(a + b\right)} \cos\left(f x + e\right) - \frac{8 \, {\left(-b \cos\left(f x + e\right)^{2} + a + b\right)}^{\frac{5}{2}} \cos\left(f x + e\right)}{b} + \frac{2 \, {\left(-b \cos\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} {\left(a + b\right)} \cos\left(f x + e\right)}{b} + \frac{3 \, \sqrt{-b \cos\left(f x + e\right)^{2} + a + b} {\left(a + b\right)}^{2} \cos\left(f x + e\right)}{b}}{48 \, f}"," ",0,"1/48*(3*(a + b)^2*a*arcsin(b*cos(f*x + e)/sqrt((a + b)*b))/b^(3/2) + 3*(a + b)^2*arcsin(b*cos(f*x + e)/sqrt((a + b)*b))/sqrt(b) - 18*(a + b)*a*arcsin(b*cos(f*x + e)/sqrt((a + b)*b))/sqrt(b) - 18*(a + b)*sqrt(b)*arcsin(b*cos(f*x + e)/sqrt((a + b)*b)) - 12*(-b*cos(f*x + e)^2 + a + b)^(3/2)*cos(f*x + e) - 18*sqrt(-b*cos(f*x + e)^2 + a + b)*(a + b)*cos(f*x + e) - 8*(-b*cos(f*x + e)^2 + a + b)^(5/2)*cos(f*x + e)/b + 2*(-b*cos(f*x + e)^2 + a + b)^(3/2)*(a + b)*cos(f*x + e)/b + 3*sqrt(-b*cos(f*x + e)^2 + a + b)*(a + b)^2*cos(f*x + e)/b)/f","A",0
133,1,106,0,0.431792," ","integrate(sin(f*x+e)*(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","-\frac{\frac{3 \, {\left(a + b\right)} a \arcsin\left(\frac{b \cos\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{b}} + 3 \, {\left(a + b\right)} \sqrt{b} \arcsin\left(\frac{b \cos\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right) + 2 \, {\left(-b \cos\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} \cos\left(f x + e\right) + 3 \, \sqrt{-b \cos\left(f x + e\right)^{2} + a + b} {\left(a + b\right)} \cos\left(f x + e\right)}{8 \, f}"," ",0,"-1/8*(3*(a + b)*a*arcsin(b*cos(f*x + e)/sqrt((a + b)*b))/sqrt(b) + 3*(a + b)*sqrt(b)*arcsin(b*cos(f*x + e)/sqrt((a + b)*b)) + 2*(-b*cos(f*x + e)^2 + a + b)^(3/2)*cos(f*x + e) + 3*sqrt(-b*cos(f*x + e)^2 + a + b)*(a + b)*cos(f*x + e))/f","A",0
134,1,179,0,0.480620," ","integrate(csc(f*x+e)*(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","-\frac{3 \, a \sqrt{b} \arcsin\left(\frac{b \cos\left(f x + e\right)}{\sqrt{a b + b^{2}}}\right) + b^{\frac{3}{2}} \arcsin\left(\frac{b \cos\left(f x + e\right)}{\sqrt{a b + b^{2}}}\right) + \sqrt{-b \cos\left(f x + e\right)^{2} + a + b} b \cos\left(f x + e\right) + a^{\frac{3}{2}} \log\left(b - \frac{\sqrt{-b \cos\left(f x + e\right)^{2} + a + b} \sqrt{a}}{\cos\left(f x + e\right) - 1} - \frac{a}{\cos\left(f x + e\right) - 1}\right) - a^{\frac{3}{2}} \log\left(-b + \frac{\sqrt{-b \cos\left(f x + e\right)^{2} + a + b} \sqrt{a}}{\cos\left(f x + e\right) + 1} + \frac{a}{\cos\left(f x + e\right) + 1}\right)}{2 \, f}"," ",0,"-1/2*(3*a*sqrt(b)*arcsin(b*cos(f*x + e)/sqrt(a*b + b^2)) + b^(3/2)*arcsin(b*cos(f*x + e)/sqrt(a*b + b^2)) + sqrt(-b*cos(f*x + e)^2 + a + b)*b*cos(f*x + e) + a^(3/2)*log(b - sqrt(-b*cos(f*x + e)^2 + a + b)*sqrt(a)/(cos(f*x + e) - 1) - a/(cos(f*x + e) - 1)) - a^(3/2)*log(-b + sqrt(-b*cos(f*x + e)^2 + a + b)*sqrt(a)/(cos(f*x + e) + 1) + a/(cos(f*x + e) + 1)))/f","A",0
135,0,0,0,0.000000," ","integrate(csc(f*x+e)^3*(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \csc\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^(3/2)*csc(f*x + e)^3, x)","F",0
136,0,0,0,0.000000," ","integrate(csc(f*x+e)^5*(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \csc\left(f x + e\right)^{5}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^(3/2)*csc(f*x + e)^5, x)","F",0
137,0,0,0,0.000000," ","integrate(csc(f*x+e)^7*(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \csc\left(f x + e\right)^{7}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^(3/2)*csc(f*x + e)^7, x)","F",0
138,0,0,0,0.000000," ","integrate(sin(f*x+e)^4*(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \sin\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^(3/2)*sin(f*x + e)^4, x)","F",0
139,0,0,0,0.000000," ","integrate(sin(f*x+e)^2*(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \sin\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^(3/2)*sin(f*x + e)^2, x)","F",0
140,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^(3/2), x)","F",0
141,0,0,0,0.000000," ","integrate(csc(f*x+e)^2*(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \csc\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^(3/2)*csc(f*x + e)^2, x)","F",0
142,0,0,0,0.000000," ","integrate(csc(f*x+e)^4*(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \csc\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^(3/2)*csc(f*x + e)^4, x)","F",0
143,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c)^2)^(5/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right)^{2} + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*sin(d*x + c)^2 + a)^(5/2), x)","F",0
144,1,75,0,0.430724," ","integrate(sin(f*x+e)^3/(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\frac{\frac{a \arcsin\left(\frac{b \cos\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{b^{\frac{3}{2}}} - \frac{\arcsin\left(\frac{b \cos\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{b}} - \frac{\sqrt{-b \cos\left(f x + e\right)^{2} + a + b} \cos\left(f x + e\right)}{b}}{2 \, f}"," ",0,"1/2*(a*arcsin(b*cos(f*x + e)/sqrt((a + b)*b))/b^(3/2) - arcsin(b*cos(f*x + e)/sqrt((a + b)*b))/sqrt(b) - sqrt(-b*cos(f*x + e)^2 + a + b)*cos(f*x + e)/b)/f","A",0
145,1,24,0,0.441920," ","integrate(sin(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","-\frac{\arcsin\left(\frac{b \cos\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{\sqrt{b} f}"," ",0,"-arcsin(b*cos(f*x + e)/sqrt((a + b)*b))/(sqrt(b)*f)","A",0
146,1,109,0,0.437908," ","integrate(csc(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","-\frac{\frac{\log\left(b - \frac{\sqrt{-b \cos\left(f x + e\right)^{2} + a + b} \sqrt{a}}{\cos\left(f x + e\right) - 1} - \frac{a}{\cos\left(f x + e\right) - 1}\right)}{\sqrt{a}} - \frac{\log\left(-b + \frac{\sqrt{-b \cos\left(f x + e\right)^{2} + a + b} \sqrt{a}}{\cos\left(f x + e\right) + 1} + \frac{a}{\cos\left(f x + e\right) + 1}\right)}{\sqrt{a}}}{2 \, f}"," ",0,"-1/2*(log(b - sqrt(-b*cos(f*x + e)^2 + a + b)*sqrt(a)/(cos(f*x + e) - 1) - a/(cos(f*x + e) - 1))/sqrt(a) - log(-b + sqrt(-b*cos(f*x + e)^2 + a + b)*sqrt(a)/(cos(f*x + e) + 1) + a/(cos(f*x + e) + 1))/sqrt(a))/f","B",0
147,0,0,0,0.000000," ","integrate(csc(f*x+e)^3/(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\csc\left(f x + e\right)^{3}}{\sqrt{b \sin\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(csc(f*x + e)^3/sqrt(b*sin(f*x + e)^2 + a), x)","F",0
148,0,0,0,0.000000," ","integrate(sin(f*x+e)^4/(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\sin\left(f x + e\right)^{4}}{\sqrt{b \sin\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(sin(f*x + e)^4/sqrt(b*sin(f*x + e)^2 + a), x)","F",0
149,0,0,0,0.000000," ","integrate(sin(f*x+e)^2/(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\sin\left(f x + e\right)^{2}}{\sqrt{b \sin\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(sin(f*x + e)^2/sqrt(b*sin(f*x + e)^2 + a), x)","F",0
150,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \sin\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(1/sqrt(b*sin(f*x + e)^2 + a), x)","F",0
151,0,0,0,0.000000," ","integrate(csc(f*x+e)^2/(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\csc\left(f x + e\right)^{2}}{\sqrt{b \sin\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(csc(f*x + e)^2/sqrt(b*sin(f*x + e)^2 + a), x)","F",0
152,0,0,0,0.000000," ","integrate(csc(f*x+e)^4/(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\csc\left(f x + e\right)^{4}}{\sqrt{b \sin\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(csc(f*x + e)^4/sqrt(b*sin(f*x + e)^2 + a), x)","F",0
153,1,81,0,0.584592," ","integrate(sin(f*x+e)^3/(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","-\frac{\frac{\arcsin\left(\frac{b \cos\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{b^{\frac{3}{2}}} + \frac{\cos\left(f x + e\right)}{\sqrt{-b \cos\left(f x + e\right)^{2} + a + b} {\left(a + b\right)}} - \frac{\cos\left(f x + e\right)}{\sqrt{-b \cos\left(f x + e\right)^{2} + a + b} b}}{f}"," ",0,"-(arcsin(b*cos(f*x + e)/sqrt((a + b)*b))/b^(3/2) + cos(f*x + e)/(sqrt(-b*cos(f*x + e)^2 + a + b)*(a + b)) - cos(f*x + e)/(sqrt(-b*cos(f*x + e)^2 + a + b)*b))/f","A",0
154,1,32,0,0.388143," ","integrate(sin(f*x+e)/(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","-\frac{\cos\left(f x + e\right)}{\sqrt{-b \cos\left(f x + e\right)^{2} + a + b} {\left(a + b\right)} f}"," ",0,"-cos(f*x + e)/(sqrt(-b*cos(f*x + e)^2 + a + b)*(a + b)*f)","A",0
155,1,165,0,0.486794," ","integrate(csc(f*x+e)/(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\frac{\frac{2 \, b^{2} \cos\left(f x + e\right)}{\sqrt{-b \cos\left(f x + e\right)^{2} + a + b} a^{2} b + \sqrt{-b \cos\left(f x + e\right)^{2} + a + b} a b^{2}} - \frac{\log\left(b - \frac{\sqrt{-b \cos\left(f x + e\right)^{2} + a + b} \sqrt{a}}{\cos\left(f x + e\right) - 1} - \frac{a}{\cos\left(f x + e\right) - 1}\right)}{a^{\frac{3}{2}}} + \frac{\log\left(-b + \frac{\sqrt{-b \cos\left(f x + e\right)^{2} + a + b} \sqrt{a}}{\cos\left(f x + e\right) + 1} + \frac{a}{\cos\left(f x + e\right) + 1}\right)}{a^{\frac{3}{2}}}}{2 \, f}"," ",0,"1/2*(2*b^2*cos(f*x + e)/(sqrt(-b*cos(f*x + e)^2 + a + b)*a^2*b + sqrt(-b*cos(f*x + e)^2 + a + b)*a*b^2) - log(b - sqrt(-b*cos(f*x + e)^2 + a + b)*sqrt(a)/(cos(f*x + e) - 1) - a/(cos(f*x + e) - 1))/a^(3/2) + log(-b + sqrt(-b*cos(f*x + e)^2 + a + b)*sqrt(a)/(cos(f*x + e) + 1) + a/(cos(f*x + e) + 1))/a^(3/2))/f","B",0
156,0,0,0,0.000000," ","integrate(csc(f*x+e)^3/(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\csc\left(f x + e\right)^{3}}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(csc(f*x + e)^3/(b*sin(f*x + e)^2 + a)^(3/2), x)","F",0
157,0,0,0,0.000000," ","integrate(sin(f*x+e)^6/(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\sin\left(f x + e\right)^{6}}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sin(f*x + e)^6/(b*sin(f*x + e)^2 + a)^(3/2), x)","F",0
158,0,0,0,0.000000," ","integrate(sin(f*x+e)^4/(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\sin\left(f x + e\right)^{4}}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sin(f*x + e)^4/(b*sin(f*x + e)^2 + a)^(3/2), x)","F",0
159,0,0,0,0.000000," ","integrate(sin(f*x+e)^2/(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\sin\left(f x + e\right)^{2}}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sin(f*x + e)^2/(b*sin(f*x + e)^2 + a)^(3/2), x)","F",0
160,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^(-3/2), x)","F",0
161,0,0,0,0.000000," ","integrate(csc(f*x+e)^2/(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\csc\left(f x + e\right)^{2}}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(csc(f*x + e)^2/(b*sin(f*x + e)^2 + a)^(3/2), x)","F",0
162,1,283,0,0.460434," ","integrate(sin(f*x+e)^5/(a+b*sin(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","-\frac{{\left(\frac{3 \, \cos\left(f x + e\right)^{2}}{{\left(-b \cos\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} b} - \frac{2 \, a}{{\left(-b \cos\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} b^{2}} - \frac{2}{{\left(-b \cos\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} b}\right)} \cos\left(f x + e\right) + \frac{3 \, \arcsin\left(\frac{b \cos\left(f x + e\right)}{\sqrt{{\left(a + b\right)} b}}\right)}{b^{\frac{5}{2}}} + \frac{2 \, \cos\left(f x + e\right)}{\sqrt{-b \cos\left(f x + e\right)^{2} + a + b} {\left(a + b\right)}^{2}} + \frac{\cos\left(f x + e\right)}{{\left(-b \cos\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} {\left(a + b\right)}} - \frac{3 \, \cos\left(f x + e\right)}{\sqrt{-b \cos\left(f x + e\right)^{2} + a + b} b^{2}} + \frac{2 \, a \cos\left(f x + e\right)}{\sqrt{-b \cos\left(f x + e\right)^{2} + a + b} {\left(a + b\right)} b^{2}} - \frac{2 \, \cos\left(f x + e\right)}{{\left(-b \cos\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} b} + \frac{4 \, \cos\left(f x + e\right)}{\sqrt{-b \cos\left(f x + e\right)^{2} + a + b} {\left(a + b\right)} b}}{3 \, f}"," ",0,"-1/3*((3*cos(f*x + e)^2/((-b*cos(f*x + e)^2 + a + b)^(3/2)*b) - 2*a/((-b*cos(f*x + e)^2 + a + b)^(3/2)*b^2) - 2/((-b*cos(f*x + e)^2 + a + b)^(3/2)*b))*cos(f*x + e) + 3*arcsin(b*cos(f*x + e)/sqrt((a + b)*b))/b^(5/2) + 2*cos(f*x + e)/(sqrt(-b*cos(f*x + e)^2 + a + b)*(a + b)^2) + cos(f*x + e)/((-b*cos(f*x + e)^2 + a + b)^(3/2)*(a + b)) - 3*cos(f*x + e)/(sqrt(-b*cos(f*x + e)^2 + a + b)*b^2) + 2*a*cos(f*x + e)/(sqrt(-b*cos(f*x + e)^2 + a + b)*(a + b)*b^2) - 2*cos(f*x + e)/((-b*cos(f*x + e)^2 + a + b)^(3/2)*b) + 4*cos(f*x + e)/(sqrt(-b*cos(f*x + e)^2 + a + b)*(a + b)*b))/f","B",0
163,1,121,0,0.345315," ","integrate(sin(f*x+e)^3/(a+b*sin(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","-\frac{\frac{2 \, \cos\left(f x + e\right)}{\sqrt{-b \cos\left(f x + e\right)^{2} + a + b} {\left(a + b\right)}^{2}} + \frac{\cos\left(f x + e\right)}{{\left(-b \cos\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} {\left(a + b\right)}} - \frac{\cos\left(f x + e\right)}{{\left(-b \cos\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} b} + \frac{\cos\left(f x + e\right)}{\sqrt{-b \cos\left(f x + e\right)^{2} + a + b} {\left(a + b\right)} b}}{3 \, f}"," ",0,"-1/3*(2*cos(f*x + e)/(sqrt(-b*cos(f*x + e)^2 + a + b)*(a + b)^2) + cos(f*x + e)/((-b*cos(f*x + e)^2 + a + b)^(3/2)*(a + b)) - cos(f*x + e)/((-b*cos(f*x + e)^2 + a + b)^(3/2)*b) + cos(f*x + e)/(sqrt(-b*cos(f*x + e)^2 + a + b)*(a + b)*b))/f","A",0
164,1,63,0,0.365897," ","integrate(sin(f*x+e)/(a+b*sin(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","-\frac{\frac{2 \, \cos\left(f x + e\right)}{\sqrt{-b \cos\left(f x + e\right)^{2} + a + b} {\left(a + b\right)}^{2}} + \frac{\cos\left(f x + e\right)}{{\left(-b \cos\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} {\left(a + b\right)}}}{3 \, f}"," ",0,"-1/3*(2*cos(f*x + e)/(sqrt(-b*cos(f*x + e)^2 + a + b)*(a + b)^2) + cos(f*x + e)/((-b*cos(f*x + e)^2 + a + b)^(3/2)*(a + b)))/f","A",0
165,1,306,0,0.529892," ","integrate(csc(f*x+e)/(a+b*sin(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\frac{\frac{4 \, b^{3} \cos\left(f x + e\right)}{\sqrt{-b \cos\left(f x + e\right)^{2} + a + b} a^{3} b^{2} + 2 \, \sqrt{-b \cos\left(f x + e\right)^{2} + a + b} a^{2} b^{3} + \sqrt{-b \cos\left(f x + e\right)^{2} + a + b} a b^{4}} + \frac{2 \, b^{2} \cos\left(f x + e\right)}{{\left(-b \cos\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} a^{2} b + {\left(-b \cos\left(f x + e\right)^{2} + a + b\right)}^{\frac{3}{2}} a b^{2}} + \frac{6 \, b^{2} \cos\left(f x + e\right)}{\sqrt{-b \cos\left(f x + e\right)^{2} + a + b} a^{3} b + \sqrt{-b \cos\left(f x + e\right)^{2} + a + b} a^{2} b^{2}} - \frac{3 \, \log\left(b - \frac{\sqrt{-b \cos\left(f x + e\right)^{2} + a + b} \sqrt{a}}{\cos\left(f x + e\right) - 1} - \frac{a}{\cos\left(f x + e\right) - 1}\right)}{a^{\frac{5}{2}}} + \frac{3 \, \log\left(-b + \frac{\sqrt{-b \cos\left(f x + e\right)^{2} + a + b} \sqrt{a}}{\cos\left(f x + e\right) + 1} + \frac{a}{\cos\left(f x + e\right) + 1}\right)}{a^{\frac{5}{2}}}}{6 \, f}"," ",0,"1/6*(4*b^3*cos(f*x + e)/(sqrt(-b*cos(f*x + e)^2 + a + b)*a^3*b^2 + 2*sqrt(-b*cos(f*x + e)^2 + a + b)*a^2*b^3 + sqrt(-b*cos(f*x + e)^2 + a + b)*a*b^4) + 2*b^2*cos(f*x + e)/((-b*cos(f*x + e)^2 + a + b)^(3/2)*a^2*b + (-b*cos(f*x + e)^2 + a + b)^(3/2)*a*b^2) + 6*b^2*cos(f*x + e)/(sqrt(-b*cos(f*x + e)^2 + a + b)*a^3*b + sqrt(-b*cos(f*x + e)^2 + a + b)*a^2*b^2) - 3*log(b - sqrt(-b*cos(f*x + e)^2 + a + b)*sqrt(a)/(cos(f*x + e) - 1) - a/(cos(f*x + e) - 1))/a^(5/2) + 3*log(-b + sqrt(-b*cos(f*x + e)^2 + a + b)*sqrt(a)/(cos(f*x + e) + 1) + a/(cos(f*x + e) + 1))/a^(5/2))/f","B",0
166,0,0,0,0.000000," ","integrate(sin(f*x+e)^6/(a+b*sin(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\sin\left(f x + e\right)^{6}}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sin(f*x + e)^6/(b*sin(f*x + e)^2 + a)^(5/2), x)","F",0
167,0,0,0,0.000000," ","integrate(sin(f*x+e)^4/(a+b*sin(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\sin\left(f x + e\right)^{4}}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sin(f*x + e)^4/(b*sin(f*x + e)^2 + a)^(5/2), x)","F",0
168,0,0,0,0.000000," ","integrate(sin(f*x+e)^2/(a+b*sin(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\sin\left(f x + e\right)^{2}}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sin(f*x + e)^2/(b*sin(f*x + e)^2 + a)^(5/2), x)","F",0
169,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^(-5/2), x)","F",0
170,0,0,0,0.000000," ","integrate(csc(f*x+e)^2/(a+b*sin(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\csc\left(f x + e\right)^{2}}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(csc(f*x + e)^2/(b*sin(f*x + e)^2 + a)^(5/2), x)","F",0
171,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^m*(a+b*sin(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{p} \left(d \sin\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^p*(d*sin(f*x + e))^m, x)","F",0
172,0,0,0,0.000000," ","integrate(sin(f*x+e)^5*(a+b*sin(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{p} \sin\left(f x + e\right)^{5}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^p*sin(f*x + e)^5, x)","F",0
173,0,0,0,0.000000," ","integrate(sin(f*x+e)^3*(a+b*sin(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{p} \sin\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^p*sin(f*x + e)^3, x)","F",0
174,0,0,0,0.000000," ","integrate(sin(f*x+e)*(a+b*sin(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{p} \sin\left(f x + e\right)\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^p*sin(f*x + e), x)","F",0
175,0,0,0,0.000000," ","integrate(csc(f*x+e)*(a+b*sin(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{p} \csc\left(f x + e\right)\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^p*csc(f*x + e), x)","F",0
176,0,0,0,0.000000," ","integrate(csc(f*x+e)^3*(a+b*sin(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{p} \csc\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^p*csc(f*x + e)^3, x)","F",0
177,0,0,0,0.000000," ","integrate(csc(f*x+e)^5*(a+b*sin(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{p} \csc\left(f x + e\right)^{5}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^p*csc(f*x + e)^5, x)","F",0
178,0,0,0,0.000000," ","integrate(sin(f*x+e)^4*(a+b*sin(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{p} \sin\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^p*sin(f*x + e)^4, x)","F",0
179,0,0,0,0.000000," ","integrate(sin(f*x+e)^2*(a+b*sin(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{p} \sin\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^p*sin(f*x + e)^2, x)","F",0
180,0,0,0,0.000000," ","integrate(csc(f*x+e)^2*(a+b*sin(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{p} \csc\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^p*csc(f*x + e)^2, x)","F",0
181,0,0,0,0.000000," ","integrate(csc(f*x+e)^4*(a+b*sin(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{p} \csc\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^p*csc(f*x + e)^4, x)","F",0
182,-1,0,0,0.000000," ","integrate(sin(d*x+c)^7/(a+b*sin(d*x+c)^3),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
183,-1,0,0,0.000000," ","integrate(sin(d*x+c)^5/(a+b*sin(d*x+c)^3),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
184,0,0,0,0.000000," ","integrate(sin(d*x+c)^3/(a+b*sin(d*x+c)^3),x, algorithm=""maxima"")","\frac{-8 \, a b \int \frac{8 \, a \cos\left(3 \, d x + 3 \, c\right)^{2} - b \cos\left(3 \, d x + 3 \, c\right) \sin\left(6 \, d x + 6 \, c\right) + 3 \, b \cos\left(3 \, d x + 3 \, c\right) \sin\left(4 \, d x + 4 \, c\right) + b \cos\left(6 \, d x + 6 \, c\right) \sin\left(3 \, d x + 3 \, c\right) - 3 \, b \cos\left(4 \, d x + 4 \, c\right) \sin\left(3 \, d x + 3 \, c\right) + 8 \, a \sin\left(3 \, d x + 3 \, c\right)^{2} - 3 \, b \cos\left(3 \, d x + 3 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + {\left(3 \, b \cos\left(2 \, d x + 2 \, c\right) - b\right)} \sin\left(3 \, d x + 3 \, c\right)}{b^{3} \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, b^{3} \cos\left(4 \, d x + 4 \, c\right)^{2} + 64 \, a^{2} b \cos\left(3 \, d x + 3 \, c\right)^{2} + 9 \, b^{3} \cos\left(2 \, d x + 2 \, c\right)^{2} + b^{3} \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, b^{3} \sin\left(4 \, d x + 4 \, c\right)^{2} + 64 \, a^{2} b \sin\left(3 \, d x + 3 \, c\right)^{2} - 48 \, a b^{2} \cos\left(3 \, d x + 3 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, b^{3} \sin\left(2 \, d x + 2 \, c\right)^{2} - 6 \, b^{3} \cos\left(2 \, d x + 2 \, c\right) + b^{3} - 2 \, {\left(3 \, b^{3} \cos\left(4 \, d x + 4 \, c\right) - 3 \, b^{3} \cos\left(2 \, d x + 2 \, c\right) - 8 \, a b^{2} \sin\left(3 \, d x + 3 \, c\right) + b^{3}\right)} \cos\left(6 \, d x + 6 \, c\right) - 6 \, {\left(3 \, b^{3} \cos\left(2 \, d x + 2 \, c\right) + 8 \, a b^{2} \sin\left(3 \, d x + 3 \, c\right) - b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right) - 2 \, {\left(8 \, a b^{2} \cos\left(3 \, d x + 3 \, c\right) + 3 \, b^{3} \sin\left(4 \, d x + 4 \, c\right) - 3 \, b^{3} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 6 \, {\left(8 \, a b^{2} \cos\left(3 \, d x + 3 \, c\right) - 3 \, b^{3} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) + 16 \, {\left(3 \, a b^{2} \cos\left(2 \, d x + 2 \, c\right) - a b^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)}\,{d x} + x}{b}"," ",0,"(8*a*b*integrate(-(8*a*cos(3*d*x + 3*c)^2 - b*cos(3*d*x + 3*c)*sin(6*d*x + 6*c) + 3*b*cos(3*d*x + 3*c)*sin(4*d*x + 4*c) + b*cos(6*d*x + 6*c)*sin(3*d*x + 3*c) - 3*b*cos(4*d*x + 4*c)*sin(3*d*x + 3*c) + 8*a*sin(3*d*x + 3*c)^2 - 3*b*cos(3*d*x + 3*c)*sin(2*d*x + 2*c) + (3*b*cos(2*d*x + 2*c) - b)*sin(3*d*x + 3*c))/(b^3*cos(6*d*x + 6*c)^2 + 9*b^3*cos(4*d*x + 4*c)^2 + 64*a^2*b*cos(3*d*x + 3*c)^2 + 9*b^3*cos(2*d*x + 2*c)^2 + b^3*sin(6*d*x + 6*c)^2 + 9*b^3*sin(4*d*x + 4*c)^2 + 64*a^2*b*sin(3*d*x + 3*c)^2 - 48*a*b^2*cos(3*d*x + 3*c)*sin(2*d*x + 2*c) + 9*b^3*sin(2*d*x + 2*c)^2 - 6*b^3*cos(2*d*x + 2*c) + b^3 - 2*(3*b^3*cos(4*d*x + 4*c) - 3*b^3*cos(2*d*x + 2*c) - 8*a*b^2*sin(3*d*x + 3*c) + b^3)*cos(6*d*x + 6*c) - 6*(3*b^3*cos(2*d*x + 2*c) + 8*a*b^2*sin(3*d*x + 3*c) - b^3)*cos(4*d*x + 4*c) - 2*(8*a*b^2*cos(3*d*x + 3*c) + 3*b^3*sin(4*d*x + 4*c) - 3*b^3*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 6*(8*a*b^2*cos(3*d*x + 3*c) - 3*b^3*sin(2*d*x + 2*c))*sin(4*d*x + 4*c) + 16*(3*a*b^2*cos(2*d*x + 2*c) - a*b^2)*sin(3*d*x + 3*c)), x) + x)/b","F",0
185,0,0,0,0.000000," ","integrate(sin(d*x+c)/(a+b*sin(d*x+c)^3),x, algorithm=""maxima"")","\int \frac{\sin\left(d x + c\right)}{b \sin\left(d x + c\right)^{3} + a}\,{d x}"," ",0,"integrate(sin(d*x + c)/(b*sin(d*x + c)^3 + a), x)","F",0
186,-1,0,0,0.000000," ","integrate(csc(d*x+c)/(a+b*sin(d*x+c)^3),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
187,0,0,0,0.000000," ","integrate(csc(d*x+c)^3/(a+b*sin(d*x+c)^3),x, algorithm=""maxima"")","\frac{4 \, {\left(\cos\left(3 \, d x + 3 \, c\right) + \cos\left(d x + c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) - 1\right)} \cos\left(3 \, d x + 3 \, c\right) - 8 \, \cos\left(2 \, d x + 2 \, c\right) \cos\left(d x + c\right) - 32 \, {\left(a b d \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, a b d \cos\left(2 \, d x + 2 \, c\right)^{2} + a b d \sin\left(4 \, d x + 4 \, c\right)^{2} - 4 \, a b d \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, a b d \sin\left(2 \, d x + 2 \, c\right)^{2} - 4 \, a b d \cos\left(2 \, d x + 2 \, c\right) + a b d - 2 \, {\left(2 \, a b d \cos\left(2 \, d x + 2 \, c\right) - a b d\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \int \frac{8 \, a \cos\left(3 \, d x + 3 \, c\right)^{2} - b \cos\left(3 \, d x + 3 \, c\right) \sin\left(6 \, d x + 6 \, c\right) + 3 \, b \cos\left(3 \, d x + 3 \, c\right) \sin\left(4 \, d x + 4 \, c\right) + b \cos\left(6 \, d x + 6 \, c\right) \sin\left(3 \, d x + 3 \, c\right) - 3 \, b \cos\left(4 \, d x + 4 \, c\right) \sin\left(3 \, d x + 3 \, c\right) + 8 \, a \sin\left(3 \, d x + 3 \, c\right)^{2} - 3 \, b \cos\left(3 \, d x + 3 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + {\left(3 \, b \cos\left(2 \, d x + 2 \, c\right) - b\right)} \sin\left(3 \, d x + 3 \, c\right)}{a b^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a b^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 64 \, a^{3} \cos\left(3 \, d x + 3 \, c\right)^{2} + 9 \, a b^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a b^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a b^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 64 \, a^{3} \sin\left(3 \, d x + 3 \, c\right)^{2} - 48 \, a^{2} b \cos\left(3 \, d x + 3 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, a b^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} - 6 \, a b^{2} \cos\left(2 \, d x + 2 \, c\right) + a b^{2} - 2 \, {\left(3 \, a b^{2} \cos\left(4 \, d x + 4 \, c\right) - 3 \, a b^{2} \cos\left(2 \, d x + 2 \, c\right) - 8 \, a^{2} b \sin\left(3 \, d x + 3 \, c\right) + a b^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) - 6 \, {\left(3 \, a b^{2} \cos\left(2 \, d x + 2 \, c\right) + 8 \, a^{2} b \sin\left(3 \, d x + 3 \, c\right) - a b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) - 2 \, {\left(8 \, a^{2} b \cos\left(3 \, d x + 3 \, c\right) + 3 \, a b^{2} \sin\left(4 \, d x + 4 \, c\right) - 3 \, a b^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 6 \, {\left(8 \, a^{2} b \cos\left(3 \, d x + 3 \, c\right) - 3 \, a b^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) + 16 \, {\left(3 \, a^{2} b \cos\left(2 \, d x + 2 \, c\right) - a^{2} b\right)} \sin\left(3 \, d x + 3 \, c\right)}\,{d x} + {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) - 1\right)} \cos\left(4 \, d x + 4 \, c\right) - \cos\left(4 \, d x + 4 \, c\right)^{2} - 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} - \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) - 1\right)} \log\left(\cos\left(d x\right)^{2} + 2 \, \cos\left(d x\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(d x\right)^{2} - 2 \, \sin\left(d x\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right) - {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) - 1\right)} \cos\left(4 \, d x + 4 \, c\right) - \cos\left(4 \, d x + 4 \, c\right)^{2} - 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} - \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) - 1\right)} \log\left(\cos\left(d x\right)^{2} - 2 \, \cos\left(d x\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(d x\right)^{2} + 2 \, \sin\left(d x\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right) + 4 \, {\left(\sin\left(3 \, d x + 3 \, c\right) + \sin\left(d x + c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) - 8 \, \sin\left(3 \, d x + 3 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 8 \, \sin\left(2 \, d x + 2 \, c\right) \sin\left(d x + c\right) + 4 \, \cos\left(d x + c\right)}{4 \, {\left(a d \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, a d \cos\left(2 \, d x + 2 \, c\right)^{2} + a d \sin\left(4 \, d x + 4 \, c\right)^{2} - 4 \, a d \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, a d \sin\left(2 \, d x + 2 \, c\right)^{2} - 4 \, a d \cos\left(2 \, d x + 2 \, c\right) + a d - 2 \, {\left(2 \, a d \cos\left(2 \, d x + 2 \, c\right) - a d\right)} \cos\left(4 \, d x + 4 \, c\right)\right)}}"," ",0,"1/4*(4*(cos(3*d*x + 3*c) + cos(d*x + c))*cos(4*d*x + 4*c) - 4*(2*cos(2*d*x + 2*c) - 1)*cos(3*d*x + 3*c) - 8*cos(2*d*x + 2*c)*cos(d*x + c) + 32*(a*b*d*cos(4*d*x + 4*c)^2 + 4*a*b*d*cos(2*d*x + 2*c)^2 + a*b*d*sin(4*d*x + 4*c)^2 - 4*a*b*d*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*a*b*d*sin(2*d*x + 2*c)^2 - 4*a*b*d*cos(2*d*x + 2*c) + a*b*d - 2*(2*a*b*d*cos(2*d*x + 2*c) - a*b*d)*cos(4*d*x + 4*c))*integrate(-(8*a*cos(3*d*x + 3*c)^2 - b*cos(3*d*x + 3*c)*sin(6*d*x + 6*c) + 3*b*cos(3*d*x + 3*c)*sin(4*d*x + 4*c) + b*cos(6*d*x + 6*c)*sin(3*d*x + 3*c) - 3*b*cos(4*d*x + 4*c)*sin(3*d*x + 3*c) + 8*a*sin(3*d*x + 3*c)^2 - 3*b*cos(3*d*x + 3*c)*sin(2*d*x + 2*c) + (3*b*cos(2*d*x + 2*c) - b)*sin(3*d*x + 3*c))/(a*b^2*cos(6*d*x + 6*c)^2 + 9*a*b^2*cos(4*d*x + 4*c)^2 + 64*a^3*cos(3*d*x + 3*c)^2 + 9*a*b^2*cos(2*d*x + 2*c)^2 + a*b^2*sin(6*d*x + 6*c)^2 + 9*a*b^2*sin(4*d*x + 4*c)^2 + 64*a^3*sin(3*d*x + 3*c)^2 - 48*a^2*b*cos(3*d*x + 3*c)*sin(2*d*x + 2*c) + 9*a*b^2*sin(2*d*x + 2*c)^2 - 6*a*b^2*cos(2*d*x + 2*c) + a*b^2 - 2*(3*a*b^2*cos(4*d*x + 4*c) - 3*a*b^2*cos(2*d*x + 2*c) - 8*a^2*b*sin(3*d*x + 3*c) + a*b^2)*cos(6*d*x + 6*c) - 6*(3*a*b^2*cos(2*d*x + 2*c) + 8*a^2*b*sin(3*d*x + 3*c) - a*b^2)*cos(4*d*x + 4*c) - 2*(8*a^2*b*cos(3*d*x + 3*c) + 3*a*b^2*sin(4*d*x + 4*c) - 3*a*b^2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 6*(8*a^2*b*cos(3*d*x + 3*c) - 3*a*b^2*sin(2*d*x + 2*c))*sin(4*d*x + 4*c) + 16*(3*a^2*b*cos(2*d*x + 2*c) - a^2*b)*sin(3*d*x + 3*c)), x) + (2*(2*cos(2*d*x + 2*c) - 1)*cos(4*d*x + 4*c) - cos(4*d*x + 4*c)^2 - 4*cos(2*d*x + 2*c)^2 - sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) - 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) - 1)*log(cos(d*x)^2 + 2*cos(d*x)*cos(c) + cos(c)^2 + sin(d*x)^2 - 2*sin(d*x)*sin(c) + sin(c)^2) - (2*(2*cos(2*d*x + 2*c) - 1)*cos(4*d*x + 4*c) - cos(4*d*x + 4*c)^2 - 4*cos(2*d*x + 2*c)^2 - sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) - 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) - 1)*log(cos(d*x)^2 - 2*cos(d*x)*cos(c) + cos(c)^2 + sin(d*x)^2 + 2*sin(d*x)*sin(c) + sin(c)^2) + 4*(sin(3*d*x + 3*c) + sin(d*x + c))*sin(4*d*x + 4*c) - 8*sin(3*d*x + 3*c)*sin(2*d*x + 2*c) - 8*sin(2*d*x + 2*c)*sin(d*x + c) + 4*cos(d*x + c))/(a*d*cos(4*d*x + 4*c)^2 + 4*a*d*cos(2*d*x + 2*c)^2 + a*d*sin(4*d*x + 4*c)^2 - 4*a*d*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*a*d*sin(2*d*x + 2*c)^2 - 4*a*d*cos(2*d*x + 2*c) + a*d - 2*(2*a*d*cos(2*d*x + 2*c) - a*d)*cos(4*d*x + 4*c))","F",0
188,-1,0,0,0.000000," ","integrate(csc(d*x+c)^5/(a+b*sin(d*x+c)^3),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
189,0,0,0,0.000000," ","integrate(sin(d*x+c)^6/(a+b*sin(d*x+c)^3),x, algorithm=""maxima"")","-\frac{-96 \, a^{2} b^{2} d \int \frac{8 \, a \cos\left(3 \, d x + 3 \, c\right)^{2} - b \cos\left(3 \, d x + 3 \, c\right) \sin\left(6 \, d x + 6 \, c\right) + 3 \, b \cos\left(3 \, d x + 3 \, c\right) \sin\left(4 \, d x + 4 \, c\right) + b \cos\left(6 \, d x + 6 \, c\right) \sin\left(3 \, d x + 3 \, c\right) - 3 \, b \cos\left(4 \, d x + 4 \, c\right) \sin\left(3 \, d x + 3 \, c\right) + 8 \, a \sin\left(3 \, d x + 3 \, c\right)^{2} - 3 \, b \cos\left(3 \, d x + 3 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + {\left(3 \, b \cos\left(2 \, d x + 2 \, c\right) - b\right)} \sin\left(3 \, d x + 3 \, c\right)}{b^{4} \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, b^{4} \cos\left(4 \, d x + 4 \, c\right)^{2} + 64 \, a^{2} b^{2} \cos\left(3 \, d x + 3 \, c\right)^{2} + 9 \, b^{4} \cos\left(2 \, d x + 2 \, c\right)^{2} + b^{4} \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, b^{4} \sin\left(4 \, d x + 4 \, c\right)^{2} + 64 \, a^{2} b^{2} \sin\left(3 \, d x + 3 \, c\right)^{2} - 48 \, a b^{3} \cos\left(3 \, d x + 3 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, b^{4} \sin\left(2 \, d x + 2 \, c\right)^{2} - 6 \, b^{4} \cos\left(2 \, d x + 2 \, c\right) + b^{4} - 2 \, {\left(3 \, b^{4} \cos\left(4 \, d x + 4 \, c\right) - 3 \, b^{4} \cos\left(2 \, d x + 2 \, c\right) - 8 \, a b^{3} \sin\left(3 \, d x + 3 \, c\right) + b^{4}\right)} \cos\left(6 \, d x + 6 \, c\right) - 6 \, {\left(3 \, b^{4} \cos\left(2 \, d x + 2 \, c\right) + 8 \, a b^{3} \sin\left(3 \, d x + 3 \, c\right) - b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right) - 2 \, {\left(8 \, a b^{3} \cos\left(3 \, d x + 3 \, c\right) + 3 \, b^{4} \sin\left(4 \, d x + 4 \, c\right) - 3 \, b^{4} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 6 \, {\left(8 \, a b^{3} \cos\left(3 \, d x + 3 \, c\right) - 3 \, b^{4} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) + 16 \, {\left(3 \, a b^{3} \cos\left(2 \, d x + 2 \, c\right) - a b^{3}\right)} \sin\left(3 \, d x + 3 \, c\right)}\,{d x} + 12 \, a d x - b \cos\left(3 \, d x + 3 \, c\right) + 9 \, b \cos\left(d x + c\right)}{12 \, b^{2} d}"," ",0,"-1/12*(96*a^2*b^2*d*integrate(-(8*a*cos(3*d*x + 3*c)^2 - b*cos(3*d*x + 3*c)*sin(6*d*x + 6*c) + 3*b*cos(3*d*x + 3*c)*sin(4*d*x + 4*c) + b*cos(6*d*x + 6*c)*sin(3*d*x + 3*c) - 3*b*cos(4*d*x + 4*c)*sin(3*d*x + 3*c) + 8*a*sin(3*d*x + 3*c)^2 - 3*b*cos(3*d*x + 3*c)*sin(2*d*x + 2*c) + (3*b*cos(2*d*x + 2*c) - b)*sin(3*d*x + 3*c))/(b^4*cos(6*d*x + 6*c)^2 + 9*b^4*cos(4*d*x + 4*c)^2 + 64*a^2*b^2*cos(3*d*x + 3*c)^2 + 9*b^4*cos(2*d*x + 2*c)^2 + b^4*sin(6*d*x + 6*c)^2 + 9*b^4*sin(4*d*x + 4*c)^2 + 64*a^2*b^2*sin(3*d*x + 3*c)^2 - 48*a*b^3*cos(3*d*x + 3*c)*sin(2*d*x + 2*c) + 9*b^4*sin(2*d*x + 2*c)^2 - 6*b^4*cos(2*d*x + 2*c) + b^4 - 2*(3*b^4*cos(4*d*x + 4*c) - 3*b^4*cos(2*d*x + 2*c) - 8*a*b^3*sin(3*d*x + 3*c) + b^4)*cos(6*d*x + 6*c) - 6*(3*b^4*cos(2*d*x + 2*c) + 8*a*b^3*sin(3*d*x + 3*c) - b^4)*cos(4*d*x + 4*c) - 2*(8*a*b^3*cos(3*d*x + 3*c) + 3*b^4*sin(4*d*x + 4*c) - 3*b^4*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 6*(8*a*b^3*cos(3*d*x + 3*c) - 3*b^4*sin(2*d*x + 2*c))*sin(4*d*x + 4*c) + 16*(3*a*b^3*cos(2*d*x + 2*c) - a*b^3)*sin(3*d*x + 3*c)), x) + 12*a*d*x - b*cos(3*d*x + 3*c) + 9*b*cos(d*x + c))/(b^2*d)","F",0
190,-1,0,0,0.000000," ","integrate(sin(d*x+c)^4/(a+b*sin(d*x+c)^3),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
191,0,0,0,0.000000," ","integrate(sin(d*x+c)^2/(a+b*sin(d*x+c)^3),x, algorithm=""maxima"")","\int \frac{\sin\left(d x + c\right)^{2}}{b \sin\left(d x + c\right)^{3} + a}\,{d x}"," ",0,"integrate(sin(d*x + c)^2/(b*sin(d*x + c)^3 + a), x)","F",0
192,0,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c)^3),x, algorithm=""maxima"")","\int \frac{1}{b \sin\left(d x + c\right)^{3} + a}\,{d x}"," ",0,"integrate(1/(b*sin(d*x + c)^3 + a), x)","F",0
193,-1,0,0,0.000000," ","integrate(csc(d*x+c)^2/(a+b*sin(d*x+c)^3),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
194,-1,0,0,0.000000," ","integrate(csc(d*x+c)^4/(a+b*sin(d*x+c)^3),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
195,0,0,0,0.000000," ","integrate(sin(d*x+c)^9/(a-b*sin(d*x+c)^4),x, algorithm=""maxima"")","\frac{1920 \, b^{2} d \int \frac{4 \, a^{2} b \cos\left(3 \, d x + 3 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 2 \, {\left(8 \, a^{3} - 3 \, a^{2} b\right)} \cos\left(3 \, d x + 3 \, c\right) \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(8 \, a^{3} - 3 \, a^{2} b\right)} \cos\left(4 \, d x + 4 \, c\right) \sin\left(3 \, d x + 3 \, c\right) - {\left(a^{2} b \sin\left(5 \, d x + 5 \, c\right) - a^{2} b \sin\left(3 \, d x + 3 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) + 4 \, {\left(a^{2} b \sin\left(5 \, d x + 5 \, c\right) - a^{2} b \sin\left(3 \, d x + 3 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left(2 \, a^{2} b \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a^{3} - 3 \, a^{2} b\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left(a^{2} b \cos\left(5 \, d x + 5 \, c\right) - a^{2} b \cos\left(3 \, d x + 3 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) - 4 \, {\left(a^{2} b \cos\left(5 \, d x + 5 \, c\right) - a^{2} b \cos\left(3 \, d x + 3 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + {\left(4 \, a^{2} b \cos\left(2 \, d x + 2 \, c\right) - a^{2} b + 2 \, {\left(8 \, a^{3} - 3 \, a^{2} b\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \sin\left(5 \, d x + 5 \, c\right) - {\left(4 \, a^{2} b \cos\left(2 \, d x + 2 \, c\right) - a^{2} b\right)} \sin\left(3 \, d x + 3 \, c\right)}{b^{4} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, b^{4} \cos\left(6 \, d x + 6 \, c\right)^{2} + 16 \, b^{4} \cos\left(2 \, d x + 2 \, c\right)^{2} + b^{4} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, b^{4} \sin\left(6 \, d x + 6 \, c\right)^{2} + 16 \, b^{4} \sin\left(2 \, d x + 2 \, c\right)^{2} - 8 \, b^{4} \cos\left(2 \, d x + 2 \, c\right) + b^{4} + 4 \, {\left(64 \, a^{2} b^{2} - 48 \, a b^{3} + 9 \, b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(64 \, a^{2} b^{2} - 48 \, a b^{3} + 9 \, b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(8 \, a b^{3} - 3 \, b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 2 \, {\left(4 \, b^{4} \cos\left(6 \, d x + 6 \, c\right) + 4 \, b^{4} \cos\left(2 \, d x + 2 \, c\right) - b^{4} + 2 \, {\left(8 \, a b^{3} - 3 \, b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(4 \, b^{4} \cos\left(2 \, d x + 2 \, c\right) - b^{4} + 2 \, {\left(8 \, a b^{3} - 3 \, b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(8 \, a b^{3} - 3 \, b^{4} - 4 \, {\left(8 \, a b^{3} - 3 \, b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(2 \, b^{4} \sin\left(6 \, d x + 6 \, c\right) + 2 \, b^{4} \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a b^{3} - 3 \, b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(2 \, b^{4} \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a b^{3} - 3 \, b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}\,{d x} + 3 \, b \cos\left(5 \, d x + 5 \, c\right) - 25 \, b \cos\left(3 \, d x + 3 \, c\right) + 30 \, {\left(8 \, a + 5 \, b\right)} \cos\left(d x + c\right)}{240 \, b^{2} d}"," ",0,"1/240*(240*b^2*d*integrate(8*(4*a^2*b*cos(3*d*x + 3*c)*sin(2*d*x + 2*c) + 2*(8*a^3 - 3*a^2*b)*cos(3*d*x + 3*c)*sin(4*d*x + 4*c) - 2*(8*a^3 - 3*a^2*b)*cos(4*d*x + 4*c)*sin(3*d*x + 3*c) - (a^2*b*sin(5*d*x + 5*c) - a^2*b*sin(3*d*x + 3*c))*cos(8*d*x + 8*c) + 4*(a^2*b*sin(5*d*x + 5*c) - a^2*b*sin(3*d*x + 3*c))*cos(6*d*x + 6*c) - 2*(2*a^2*b*sin(2*d*x + 2*c) + (8*a^3 - 3*a^2*b)*sin(4*d*x + 4*c))*cos(5*d*x + 5*c) + (a^2*b*cos(5*d*x + 5*c) - a^2*b*cos(3*d*x + 3*c))*sin(8*d*x + 8*c) - 4*(a^2*b*cos(5*d*x + 5*c) - a^2*b*cos(3*d*x + 3*c))*sin(6*d*x + 6*c) + (4*a^2*b*cos(2*d*x + 2*c) - a^2*b + 2*(8*a^3 - 3*a^2*b)*cos(4*d*x + 4*c))*sin(5*d*x + 5*c) - (4*a^2*b*cos(2*d*x + 2*c) - a^2*b)*sin(3*d*x + 3*c))/(b^4*cos(8*d*x + 8*c)^2 + 16*b^4*cos(6*d*x + 6*c)^2 + 16*b^4*cos(2*d*x + 2*c)^2 + b^4*sin(8*d*x + 8*c)^2 + 16*b^4*sin(6*d*x + 6*c)^2 + 16*b^4*sin(2*d*x + 2*c)^2 - 8*b^4*cos(2*d*x + 2*c) + b^4 + 4*(64*a^2*b^2 - 48*a*b^3 + 9*b^4)*cos(4*d*x + 4*c)^2 + 4*(64*a^2*b^2 - 48*a*b^3 + 9*b^4)*sin(4*d*x + 4*c)^2 + 16*(8*a*b^3 - 3*b^4)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) - 2*(4*b^4*cos(6*d*x + 6*c) + 4*b^4*cos(2*d*x + 2*c) - b^4 + 2*(8*a*b^3 - 3*b^4)*cos(4*d*x + 4*c))*cos(8*d*x + 8*c) + 8*(4*b^4*cos(2*d*x + 2*c) - b^4 + 2*(8*a*b^3 - 3*b^4)*cos(4*d*x + 4*c))*cos(6*d*x + 6*c) - 4*(8*a*b^3 - 3*b^4 - 4*(8*a*b^3 - 3*b^4)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 4*(2*b^4*sin(6*d*x + 6*c) + 2*b^4*sin(2*d*x + 2*c) + (8*a*b^3 - 3*b^4)*sin(4*d*x + 4*c))*sin(8*d*x + 8*c) + 16*(2*b^4*sin(2*d*x + 2*c) + (8*a*b^3 - 3*b^4)*sin(4*d*x + 4*c))*sin(6*d*x + 6*c)), x) + 3*b*cos(5*d*x + 5*c) - 25*b*cos(3*d*x + 3*c) + 30*(8*a + 5*b)*cos(d*x + c))/(b^2*d)","F",0
196,0,0,0,0.000000," ","integrate(sin(d*x+c)^7/(a-b*sin(d*x+c)^4),x, algorithm=""maxima"")","-\frac{-24 \, b d \int \frac{12 \, a b \cos\left(3 \, d x + 3 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 4 \, a b \cos\left(d x + c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, a b \cos\left(2 \, d x + 2 \, c\right) \sin\left(d x + c\right) - a b \sin\left(d x + c\right) + {\left(a b \sin\left(7 \, d x + 7 \, c\right) - 3 \, a b \sin\left(5 \, d x + 5 \, c\right) + 3 \, a b \sin\left(3 \, d x + 3 \, c\right) - a b \sin\left(d x + c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) + 2 \, {\left(2 \, a b \sin\left(6 \, d x + 6 \, c\right) + 2 \, a b \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a^{2} - 3 \, a b\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \cos\left(7 \, d x + 7 \, c\right) + 4 \, {\left(3 \, a b \sin\left(5 \, d x + 5 \, c\right) - 3 \, a b \sin\left(3 \, d x + 3 \, c\right) + a b \sin\left(d x + c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 6 \, {\left(2 \, a b \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a^{2} - 3 \, a b\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \cos\left(5 \, d x + 5 \, c\right) - 2 \, {\left(3 \, {\left(8 \, a^{2} - 3 \, a b\right)} \sin\left(3 \, d x + 3 \, c\right) - {\left(8 \, a^{2} - 3 \, a b\right)} \sin\left(d x + c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - {\left(a b \cos\left(7 \, d x + 7 \, c\right) - 3 \, a b \cos\left(5 \, d x + 5 \, c\right) + 3 \, a b \cos\left(3 \, d x + 3 \, c\right) - a b \cos\left(d x + c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) - {\left(4 \, a b \cos\left(6 \, d x + 6 \, c\right) + 4 \, a b \cos\left(2 \, d x + 2 \, c\right) - a b + 2 \, {\left(8 \, a^{2} - 3 \, a b\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \sin\left(7 \, d x + 7 \, c\right) - 4 \, {\left(3 \, a b \cos\left(5 \, d x + 5 \, c\right) - 3 \, a b \cos\left(3 \, d x + 3 \, c\right) + a b \cos\left(d x + c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 3 \, {\left(4 \, a b \cos\left(2 \, d x + 2 \, c\right) - a b + 2 \, {\left(8 \, a^{2} - 3 \, a b\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \sin\left(5 \, d x + 5 \, c\right) + 2 \, {\left(3 \, {\left(8 \, a^{2} - 3 \, a b\right)} \cos\left(3 \, d x + 3 \, c\right) - {\left(8 \, a^{2} - 3 \, a b\right)} \cos\left(d x + c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) - 3 \, {\left(4 \, a b \cos\left(2 \, d x + 2 \, c\right) - a b\right)} \sin\left(3 \, d x + 3 \, c\right)}{b^{3} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, b^{3} \cos\left(6 \, d x + 6 \, c\right)^{2} + 16 \, b^{3} \cos\left(2 \, d x + 2 \, c\right)^{2} + b^{3} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, b^{3} \sin\left(6 \, d x + 6 \, c\right)^{2} + 16 \, b^{3} \sin\left(2 \, d x + 2 \, c\right)^{2} - 8 \, b^{3} \cos\left(2 \, d x + 2 \, c\right) + b^{3} + 4 \, {\left(64 \, a^{2} b - 48 \, a b^{2} + 9 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(64 \, a^{2} b - 48 \, a b^{2} + 9 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(8 \, a b^{2} - 3 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 2 \, {\left(4 \, b^{3} \cos\left(6 \, d x + 6 \, c\right) + 4 \, b^{3} \cos\left(2 \, d x + 2 \, c\right) - b^{3} + 2 \, {\left(8 \, a b^{2} - 3 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(4 \, b^{3} \cos\left(2 \, d x + 2 \, c\right) - b^{3} + 2 \, {\left(8 \, a b^{2} - 3 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(8 \, a b^{2} - 3 \, b^{3} - 4 \, {\left(8 \, a b^{2} - 3 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(2 \, b^{3} \sin\left(6 \, d x + 6 \, c\right) + 2 \, b^{3} \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a b^{2} - 3 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(2 \, b^{3} \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a b^{2} - 3 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}\,{d x} + \cos\left(3 \, d x + 3 \, c\right) - 9 \, \cos\left(d x + c\right)}{12 \, b d}"," ",0,"-1/12*(12*b*d*integrate(-2*(12*a*b*cos(3*d*x + 3*c)*sin(2*d*x + 2*c) - 4*a*b*cos(d*x + c)*sin(2*d*x + 2*c) + 4*a*b*cos(2*d*x + 2*c)*sin(d*x + c) - a*b*sin(d*x + c) + (a*b*sin(7*d*x + 7*c) - 3*a*b*sin(5*d*x + 5*c) + 3*a*b*sin(3*d*x + 3*c) - a*b*sin(d*x + c))*cos(8*d*x + 8*c) + 2*(2*a*b*sin(6*d*x + 6*c) + 2*a*b*sin(2*d*x + 2*c) + (8*a^2 - 3*a*b)*sin(4*d*x + 4*c))*cos(7*d*x + 7*c) + 4*(3*a*b*sin(5*d*x + 5*c) - 3*a*b*sin(3*d*x + 3*c) + a*b*sin(d*x + c))*cos(6*d*x + 6*c) - 6*(2*a*b*sin(2*d*x + 2*c) + (8*a^2 - 3*a*b)*sin(4*d*x + 4*c))*cos(5*d*x + 5*c) - 2*(3*(8*a^2 - 3*a*b)*sin(3*d*x + 3*c) - (8*a^2 - 3*a*b)*sin(d*x + c))*cos(4*d*x + 4*c) - (a*b*cos(7*d*x + 7*c) - 3*a*b*cos(5*d*x + 5*c) + 3*a*b*cos(3*d*x + 3*c) - a*b*cos(d*x + c))*sin(8*d*x + 8*c) - (4*a*b*cos(6*d*x + 6*c) + 4*a*b*cos(2*d*x + 2*c) - a*b + 2*(8*a^2 - 3*a*b)*cos(4*d*x + 4*c))*sin(7*d*x + 7*c) - 4*(3*a*b*cos(5*d*x + 5*c) - 3*a*b*cos(3*d*x + 3*c) + a*b*cos(d*x + c))*sin(6*d*x + 6*c) + 3*(4*a*b*cos(2*d*x + 2*c) - a*b + 2*(8*a^2 - 3*a*b)*cos(4*d*x + 4*c))*sin(5*d*x + 5*c) + 2*(3*(8*a^2 - 3*a*b)*cos(3*d*x + 3*c) - (8*a^2 - 3*a*b)*cos(d*x + c))*sin(4*d*x + 4*c) - 3*(4*a*b*cos(2*d*x + 2*c) - a*b)*sin(3*d*x + 3*c))/(b^3*cos(8*d*x + 8*c)^2 + 16*b^3*cos(6*d*x + 6*c)^2 + 16*b^3*cos(2*d*x + 2*c)^2 + b^3*sin(8*d*x + 8*c)^2 + 16*b^3*sin(6*d*x + 6*c)^2 + 16*b^3*sin(2*d*x + 2*c)^2 - 8*b^3*cos(2*d*x + 2*c) + b^3 + 4*(64*a^2*b - 48*a*b^2 + 9*b^3)*cos(4*d*x + 4*c)^2 + 4*(64*a^2*b - 48*a*b^2 + 9*b^3)*sin(4*d*x + 4*c)^2 + 16*(8*a*b^2 - 3*b^3)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) - 2*(4*b^3*cos(6*d*x + 6*c) + 4*b^3*cos(2*d*x + 2*c) - b^3 + 2*(8*a*b^2 - 3*b^3)*cos(4*d*x + 4*c))*cos(8*d*x + 8*c) + 8*(4*b^3*cos(2*d*x + 2*c) - b^3 + 2*(8*a*b^2 - 3*b^3)*cos(4*d*x + 4*c))*cos(6*d*x + 6*c) - 4*(8*a*b^2 - 3*b^3 - 4*(8*a*b^2 - 3*b^3)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 4*(2*b^3*sin(6*d*x + 6*c) + 2*b^3*sin(2*d*x + 2*c) + (8*a*b^2 - 3*b^3)*sin(4*d*x + 4*c))*sin(8*d*x + 8*c) + 16*(2*b^3*sin(2*d*x + 2*c) + (8*a*b^2 - 3*b^3)*sin(4*d*x + 4*c))*sin(6*d*x + 6*c)), x) + cos(3*d*x + 3*c) - 9*cos(d*x + c))/(b*d)","F",0
197,0,0,0,0.000000," ","integrate(sin(d*x+c)^5/(a-b*sin(d*x+c)^4),x, algorithm=""maxima"")","\frac{8 \, b d \int \frac{4 \, a b \cos\left(3 \, d x + 3 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 2 \, {\left(8 \, a^{2} - 3 \, a b\right)} \cos\left(3 \, d x + 3 \, c\right) \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(8 \, a^{2} - 3 \, a b\right)} \cos\left(4 \, d x + 4 \, c\right) \sin\left(3 \, d x + 3 \, c\right) - {\left(a b \sin\left(5 \, d x + 5 \, c\right) - a b \sin\left(3 \, d x + 3 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) + 4 \, {\left(a b \sin\left(5 \, d x + 5 \, c\right) - a b \sin\left(3 \, d x + 3 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left(2 \, a b \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a^{2} - 3 \, a b\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left(a b \cos\left(5 \, d x + 5 \, c\right) - a b \cos\left(3 \, d x + 3 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) - 4 \, {\left(a b \cos\left(5 \, d x + 5 \, c\right) - a b \cos\left(3 \, d x + 3 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + {\left(4 \, a b \cos\left(2 \, d x + 2 \, c\right) - a b + 2 \, {\left(8 \, a^{2} - 3 \, a b\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \sin\left(5 \, d x + 5 \, c\right) - {\left(4 \, a b \cos\left(2 \, d x + 2 \, c\right) - a b\right)} \sin\left(3 \, d x + 3 \, c\right)}{b^{3} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, b^{3} \cos\left(6 \, d x + 6 \, c\right)^{2} + 16 \, b^{3} \cos\left(2 \, d x + 2 \, c\right)^{2} + b^{3} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, b^{3} \sin\left(6 \, d x + 6 \, c\right)^{2} + 16 \, b^{3} \sin\left(2 \, d x + 2 \, c\right)^{2} - 8 \, b^{3} \cos\left(2 \, d x + 2 \, c\right) + b^{3} + 4 \, {\left(64 \, a^{2} b - 48 \, a b^{2} + 9 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(64 \, a^{2} b - 48 \, a b^{2} + 9 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(8 \, a b^{2} - 3 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 2 \, {\left(4 \, b^{3} \cos\left(6 \, d x + 6 \, c\right) + 4 \, b^{3} \cos\left(2 \, d x + 2 \, c\right) - b^{3} + 2 \, {\left(8 \, a b^{2} - 3 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(4 \, b^{3} \cos\left(2 \, d x + 2 \, c\right) - b^{3} + 2 \, {\left(8 \, a b^{2} - 3 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(8 \, a b^{2} - 3 \, b^{3} - 4 \, {\left(8 \, a b^{2} - 3 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(2 \, b^{3} \sin\left(6 \, d x + 6 \, c\right) + 2 \, b^{3} \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a b^{2} - 3 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(2 \, b^{3} \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a b^{2} - 3 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}\,{d x} + \cos\left(d x + c\right)}{b d}"," ",0,"(b*d*integrate(8*(4*a*b*cos(3*d*x + 3*c)*sin(2*d*x + 2*c) + 2*(8*a^2 - 3*a*b)*cos(3*d*x + 3*c)*sin(4*d*x + 4*c) - 2*(8*a^2 - 3*a*b)*cos(4*d*x + 4*c)*sin(3*d*x + 3*c) - (a*b*sin(5*d*x + 5*c) - a*b*sin(3*d*x + 3*c))*cos(8*d*x + 8*c) + 4*(a*b*sin(5*d*x + 5*c) - a*b*sin(3*d*x + 3*c))*cos(6*d*x + 6*c) - 2*(2*a*b*sin(2*d*x + 2*c) + (8*a^2 - 3*a*b)*sin(4*d*x + 4*c))*cos(5*d*x + 5*c) + (a*b*cos(5*d*x + 5*c) - a*b*cos(3*d*x + 3*c))*sin(8*d*x + 8*c) - 4*(a*b*cos(5*d*x + 5*c) - a*b*cos(3*d*x + 3*c))*sin(6*d*x + 6*c) + (4*a*b*cos(2*d*x + 2*c) - a*b + 2*(8*a^2 - 3*a*b)*cos(4*d*x + 4*c))*sin(5*d*x + 5*c) - (4*a*b*cos(2*d*x + 2*c) - a*b)*sin(3*d*x + 3*c))/(b^3*cos(8*d*x + 8*c)^2 + 16*b^3*cos(6*d*x + 6*c)^2 + 16*b^3*cos(2*d*x + 2*c)^2 + b^3*sin(8*d*x + 8*c)^2 + 16*b^3*sin(6*d*x + 6*c)^2 + 16*b^3*sin(2*d*x + 2*c)^2 - 8*b^3*cos(2*d*x + 2*c) + b^3 + 4*(64*a^2*b - 48*a*b^2 + 9*b^3)*cos(4*d*x + 4*c)^2 + 4*(64*a^2*b - 48*a*b^2 + 9*b^3)*sin(4*d*x + 4*c)^2 + 16*(8*a*b^2 - 3*b^3)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) - 2*(4*b^3*cos(6*d*x + 6*c) + 4*b^3*cos(2*d*x + 2*c) - b^3 + 2*(8*a*b^2 - 3*b^3)*cos(4*d*x + 4*c))*cos(8*d*x + 8*c) + 8*(4*b^3*cos(2*d*x + 2*c) - b^3 + 2*(8*a*b^2 - 3*b^3)*cos(4*d*x + 4*c))*cos(6*d*x + 6*c) - 4*(8*a*b^2 - 3*b^3 - 4*(8*a*b^2 - 3*b^3)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 4*(2*b^3*sin(6*d*x + 6*c) + 2*b^3*sin(2*d*x + 2*c) + (8*a*b^2 - 3*b^3)*sin(4*d*x + 4*c))*sin(8*d*x + 8*c) + 16*(2*b^3*sin(2*d*x + 2*c) + (8*a*b^2 - 3*b^3)*sin(4*d*x + 4*c))*sin(6*d*x + 6*c)), x) + cos(d*x + c))/(b*d)","F",0
198,0,0,0,0.000000," ","integrate(sin(d*x+c)^3/(a-b*sin(d*x+c)^4),x, algorithm=""maxima"")","-\int \frac{\sin\left(d x + c\right)^{3}}{b \sin\left(d x + c\right)^{4} - a}\,{d x}"," ",0,"-integrate(sin(d*x + c)^3/(b*sin(d*x + c)^4 - a), x)","F",0
199,0,0,0,0.000000," ","integrate(sin(d*x+c)/(a-b*sin(d*x+c)^4),x, algorithm=""maxima"")","-\int \frac{\sin\left(d x + c\right)}{b \sin\left(d x + c\right)^{4} - a}\,{d x}"," ",0,"-integrate(sin(d*x + c)/(b*sin(d*x + c)^4 - a), x)","F",0
200,0,0,0,0.000000," ","integrate(csc(d*x+c)/(a-b*sin(d*x+c)^4),x, algorithm=""maxima"")","-\frac{-4 \, a d \int \frac{12 \, b^{2} \cos\left(3 \, d x + 3 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 4 \, b^{2} \cos\left(d x + c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(d x + c\right) - b^{2} \sin\left(d x + c\right) + {\left(b^{2} \sin\left(7 \, d x + 7 \, c\right) - 3 \, b^{2} \sin\left(5 \, d x + 5 \, c\right) + 3 \, b^{2} \sin\left(3 \, d x + 3 \, c\right) - b^{2} \sin\left(d x + c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) + 2 \, {\left(2 \, b^{2} \sin\left(6 \, d x + 6 \, c\right) + 2 \, b^{2} \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a b - 3 \, b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \cos\left(7 \, d x + 7 \, c\right) + 4 \, {\left(3 \, b^{2} \sin\left(5 \, d x + 5 \, c\right) - 3 \, b^{2} \sin\left(3 \, d x + 3 \, c\right) + b^{2} \sin\left(d x + c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 6 \, {\left(2 \, b^{2} \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a b - 3 \, b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \cos\left(5 \, d x + 5 \, c\right) - 2 \, {\left(3 \, {\left(8 \, a b - 3 \, b^{2}\right)} \sin\left(3 \, d x + 3 \, c\right) - {\left(8 \, a b - 3 \, b^{2}\right)} \sin\left(d x + c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - {\left(b^{2} \cos\left(7 \, d x + 7 \, c\right) - 3 \, b^{2} \cos\left(5 \, d x + 5 \, c\right) + 3 \, b^{2} \cos\left(3 \, d x + 3 \, c\right) - b^{2} \cos\left(d x + c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) - {\left(4 \, b^{2} \cos\left(6 \, d x + 6 \, c\right) + 4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) - b^{2} + 2 \, {\left(8 \, a b - 3 \, b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \sin\left(7 \, d x + 7 \, c\right) - 4 \, {\left(3 \, b^{2} \cos\left(5 \, d x + 5 \, c\right) - 3 \, b^{2} \cos\left(3 \, d x + 3 \, c\right) + b^{2} \cos\left(d x + c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 3 \, {\left(4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) - b^{2} + 2 \, {\left(8 \, a b - 3 \, b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \sin\left(5 \, d x + 5 \, c\right) + 2 \, {\left(3 \, {\left(8 \, a b - 3 \, b^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) - {\left(8 \, a b - 3 \, b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) - 3 \, {\left(4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) - b^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)}{a b^{2} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a b^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 16 \, a b^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a b^{2} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a b^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 16 \, a b^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} - 8 \, a b^{2} \cos\left(2 \, d x + 2 \, c\right) + a b^{2} + 4 \, {\left(64 \, a^{3} - 48 \, a^{2} b + 9 \, a b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(64 \, a^{3} - 48 \, a^{2} b + 9 \, a b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(8 \, a^{2} b - 3 \, a b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 2 \, {\left(4 \, a b^{2} \cos\left(6 \, d x + 6 \, c\right) + 4 \, a b^{2} \cos\left(2 \, d x + 2 \, c\right) - a b^{2} + 2 \, {\left(8 \, a^{2} b - 3 \, a b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(4 \, a b^{2} \cos\left(2 \, d x + 2 \, c\right) - a b^{2} + 2 \, {\left(8 \, a^{2} b - 3 \, a b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(8 \, a^{2} b - 3 \, a b^{2} - 4 \, {\left(8 \, a^{2} b - 3 \, a b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(2 \, a b^{2} \sin\left(6 \, d x + 6 \, c\right) + 2 \, a b^{2} \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a^{2} b - 3 \, a b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(2 \, a b^{2} \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a^{2} b - 3 \, a b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}\,{d x} + \log\left(\cos\left(d x\right)^{2} + 2 \, \cos\left(d x\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(d x\right)^{2} - 2 \, \sin\left(d x\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right) - \log\left(\cos\left(d x\right)^{2} - 2 \, \cos\left(d x\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(d x\right)^{2} + 2 \, \sin\left(d x\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right)}{2 \, a d}"," ",0,"-1/2*(2*a*d*integrate(-2*(12*b^2*cos(3*d*x + 3*c)*sin(2*d*x + 2*c) - 4*b^2*cos(d*x + c)*sin(2*d*x + 2*c) + 4*b^2*cos(2*d*x + 2*c)*sin(d*x + c) - b^2*sin(d*x + c) + (b^2*sin(7*d*x + 7*c) - 3*b^2*sin(5*d*x + 5*c) + 3*b^2*sin(3*d*x + 3*c) - b^2*sin(d*x + c))*cos(8*d*x + 8*c) + 2*(2*b^2*sin(6*d*x + 6*c) + 2*b^2*sin(2*d*x + 2*c) + (8*a*b - 3*b^2)*sin(4*d*x + 4*c))*cos(7*d*x + 7*c) + 4*(3*b^2*sin(5*d*x + 5*c) - 3*b^2*sin(3*d*x + 3*c) + b^2*sin(d*x + c))*cos(6*d*x + 6*c) - 6*(2*b^2*sin(2*d*x + 2*c) + (8*a*b - 3*b^2)*sin(4*d*x + 4*c))*cos(5*d*x + 5*c) - 2*(3*(8*a*b - 3*b^2)*sin(3*d*x + 3*c) - (8*a*b - 3*b^2)*sin(d*x + c))*cos(4*d*x + 4*c) - (b^2*cos(7*d*x + 7*c) - 3*b^2*cos(5*d*x + 5*c) + 3*b^2*cos(3*d*x + 3*c) - b^2*cos(d*x + c))*sin(8*d*x + 8*c) - (4*b^2*cos(6*d*x + 6*c) + 4*b^2*cos(2*d*x + 2*c) - b^2 + 2*(8*a*b - 3*b^2)*cos(4*d*x + 4*c))*sin(7*d*x + 7*c) - 4*(3*b^2*cos(5*d*x + 5*c) - 3*b^2*cos(3*d*x + 3*c) + b^2*cos(d*x + c))*sin(6*d*x + 6*c) + 3*(4*b^2*cos(2*d*x + 2*c) - b^2 + 2*(8*a*b - 3*b^2)*cos(4*d*x + 4*c))*sin(5*d*x + 5*c) + 2*(3*(8*a*b - 3*b^2)*cos(3*d*x + 3*c) - (8*a*b - 3*b^2)*cos(d*x + c))*sin(4*d*x + 4*c) - 3*(4*b^2*cos(2*d*x + 2*c) - b^2)*sin(3*d*x + 3*c))/(a*b^2*cos(8*d*x + 8*c)^2 + 16*a*b^2*cos(6*d*x + 6*c)^2 + 16*a*b^2*cos(2*d*x + 2*c)^2 + a*b^2*sin(8*d*x + 8*c)^2 + 16*a*b^2*sin(6*d*x + 6*c)^2 + 16*a*b^2*sin(2*d*x + 2*c)^2 - 8*a*b^2*cos(2*d*x + 2*c) + a*b^2 + 4*(64*a^3 - 48*a^2*b + 9*a*b^2)*cos(4*d*x + 4*c)^2 + 4*(64*a^3 - 48*a^2*b + 9*a*b^2)*sin(4*d*x + 4*c)^2 + 16*(8*a^2*b - 3*a*b^2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) - 2*(4*a*b^2*cos(6*d*x + 6*c) + 4*a*b^2*cos(2*d*x + 2*c) - a*b^2 + 2*(8*a^2*b - 3*a*b^2)*cos(4*d*x + 4*c))*cos(8*d*x + 8*c) + 8*(4*a*b^2*cos(2*d*x + 2*c) - a*b^2 + 2*(8*a^2*b - 3*a*b^2)*cos(4*d*x + 4*c))*cos(6*d*x + 6*c) - 4*(8*a^2*b - 3*a*b^2 - 4*(8*a^2*b - 3*a*b^2)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 4*(2*a*b^2*sin(6*d*x + 6*c) + 2*a*b^2*sin(2*d*x + 2*c) + (8*a^2*b - 3*a*b^2)*sin(4*d*x + 4*c))*sin(8*d*x + 8*c) + 16*(2*a*b^2*sin(2*d*x + 2*c) + (8*a^2*b - 3*a*b^2)*sin(4*d*x + 4*c))*sin(6*d*x + 6*c)), x) + log(cos(d*x)^2 + 2*cos(d*x)*cos(c) + cos(c)^2 + sin(d*x)^2 - 2*sin(d*x)*sin(c) + sin(c)^2) - log(cos(d*x)^2 - 2*cos(d*x)*cos(c) + cos(c)^2 + sin(d*x)^2 + 2*sin(d*x)*sin(c) + sin(c)^2))/(a*d)","F",0
201,0,0,0,0.000000," ","integrate(csc(d*x+c)^3/(a-b*sin(d*x+c)^4),x, algorithm=""maxima"")","\frac{4 \, {\left(\cos\left(3 \, d x + 3 \, c\right) + \cos\left(d x + c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) - 1\right)} \cos\left(3 \, d x + 3 \, c\right) - 8 \, \cos\left(2 \, d x + 2 \, c\right) \cos\left(d x + c\right) + 32 \, {\left(a d \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, a d \cos\left(2 \, d x + 2 \, c\right)^{2} + a d \sin\left(4 \, d x + 4 \, c\right)^{2} - 4 \, a d \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, a d \sin\left(2 \, d x + 2 \, c\right)^{2} - 4 \, a d \cos\left(2 \, d x + 2 \, c\right) + a d - 2 \, {\left(2 \, a d \cos\left(2 \, d x + 2 \, c\right) - a d\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \int \frac{4 \, b^{2} \cos\left(3 \, d x + 3 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 2 \, {\left(8 \, a b - 3 \, b^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(8 \, a b - 3 \, b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) \sin\left(3 \, d x + 3 \, c\right) - {\left(b^{2} \sin\left(5 \, d x + 5 \, c\right) - b^{2} \sin\left(3 \, d x + 3 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) + 4 \, {\left(b^{2} \sin\left(5 \, d x + 5 \, c\right) - b^{2} \sin\left(3 \, d x + 3 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left(2 \, b^{2} \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a b - 3 \, b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left(b^{2} \cos\left(5 \, d x + 5 \, c\right) - b^{2} \cos\left(3 \, d x + 3 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) - 4 \, {\left(b^{2} \cos\left(5 \, d x + 5 \, c\right) - b^{2} \cos\left(3 \, d x + 3 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + {\left(4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) - b^{2} + 2 \, {\left(8 \, a b - 3 \, b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \sin\left(5 \, d x + 5 \, c\right) - {\left(4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) - b^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)}{a b^{2} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a b^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 16 \, a b^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a b^{2} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a b^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 16 \, a b^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} - 8 \, a b^{2} \cos\left(2 \, d x + 2 \, c\right) + a b^{2} + 4 \, {\left(64 \, a^{3} - 48 \, a^{2} b + 9 \, a b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(64 \, a^{3} - 48 \, a^{2} b + 9 \, a b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(8 \, a^{2} b - 3 \, a b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 2 \, {\left(4 \, a b^{2} \cos\left(6 \, d x + 6 \, c\right) + 4 \, a b^{2} \cos\left(2 \, d x + 2 \, c\right) - a b^{2} + 2 \, {\left(8 \, a^{2} b - 3 \, a b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(4 \, a b^{2} \cos\left(2 \, d x + 2 \, c\right) - a b^{2} + 2 \, {\left(8 \, a^{2} b - 3 \, a b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(8 \, a^{2} b - 3 \, a b^{2} - 4 \, {\left(8 \, a^{2} b - 3 \, a b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(2 \, a b^{2} \sin\left(6 \, d x + 6 \, c\right) + 2 \, a b^{2} \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a^{2} b - 3 \, a b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(2 \, a b^{2} \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a^{2} b - 3 \, a b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}\,{d x} + {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) - 1\right)} \cos\left(4 \, d x + 4 \, c\right) - \cos\left(4 \, d x + 4 \, c\right)^{2} - 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} - \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) - 1\right)} \log\left(\cos\left(d x\right)^{2} + 2 \, \cos\left(d x\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(d x\right)^{2} - 2 \, \sin\left(d x\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right) - {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) - 1\right)} \cos\left(4 \, d x + 4 \, c\right) - \cos\left(4 \, d x + 4 \, c\right)^{2} - 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} - \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) - 1\right)} \log\left(\cos\left(d x\right)^{2} - 2 \, \cos\left(d x\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(d x\right)^{2} + 2 \, \sin\left(d x\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right) + 4 \, {\left(\sin\left(3 \, d x + 3 \, c\right) + \sin\left(d x + c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) - 8 \, \sin\left(3 \, d x + 3 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 8 \, \sin\left(2 \, d x + 2 \, c\right) \sin\left(d x + c\right) + 4 \, \cos\left(d x + c\right)}{4 \, {\left(a d \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, a d \cos\left(2 \, d x + 2 \, c\right)^{2} + a d \sin\left(4 \, d x + 4 \, c\right)^{2} - 4 \, a d \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, a d \sin\left(2 \, d x + 2 \, c\right)^{2} - 4 \, a d \cos\left(2 \, d x + 2 \, c\right) + a d - 2 \, {\left(2 \, a d \cos\left(2 \, d x + 2 \, c\right) - a d\right)} \cos\left(4 \, d x + 4 \, c\right)\right)}}"," ",0,"1/4*(4*(cos(3*d*x + 3*c) + cos(d*x + c))*cos(4*d*x + 4*c) - 4*(2*cos(2*d*x + 2*c) - 1)*cos(3*d*x + 3*c) - 8*cos(2*d*x + 2*c)*cos(d*x + c) + 4*(a*d*cos(4*d*x + 4*c)^2 + 4*a*d*cos(2*d*x + 2*c)^2 + a*d*sin(4*d*x + 4*c)^2 - 4*a*d*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*a*d*sin(2*d*x + 2*c)^2 - 4*a*d*cos(2*d*x + 2*c) + a*d - 2*(2*a*d*cos(2*d*x + 2*c) - a*d)*cos(4*d*x + 4*c))*integrate(8*(4*b^2*cos(3*d*x + 3*c)*sin(2*d*x + 2*c) + 2*(8*a*b - 3*b^2)*cos(3*d*x + 3*c)*sin(4*d*x + 4*c) - 2*(8*a*b - 3*b^2)*cos(4*d*x + 4*c)*sin(3*d*x + 3*c) - (b^2*sin(5*d*x + 5*c) - b^2*sin(3*d*x + 3*c))*cos(8*d*x + 8*c) + 4*(b^2*sin(5*d*x + 5*c) - b^2*sin(3*d*x + 3*c))*cos(6*d*x + 6*c) - 2*(2*b^2*sin(2*d*x + 2*c) + (8*a*b - 3*b^2)*sin(4*d*x + 4*c))*cos(5*d*x + 5*c) + (b^2*cos(5*d*x + 5*c) - b^2*cos(3*d*x + 3*c))*sin(8*d*x + 8*c) - 4*(b^2*cos(5*d*x + 5*c) - b^2*cos(3*d*x + 3*c))*sin(6*d*x + 6*c) + (4*b^2*cos(2*d*x + 2*c) - b^2 + 2*(8*a*b - 3*b^2)*cos(4*d*x + 4*c))*sin(5*d*x + 5*c) - (4*b^2*cos(2*d*x + 2*c) - b^2)*sin(3*d*x + 3*c))/(a*b^2*cos(8*d*x + 8*c)^2 + 16*a*b^2*cos(6*d*x + 6*c)^2 + 16*a*b^2*cos(2*d*x + 2*c)^2 + a*b^2*sin(8*d*x + 8*c)^2 + 16*a*b^2*sin(6*d*x + 6*c)^2 + 16*a*b^2*sin(2*d*x + 2*c)^2 - 8*a*b^2*cos(2*d*x + 2*c) + a*b^2 + 4*(64*a^3 - 48*a^2*b + 9*a*b^2)*cos(4*d*x + 4*c)^2 + 4*(64*a^3 - 48*a^2*b + 9*a*b^2)*sin(4*d*x + 4*c)^2 + 16*(8*a^2*b - 3*a*b^2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) - 2*(4*a*b^2*cos(6*d*x + 6*c) + 4*a*b^2*cos(2*d*x + 2*c) - a*b^2 + 2*(8*a^2*b - 3*a*b^2)*cos(4*d*x + 4*c))*cos(8*d*x + 8*c) + 8*(4*a*b^2*cos(2*d*x + 2*c) - a*b^2 + 2*(8*a^2*b - 3*a*b^2)*cos(4*d*x + 4*c))*cos(6*d*x + 6*c) - 4*(8*a^2*b - 3*a*b^2 - 4*(8*a^2*b - 3*a*b^2)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 4*(2*a*b^2*sin(6*d*x + 6*c) + 2*a*b^2*sin(2*d*x + 2*c) + (8*a^2*b - 3*a*b^2)*sin(4*d*x + 4*c))*sin(8*d*x + 8*c) + 16*(2*a*b^2*sin(2*d*x + 2*c) + (8*a^2*b - 3*a*b^2)*sin(4*d*x + 4*c))*sin(6*d*x + 6*c)), x) + (2*(2*cos(2*d*x + 2*c) - 1)*cos(4*d*x + 4*c) - cos(4*d*x + 4*c)^2 - 4*cos(2*d*x + 2*c)^2 - sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) - 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) - 1)*log(cos(d*x)^2 + 2*cos(d*x)*cos(c) + cos(c)^2 + sin(d*x)^2 - 2*sin(d*x)*sin(c) + sin(c)^2) - (2*(2*cos(2*d*x + 2*c) - 1)*cos(4*d*x + 4*c) - cos(4*d*x + 4*c)^2 - 4*cos(2*d*x + 2*c)^2 - sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) - 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) - 1)*log(cos(d*x)^2 - 2*cos(d*x)*cos(c) + cos(c)^2 + sin(d*x)^2 + 2*sin(d*x)*sin(c) + sin(c)^2) + 4*(sin(3*d*x + 3*c) + sin(d*x + c))*sin(4*d*x + 4*c) - 8*sin(3*d*x + 3*c)*sin(2*d*x + 2*c) - 8*sin(2*d*x + 2*c)*sin(d*x + c) + 4*cos(d*x + c))/(a*d*cos(4*d*x + 4*c)^2 + 4*a*d*cos(2*d*x + 2*c)^2 + a*d*sin(4*d*x + 4*c)^2 - 4*a*d*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*a*d*sin(2*d*x + 2*c)^2 - 4*a*d*cos(2*d*x + 2*c) + a*d - 2*(2*a*d*cos(2*d*x + 2*c) - a*d)*cos(4*d*x + 4*c))","F",0
202,0,0,0,0.000000," ","integrate(csc(d*x+c)^5/(a-b*sin(d*x+c)^4),x, algorithm=""maxima"")","-\frac{48 \, a \cos\left(2 \, d x + 2 \, c\right) \cos\left(d x + c\right) - 176 \, a \sin\left(3 \, d x + 3 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 48 \, a \sin\left(2 \, d x + 2 \, c\right) \sin\left(d x + c\right) - 4 \, {\left(3 \, a \cos\left(7 \, d x + 7 \, c\right) - 11 \, a \cos\left(5 \, d x + 5 \, c\right) - 11 \, a \cos\left(3 \, d x + 3 \, c\right) + 3 \, a \cos\left(d x + c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) + 12 \, {\left(4 \, a \cos\left(6 \, d x + 6 \, c\right) - 6 \, a \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) - a\right)} \cos\left(7 \, d x + 7 \, c\right) - 16 \, {\left(11 \, a \cos\left(5 \, d x + 5 \, c\right) + 11 \, a \cos\left(3 \, d x + 3 \, c\right) - 3 \, a \cos\left(d x + c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) + 44 \, {\left(6 \, a \cos\left(4 \, d x + 4 \, c\right) - 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(5 \, d x + 5 \, c\right) + 24 \, {\left(11 \, a \cos\left(3 \, d x + 3 \, c\right) - 3 \, a \cos\left(d x + c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 44 \, {\left(4 \, a \cos\left(2 \, d x + 2 \, c\right) - a\right)} \cos\left(3 \, d x + 3 \, c\right) - 12 \, a \cos\left(d x + c\right) - 32 \, {\left(a^{2} d \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a^{2} d \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a^{2} d \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, a^{2} d \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} d \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a^{2} d \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a^{2} d \sin\left(4 \, d x + 4 \, c\right)^{2} - 48 \, a^{2} d \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, a^{2} d \sin\left(2 \, d x + 2 \, c\right)^{2} - 8 \, a^{2} d \cos\left(2 \, d x + 2 \, c\right) + a^{2} d - 2 \, {\left(4 \, a^{2} d \cos\left(6 \, d x + 6 \, c\right) - 6 \, a^{2} d \cos\left(4 \, d x + 4 \, c\right) + 4 \, a^{2} d \cos\left(2 \, d x + 2 \, c\right) - a^{2} d\right)} \cos\left(8 \, d x + 8 \, c\right) - 8 \, {\left(6 \, a^{2} d \cos\left(4 \, d x + 4 \, c\right) - 4 \, a^{2} d \cos\left(2 \, d x + 2 \, c\right) + a^{2} d\right)} \cos\left(6 \, d x + 6 \, c\right) - 12 \, {\left(4 \, a^{2} d \cos\left(2 \, d x + 2 \, c\right) - a^{2} d\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(2 \, a^{2} d \sin\left(6 \, d x + 6 \, c\right) - 3 \, a^{2} d \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) - 16 \, {\left(3 \, a^{2} d \sin\left(4 \, d x + 4 \, c\right) - 2 \, a^{2} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \int \frac{12 \, b^{3} \cos\left(3 \, d x + 3 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 4 \, b^{3} \cos\left(d x + c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, b^{3} \cos\left(2 \, d x + 2 \, c\right) \sin\left(d x + c\right) - b^{3} \sin\left(d x + c\right) + {\left(b^{3} \sin\left(7 \, d x + 7 \, c\right) - 3 \, b^{3} \sin\left(5 \, d x + 5 \, c\right) + 3 \, b^{3} \sin\left(3 \, d x + 3 \, c\right) - b^{3} \sin\left(d x + c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) + 2 \, {\left(2 \, b^{3} \sin\left(6 \, d x + 6 \, c\right) + 2 \, b^{3} \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a b^{2} - 3 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \cos\left(7 \, d x + 7 \, c\right) + 4 \, {\left(3 \, b^{3} \sin\left(5 \, d x + 5 \, c\right) - 3 \, b^{3} \sin\left(3 \, d x + 3 \, c\right) + b^{3} \sin\left(d x + c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 6 \, {\left(2 \, b^{3} \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a b^{2} - 3 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \cos\left(5 \, d x + 5 \, c\right) - 2 \, {\left(3 \, {\left(8 \, a b^{2} - 3 \, b^{3}\right)} \sin\left(3 \, d x + 3 \, c\right) - {\left(8 \, a b^{2} - 3 \, b^{3}\right)} \sin\left(d x + c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - {\left(b^{3} \cos\left(7 \, d x + 7 \, c\right) - 3 \, b^{3} \cos\left(5 \, d x + 5 \, c\right) + 3 \, b^{3} \cos\left(3 \, d x + 3 \, c\right) - b^{3} \cos\left(d x + c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) - {\left(4 \, b^{3} \cos\left(6 \, d x + 6 \, c\right) + 4 \, b^{3} \cos\left(2 \, d x + 2 \, c\right) - b^{3} + 2 \, {\left(8 \, a b^{2} - 3 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \sin\left(7 \, d x + 7 \, c\right) - 4 \, {\left(3 \, b^{3} \cos\left(5 \, d x + 5 \, c\right) - 3 \, b^{3} \cos\left(3 \, d x + 3 \, c\right) + b^{3} \cos\left(d x + c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 3 \, {\left(4 \, b^{3} \cos\left(2 \, d x + 2 \, c\right) - b^{3} + 2 \, {\left(8 \, a b^{2} - 3 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \sin\left(5 \, d x + 5 \, c\right) + 2 \, {\left(3 \, {\left(8 \, a b^{2} - 3 \, b^{3}\right)} \cos\left(3 \, d x + 3 \, c\right) - {\left(8 \, a b^{2} - 3 \, b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) - 3 \, {\left(4 \, b^{3} \cos\left(2 \, d x + 2 \, c\right) - b^{3}\right)} \sin\left(3 \, d x + 3 \, c\right)}{a^{2} b^{2} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a^{2} b^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 16 \, a^{2} b^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} b^{2} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a^{2} b^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 16 \, a^{2} b^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} - 8 \, a^{2} b^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2} b^{2} + 4 \, {\left(64 \, a^{4} - 48 \, a^{3} b + 9 \, a^{2} b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(64 \, a^{4} - 48 \, a^{3} b + 9 \, a^{2} b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(8 \, a^{3} b - 3 \, a^{2} b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 2 \, {\left(4 \, a^{2} b^{2} \cos\left(6 \, d x + 6 \, c\right) + 4 \, a^{2} b^{2} \cos\left(2 \, d x + 2 \, c\right) - a^{2} b^{2} + 2 \, {\left(8 \, a^{3} b - 3 \, a^{2} b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(4 \, a^{2} b^{2} \cos\left(2 \, d x + 2 \, c\right) - a^{2} b^{2} + 2 \, {\left(8 \, a^{3} b - 3 \, a^{2} b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(8 \, a^{3} b - 3 \, a^{2} b^{2} - 4 \, {\left(8 \, a^{3} b - 3 \, a^{2} b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(2 \, a^{2} b^{2} \sin\left(6 \, d x + 6 \, c\right) + 2 \, a^{2} b^{2} \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a^{3} b - 3 \, a^{2} b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(2 \, a^{2} b^{2} \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a^{3} b - 3 \, a^{2} b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}\,{d x} + {\left({\left(3 \, a + 8 \, b\right)} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, a + 8 \, b\right)} \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, {\left(3 \, a + 8 \, b\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(3 \, a + 8 \, b\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(3 \, a + 8 \, b\right)} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, a + 8 \, b\right)} \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, {\left(3 \, a + 8 \, b\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} - 48 \, {\left(3 \, a + 8 \, b\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, {\left(3 \, a + 8 \, b\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, {\left(4 \, {\left(3 \, a + 8 \, b\right)} \cos\left(6 \, d x + 6 \, c\right) - 6 \, {\left(3 \, a + 8 \, b\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(3 \, a + 8 \, b\right)} \cos\left(2 \, d x + 2 \, c\right) - 3 \, a - 8 \, b\right)} \cos\left(8 \, d x + 8 \, c\right) - 8 \, {\left(6 \, {\left(3 \, a + 8 \, b\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(3 \, a + 8 \, b\right)} \cos\left(2 \, d x + 2 \, c\right) + 3 \, a + 8 \, b\right)} \cos\left(6 \, d x + 6 \, c\right) - 12 \, {\left(4 \, {\left(3 \, a + 8 \, b\right)} \cos\left(2 \, d x + 2 \, c\right) - 3 \, a - 8 \, b\right)} \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(3 \, a + 8 \, b\right)} \cos\left(2 \, d x + 2 \, c\right) - 4 \, {\left(2 \, {\left(3 \, a + 8 \, b\right)} \sin\left(6 \, d x + 6 \, c\right) - 3 \, {\left(3 \, a + 8 \, b\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(3 \, a + 8 \, b\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) - 16 \, {\left(3 \, {\left(3 \, a + 8 \, b\right)} \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(3 \, a + 8 \, b\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 3 \, a + 8 \, b\right)} \log\left(\cos\left(d x\right)^{2} + 2 \, \cos\left(d x\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(d x\right)^{2} - 2 \, \sin\left(d x\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right) - {\left({\left(3 \, a + 8 \, b\right)} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, a + 8 \, b\right)} \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, {\left(3 \, a + 8 \, b\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(3 \, a + 8 \, b\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(3 \, a + 8 \, b\right)} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, a + 8 \, b\right)} \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, {\left(3 \, a + 8 \, b\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} - 48 \, {\left(3 \, a + 8 \, b\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, {\left(3 \, a + 8 \, b\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, {\left(4 \, {\left(3 \, a + 8 \, b\right)} \cos\left(6 \, d x + 6 \, c\right) - 6 \, {\left(3 \, a + 8 \, b\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(3 \, a + 8 \, b\right)} \cos\left(2 \, d x + 2 \, c\right) - 3 \, a - 8 \, b\right)} \cos\left(8 \, d x + 8 \, c\right) - 8 \, {\left(6 \, {\left(3 \, a + 8 \, b\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(3 \, a + 8 \, b\right)} \cos\left(2 \, d x + 2 \, c\right) + 3 \, a + 8 \, b\right)} \cos\left(6 \, d x + 6 \, c\right) - 12 \, {\left(4 \, {\left(3 \, a + 8 \, b\right)} \cos\left(2 \, d x + 2 \, c\right) - 3 \, a - 8 \, b\right)} \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(3 \, a + 8 \, b\right)} \cos\left(2 \, d x + 2 \, c\right) - 4 \, {\left(2 \, {\left(3 \, a + 8 \, b\right)} \sin\left(6 \, d x + 6 \, c\right) - 3 \, {\left(3 \, a + 8 \, b\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(3 \, a + 8 \, b\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) - 16 \, {\left(3 \, {\left(3 \, a + 8 \, b\right)} \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(3 \, a + 8 \, b\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 3 \, a + 8 \, b\right)} \log\left(\cos\left(d x\right)^{2} - 2 \, \cos\left(d x\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(d x\right)^{2} + 2 \, \sin\left(d x\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right) - 4 \, {\left(3 \, a \sin\left(7 \, d x + 7 \, c\right) - 11 \, a \sin\left(5 \, d x + 5 \, c\right) - 11 \, a \sin\left(3 \, d x + 3 \, c\right) + 3 \, a \sin\left(d x + c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 24 \, {\left(2 \, a \sin\left(6 \, d x + 6 \, c\right) - 3 \, a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(7 \, d x + 7 \, c\right) - 16 \, {\left(11 \, a \sin\left(5 \, d x + 5 \, c\right) + 11 \, a \sin\left(3 \, d x + 3 \, c\right) - 3 \, a \sin\left(d x + c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 88 \, {\left(3 \, a \sin\left(4 \, d x + 4 \, c\right) - 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(5 \, d x + 5 \, c\right) + 24 \, {\left(11 \, a \sin\left(3 \, d x + 3 \, c\right) - 3 \, a \sin\left(d x + c\right)\right)} \sin\left(4 \, d x + 4 \, c\right)}{16 \, {\left(a^{2} d \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a^{2} d \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a^{2} d \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, a^{2} d \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} d \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a^{2} d \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a^{2} d \sin\left(4 \, d x + 4 \, c\right)^{2} - 48 \, a^{2} d \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, a^{2} d \sin\left(2 \, d x + 2 \, c\right)^{2} - 8 \, a^{2} d \cos\left(2 \, d x + 2 \, c\right) + a^{2} d - 2 \, {\left(4 \, a^{2} d \cos\left(6 \, d x + 6 \, c\right) - 6 \, a^{2} d \cos\left(4 \, d x + 4 \, c\right) + 4 \, a^{2} d \cos\left(2 \, d x + 2 \, c\right) - a^{2} d\right)} \cos\left(8 \, d x + 8 \, c\right) - 8 \, {\left(6 \, a^{2} d \cos\left(4 \, d x + 4 \, c\right) - 4 \, a^{2} d \cos\left(2 \, d x + 2 \, c\right) + a^{2} d\right)} \cos\left(6 \, d x + 6 \, c\right) - 12 \, {\left(4 \, a^{2} d \cos\left(2 \, d x + 2 \, c\right) - a^{2} d\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(2 \, a^{2} d \sin\left(6 \, d x + 6 \, c\right) - 3 \, a^{2} d \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) - 16 \, {\left(3 \, a^{2} d \sin\left(4 \, d x + 4 \, c\right) - 2 \, a^{2} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)}}"," ",0,"-1/16*(48*a*cos(2*d*x + 2*c)*cos(d*x + c) - 176*a*sin(3*d*x + 3*c)*sin(2*d*x + 2*c) + 48*a*sin(2*d*x + 2*c)*sin(d*x + c) - 4*(3*a*cos(7*d*x + 7*c) - 11*a*cos(5*d*x + 5*c) - 11*a*cos(3*d*x + 3*c) + 3*a*cos(d*x + c))*cos(8*d*x + 8*c) + 12*(4*a*cos(6*d*x + 6*c) - 6*a*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) - a)*cos(7*d*x + 7*c) - 16*(11*a*cos(5*d*x + 5*c) + 11*a*cos(3*d*x + 3*c) - 3*a*cos(d*x + c))*cos(6*d*x + 6*c) + 44*(6*a*cos(4*d*x + 4*c) - 4*a*cos(2*d*x + 2*c) + a)*cos(5*d*x + 5*c) + 24*(11*a*cos(3*d*x + 3*c) - 3*a*cos(d*x + c))*cos(4*d*x + 4*c) - 44*(4*a*cos(2*d*x + 2*c) - a)*cos(3*d*x + 3*c) - 12*a*cos(d*x + c) + 16*(a^2*d*cos(8*d*x + 8*c)^2 + 16*a^2*d*cos(6*d*x + 6*c)^2 + 36*a^2*d*cos(4*d*x + 4*c)^2 + 16*a^2*d*cos(2*d*x + 2*c)^2 + a^2*d*sin(8*d*x + 8*c)^2 + 16*a^2*d*sin(6*d*x + 6*c)^2 + 36*a^2*d*sin(4*d*x + 4*c)^2 - 48*a^2*d*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*a^2*d*sin(2*d*x + 2*c)^2 - 8*a^2*d*cos(2*d*x + 2*c) + a^2*d - 2*(4*a^2*d*cos(6*d*x + 6*c) - 6*a^2*d*cos(4*d*x + 4*c) + 4*a^2*d*cos(2*d*x + 2*c) - a^2*d)*cos(8*d*x + 8*c) - 8*(6*a^2*d*cos(4*d*x + 4*c) - 4*a^2*d*cos(2*d*x + 2*c) + a^2*d)*cos(6*d*x + 6*c) - 12*(4*a^2*d*cos(2*d*x + 2*c) - a^2*d)*cos(4*d*x + 4*c) - 4*(2*a^2*d*sin(6*d*x + 6*c) - 3*a^2*d*sin(4*d*x + 4*c) + 2*a^2*d*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) - 16*(3*a^2*d*sin(4*d*x + 4*c) - 2*a^2*d*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*integrate(-2*(12*b^3*cos(3*d*x + 3*c)*sin(2*d*x + 2*c) - 4*b^3*cos(d*x + c)*sin(2*d*x + 2*c) + 4*b^3*cos(2*d*x + 2*c)*sin(d*x + c) - b^3*sin(d*x + c) + (b^3*sin(7*d*x + 7*c) - 3*b^3*sin(5*d*x + 5*c) + 3*b^3*sin(3*d*x + 3*c) - b^3*sin(d*x + c))*cos(8*d*x + 8*c) + 2*(2*b^3*sin(6*d*x + 6*c) + 2*b^3*sin(2*d*x + 2*c) + (8*a*b^2 - 3*b^3)*sin(4*d*x + 4*c))*cos(7*d*x + 7*c) + 4*(3*b^3*sin(5*d*x + 5*c) - 3*b^3*sin(3*d*x + 3*c) + b^3*sin(d*x + c))*cos(6*d*x + 6*c) - 6*(2*b^3*sin(2*d*x + 2*c) + (8*a*b^2 - 3*b^3)*sin(4*d*x + 4*c))*cos(5*d*x + 5*c) - 2*(3*(8*a*b^2 - 3*b^3)*sin(3*d*x + 3*c) - (8*a*b^2 - 3*b^3)*sin(d*x + c))*cos(4*d*x + 4*c) - (b^3*cos(7*d*x + 7*c) - 3*b^3*cos(5*d*x + 5*c) + 3*b^3*cos(3*d*x + 3*c) - b^3*cos(d*x + c))*sin(8*d*x + 8*c) - (4*b^3*cos(6*d*x + 6*c) + 4*b^3*cos(2*d*x + 2*c) - b^3 + 2*(8*a*b^2 - 3*b^3)*cos(4*d*x + 4*c))*sin(7*d*x + 7*c) - 4*(3*b^3*cos(5*d*x + 5*c) - 3*b^3*cos(3*d*x + 3*c) + b^3*cos(d*x + c))*sin(6*d*x + 6*c) + 3*(4*b^3*cos(2*d*x + 2*c) - b^3 + 2*(8*a*b^2 - 3*b^3)*cos(4*d*x + 4*c))*sin(5*d*x + 5*c) + 2*(3*(8*a*b^2 - 3*b^3)*cos(3*d*x + 3*c) - (8*a*b^2 - 3*b^3)*cos(d*x + c))*sin(4*d*x + 4*c) - 3*(4*b^3*cos(2*d*x + 2*c) - b^3)*sin(3*d*x + 3*c))/(a^2*b^2*cos(8*d*x + 8*c)^2 + 16*a^2*b^2*cos(6*d*x + 6*c)^2 + 16*a^2*b^2*cos(2*d*x + 2*c)^2 + a^2*b^2*sin(8*d*x + 8*c)^2 + 16*a^2*b^2*sin(6*d*x + 6*c)^2 + 16*a^2*b^2*sin(2*d*x + 2*c)^2 - 8*a^2*b^2*cos(2*d*x + 2*c) + a^2*b^2 + 4*(64*a^4 - 48*a^3*b + 9*a^2*b^2)*cos(4*d*x + 4*c)^2 + 4*(64*a^4 - 48*a^3*b + 9*a^2*b^2)*sin(4*d*x + 4*c)^2 + 16*(8*a^3*b - 3*a^2*b^2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) - 2*(4*a^2*b^2*cos(6*d*x + 6*c) + 4*a^2*b^2*cos(2*d*x + 2*c) - a^2*b^2 + 2*(8*a^3*b - 3*a^2*b^2)*cos(4*d*x + 4*c))*cos(8*d*x + 8*c) + 8*(4*a^2*b^2*cos(2*d*x + 2*c) - a^2*b^2 + 2*(8*a^3*b - 3*a^2*b^2)*cos(4*d*x + 4*c))*cos(6*d*x + 6*c) - 4*(8*a^3*b - 3*a^2*b^2 - 4*(8*a^3*b - 3*a^2*b^2)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 4*(2*a^2*b^2*sin(6*d*x + 6*c) + 2*a^2*b^2*sin(2*d*x + 2*c) + (8*a^3*b - 3*a^2*b^2)*sin(4*d*x + 4*c))*sin(8*d*x + 8*c) + 16*(2*a^2*b^2*sin(2*d*x + 2*c) + (8*a^3*b - 3*a^2*b^2)*sin(4*d*x + 4*c))*sin(6*d*x + 6*c)), x) + ((3*a + 8*b)*cos(8*d*x + 8*c)^2 + 16*(3*a + 8*b)*cos(6*d*x + 6*c)^2 + 36*(3*a + 8*b)*cos(4*d*x + 4*c)^2 + 16*(3*a + 8*b)*cos(2*d*x + 2*c)^2 + (3*a + 8*b)*sin(8*d*x + 8*c)^2 + 16*(3*a + 8*b)*sin(6*d*x + 6*c)^2 + 36*(3*a + 8*b)*sin(4*d*x + 4*c)^2 - 48*(3*a + 8*b)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*(3*a + 8*b)*sin(2*d*x + 2*c)^2 - 2*(4*(3*a + 8*b)*cos(6*d*x + 6*c) - 6*(3*a + 8*b)*cos(4*d*x + 4*c) + 4*(3*a + 8*b)*cos(2*d*x + 2*c) - 3*a - 8*b)*cos(8*d*x + 8*c) - 8*(6*(3*a + 8*b)*cos(4*d*x + 4*c) - 4*(3*a + 8*b)*cos(2*d*x + 2*c) + 3*a + 8*b)*cos(6*d*x + 6*c) - 12*(4*(3*a + 8*b)*cos(2*d*x + 2*c) - 3*a - 8*b)*cos(4*d*x + 4*c) - 8*(3*a + 8*b)*cos(2*d*x + 2*c) - 4*(2*(3*a + 8*b)*sin(6*d*x + 6*c) - 3*(3*a + 8*b)*sin(4*d*x + 4*c) + 2*(3*a + 8*b)*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) - 16*(3*(3*a + 8*b)*sin(4*d*x + 4*c) - 2*(3*a + 8*b)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 3*a + 8*b)*log(cos(d*x)^2 + 2*cos(d*x)*cos(c) + cos(c)^2 + sin(d*x)^2 - 2*sin(d*x)*sin(c) + sin(c)^2) - ((3*a + 8*b)*cos(8*d*x + 8*c)^2 + 16*(3*a + 8*b)*cos(6*d*x + 6*c)^2 + 36*(3*a + 8*b)*cos(4*d*x + 4*c)^2 + 16*(3*a + 8*b)*cos(2*d*x + 2*c)^2 + (3*a + 8*b)*sin(8*d*x + 8*c)^2 + 16*(3*a + 8*b)*sin(6*d*x + 6*c)^2 + 36*(3*a + 8*b)*sin(4*d*x + 4*c)^2 - 48*(3*a + 8*b)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*(3*a + 8*b)*sin(2*d*x + 2*c)^2 - 2*(4*(3*a + 8*b)*cos(6*d*x + 6*c) - 6*(3*a + 8*b)*cos(4*d*x + 4*c) + 4*(3*a + 8*b)*cos(2*d*x + 2*c) - 3*a - 8*b)*cos(8*d*x + 8*c) - 8*(6*(3*a + 8*b)*cos(4*d*x + 4*c) - 4*(3*a + 8*b)*cos(2*d*x + 2*c) + 3*a + 8*b)*cos(6*d*x + 6*c) - 12*(4*(3*a + 8*b)*cos(2*d*x + 2*c) - 3*a - 8*b)*cos(4*d*x + 4*c) - 8*(3*a + 8*b)*cos(2*d*x + 2*c) - 4*(2*(3*a + 8*b)*sin(6*d*x + 6*c) - 3*(3*a + 8*b)*sin(4*d*x + 4*c) + 2*(3*a + 8*b)*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) - 16*(3*(3*a + 8*b)*sin(4*d*x + 4*c) - 2*(3*a + 8*b)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 3*a + 8*b)*log(cos(d*x)^2 - 2*cos(d*x)*cos(c) + cos(c)^2 + sin(d*x)^2 + 2*sin(d*x)*sin(c) + sin(c)^2) - 4*(3*a*sin(7*d*x + 7*c) - 11*a*sin(5*d*x + 5*c) - 11*a*sin(3*d*x + 3*c) + 3*a*sin(d*x + c))*sin(8*d*x + 8*c) + 24*(2*a*sin(6*d*x + 6*c) - 3*a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*sin(7*d*x + 7*c) - 16*(11*a*sin(5*d*x + 5*c) + 11*a*sin(3*d*x + 3*c) - 3*a*sin(d*x + c))*sin(6*d*x + 6*c) + 88*(3*a*sin(4*d*x + 4*c) - 2*a*sin(2*d*x + 2*c))*sin(5*d*x + 5*c) + 24*(11*a*sin(3*d*x + 3*c) - 3*a*sin(d*x + c))*sin(4*d*x + 4*c))/(a^2*d*cos(8*d*x + 8*c)^2 + 16*a^2*d*cos(6*d*x + 6*c)^2 + 36*a^2*d*cos(4*d*x + 4*c)^2 + 16*a^2*d*cos(2*d*x + 2*c)^2 + a^2*d*sin(8*d*x + 8*c)^2 + 16*a^2*d*sin(6*d*x + 6*c)^2 + 36*a^2*d*sin(4*d*x + 4*c)^2 - 48*a^2*d*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*a^2*d*sin(2*d*x + 2*c)^2 - 8*a^2*d*cos(2*d*x + 2*c) + a^2*d - 2*(4*a^2*d*cos(6*d*x + 6*c) - 6*a^2*d*cos(4*d*x + 4*c) + 4*a^2*d*cos(2*d*x + 2*c) - a^2*d)*cos(8*d*x + 8*c) - 8*(6*a^2*d*cos(4*d*x + 4*c) - 4*a^2*d*cos(2*d*x + 2*c) + a^2*d)*cos(6*d*x + 6*c) - 12*(4*a^2*d*cos(2*d*x + 2*c) - a^2*d)*cos(4*d*x + 4*c) - 4*(2*a^2*d*sin(6*d*x + 6*c) - 3*a^2*d*sin(4*d*x + 4*c) + 2*a^2*d*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) - 16*(3*a^2*d*sin(4*d*x + 4*c) - 2*a^2*d*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))","F",0
203,-1,0,0,0.000000," ","integrate(sin(d*x+c)^8/(a-b*sin(d*x+c)^4),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
204,0,0,0,0.000000," ","integrate(sin(d*x+c)^6/(a-b*sin(d*x+c)^4),x, algorithm=""maxima"")","\frac{-16 \, b d \int \frac{4 \, a b \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, a b \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, a b \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, a b \sin\left(2 \, d x + 2 \, c\right)^{2} - 4 \, {\left(8 \, a^{2} - 3 \, a b\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} - a b \cos\left(2 \, d x + 2 \, c\right) - 4 \, {\left(8 \, a^{2} - 3 \, a b\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, {\left(8 \, a^{2} - 7 \, a b\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - {\left(a b \cos\left(6 \, d x + 6 \, c\right) - 2 \, a b \cos\left(4 \, d x + 4 \, c\right) + a b \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) + {\left(8 \, a b \cos\left(2 \, d x + 2 \, c\right) - a b + 2 \, {\left(8 \, a^{2} - 7 \, a b\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) + 2 \, {\left(a b + {\left(8 \, a^{2} - 7 \, a b\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - {\left(a b \sin\left(6 \, d x + 6 \, c\right) - 2 \, a b \sin\left(4 \, d x + 4 \, c\right) + a b \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 2 \, {\left(4 \, a b \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a^{2} - 7 \, a b\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}{b^{3} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, b^{3} \cos\left(6 \, d x + 6 \, c\right)^{2} + 16 \, b^{3} \cos\left(2 \, d x + 2 \, c\right)^{2} + b^{3} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, b^{3} \sin\left(6 \, d x + 6 \, c\right)^{2} + 16 \, b^{3} \sin\left(2 \, d x + 2 \, c\right)^{2} - 8 \, b^{3} \cos\left(2 \, d x + 2 \, c\right) + b^{3} + 4 \, {\left(64 \, a^{2} b - 48 \, a b^{2} + 9 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(64 \, a^{2} b - 48 \, a b^{2} + 9 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(8 \, a b^{2} - 3 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 2 \, {\left(4 \, b^{3} \cos\left(6 \, d x + 6 \, c\right) + 4 \, b^{3} \cos\left(2 \, d x + 2 \, c\right) - b^{3} + 2 \, {\left(8 \, a b^{2} - 3 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(4 \, b^{3} \cos\left(2 \, d x + 2 \, c\right) - b^{3} + 2 \, {\left(8 \, a b^{2} - 3 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(8 \, a b^{2} - 3 \, b^{3} - 4 \, {\left(8 \, a b^{2} - 3 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(2 \, b^{3} \sin\left(6 \, d x + 6 \, c\right) + 2 \, b^{3} \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a b^{2} - 3 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(2 \, b^{3} \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a b^{2} - 3 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}\,{d x} - 2 \, d x + \sin\left(2 \, d x + 2 \, c\right)}{4 \, b d}"," ",0,"1/4*(4*b*d*integrate(-4*(4*a*b*cos(6*d*x + 6*c)^2 + 4*a*b*cos(2*d*x + 2*c)^2 + 4*a*b*sin(6*d*x + 6*c)^2 + 4*a*b*sin(2*d*x + 2*c)^2 - 4*(8*a^2 - 3*a*b)*cos(4*d*x + 4*c)^2 - a*b*cos(2*d*x + 2*c) - 4*(8*a^2 - 3*a*b)*sin(4*d*x + 4*c)^2 + 2*(8*a^2 - 7*a*b)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) - (a*b*cos(6*d*x + 6*c) - 2*a*b*cos(4*d*x + 4*c) + a*b*cos(2*d*x + 2*c))*cos(8*d*x + 8*c) + (8*a*b*cos(2*d*x + 2*c) - a*b + 2*(8*a^2 - 7*a*b)*cos(4*d*x + 4*c))*cos(6*d*x + 6*c) + 2*(a*b + (8*a^2 - 7*a*b)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - (a*b*sin(6*d*x + 6*c) - 2*a*b*sin(4*d*x + 4*c) + a*b*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 2*(4*a*b*sin(2*d*x + 2*c) + (8*a^2 - 7*a*b)*sin(4*d*x + 4*c))*sin(6*d*x + 6*c))/(b^3*cos(8*d*x + 8*c)^2 + 16*b^3*cos(6*d*x + 6*c)^2 + 16*b^3*cos(2*d*x + 2*c)^2 + b^3*sin(8*d*x + 8*c)^2 + 16*b^3*sin(6*d*x + 6*c)^2 + 16*b^3*sin(2*d*x + 2*c)^2 - 8*b^3*cos(2*d*x + 2*c) + b^3 + 4*(64*a^2*b - 48*a*b^2 + 9*b^3)*cos(4*d*x + 4*c)^2 + 4*(64*a^2*b - 48*a*b^2 + 9*b^3)*sin(4*d*x + 4*c)^2 + 16*(8*a*b^2 - 3*b^3)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) - 2*(4*b^3*cos(6*d*x + 6*c) + 4*b^3*cos(2*d*x + 2*c) - b^3 + 2*(8*a*b^2 - 3*b^3)*cos(4*d*x + 4*c))*cos(8*d*x + 8*c) + 8*(4*b^3*cos(2*d*x + 2*c) - b^3 + 2*(8*a*b^2 - 3*b^3)*cos(4*d*x + 4*c))*cos(6*d*x + 6*c) - 4*(8*a*b^2 - 3*b^3 - 4*(8*a*b^2 - 3*b^3)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 4*(2*b^3*sin(6*d*x + 6*c) + 2*b^3*sin(2*d*x + 2*c) + (8*a*b^2 - 3*b^3)*sin(4*d*x + 4*c))*sin(8*d*x + 8*c) + 16*(2*b^3*sin(2*d*x + 2*c) + (8*a*b^2 - 3*b^3)*sin(4*d*x + 4*c))*sin(6*d*x + 6*c)), x) - 2*d*x + sin(2*d*x + 2*c))/(b*d)","F",0
205,-1,0,0,0.000000," ","integrate(sin(d*x+c)^4/(a-b*sin(d*x+c)^4),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
206,0,0,0,0.000000," ","integrate(sin(d*x+c)^2/(a-b*sin(d*x+c)^4),x, algorithm=""maxima"")","-\int \frac{\sin\left(d x + c\right)^{2}}{b \sin\left(d x + c\right)^{4} - a}\,{d x}"," ",0,"-integrate(sin(d*x + c)^2/(b*sin(d*x + c)^4 - a), x)","F",0
207,0,0,0,0.000000," ","integrate(1/(a-b*sin(d*x+c)^4),x, algorithm=""maxima"")","-\int \frac{1}{b \sin\left(d x + c\right)^{4} - a}\,{d x}"," ",0,"-integrate(1/(b*sin(d*x + c)^4 - a), x)","F",0
208,0,0,0,0.000000," ","integrate(csc(d*x+c)^2/(a-b*sin(d*x+c)^4),x, algorithm=""maxima"")","\frac{-4 \, {\left(a d \cos\left(2 \, d x + 2 \, c\right)^{2} + a d \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, a d \cos\left(2 \, d x + 2 \, c\right) + a d\right)} \int \frac{4 \, b^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, b^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, b^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} - 4 \, {\left(8 \, a b - 3 \, b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} - b^{2} \cos\left(2 \, d x + 2 \, c\right) - 4 \, {\left(8 \, a b - 3 \, b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, {\left(8 \, a b - 7 \, b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - {\left(b^{2} \cos\left(6 \, d x + 6 \, c\right) - 2 \, b^{2} \cos\left(4 \, d x + 4 \, c\right) + b^{2} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) + {\left(8 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) - b^{2} + 2 \, {\left(8 \, a b - 7 \, b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) + 2 \, {\left(b^{2} + {\left(8 \, a b - 7 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - {\left(b^{2} \sin\left(6 \, d x + 6 \, c\right) - 2 \, b^{2} \sin\left(4 \, d x + 4 \, c\right) + b^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 2 \, {\left(4 \, b^{2} \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a b - 7 \, b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}{a b^{2} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a b^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 16 \, a b^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a b^{2} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a b^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 16 \, a b^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} - 8 \, a b^{2} \cos\left(2 \, d x + 2 \, c\right) + a b^{2} + 4 \, {\left(64 \, a^{3} - 48 \, a^{2} b + 9 \, a b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(64 \, a^{3} - 48 \, a^{2} b + 9 \, a b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(8 \, a^{2} b - 3 \, a b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 2 \, {\left(4 \, a b^{2} \cos\left(6 \, d x + 6 \, c\right) + 4 \, a b^{2} \cos\left(2 \, d x + 2 \, c\right) - a b^{2} + 2 \, {\left(8 \, a^{2} b - 3 \, a b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(4 \, a b^{2} \cos\left(2 \, d x + 2 \, c\right) - a b^{2} + 2 \, {\left(8 \, a^{2} b - 3 \, a b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(8 \, a^{2} b - 3 \, a b^{2} - 4 \, {\left(8 \, a^{2} b - 3 \, a b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(2 \, a b^{2} \sin\left(6 \, d x + 6 \, c\right) + 2 \, a b^{2} \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a^{2} b - 3 \, a b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(2 \, a b^{2} \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a^{2} b - 3 \, a b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}\,{d x} - 2 \, \sin\left(2 \, d x + 2 \, c\right)}{a d \cos\left(2 \, d x + 2 \, c\right)^{2} + a d \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, a d \cos\left(2 \, d x + 2 \, c\right) + a d}"," ",0,"((a*d*cos(2*d*x + 2*c)^2 + a*d*sin(2*d*x + 2*c)^2 - 2*a*d*cos(2*d*x + 2*c) + a*d)*integrate(-4*(4*b^2*cos(6*d*x + 6*c)^2 + 4*b^2*cos(2*d*x + 2*c)^2 + 4*b^2*sin(6*d*x + 6*c)^2 + 4*b^2*sin(2*d*x + 2*c)^2 - 4*(8*a*b - 3*b^2)*cos(4*d*x + 4*c)^2 - b^2*cos(2*d*x + 2*c) - 4*(8*a*b - 3*b^2)*sin(4*d*x + 4*c)^2 + 2*(8*a*b - 7*b^2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) - (b^2*cos(6*d*x + 6*c) - 2*b^2*cos(4*d*x + 4*c) + b^2*cos(2*d*x + 2*c))*cos(8*d*x + 8*c) + (8*b^2*cos(2*d*x + 2*c) - b^2 + 2*(8*a*b - 7*b^2)*cos(4*d*x + 4*c))*cos(6*d*x + 6*c) + 2*(b^2 + (8*a*b - 7*b^2)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - (b^2*sin(6*d*x + 6*c) - 2*b^2*sin(4*d*x + 4*c) + b^2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 2*(4*b^2*sin(2*d*x + 2*c) + (8*a*b - 7*b^2)*sin(4*d*x + 4*c))*sin(6*d*x + 6*c))/(a*b^2*cos(8*d*x + 8*c)^2 + 16*a*b^2*cos(6*d*x + 6*c)^2 + 16*a*b^2*cos(2*d*x + 2*c)^2 + a*b^2*sin(8*d*x + 8*c)^2 + 16*a*b^2*sin(6*d*x + 6*c)^2 + 16*a*b^2*sin(2*d*x + 2*c)^2 - 8*a*b^2*cos(2*d*x + 2*c) + a*b^2 + 4*(64*a^3 - 48*a^2*b + 9*a*b^2)*cos(4*d*x + 4*c)^2 + 4*(64*a^3 - 48*a^2*b + 9*a*b^2)*sin(4*d*x + 4*c)^2 + 16*(8*a^2*b - 3*a*b^2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) - 2*(4*a*b^2*cos(6*d*x + 6*c) + 4*a*b^2*cos(2*d*x + 2*c) - a*b^2 + 2*(8*a^2*b - 3*a*b^2)*cos(4*d*x + 4*c))*cos(8*d*x + 8*c) + 8*(4*a*b^2*cos(2*d*x + 2*c) - a*b^2 + 2*(8*a^2*b - 3*a*b^2)*cos(4*d*x + 4*c))*cos(6*d*x + 6*c) - 4*(8*a^2*b - 3*a*b^2 - 4*(8*a^2*b - 3*a*b^2)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 4*(2*a*b^2*sin(6*d*x + 6*c) + 2*a*b^2*sin(2*d*x + 2*c) + (8*a^2*b - 3*a*b^2)*sin(4*d*x + 4*c))*sin(8*d*x + 8*c) + 16*(2*a*b^2*sin(2*d*x + 2*c) + (8*a^2*b - 3*a*b^2)*sin(4*d*x + 4*c))*sin(6*d*x + 6*c)), x) - 2*sin(2*d*x + 2*c))/(a*d*cos(2*d*x + 2*c)^2 + a*d*sin(2*d*x + 2*c)^2 - 2*a*d*cos(2*d*x + 2*c) + a*d)","F",0
209,-1,0,0,0.000000," ","integrate(csc(d*x+c)^4/(a-b*sin(d*x+c)^4),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
210,0,0,0,0.000000," ","integrate(csc(d*x+c)^6/(a-b*sin(d*x+c)^4),x, algorithm=""maxima"")","\frac{300 \, b \cos\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 10 \, {\left(3 \, b \sin\left(8 \, d x + 8 \, c\right) - 12 \, b \sin\left(6 \, d x + 6 \, c\right) + 2 \, {\left(8 \, a + 9 \, b\right)} \sin\left(4 \, d x + 4 \, c\right) - 4 \, {\left(2 \, a + 3 \, b\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(10 \, d x + 10 \, c\right) + 50 \, {\left(6 \, b \sin\left(6 \, d x + 6 \, c\right) - 4 \, {\left(4 \, a + 3 \, b\right)} \sin\left(4 \, d x + 4 \, c\right) + {\left(8 \, a + 9 \, b\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) + 200 \, {\left({\left(8 \, a + 3 \, b\right)} \sin\left(4 \, d x + 4 \, c\right) - {\left(4 \, a + 3 \, b\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 60 \, {\left(a^{2} d \cos\left(10 \, d x + 10 \, c\right)^{2} + 25 \, a^{2} d \cos\left(8 \, d x + 8 \, c\right)^{2} + 100 \, a^{2} d \cos\left(6 \, d x + 6 \, c\right)^{2} + 100 \, a^{2} d \cos\left(4 \, d x + 4 \, c\right)^{2} + 25 \, a^{2} d \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} d \sin\left(10 \, d x + 10 \, c\right)^{2} + 25 \, a^{2} d \sin\left(8 \, d x + 8 \, c\right)^{2} + 100 \, a^{2} d \sin\left(6 \, d x + 6 \, c\right)^{2} + 100 \, a^{2} d \sin\left(4 \, d x + 4 \, c\right)^{2} - 100 \, a^{2} d \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 25 \, a^{2} d \sin\left(2 \, d x + 2 \, c\right)^{2} - 10 \, a^{2} d \cos\left(2 \, d x + 2 \, c\right) + a^{2} d - 2 \, {\left(5 \, a^{2} d \cos\left(8 \, d x + 8 \, c\right) - 10 \, a^{2} d \cos\left(6 \, d x + 6 \, c\right) + 10 \, a^{2} d \cos\left(4 \, d x + 4 \, c\right) - 5 \, a^{2} d \cos\left(2 \, d x + 2 \, c\right) + a^{2} d\right)} \cos\left(10 \, d x + 10 \, c\right) - 10 \, {\left(10 \, a^{2} d \cos\left(6 \, d x + 6 \, c\right) - 10 \, a^{2} d \cos\left(4 \, d x + 4 \, c\right) + 5 \, a^{2} d \cos\left(2 \, d x + 2 \, c\right) - a^{2} d\right)} \cos\left(8 \, d x + 8 \, c\right) - 20 \, {\left(10 \, a^{2} d \cos\left(4 \, d x + 4 \, c\right) - 5 \, a^{2} d \cos\left(2 \, d x + 2 \, c\right) + a^{2} d\right)} \cos\left(6 \, d x + 6 \, c\right) - 20 \, {\left(5 \, a^{2} d \cos\left(2 \, d x + 2 \, c\right) - a^{2} d\right)} \cos\left(4 \, d x + 4 \, c\right) - 10 \, {\left(a^{2} d \sin\left(8 \, d x + 8 \, c\right) - 2 \, a^{2} d \sin\left(6 \, d x + 6 \, c\right) + 2 \, a^{2} d \sin\left(4 \, d x + 4 \, c\right) - a^{2} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) - 50 \, {\left(2 \, a^{2} d \sin\left(6 \, d x + 6 \, c\right) - 2 \, a^{2} d \sin\left(4 \, d x + 4 \, c\right) + a^{2} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) - 100 \, {\left(2 \, a^{2} d \sin\left(4 \, d x + 4 \, c\right) - a^{2} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \int \frac{4 \, b^{3} \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, b^{3} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, b^{3} \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, b^{3} \sin\left(2 \, d x + 2 \, c\right)^{2} - b^{3} \cos\left(2 \, d x + 2 \, c\right) - 4 \, {\left(8 \, a b^{2} - 3 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} - 4 \, {\left(8 \, a b^{2} - 3 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, {\left(8 \, a b^{2} - 7 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - {\left(b^{3} \cos\left(6 \, d x + 6 \, c\right) - 2 \, b^{3} \cos\left(4 \, d x + 4 \, c\right) + b^{3} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) + {\left(8 \, b^{3} \cos\left(2 \, d x + 2 \, c\right) - b^{3} + 2 \, {\left(8 \, a b^{2} - 7 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) + 2 \, {\left(b^{3} + {\left(8 \, a b^{2} - 7 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - {\left(b^{3} \sin\left(6 \, d x + 6 \, c\right) - 2 \, b^{3} \sin\left(4 \, d x + 4 \, c\right) + b^{3} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 2 \, {\left(4 \, b^{3} \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a b^{2} - 7 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}{a^{2} b^{2} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a^{2} b^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 16 \, a^{2} b^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} b^{2} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a^{2} b^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 16 \, a^{2} b^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} - 8 \, a^{2} b^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2} b^{2} + 4 \, {\left(64 \, a^{4} - 48 \, a^{3} b + 9 \, a^{2} b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(64 \, a^{4} - 48 \, a^{3} b + 9 \, a^{2} b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(8 \, a^{3} b - 3 \, a^{2} b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 2 \, {\left(4 \, a^{2} b^{2} \cos\left(6 \, d x + 6 \, c\right) + 4 \, a^{2} b^{2} \cos\left(2 \, d x + 2 \, c\right) - a^{2} b^{2} + 2 \, {\left(8 \, a^{3} b - 3 \, a^{2} b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(4 \, a^{2} b^{2} \cos\left(2 \, d x + 2 \, c\right) - a^{2} b^{2} + 2 \, {\left(8 \, a^{3} b - 3 \, a^{2} b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(8 \, a^{3} b - 3 \, a^{2} b^{2} - 4 \, {\left(8 \, a^{3} b - 3 \, a^{2} b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(2 \, a^{2} b^{2} \sin\left(6 \, d x + 6 \, c\right) + 2 \, a^{2} b^{2} \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a^{3} b - 3 \, a^{2} b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(2 \, a^{2} b^{2} \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a^{3} b - 3 \, a^{2} b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}\,{d x} - 2 \, {\left(15 \, b \cos\left(8 \, d x + 8 \, c\right) - 60 \, b \cos\left(6 \, d x + 6 \, c\right) + 10 \, {\left(8 \, a + 9 \, b\right)} \cos\left(4 \, d x + 4 \, c\right) - 20 \, {\left(2 \, a + 3 \, b\right)} \cos\left(2 \, d x + 2 \, c\right) + 8 \, a + 15 \, b\right)} \sin\left(10 \, d x + 10 \, c\right) - 10 \, {\left(30 \, b \cos\left(6 \, d x + 6 \, c\right) - 20 \, {\left(4 \, a + 3 \, b\right)} \cos\left(4 \, d x + 4 \, c\right) + 5 \, {\left(8 \, a + 9 \, b\right)} \cos\left(2 \, d x + 2 \, c\right) - 8 \, a - 12 \, b\right)} \sin\left(8 \, d x + 8 \, c\right) - 20 \, {\left(10 \, {\left(8 \, a + 3 \, b\right)} \cos\left(4 \, d x + 4 \, c\right) - 10 \, {\left(4 \, a + 3 \, b\right)} \cos\left(2 \, d x + 2 \, c\right) + 8 \, a + 9 \, b\right)} \sin\left(6 \, d x + 6 \, c\right) - 60 \, {\left(5 \, b \cos\left(2 \, d x + 2 \, c\right) - 2 \, b\right)} \sin\left(4 \, d x + 4 \, c\right) - 30 \, b \sin\left(2 \, d x + 2 \, c\right)}{15 \, {\left(a^{2} d \cos\left(10 \, d x + 10 \, c\right)^{2} + 25 \, a^{2} d \cos\left(8 \, d x + 8 \, c\right)^{2} + 100 \, a^{2} d \cos\left(6 \, d x + 6 \, c\right)^{2} + 100 \, a^{2} d \cos\left(4 \, d x + 4 \, c\right)^{2} + 25 \, a^{2} d \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} d \sin\left(10 \, d x + 10 \, c\right)^{2} + 25 \, a^{2} d \sin\left(8 \, d x + 8 \, c\right)^{2} + 100 \, a^{2} d \sin\left(6 \, d x + 6 \, c\right)^{2} + 100 \, a^{2} d \sin\left(4 \, d x + 4 \, c\right)^{2} - 100 \, a^{2} d \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 25 \, a^{2} d \sin\left(2 \, d x + 2 \, c\right)^{2} - 10 \, a^{2} d \cos\left(2 \, d x + 2 \, c\right) + a^{2} d - 2 \, {\left(5 \, a^{2} d \cos\left(8 \, d x + 8 \, c\right) - 10 \, a^{2} d \cos\left(6 \, d x + 6 \, c\right) + 10 \, a^{2} d \cos\left(4 \, d x + 4 \, c\right) - 5 \, a^{2} d \cos\left(2 \, d x + 2 \, c\right) + a^{2} d\right)} \cos\left(10 \, d x + 10 \, c\right) - 10 \, {\left(10 \, a^{2} d \cos\left(6 \, d x + 6 \, c\right) - 10 \, a^{2} d \cos\left(4 \, d x + 4 \, c\right) + 5 \, a^{2} d \cos\left(2 \, d x + 2 \, c\right) - a^{2} d\right)} \cos\left(8 \, d x + 8 \, c\right) - 20 \, {\left(10 \, a^{2} d \cos\left(4 \, d x + 4 \, c\right) - 5 \, a^{2} d \cos\left(2 \, d x + 2 \, c\right) + a^{2} d\right)} \cos\left(6 \, d x + 6 \, c\right) - 20 \, {\left(5 \, a^{2} d \cos\left(2 \, d x + 2 \, c\right) - a^{2} d\right)} \cos\left(4 \, d x + 4 \, c\right) - 10 \, {\left(a^{2} d \sin\left(8 \, d x + 8 \, c\right) - 2 \, a^{2} d \sin\left(6 \, d x + 6 \, c\right) + 2 \, a^{2} d \sin\left(4 \, d x + 4 \, c\right) - a^{2} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) - 50 \, {\left(2 \, a^{2} d \sin\left(6 \, d x + 6 \, c\right) - 2 \, a^{2} d \sin\left(4 \, d x + 4 \, c\right) + a^{2} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) - 100 \, {\left(2 \, a^{2} d \sin\left(4 \, d x + 4 \, c\right) - a^{2} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)}}"," ",0,"1/15*(300*b*cos(4*d*x + 4*c)*sin(2*d*x + 2*c) + 10*(3*b*sin(8*d*x + 8*c) - 12*b*sin(6*d*x + 6*c) + 2*(8*a + 9*b)*sin(4*d*x + 4*c) - 4*(2*a + 3*b)*sin(2*d*x + 2*c))*cos(10*d*x + 10*c) + 50*(6*b*sin(6*d*x + 6*c) - 4*(4*a + 3*b)*sin(4*d*x + 4*c) + (8*a + 9*b)*sin(2*d*x + 2*c))*cos(8*d*x + 8*c) + 200*((8*a + 3*b)*sin(4*d*x + 4*c) - (4*a + 3*b)*sin(2*d*x + 2*c))*cos(6*d*x + 6*c) + 15*(a^2*d*cos(10*d*x + 10*c)^2 + 25*a^2*d*cos(8*d*x + 8*c)^2 + 100*a^2*d*cos(6*d*x + 6*c)^2 + 100*a^2*d*cos(4*d*x + 4*c)^2 + 25*a^2*d*cos(2*d*x + 2*c)^2 + a^2*d*sin(10*d*x + 10*c)^2 + 25*a^2*d*sin(8*d*x + 8*c)^2 + 100*a^2*d*sin(6*d*x + 6*c)^2 + 100*a^2*d*sin(4*d*x + 4*c)^2 - 100*a^2*d*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 25*a^2*d*sin(2*d*x + 2*c)^2 - 10*a^2*d*cos(2*d*x + 2*c) + a^2*d - 2*(5*a^2*d*cos(8*d*x + 8*c) - 10*a^2*d*cos(6*d*x + 6*c) + 10*a^2*d*cos(4*d*x + 4*c) - 5*a^2*d*cos(2*d*x + 2*c) + a^2*d)*cos(10*d*x + 10*c) - 10*(10*a^2*d*cos(6*d*x + 6*c) - 10*a^2*d*cos(4*d*x + 4*c) + 5*a^2*d*cos(2*d*x + 2*c) - a^2*d)*cos(8*d*x + 8*c) - 20*(10*a^2*d*cos(4*d*x + 4*c) - 5*a^2*d*cos(2*d*x + 2*c) + a^2*d)*cos(6*d*x + 6*c) - 20*(5*a^2*d*cos(2*d*x + 2*c) - a^2*d)*cos(4*d*x + 4*c) - 10*(a^2*d*sin(8*d*x + 8*c) - 2*a^2*d*sin(6*d*x + 6*c) + 2*a^2*d*sin(4*d*x + 4*c) - a^2*d*sin(2*d*x + 2*c))*sin(10*d*x + 10*c) - 50*(2*a^2*d*sin(6*d*x + 6*c) - 2*a^2*d*sin(4*d*x + 4*c) + a^2*d*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) - 100*(2*a^2*d*sin(4*d*x + 4*c) - a^2*d*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*integrate(-4*(4*b^3*cos(6*d*x + 6*c)^2 + 4*b^3*cos(2*d*x + 2*c)^2 + 4*b^3*sin(6*d*x + 6*c)^2 + 4*b^3*sin(2*d*x + 2*c)^2 - b^3*cos(2*d*x + 2*c) - 4*(8*a*b^2 - 3*b^3)*cos(4*d*x + 4*c)^2 - 4*(8*a*b^2 - 3*b^3)*sin(4*d*x + 4*c)^2 + 2*(8*a*b^2 - 7*b^3)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) - (b^3*cos(6*d*x + 6*c) - 2*b^3*cos(4*d*x + 4*c) + b^3*cos(2*d*x + 2*c))*cos(8*d*x + 8*c) + (8*b^3*cos(2*d*x + 2*c) - b^3 + 2*(8*a*b^2 - 7*b^3)*cos(4*d*x + 4*c))*cos(6*d*x + 6*c) + 2*(b^3 + (8*a*b^2 - 7*b^3)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - (b^3*sin(6*d*x + 6*c) - 2*b^3*sin(4*d*x + 4*c) + b^3*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 2*(4*b^3*sin(2*d*x + 2*c) + (8*a*b^2 - 7*b^3)*sin(4*d*x + 4*c))*sin(6*d*x + 6*c))/(a^2*b^2*cos(8*d*x + 8*c)^2 + 16*a^2*b^2*cos(6*d*x + 6*c)^2 + 16*a^2*b^2*cos(2*d*x + 2*c)^2 + a^2*b^2*sin(8*d*x + 8*c)^2 + 16*a^2*b^2*sin(6*d*x + 6*c)^2 + 16*a^2*b^2*sin(2*d*x + 2*c)^2 - 8*a^2*b^2*cos(2*d*x + 2*c) + a^2*b^2 + 4*(64*a^4 - 48*a^3*b + 9*a^2*b^2)*cos(4*d*x + 4*c)^2 + 4*(64*a^4 - 48*a^3*b + 9*a^2*b^2)*sin(4*d*x + 4*c)^2 + 16*(8*a^3*b - 3*a^2*b^2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) - 2*(4*a^2*b^2*cos(6*d*x + 6*c) + 4*a^2*b^2*cos(2*d*x + 2*c) - a^2*b^2 + 2*(8*a^3*b - 3*a^2*b^2)*cos(4*d*x + 4*c))*cos(8*d*x + 8*c) + 8*(4*a^2*b^2*cos(2*d*x + 2*c) - a^2*b^2 + 2*(8*a^3*b - 3*a^2*b^2)*cos(4*d*x + 4*c))*cos(6*d*x + 6*c) - 4*(8*a^3*b - 3*a^2*b^2 - 4*(8*a^3*b - 3*a^2*b^2)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 4*(2*a^2*b^2*sin(6*d*x + 6*c) + 2*a^2*b^2*sin(2*d*x + 2*c) + (8*a^3*b - 3*a^2*b^2)*sin(4*d*x + 4*c))*sin(8*d*x + 8*c) + 16*(2*a^2*b^2*sin(2*d*x + 2*c) + (8*a^3*b - 3*a^2*b^2)*sin(4*d*x + 4*c))*sin(6*d*x + 6*c)), x) - 2*(15*b*cos(8*d*x + 8*c) - 60*b*cos(6*d*x + 6*c) + 10*(8*a + 9*b)*cos(4*d*x + 4*c) - 20*(2*a + 3*b)*cos(2*d*x + 2*c) + 8*a + 15*b)*sin(10*d*x + 10*c) - 10*(30*b*cos(6*d*x + 6*c) - 20*(4*a + 3*b)*cos(4*d*x + 4*c) + 5*(8*a + 9*b)*cos(2*d*x + 2*c) - 8*a - 12*b)*sin(8*d*x + 8*c) - 20*(10*(8*a + 3*b)*cos(4*d*x + 4*c) - 10*(4*a + 3*b)*cos(2*d*x + 2*c) + 8*a + 9*b)*sin(6*d*x + 6*c) - 60*(5*b*cos(2*d*x + 2*c) - 2*b)*sin(4*d*x + 4*c) - 30*b*sin(2*d*x + 2*c))/(a^2*d*cos(10*d*x + 10*c)^2 + 25*a^2*d*cos(8*d*x + 8*c)^2 + 100*a^2*d*cos(6*d*x + 6*c)^2 + 100*a^2*d*cos(4*d*x + 4*c)^2 + 25*a^2*d*cos(2*d*x + 2*c)^2 + a^2*d*sin(10*d*x + 10*c)^2 + 25*a^2*d*sin(8*d*x + 8*c)^2 + 100*a^2*d*sin(6*d*x + 6*c)^2 + 100*a^2*d*sin(4*d*x + 4*c)^2 - 100*a^2*d*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 25*a^2*d*sin(2*d*x + 2*c)^2 - 10*a^2*d*cos(2*d*x + 2*c) + a^2*d - 2*(5*a^2*d*cos(8*d*x + 8*c) - 10*a^2*d*cos(6*d*x + 6*c) + 10*a^2*d*cos(4*d*x + 4*c) - 5*a^2*d*cos(2*d*x + 2*c) + a^2*d)*cos(10*d*x + 10*c) - 10*(10*a^2*d*cos(6*d*x + 6*c) - 10*a^2*d*cos(4*d*x + 4*c) + 5*a^2*d*cos(2*d*x + 2*c) - a^2*d)*cos(8*d*x + 8*c) - 20*(10*a^2*d*cos(4*d*x + 4*c) - 5*a^2*d*cos(2*d*x + 2*c) + a^2*d)*cos(6*d*x + 6*c) - 20*(5*a^2*d*cos(2*d*x + 2*c) - a^2*d)*cos(4*d*x + 4*c) - 10*(a^2*d*sin(8*d*x + 8*c) - 2*a^2*d*sin(6*d*x + 6*c) + 2*a^2*d*sin(4*d*x + 4*c) - a^2*d*sin(2*d*x + 2*c))*sin(10*d*x + 10*c) - 50*(2*a^2*d*sin(6*d*x + 6*c) - 2*a^2*d*sin(4*d*x + 4*c) + a^2*d*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) - 100*(2*a^2*d*sin(4*d*x + 4*c) - a^2*d*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))","F",0
211,-1,0,0,0.000000," ","integrate(csc(d*x+c)^8/(a-b*sin(d*x+c)^4),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
212,0,0,0,0.000000," ","integrate(sin(d*x+c)^9/(a-b*sin(d*x+c)^4)^2,x, algorithm=""maxima"")","\frac{{\left(2 \, a b^{2} - 3 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right) \cos\left(d x + c\right) - 4 \, {\left(2 \, a b^{2} - 3 \, b^{3}\right)} \sin\left(3 \, d x + 3 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + {\left(2 \, a b^{2} - 3 \, b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right) \sin\left(d x + c\right) - {\left({\left(a b^{2} - b^{3}\right)} \cos\left(9 \, d x + 9 \, c\right) - 4 \, {\left(a b^{2} - b^{3}\right)} \cos\left(7 \, d x + 7 \, c\right) - 2 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} \cos\left(5 \, d x + 5 \, c\right) - 4 \, {\left(a b^{2} - b^{3}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(a b^{2} - b^{3}\right)} \cos\left(d x + c\right)\right)} \cos\left(10 \, d x + 10 \, c\right) - {\left(a b^{2} - b^{3} - {\left(2 \, a b^{2} - 3 \, b^{3}\right)} \cos\left(8 \, d x + 8 \, c\right) - {\left(20 \, a^{2} b - 17 \, a b^{2} + 2 \, b^{3}\right)} \cos\left(6 \, d x + 6 \, c\right) - {\left(20 \, a^{2} b - 17 \, a b^{2} + 2 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right) - {\left(2 \, a b^{2} - 3 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(9 \, d x + 9 \, c\right) - {\left(4 \, {\left(2 \, a b^{2} - 3 \, b^{3}\right)} \cos\left(7 \, d x + 7 \, c\right) + 2 \, {\left(16 \, a^{2} b - 30 \, a b^{2} + 9 \, b^{3}\right)} \cos\left(5 \, d x + 5 \, c\right) + 4 \, {\left(2 \, a b^{2} - 3 \, b^{3}\right)} \cos\left(3 \, d x + 3 \, c\right) - {\left(2 \, a b^{2} - 3 \, b^{3}\right)} \cos\left(d x + c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) + 4 \, {\left(a b^{2} - b^{3} - {\left(20 \, a^{2} b - 17 \, a b^{2} + 2 \, b^{3}\right)} \cos\left(6 \, d x + 6 \, c\right) - {\left(20 \, a^{2} b - 17 \, a b^{2} + 2 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right) - {\left(2 \, a b^{2} - 3 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(7 \, d x + 7 \, c\right) - {\left(2 \, {\left(160 \, a^{3} - 196 \, a^{2} b + 67 \, a b^{2} - 6 \, b^{3}\right)} \cos\left(5 \, d x + 5 \, c\right) + 4 \, {\left(20 \, a^{2} b - 17 \, a b^{2} + 2 \, b^{3}\right)} \cos\left(3 \, d x + 3 \, c\right) - {\left(20 \, a^{2} b - 17 \, a b^{2} + 2 \, b^{3}\right)} \cos\left(d x + c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) + 2 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3} - {\left(160 \, a^{3} - 196 \, a^{2} b + 67 \, a b^{2} - 6 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right) - {\left(16 \, a^{2} b - 30 \, a b^{2} + 9 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(5 \, d x + 5 \, c\right) - {\left(4 \, {\left(20 \, a^{2} b - 17 \, a b^{2} + 2 \, b^{3}\right)} \cos\left(3 \, d x + 3 \, c\right) - {\left(20 \, a^{2} b - 17 \, a b^{2} + 2 \, b^{3}\right)} \cos\left(d x + c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a b^{2} - b^{3} - {\left(2 \, a b^{2} - 3 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(3 \, d x + 3 \, c\right) - {\left(a b^{2} - b^{3}\right)} \cos\left(d x + c\right) - {\left({\left(a b^{4} - b^{5}\right)} d \cos\left(9 \, d x + 9 \, c\right)^{2} + 16 \, {\left(a b^{4} - b^{5}\right)} d \cos\left(7 \, d x + 7 \, c\right)^{2} + 4 \, {\left(64 \, a^{3} b^{2} - 112 \, a^{2} b^{3} + 57 \, a b^{4} - 9 \, b^{5}\right)} d \cos\left(5 \, d x + 5 \, c\right)^{2} + 16 \, {\left(a b^{4} - b^{5}\right)} d \cos\left(3 \, d x + 3 \, c\right)^{2} - 8 \, {\left(a b^{4} - b^{5}\right)} d \cos\left(3 \, d x + 3 \, c\right) \cos\left(d x + c\right) + {\left(a b^{4} - b^{5}\right)} d \cos\left(d x + c\right)^{2} + {\left(a b^{4} - b^{5}\right)} d \sin\left(9 \, d x + 9 \, c\right)^{2} + 16 \, {\left(a b^{4} - b^{5}\right)} d \sin\left(7 \, d x + 7 \, c\right)^{2} + 4 \, {\left(64 \, a^{3} b^{2} - 112 \, a^{2} b^{3} + 57 \, a b^{4} - 9 \, b^{5}\right)} d \sin\left(5 \, d x + 5 \, c\right)^{2} + 16 \, {\left(a b^{4} - b^{5}\right)} d \sin\left(3 \, d x + 3 \, c\right)^{2} - 8 \, {\left(a b^{4} - b^{5}\right)} d \sin\left(3 \, d x + 3 \, c\right) \sin\left(d x + c\right) + {\left(a b^{4} - b^{5}\right)} d \sin\left(d x + c\right)^{2} - 2 \, {\left(4 \, {\left(a b^{4} - b^{5}\right)} d \cos\left(7 \, d x + 7 \, c\right) + 2 \, {\left(8 \, a^{2} b^{3} - 11 \, a b^{4} + 3 \, b^{5}\right)} d \cos\left(5 \, d x + 5 \, c\right) + 4 \, {\left(a b^{4} - b^{5}\right)} d \cos\left(3 \, d x + 3 \, c\right) - {\left(a b^{4} - b^{5}\right)} d \cos\left(d x + c\right)\right)} \cos\left(9 \, d x + 9 \, c\right) + 8 \, {\left(2 \, {\left(8 \, a^{2} b^{3} - 11 \, a b^{4} + 3 \, b^{5}\right)} d \cos\left(5 \, d x + 5 \, c\right) + 4 \, {\left(a b^{4} - b^{5}\right)} d \cos\left(3 \, d x + 3 \, c\right) - {\left(a b^{4} - b^{5}\right)} d \cos\left(d x + c\right)\right)} \cos\left(7 \, d x + 7 \, c\right) + 4 \, {\left(4 \, {\left(8 \, a^{2} b^{3} - 11 \, a b^{4} + 3 \, b^{5}\right)} d \cos\left(3 \, d x + 3 \, c\right) - {\left(8 \, a^{2} b^{3} - 11 \, a b^{4} + 3 \, b^{5}\right)} d \cos\left(d x + c\right)\right)} \cos\left(5 \, d x + 5 \, c\right) - 2 \, {\left(4 \, {\left(a b^{4} - b^{5}\right)} d \sin\left(7 \, d x + 7 \, c\right) + 2 \, {\left(8 \, a^{2} b^{3} - 11 \, a b^{4} + 3 \, b^{5}\right)} d \sin\left(5 \, d x + 5 \, c\right) + 4 \, {\left(a b^{4} - b^{5}\right)} d \sin\left(3 \, d x + 3 \, c\right) - {\left(a b^{4} - b^{5}\right)} d \sin\left(d x + c\right)\right)} \sin\left(9 \, d x + 9 \, c\right) + 8 \, {\left(2 \, {\left(8 \, a^{2} b^{3} - 11 \, a b^{4} + 3 \, b^{5}\right)} d \sin\left(5 \, d x + 5 \, c\right) + 4 \, {\left(a b^{4} - b^{5}\right)} d \sin\left(3 \, d x + 3 \, c\right) - {\left(a b^{4} - b^{5}\right)} d \sin\left(d x + c\right)\right)} \sin\left(7 \, d x + 7 \, c\right) + 4 \, {\left(4 \, {\left(8 \, a^{2} b^{3} - 11 \, a b^{4} + 3 \, b^{5}\right)} d \sin\left(3 \, d x + 3 \, c\right) - {\left(8 \, a^{2} b^{3} - 11 \, a b^{4} + 3 \, b^{5}\right)} d \sin\left(d x + c\right)\right)} \sin\left(5 \, d x + 5 \, c\right)\right)} \int \frac{4 \, a b^{2} \cos\left(d x + c\right) \sin\left(2 \, d x + 2 \, c\right) - 4 \, a b^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(d x + c\right) + a b^{2} \sin\left(d x + c\right) + 4 \, {\left(20 \, a^{2} b - 27 \, a b^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - {\left(a b^{2} \sin\left(7 \, d x + 7 \, c\right) - a b^{2} \sin\left(d x + c\right) + {\left(20 \, a^{2} b - 27 \, a b^{2}\right)} \sin\left(5 \, d x + 5 \, c\right) - {\left(20 \, a^{2} b - 27 \, a b^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) - 2 \, {\left(2 \, a b^{2} \sin\left(6 \, d x + 6 \, c\right) + 2 \, a b^{2} \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a^{2} b - 3 \, a b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \cos\left(7 \, d x + 7 \, c\right) - 4 \, {\left(a b^{2} \sin\left(d x + c\right) - {\left(20 \, a^{2} b - 27 \, a b^{2}\right)} \sin\left(5 \, d x + 5 \, c\right) + {\left(20 \, a^{2} b - 27 \, a b^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left({\left(160 \, a^{3} - 276 \, a^{2} b + 81 \, a b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(20 \, a^{2} b - 27 \, a b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(5 \, d x + 5 \, c\right) - 2 \, {\left({\left(160 \, a^{3} - 276 \, a^{2} b + 81 \, a b^{2}\right)} \sin\left(3 \, d x + 3 \, c\right) + {\left(8 \, a^{2} b - 3 \, a b^{2}\right)} \sin\left(d x + c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) + {\left(a b^{2} \cos\left(7 \, d x + 7 \, c\right) - a b^{2} \cos\left(d x + c\right) + {\left(20 \, a^{2} b - 27 \, a b^{2}\right)} \cos\left(5 \, d x + 5 \, c\right) - {\left(20 \, a^{2} b - 27 \, a b^{2}\right)} \cos\left(3 \, d x + 3 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + {\left(4 \, a b^{2} \cos\left(6 \, d x + 6 \, c\right) + 4 \, a b^{2} \cos\left(2 \, d x + 2 \, c\right) - a b^{2} + 2 \, {\left(8 \, a^{2} b - 3 \, a b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \sin\left(7 \, d x + 7 \, c\right) + 4 \, {\left(a b^{2} \cos\left(d x + c\right) - {\left(20 \, a^{2} b - 27 \, a b^{2}\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left(20 \, a^{2} b - 27 \, a b^{2}\right)} \cos\left(3 \, d x + 3 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) - {\left(20 \, a^{2} b - 27 \, a b^{2} - 2 \, {\left(160 \, a^{3} - 276 \, a^{2} b + 81 \, a b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(20 \, a^{2} b - 27 \, a b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(5 \, d x + 5 \, c\right) + 2 \, {\left({\left(160 \, a^{3} - 276 \, a^{2} b + 81 \, a b^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(8 \, a^{2} b - 3 \, a b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) + {\left(20 \, a^{2} b - 27 \, a b^{2} - 4 \, {\left(20 \, a^{2} b - 27 \, a b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(3 \, d x + 3 \, c\right)}{a b^{4} - b^{5} + {\left(a b^{4} - b^{5}\right)} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a b^{4} - b^{5}\right)} \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{3} b^{2} - 112 \, a^{2} b^{3} + 57 \, a b^{4} - 9 \, b^{5}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(a b^{4} - b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a b^{4} - b^{5}\right)} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a b^{4} - b^{5}\right)} \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{3} b^{2} - 112 \, a^{2} b^{3} + 57 \, a b^{4} - 9 \, b^{5}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(8 \, a^{2} b^{3} - 11 \, a b^{4} + 3 \, b^{5}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, {\left(a b^{4} - b^{5}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a b^{4} - b^{5} - 4 \, {\left(a b^{4} - b^{5}\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left(8 \, a^{2} b^{3} - 11 \, a b^{4} + 3 \, b^{5}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a b^{4} - b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) - 8 \, {\left(a b^{4} - b^{5} - 2 \, {\left(8 \, a^{2} b^{3} - 11 \, a b^{4} + 3 \, b^{5}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a b^{4} - b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(8 \, a^{2} b^{3} - 11 \, a b^{4} + 3 \, b^{5} - 4 \, {\left(8 \, a^{2} b^{3} - 11 \, a b^{4} + 3 \, b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(a b^{4} - b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right) - 4 \, {\left(2 \, {\left(a b^{4} - b^{5}\right)} \sin\left(6 \, d x + 6 \, c\right) + {\left(8 \, a^{2} b^{3} - 11 \, a b^{4} + 3 \, b^{5}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a b^{4} - b^{5}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left({\left(8 \, a^{2} b^{3} - 11 \, a b^{4} + 3 \, b^{5}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a b^{4} - b^{5}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}\,{d x} - {\left({\left(a b^{2} - b^{3}\right)} \sin\left(9 \, d x + 9 \, c\right) - 4 \, {\left(a b^{2} - b^{3}\right)} \sin\left(7 \, d x + 7 \, c\right) - 2 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} \sin\left(5 \, d x + 5 \, c\right) - 4 \, {\left(a b^{2} - b^{3}\right)} \sin\left(3 \, d x + 3 \, c\right) + {\left(a b^{2} - b^{3}\right)} \sin\left(d x + c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + {\left({\left(2 \, a b^{2} - 3 \, b^{3}\right)} \sin\left(8 \, d x + 8 \, c\right) + {\left(20 \, a^{2} b - 17 \, a b^{2} + 2 \, b^{3}\right)} \sin\left(6 \, d x + 6 \, c\right) + {\left(20 \, a^{2} b - 17 \, a b^{2} + 2 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) + {\left(2 \, a b^{2} - 3 \, b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(9 \, d x + 9 \, c\right) - {\left(4 \, {\left(2 \, a b^{2} - 3 \, b^{3}\right)} \sin\left(7 \, d x + 7 \, c\right) + 2 \, {\left(16 \, a^{2} b - 30 \, a b^{2} + 9 \, b^{3}\right)} \sin\left(5 \, d x + 5 \, c\right) + 4 \, {\left(2 \, a b^{2} - 3 \, b^{3}\right)} \sin\left(3 \, d x + 3 \, c\right) - {\left(2 \, a b^{2} - 3 \, b^{3}\right)} \sin\left(d x + c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) - 4 \, {\left({\left(20 \, a^{2} b - 17 \, a b^{2} + 2 \, b^{3}\right)} \sin\left(6 \, d x + 6 \, c\right) + {\left(20 \, a^{2} b - 17 \, a b^{2} + 2 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) + {\left(2 \, a b^{2} - 3 \, b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(7 \, d x + 7 \, c\right) - {\left(2 \, {\left(160 \, a^{3} - 196 \, a^{2} b + 67 \, a b^{2} - 6 \, b^{3}\right)} \sin\left(5 \, d x + 5 \, c\right) + 4 \, {\left(20 \, a^{2} b - 17 \, a b^{2} + 2 \, b^{3}\right)} \sin\left(3 \, d x + 3 \, c\right) - {\left(20 \, a^{2} b - 17 \, a b^{2} + 2 \, b^{3}\right)} \sin\left(d x + c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) - 2 \, {\left({\left(160 \, a^{3} - 196 \, a^{2} b + 67 \, a b^{2} - 6 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) + {\left(16 \, a^{2} b - 30 \, a b^{2} + 9 \, b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(5 \, d x + 5 \, c\right) - {\left(4 \, {\left(20 \, a^{2} b - 17 \, a b^{2} + 2 \, b^{3}\right)} \sin\left(3 \, d x + 3 \, c\right) - {\left(20 \, a^{2} b - 17 \, a b^{2} + 2 \, b^{3}\right)} \sin\left(d x + c\right)\right)} \sin\left(4 \, d x + 4 \, c\right)}{2 \, {\left({\left(a b^{4} - b^{5}\right)} d \cos\left(9 \, d x + 9 \, c\right)^{2} + 16 \, {\left(a b^{4} - b^{5}\right)} d \cos\left(7 \, d x + 7 \, c\right)^{2} + 4 \, {\left(64 \, a^{3} b^{2} - 112 \, a^{2} b^{3} + 57 \, a b^{4} - 9 \, b^{5}\right)} d \cos\left(5 \, d x + 5 \, c\right)^{2} + 16 \, {\left(a b^{4} - b^{5}\right)} d \cos\left(3 \, d x + 3 \, c\right)^{2} - 8 \, {\left(a b^{4} - b^{5}\right)} d \cos\left(3 \, d x + 3 \, c\right) \cos\left(d x + c\right) + {\left(a b^{4} - b^{5}\right)} d \cos\left(d x + c\right)^{2} + {\left(a b^{4} - b^{5}\right)} d \sin\left(9 \, d x + 9 \, c\right)^{2} + 16 \, {\left(a b^{4} - b^{5}\right)} d \sin\left(7 \, d x + 7 \, c\right)^{2} + 4 \, {\left(64 \, a^{3} b^{2} - 112 \, a^{2} b^{3} + 57 \, a b^{4} - 9 \, b^{5}\right)} d \sin\left(5 \, d x + 5 \, c\right)^{2} + 16 \, {\left(a b^{4} - b^{5}\right)} d \sin\left(3 \, d x + 3 \, c\right)^{2} - 8 \, {\left(a b^{4} - b^{5}\right)} d \sin\left(3 \, d x + 3 \, c\right) \sin\left(d x + c\right) + {\left(a b^{4} - b^{5}\right)} d \sin\left(d x + c\right)^{2} - 2 \, {\left(4 \, {\left(a b^{4} - b^{5}\right)} d \cos\left(7 \, d x + 7 \, c\right) + 2 \, {\left(8 \, a^{2} b^{3} - 11 \, a b^{4} + 3 \, b^{5}\right)} d \cos\left(5 \, d x + 5 \, c\right) + 4 \, {\left(a b^{4} - b^{5}\right)} d \cos\left(3 \, d x + 3 \, c\right) - {\left(a b^{4} - b^{5}\right)} d \cos\left(d x + c\right)\right)} \cos\left(9 \, d x + 9 \, c\right) + 8 \, {\left(2 \, {\left(8 \, a^{2} b^{3} - 11 \, a b^{4} + 3 \, b^{5}\right)} d \cos\left(5 \, d x + 5 \, c\right) + 4 \, {\left(a b^{4} - b^{5}\right)} d \cos\left(3 \, d x + 3 \, c\right) - {\left(a b^{4} - b^{5}\right)} d \cos\left(d x + c\right)\right)} \cos\left(7 \, d x + 7 \, c\right) + 4 \, {\left(4 \, {\left(8 \, a^{2} b^{3} - 11 \, a b^{4} + 3 \, b^{5}\right)} d \cos\left(3 \, d x + 3 \, c\right) - {\left(8 \, a^{2} b^{3} - 11 \, a b^{4} + 3 \, b^{5}\right)} d \cos\left(d x + c\right)\right)} \cos\left(5 \, d x + 5 \, c\right) - 2 \, {\left(4 \, {\left(a b^{4} - b^{5}\right)} d \sin\left(7 \, d x + 7 \, c\right) + 2 \, {\left(8 \, a^{2} b^{3} - 11 \, a b^{4} + 3 \, b^{5}\right)} d \sin\left(5 \, d x + 5 \, c\right) + 4 \, {\left(a b^{4} - b^{5}\right)} d \sin\left(3 \, d x + 3 \, c\right) - {\left(a b^{4} - b^{5}\right)} d \sin\left(d x + c\right)\right)} \sin\left(9 \, d x + 9 \, c\right) + 8 \, {\left(2 \, {\left(8 \, a^{2} b^{3} - 11 \, a b^{4} + 3 \, b^{5}\right)} d \sin\left(5 \, d x + 5 \, c\right) + 4 \, {\left(a b^{4} - b^{5}\right)} d \sin\left(3 \, d x + 3 \, c\right) - {\left(a b^{4} - b^{5}\right)} d \sin\left(d x + c\right)\right)} \sin\left(7 \, d x + 7 \, c\right) + 4 \, {\left(4 \, {\left(8 \, a^{2} b^{3} - 11 \, a b^{4} + 3 \, b^{5}\right)} d \sin\left(3 \, d x + 3 \, c\right) - {\left(8 \, a^{2} b^{3} - 11 \, a b^{4} + 3 \, b^{5}\right)} d \sin\left(d x + c\right)\right)} \sin\left(5 \, d x + 5 \, c\right)\right)}}"," ",0,"1/2*((2*a*b^2 - 3*b^3)*cos(2*d*x + 2*c)*cos(d*x + c) - 4*(2*a*b^2 - 3*b^3)*sin(3*d*x + 3*c)*sin(2*d*x + 2*c) + (2*a*b^2 - 3*b^3)*sin(2*d*x + 2*c)*sin(d*x + c) - ((a*b^2 - b^3)*cos(9*d*x + 9*c) - 4*(a*b^2 - b^3)*cos(7*d*x + 7*c) - 2*(8*a^2*b - 11*a*b^2 + 3*b^3)*cos(5*d*x + 5*c) - 4*(a*b^2 - b^3)*cos(3*d*x + 3*c) + (a*b^2 - b^3)*cos(d*x + c))*cos(10*d*x + 10*c) - (a*b^2 - b^3 - (2*a*b^2 - 3*b^3)*cos(8*d*x + 8*c) - (20*a^2*b - 17*a*b^2 + 2*b^3)*cos(6*d*x + 6*c) - (20*a^2*b - 17*a*b^2 + 2*b^3)*cos(4*d*x + 4*c) - (2*a*b^2 - 3*b^3)*cos(2*d*x + 2*c))*cos(9*d*x + 9*c) - (4*(2*a*b^2 - 3*b^3)*cos(7*d*x + 7*c) + 2*(16*a^2*b - 30*a*b^2 + 9*b^3)*cos(5*d*x + 5*c) + 4*(2*a*b^2 - 3*b^3)*cos(3*d*x + 3*c) - (2*a*b^2 - 3*b^3)*cos(d*x + c))*cos(8*d*x + 8*c) + 4*(a*b^2 - b^3 - (20*a^2*b - 17*a*b^2 + 2*b^3)*cos(6*d*x + 6*c) - (20*a^2*b - 17*a*b^2 + 2*b^3)*cos(4*d*x + 4*c) - (2*a*b^2 - 3*b^3)*cos(2*d*x + 2*c))*cos(7*d*x + 7*c) - (2*(160*a^3 - 196*a^2*b + 67*a*b^2 - 6*b^3)*cos(5*d*x + 5*c) + 4*(20*a^2*b - 17*a*b^2 + 2*b^3)*cos(3*d*x + 3*c) - (20*a^2*b - 17*a*b^2 + 2*b^3)*cos(d*x + c))*cos(6*d*x + 6*c) + 2*(8*a^2*b - 11*a*b^2 + 3*b^3 - (160*a^3 - 196*a^2*b + 67*a*b^2 - 6*b^3)*cos(4*d*x + 4*c) - (16*a^2*b - 30*a*b^2 + 9*b^3)*cos(2*d*x + 2*c))*cos(5*d*x + 5*c) - (4*(20*a^2*b - 17*a*b^2 + 2*b^3)*cos(3*d*x + 3*c) - (20*a^2*b - 17*a*b^2 + 2*b^3)*cos(d*x + c))*cos(4*d*x + 4*c) + 4*(a*b^2 - b^3 - (2*a*b^2 - 3*b^3)*cos(2*d*x + 2*c))*cos(3*d*x + 3*c) - (a*b^2 - b^3)*cos(d*x + c) + 2*((a*b^4 - b^5)*d*cos(9*d*x + 9*c)^2 + 16*(a*b^4 - b^5)*d*cos(7*d*x + 7*c)^2 + 4*(64*a^3*b^2 - 112*a^2*b^3 + 57*a*b^4 - 9*b^5)*d*cos(5*d*x + 5*c)^2 + 16*(a*b^4 - b^5)*d*cos(3*d*x + 3*c)^2 - 8*(a*b^4 - b^5)*d*cos(3*d*x + 3*c)*cos(d*x + c) + (a*b^4 - b^5)*d*cos(d*x + c)^2 + (a*b^4 - b^5)*d*sin(9*d*x + 9*c)^2 + 16*(a*b^4 - b^5)*d*sin(7*d*x + 7*c)^2 + 4*(64*a^3*b^2 - 112*a^2*b^3 + 57*a*b^4 - 9*b^5)*d*sin(5*d*x + 5*c)^2 + 16*(a*b^4 - b^5)*d*sin(3*d*x + 3*c)^2 - 8*(a*b^4 - b^5)*d*sin(3*d*x + 3*c)*sin(d*x + c) + (a*b^4 - b^5)*d*sin(d*x + c)^2 - 2*(4*(a*b^4 - b^5)*d*cos(7*d*x + 7*c) + 2*(8*a^2*b^3 - 11*a*b^4 + 3*b^5)*d*cos(5*d*x + 5*c) + 4*(a*b^4 - b^5)*d*cos(3*d*x + 3*c) - (a*b^4 - b^5)*d*cos(d*x + c))*cos(9*d*x + 9*c) + 8*(2*(8*a^2*b^3 - 11*a*b^4 + 3*b^5)*d*cos(5*d*x + 5*c) + 4*(a*b^4 - b^5)*d*cos(3*d*x + 3*c) - (a*b^4 - b^5)*d*cos(d*x + c))*cos(7*d*x + 7*c) + 4*(4*(8*a^2*b^3 - 11*a*b^4 + 3*b^5)*d*cos(3*d*x + 3*c) - (8*a^2*b^3 - 11*a*b^4 + 3*b^5)*d*cos(d*x + c))*cos(5*d*x + 5*c) - 2*(4*(a*b^4 - b^5)*d*sin(7*d*x + 7*c) + 2*(8*a^2*b^3 - 11*a*b^4 + 3*b^5)*d*sin(5*d*x + 5*c) + 4*(a*b^4 - b^5)*d*sin(3*d*x + 3*c) - (a*b^4 - b^5)*d*sin(d*x + c))*sin(9*d*x + 9*c) + 8*(2*(8*a^2*b^3 - 11*a*b^4 + 3*b^5)*d*sin(5*d*x + 5*c) + 4*(a*b^4 - b^5)*d*sin(3*d*x + 3*c) - (a*b^4 - b^5)*d*sin(d*x + c))*sin(7*d*x + 7*c) + 4*(4*(8*a^2*b^3 - 11*a*b^4 + 3*b^5)*d*sin(3*d*x + 3*c) - (8*a^2*b^3 - 11*a*b^4 + 3*b^5)*d*sin(d*x + c))*sin(5*d*x + 5*c))*integrate(-1/2*(4*a*b^2*cos(d*x + c)*sin(2*d*x + 2*c) - 4*a*b^2*cos(2*d*x + 2*c)*sin(d*x + c) + a*b^2*sin(d*x + c) + 4*(20*a^2*b - 27*a*b^2)*cos(3*d*x + 3*c)*sin(2*d*x + 2*c) - (a*b^2*sin(7*d*x + 7*c) - a*b^2*sin(d*x + c) + (20*a^2*b - 27*a*b^2)*sin(5*d*x + 5*c) - (20*a^2*b - 27*a*b^2)*sin(3*d*x + 3*c))*cos(8*d*x + 8*c) - 2*(2*a*b^2*sin(6*d*x + 6*c) + 2*a*b^2*sin(2*d*x + 2*c) + (8*a^2*b - 3*a*b^2)*sin(4*d*x + 4*c))*cos(7*d*x + 7*c) - 4*(a*b^2*sin(d*x + c) - (20*a^2*b - 27*a*b^2)*sin(5*d*x + 5*c) + (20*a^2*b - 27*a*b^2)*sin(3*d*x + 3*c))*cos(6*d*x + 6*c) - 2*((160*a^3 - 276*a^2*b + 81*a*b^2)*sin(4*d*x + 4*c) + 2*(20*a^2*b - 27*a*b^2)*sin(2*d*x + 2*c))*cos(5*d*x + 5*c) - 2*((160*a^3 - 276*a^2*b + 81*a*b^2)*sin(3*d*x + 3*c) + (8*a^2*b - 3*a*b^2)*sin(d*x + c))*cos(4*d*x + 4*c) + (a*b^2*cos(7*d*x + 7*c) - a*b^2*cos(d*x + c) + (20*a^2*b - 27*a*b^2)*cos(5*d*x + 5*c) - (20*a^2*b - 27*a*b^2)*cos(3*d*x + 3*c))*sin(8*d*x + 8*c) + (4*a*b^2*cos(6*d*x + 6*c) + 4*a*b^2*cos(2*d*x + 2*c) - a*b^2 + 2*(8*a^2*b - 3*a*b^2)*cos(4*d*x + 4*c))*sin(7*d*x + 7*c) + 4*(a*b^2*cos(d*x + c) - (20*a^2*b - 27*a*b^2)*cos(5*d*x + 5*c) + (20*a^2*b - 27*a*b^2)*cos(3*d*x + 3*c))*sin(6*d*x + 6*c) - (20*a^2*b - 27*a*b^2 - 2*(160*a^3 - 276*a^2*b + 81*a*b^2)*cos(4*d*x + 4*c) - 4*(20*a^2*b - 27*a*b^2)*cos(2*d*x + 2*c))*sin(5*d*x + 5*c) + 2*((160*a^3 - 276*a^2*b + 81*a*b^2)*cos(3*d*x + 3*c) + (8*a^2*b - 3*a*b^2)*cos(d*x + c))*sin(4*d*x + 4*c) + (20*a^2*b - 27*a*b^2 - 4*(20*a^2*b - 27*a*b^2)*cos(2*d*x + 2*c))*sin(3*d*x + 3*c))/(a*b^4 - b^5 + (a*b^4 - b^5)*cos(8*d*x + 8*c)^2 + 16*(a*b^4 - b^5)*cos(6*d*x + 6*c)^2 + 4*(64*a^3*b^2 - 112*a^2*b^3 + 57*a*b^4 - 9*b^5)*cos(4*d*x + 4*c)^2 + 16*(a*b^4 - b^5)*cos(2*d*x + 2*c)^2 + (a*b^4 - b^5)*sin(8*d*x + 8*c)^2 + 16*(a*b^4 - b^5)*sin(6*d*x + 6*c)^2 + 4*(64*a^3*b^2 - 112*a^2*b^3 + 57*a*b^4 - 9*b^5)*sin(4*d*x + 4*c)^2 + 16*(8*a^2*b^3 - 11*a*b^4 + 3*b^5)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*(a*b^4 - b^5)*sin(2*d*x + 2*c)^2 + 2*(a*b^4 - b^5 - 4*(a*b^4 - b^5)*cos(6*d*x + 6*c) - 2*(8*a^2*b^3 - 11*a*b^4 + 3*b^5)*cos(4*d*x + 4*c) - 4*(a*b^4 - b^5)*cos(2*d*x + 2*c))*cos(8*d*x + 8*c) - 8*(a*b^4 - b^5 - 2*(8*a^2*b^3 - 11*a*b^4 + 3*b^5)*cos(4*d*x + 4*c) - 4*(a*b^4 - b^5)*cos(2*d*x + 2*c))*cos(6*d*x + 6*c) - 4*(8*a^2*b^3 - 11*a*b^4 + 3*b^5 - 4*(8*a^2*b^3 - 11*a*b^4 + 3*b^5)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 8*(a*b^4 - b^5)*cos(2*d*x + 2*c) - 4*(2*(a*b^4 - b^5)*sin(6*d*x + 6*c) + (8*a^2*b^3 - 11*a*b^4 + 3*b^5)*sin(4*d*x + 4*c) + 2*(a*b^4 - b^5)*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*((8*a^2*b^3 - 11*a*b^4 + 3*b^5)*sin(4*d*x + 4*c) + 2*(a*b^4 - b^5)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c)), x) - ((a*b^2 - b^3)*sin(9*d*x + 9*c) - 4*(a*b^2 - b^3)*sin(7*d*x + 7*c) - 2*(8*a^2*b - 11*a*b^2 + 3*b^3)*sin(5*d*x + 5*c) - 4*(a*b^2 - b^3)*sin(3*d*x + 3*c) + (a*b^2 - b^3)*sin(d*x + c))*sin(10*d*x + 10*c) + ((2*a*b^2 - 3*b^3)*sin(8*d*x + 8*c) + (20*a^2*b - 17*a*b^2 + 2*b^3)*sin(6*d*x + 6*c) + (20*a^2*b - 17*a*b^2 + 2*b^3)*sin(4*d*x + 4*c) + (2*a*b^2 - 3*b^3)*sin(2*d*x + 2*c))*sin(9*d*x + 9*c) - (4*(2*a*b^2 - 3*b^3)*sin(7*d*x + 7*c) + 2*(16*a^2*b - 30*a*b^2 + 9*b^3)*sin(5*d*x + 5*c) + 4*(2*a*b^2 - 3*b^3)*sin(3*d*x + 3*c) - (2*a*b^2 - 3*b^3)*sin(d*x + c))*sin(8*d*x + 8*c) - 4*((20*a^2*b - 17*a*b^2 + 2*b^3)*sin(6*d*x + 6*c) + (20*a^2*b - 17*a*b^2 + 2*b^3)*sin(4*d*x + 4*c) + (2*a*b^2 - 3*b^3)*sin(2*d*x + 2*c))*sin(7*d*x + 7*c) - (2*(160*a^3 - 196*a^2*b + 67*a*b^2 - 6*b^3)*sin(5*d*x + 5*c) + 4*(20*a^2*b - 17*a*b^2 + 2*b^3)*sin(3*d*x + 3*c) - (20*a^2*b - 17*a*b^2 + 2*b^3)*sin(d*x + c))*sin(6*d*x + 6*c) - 2*((160*a^3 - 196*a^2*b + 67*a*b^2 - 6*b^3)*sin(4*d*x + 4*c) + (16*a^2*b - 30*a*b^2 + 9*b^3)*sin(2*d*x + 2*c))*sin(5*d*x + 5*c) - (4*(20*a^2*b - 17*a*b^2 + 2*b^3)*sin(3*d*x + 3*c) - (20*a^2*b - 17*a*b^2 + 2*b^3)*sin(d*x + c))*sin(4*d*x + 4*c))/((a*b^4 - b^5)*d*cos(9*d*x + 9*c)^2 + 16*(a*b^4 - b^5)*d*cos(7*d*x + 7*c)^2 + 4*(64*a^3*b^2 - 112*a^2*b^3 + 57*a*b^4 - 9*b^5)*d*cos(5*d*x + 5*c)^2 + 16*(a*b^4 - b^5)*d*cos(3*d*x + 3*c)^2 - 8*(a*b^4 - b^5)*d*cos(3*d*x + 3*c)*cos(d*x + c) + (a*b^4 - b^5)*d*cos(d*x + c)^2 + (a*b^4 - b^5)*d*sin(9*d*x + 9*c)^2 + 16*(a*b^4 - b^5)*d*sin(7*d*x + 7*c)^2 + 4*(64*a^3*b^2 - 112*a^2*b^3 + 57*a*b^4 - 9*b^5)*d*sin(5*d*x + 5*c)^2 + 16*(a*b^4 - b^5)*d*sin(3*d*x + 3*c)^2 - 8*(a*b^4 - b^5)*d*sin(3*d*x + 3*c)*sin(d*x + c) + (a*b^4 - b^5)*d*sin(d*x + c)^2 - 2*(4*(a*b^4 - b^5)*d*cos(7*d*x + 7*c) + 2*(8*a^2*b^3 - 11*a*b^4 + 3*b^5)*d*cos(5*d*x + 5*c) + 4*(a*b^4 - b^5)*d*cos(3*d*x + 3*c) - (a*b^4 - b^5)*d*cos(d*x + c))*cos(9*d*x + 9*c) + 8*(2*(8*a^2*b^3 - 11*a*b^4 + 3*b^5)*d*cos(5*d*x + 5*c) + 4*(a*b^4 - b^5)*d*cos(3*d*x + 3*c) - (a*b^4 - b^5)*d*cos(d*x + c))*cos(7*d*x + 7*c) + 4*(4*(8*a^2*b^3 - 11*a*b^4 + 3*b^5)*d*cos(3*d*x + 3*c) - (8*a^2*b^3 - 11*a*b^4 + 3*b^5)*d*cos(d*x + c))*cos(5*d*x + 5*c) - 2*(4*(a*b^4 - b^5)*d*sin(7*d*x + 7*c) + 2*(8*a^2*b^3 - 11*a*b^4 + 3*b^5)*d*sin(5*d*x + 5*c) + 4*(a*b^4 - b^5)*d*sin(3*d*x + 3*c) - (a*b^4 - b^5)*d*sin(d*x + c))*sin(9*d*x + 9*c) + 8*(2*(8*a^2*b^3 - 11*a*b^4 + 3*b^5)*d*sin(5*d*x + 5*c) + 4*(a*b^4 - b^5)*d*sin(3*d*x + 3*c) - (a*b^4 - b^5)*d*sin(d*x + c))*sin(7*d*x + 7*c) + 4*(4*(8*a^2*b^3 - 11*a*b^4 + 3*b^5)*d*sin(3*d*x + 3*c) - (8*a^2*b^3 - 11*a*b^4 + 3*b^5)*d*sin(d*x + c))*sin(5*d*x + 5*c))","F",0
213,0,0,0,0.000000," ","integrate(sin(d*x+c)^7/(a-b*sin(d*x+c)^4)^2,x, algorithm=""maxima"")","\frac{4 \, a b \cos\left(2 \, d x + 2 \, c\right) \cos\left(d x + c\right) - 20 \, a b \sin\left(3 \, d x + 3 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, a b \sin\left(2 \, d x + 2 \, c\right) \sin\left(d x + c\right) - a b \cos\left(d x + c\right) - {\left(a b \cos\left(7 \, d x + 7 \, c\right) - 5 \, a b \cos\left(5 \, d x + 5 \, c\right) - 5 \, a b \cos\left(3 \, d x + 3 \, c\right) + a b \cos\left(d x + c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) + {\left(4 \, a b \cos\left(6 \, d x + 6 \, c\right) + 4 \, a b \cos\left(2 \, d x + 2 \, c\right) - a b + 2 \, {\left(8 \, a^{2} - 3 \, a b\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(7 \, d x + 7 \, c\right) - 4 \, {\left(5 \, a b \cos\left(5 \, d x + 5 \, c\right) + 5 \, a b \cos\left(3 \, d x + 3 \, c\right) - a b \cos\left(d x + c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 5 \, {\left(4 \, a b \cos\left(2 \, d x + 2 \, c\right) - a b + 2 \, {\left(8 \, a^{2} - 3 \, a b\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(5 \, d x + 5 \, c\right) - 2 \, {\left(5 \, {\left(8 \, a^{2} - 3 \, a b\right)} \cos\left(3 \, d x + 3 \, c\right) - {\left(8 \, a^{2} - 3 \, a b\right)} \cos\left(d x + c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 5 \, {\left(4 \, a b \cos\left(2 \, d x + 2 \, c\right) - a b\right)} \cos\left(3 \, d x + 3 \, c\right) - {\left({\left(a b^{3} - b^{4}\right)} d \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a b^{3} - b^{4}\right)} d \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{3} b - 112 \, a^{2} b^{2} + 57 \, a b^{3} - 9 \, b^{4}\right)} d \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(a b^{3} - b^{4}\right)} d \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a b^{3} - b^{4}\right)} d \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a b^{3} - b^{4}\right)} d \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{3} b - 112 \, a^{2} b^{2} + 57 \, a b^{3} - 9 \, b^{4}\right)} d \sin\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, {\left(a b^{3} - b^{4}\right)} d \sin\left(2 \, d x + 2 \, c\right)^{2} - 8 \, {\left(a b^{3} - b^{4}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a b^{3} - b^{4}\right)} d - 2 \, {\left(4 \, {\left(a b^{3} - b^{4}\right)} d \cos\left(6 \, d x + 6 \, c\right) + 2 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a b^{3} - b^{4}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(a b^{3} - b^{4}\right)} d\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(2 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a b^{3} - b^{4}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(a b^{3} - b^{4}\right)} d\right)} \cos\left(6 \, d x + 6 \, c\right) + 4 \, {\left(4 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(2 \, {\left(a b^{3} - b^{4}\right)} d \sin\left(6 \, d x + 6 \, c\right) + {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a b^{3} - b^{4}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left({\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a b^{3} - b^{4}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \int \frac{4 \, {\left(5 \, a b - 12 \, b^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 4 \, {\left(3 \, a b - 4 \, b^{2}\right)} \cos\left(d x + c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, {\left(3 \, a b - 4 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) \sin\left(d x + c\right) + {\left({\left(3 \, a b - 4 \, b^{2}\right)} \sin\left(7 \, d x + 7 \, c\right) - {\left(5 \, a b - 12 \, b^{2}\right)} \sin\left(5 \, d x + 5 \, c\right) + {\left(5 \, a b - 12 \, b^{2}\right)} \sin\left(3 \, d x + 3 \, c\right) - {\left(3 \, a b - 4 \, b^{2}\right)} \sin\left(d x + c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) + 2 \, {\left(2 \, {\left(3 \, a b - 4 \, b^{2}\right)} \sin\left(6 \, d x + 6 \, c\right) + {\left(24 \, a^{2} - 41 \, a b + 12 \, b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(3 \, a b - 4 \, b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(7 \, d x + 7 \, c\right) + 4 \, {\left({\left(5 \, a b - 12 \, b^{2}\right)} \sin\left(5 \, d x + 5 \, c\right) - {\left(5 \, a b - 12 \, b^{2}\right)} \sin\left(3 \, d x + 3 \, c\right) + {\left(3 \, a b - 4 \, b^{2}\right)} \sin\left(d x + c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left({\left(40 \, a^{2} - 111 \, a b + 36 \, b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(5 \, a b - 12 \, b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(5 \, d x + 5 \, c\right) - 2 \, {\left({\left(40 \, a^{2} - 111 \, a b + 36 \, b^{2}\right)} \sin\left(3 \, d x + 3 \, c\right) - {\left(24 \, a^{2} - 41 \, a b + 12 \, b^{2}\right)} \sin\left(d x + c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - {\left({\left(3 \, a b - 4 \, b^{2}\right)} \cos\left(7 \, d x + 7 \, c\right) - {\left(5 \, a b - 12 \, b^{2}\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left(5 \, a b - 12 \, b^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) - {\left(3 \, a b - 4 \, b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + {\left(3 \, a b - 4 \, b^{2} - 4 \, {\left(3 \, a b - 4 \, b^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left(24 \, a^{2} - 41 \, a b + 12 \, b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(3 \, a b - 4 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(7 \, d x + 7 \, c\right) - 4 \, {\left({\left(5 \, a b - 12 \, b^{2}\right)} \cos\left(5 \, d x + 5 \, c\right) - {\left(5 \, a b - 12 \, b^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(3 \, a b - 4 \, b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) - {\left(5 \, a b - 12 \, b^{2} - 2 \, {\left(40 \, a^{2} - 111 \, a b + 36 \, b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(5 \, a b - 12 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(5 \, d x + 5 \, c\right) + 2 \, {\left({\left(40 \, a^{2} - 111 \, a b + 36 \, b^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) - {\left(24 \, a^{2} - 41 \, a b + 12 \, b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) + {\left(5 \, a b - 12 \, b^{2} - 4 \, {\left(5 \, a b - 12 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(3 \, d x + 3 \, c\right) - {\left(3 \, a b - 4 \, b^{2}\right)} \sin\left(d x + c\right)}{a b^{3} - b^{4} + {\left(a b^{3} - b^{4}\right)} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a b^{3} - b^{4}\right)} \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{3} b - 112 \, a^{2} b^{2} + 57 \, a b^{3} - 9 \, b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(a b^{3} - b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a b^{3} - b^{4}\right)} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a b^{3} - b^{4}\right)} \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{3} b - 112 \, a^{2} b^{2} + 57 \, a b^{3} - 9 \, b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, {\left(a b^{3} - b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a b^{3} - b^{4} - 4 \, {\left(a b^{3} - b^{4}\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a b^{3} - b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) - 8 \, {\left(a b^{3} - b^{4} - 2 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a b^{3} - b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4} - 4 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(a b^{3} - b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right) - 4 \, {\left(2 \, {\left(a b^{3} - b^{4}\right)} \sin\left(6 \, d x + 6 \, c\right) + {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a b^{3} - b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left({\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a b^{3} - b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}\,{d x} - {\left(a b \sin\left(7 \, d x + 7 \, c\right) - 5 \, a b \sin\left(5 \, d x + 5 \, c\right) - 5 \, a b \sin\left(3 \, d x + 3 \, c\right) + a b \sin\left(d x + c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 2 \, {\left(2 \, a b \sin\left(6 \, d x + 6 \, c\right) + 2 \, a b \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a^{2} - 3 \, a b\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(7 \, d x + 7 \, c\right) - 4 \, {\left(5 \, a b \sin\left(5 \, d x + 5 \, c\right) + 5 \, a b \sin\left(3 \, d x + 3 \, c\right) - a b \sin\left(d x + c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) - 10 \, {\left(2 \, a b \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a^{2} - 3 \, a b\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(5 \, d x + 5 \, c\right) - 2 \, {\left(5 \, {\left(8 \, a^{2} - 3 \, a b\right)} \sin\left(3 \, d x + 3 \, c\right) - {\left(8 \, a^{2} - 3 \, a b\right)} \sin\left(d x + c\right)\right)} \sin\left(4 \, d x + 4 \, c\right)}{2 \, {\left({\left(a b^{3} - b^{4}\right)} d \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a b^{3} - b^{4}\right)} d \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{3} b - 112 \, a^{2} b^{2} + 57 \, a b^{3} - 9 \, b^{4}\right)} d \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(a b^{3} - b^{4}\right)} d \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a b^{3} - b^{4}\right)} d \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a b^{3} - b^{4}\right)} d \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{3} b - 112 \, a^{2} b^{2} + 57 \, a b^{3} - 9 \, b^{4}\right)} d \sin\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, {\left(a b^{3} - b^{4}\right)} d \sin\left(2 \, d x + 2 \, c\right)^{2} - 8 \, {\left(a b^{3} - b^{4}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a b^{3} - b^{4}\right)} d - 2 \, {\left(4 \, {\left(a b^{3} - b^{4}\right)} d \cos\left(6 \, d x + 6 \, c\right) + 2 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a b^{3} - b^{4}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(a b^{3} - b^{4}\right)} d\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(2 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a b^{3} - b^{4}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(a b^{3} - b^{4}\right)} d\right)} \cos\left(6 \, d x + 6 \, c\right) + 4 \, {\left(4 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(2 \, {\left(a b^{3} - b^{4}\right)} d \sin\left(6 \, d x + 6 \, c\right) + {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a b^{3} - b^{4}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left({\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a b^{3} - b^{4}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)}}"," ",0,"1/2*(4*a*b*cos(2*d*x + 2*c)*cos(d*x + c) - 20*a*b*sin(3*d*x + 3*c)*sin(2*d*x + 2*c) + 4*a*b*sin(2*d*x + 2*c)*sin(d*x + c) - a*b*cos(d*x + c) - (a*b*cos(7*d*x + 7*c) - 5*a*b*cos(5*d*x + 5*c) - 5*a*b*cos(3*d*x + 3*c) + a*b*cos(d*x + c))*cos(8*d*x + 8*c) + (4*a*b*cos(6*d*x + 6*c) + 4*a*b*cos(2*d*x + 2*c) - a*b + 2*(8*a^2 - 3*a*b)*cos(4*d*x + 4*c))*cos(7*d*x + 7*c) - 4*(5*a*b*cos(5*d*x + 5*c) + 5*a*b*cos(3*d*x + 3*c) - a*b*cos(d*x + c))*cos(6*d*x + 6*c) - 5*(4*a*b*cos(2*d*x + 2*c) - a*b + 2*(8*a^2 - 3*a*b)*cos(4*d*x + 4*c))*cos(5*d*x + 5*c) - 2*(5*(8*a^2 - 3*a*b)*cos(3*d*x + 3*c) - (8*a^2 - 3*a*b)*cos(d*x + c))*cos(4*d*x + 4*c) - 5*(4*a*b*cos(2*d*x + 2*c) - a*b)*cos(3*d*x + 3*c) + 2*((a*b^3 - b^4)*d*cos(8*d*x + 8*c)^2 + 16*(a*b^3 - b^4)*d*cos(6*d*x + 6*c)^2 + 4*(64*a^3*b - 112*a^2*b^2 + 57*a*b^3 - 9*b^4)*d*cos(4*d*x + 4*c)^2 + 16*(a*b^3 - b^4)*d*cos(2*d*x + 2*c)^2 + (a*b^3 - b^4)*d*sin(8*d*x + 8*c)^2 + 16*(a*b^3 - b^4)*d*sin(6*d*x + 6*c)^2 + 4*(64*a^3*b - 112*a^2*b^2 + 57*a*b^3 - 9*b^4)*d*sin(4*d*x + 4*c)^2 + 16*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*(a*b^3 - b^4)*d*sin(2*d*x + 2*c)^2 - 8*(a*b^3 - b^4)*d*cos(2*d*x + 2*c) + (a*b^3 - b^4)*d - 2*(4*(a*b^3 - b^4)*d*cos(6*d*x + 6*c) + 2*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cos(4*d*x + 4*c) + 4*(a*b^3 - b^4)*d*cos(2*d*x + 2*c) - (a*b^3 - b^4)*d)*cos(8*d*x + 8*c) + 8*(2*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cos(4*d*x + 4*c) + 4*(a*b^3 - b^4)*d*cos(2*d*x + 2*c) - (a*b^3 - b^4)*d)*cos(6*d*x + 6*c) + 4*(4*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cos(2*d*x + 2*c) - (8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d)*cos(4*d*x + 4*c) - 4*(2*(a*b^3 - b^4)*d*sin(6*d*x + 6*c) + (8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*sin(4*d*x + 4*c) + 2*(a*b^3 - b^4)*d*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*((8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*sin(4*d*x + 4*c) + 2*(a*b^3 - b^4)*d*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*integrate(-1/2*(4*(5*a*b - 12*b^2)*cos(3*d*x + 3*c)*sin(2*d*x + 2*c) - 4*(3*a*b - 4*b^2)*cos(d*x + c)*sin(2*d*x + 2*c) + 4*(3*a*b - 4*b^2)*cos(2*d*x + 2*c)*sin(d*x + c) + ((3*a*b - 4*b^2)*sin(7*d*x + 7*c) - (5*a*b - 12*b^2)*sin(5*d*x + 5*c) + (5*a*b - 12*b^2)*sin(3*d*x + 3*c) - (3*a*b - 4*b^2)*sin(d*x + c))*cos(8*d*x + 8*c) + 2*(2*(3*a*b - 4*b^2)*sin(6*d*x + 6*c) + (24*a^2 - 41*a*b + 12*b^2)*sin(4*d*x + 4*c) + 2*(3*a*b - 4*b^2)*sin(2*d*x + 2*c))*cos(7*d*x + 7*c) + 4*((5*a*b - 12*b^2)*sin(5*d*x + 5*c) - (5*a*b - 12*b^2)*sin(3*d*x + 3*c) + (3*a*b - 4*b^2)*sin(d*x + c))*cos(6*d*x + 6*c) - 2*((40*a^2 - 111*a*b + 36*b^2)*sin(4*d*x + 4*c) + 2*(5*a*b - 12*b^2)*sin(2*d*x + 2*c))*cos(5*d*x + 5*c) - 2*((40*a^2 - 111*a*b + 36*b^2)*sin(3*d*x + 3*c) - (24*a^2 - 41*a*b + 12*b^2)*sin(d*x + c))*cos(4*d*x + 4*c) - ((3*a*b - 4*b^2)*cos(7*d*x + 7*c) - (5*a*b - 12*b^2)*cos(5*d*x + 5*c) + (5*a*b - 12*b^2)*cos(3*d*x + 3*c) - (3*a*b - 4*b^2)*cos(d*x + c))*sin(8*d*x + 8*c) + (3*a*b - 4*b^2 - 4*(3*a*b - 4*b^2)*cos(6*d*x + 6*c) - 2*(24*a^2 - 41*a*b + 12*b^2)*cos(4*d*x + 4*c) - 4*(3*a*b - 4*b^2)*cos(2*d*x + 2*c))*sin(7*d*x + 7*c) - 4*((5*a*b - 12*b^2)*cos(5*d*x + 5*c) - (5*a*b - 12*b^2)*cos(3*d*x + 3*c) + (3*a*b - 4*b^2)*cos(d*x + c))*sin(6*d*x + 6*c) - (5*a*b - 12*b^2 - 2*(40*a^2 - 111*a*b + 36*b^2)*cos(4*d*x + 4*c) - 4*(5*a*b - 12*b^2)*cos(2*d*x + 2*c))*sin(5*d*x + 5*c) + 2*((40*a^2 - 111*a*b + 36*b^2)*cos(3*d*x + 3*c) - (24*a^2 - 41*a*b + 12*b^2)*cos(d*x + c))*sin(4*d*x + 4*c) + (5*a*b - 12*b^2 - 4*(5*a*b - 12*b^2)*cos(2*d*x + 2*c))*sin(3*d*x + 3*c) - (3*a*b - 4*b^2)*sin(d*x + c))/(a*b^3 - b^4 + (a*b^3 - b^4)*cos(8*d*x + 8*c)^2 + 16*(a*b^3 - b^4)*cos(6*d*x + 6*c)^2 + 4*(64*a^3*b - 112*a^2*b^2 + 57*a*b^3 - 9*b^4)*cos(4*d*x + 4*c)^2 + 16*(a*b^3 - b^4)*cos(2*d*x + 2*c)^2 + (a*b^3 - b^4)*sin(8*d*x + 8*c)^2 + 16*(a*b^3 - b^4)*sin(6*d*x + 6*c)^2 + 4*(64*a^3*b - 112*a^2*b^2 + 57*a*b^3 - 9*b^4)*sin(4*d*x + 4*c)^2 + 16*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*(a*b^3 - b^4)*sin(2*d*x + 2*c)^2 + 2*(a*b^3 - b^4 - 4*(a*b^3 - b^4)*cos(6*d*x + 6*c) - 2*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*cos(4*d*x + 4*c) - 4*(a*b^3 - b^4)*cos(2*d*x + 2*c))*cos(8*d*x + 8*c) - 8*(a*b^3 - b^4 - 2*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*cos(4*d*x + 4*c) - 4*(a*b^3 - b^4)*cos(2*d*x + 2*c))*cos(6*d*x + 6*c) - 4*(8*a^2*b^2 - 11*a*b^3 + 3*b^4 - 4*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 8*(a*b^3 - b^4)*cos(2*d*x + 2*c) - 4*(2*(a*b^3 - b^4)*sin(6*d*x + 6*c) + (8*a^2*b^2 - 11*a*b^3 + 3*b^4)*sin(4*d*x + 4*c) + 2*(a*b^3 - b^4)*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*((8*a^2*b^2 - 11*a*b^3 + 3*b^4)*sin(4*d*x + 4*c) + 2*(a*b^3 - b^4)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c)), x) - (a*b*sin(7*d*x + 7*c) - 5*a*b*sin(5*d*x + 5*c) - 5*a*b*sin(3*d*x + 3*c) + a*b*sin(d*x + c))*sin(8*d*x + 8*c) + 2*(2*a*b*sin(6*d*x + 6*c) + 2*a*b*sin(2*d*x + 2*c) + (8*a^2 - 3*a*b)*sin(4*d*x + 4*c))*sin(7*d*x + 7*c) - 4*(5*a*b*sin(5*d*x + 5*c) + 5*a*b*sin(3*d*x + 3*c) - a*b*sin(d*x + c))*sin(6*d*x + 6*c) - 10*(2*a*b*sin(2*d*x + 2*c) + (8*a^2 - 3*a*b)*sin(4*d*x + 4*c))*sin(5*d*x + 5*c) - 2*(5*(8*a^2 - 3*a*b)*sin(3*d*x + 3*c) - (8*a^2 - 3*a*b)*sin(d*x + c))*sin(4*d*x + 4*c))/((a*b^3 - b^4)*d*cos(8*d*x + 8*c)^2 + 16*(a*b^3 - b^4)*d*cos(6*d*x + 6*c)^2 + 4*(64*a^3*b - 112*a^2*b^2 + 57*a*b^3 - 9*b^4)*d*cos(4*d*x + 4*c)^2 + 16*(a*b^3 - b^4)*d*cos(2*d*x + 2*c)^2 + (a*b^3 - b^4)*d*sin(8*d*x + 8*c)^2 + 16*(a*b^3 - b^4)*d*sin(6*d*x + 6*c)^2 + 4*(64*a^3*b - 112*a^2*b^2 + 57*a*b^3 - 9*b^4)*d*sin(4*d*x + 4*c)^2 + 16*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*(a*b^3 - b^4)*d*sin(2*d*x + 2*c)^2 - 8*(a*b^3 - b^4)*d*cos(2*d*x + 2*c) + (a*b^3 - b^4)*d - 2*(4*(a*b^3 - b^4)*d*cos(6*d*x + 6*c) + 2*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cos(4*d*x + 4*c) + 4*(a*b^3 - b^4)*d*cos(2*d*x + 2*c) - (a*b^3 - b^4)*d)*cos(8*d*x + 8*c) + 8*(2*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cos(4*d*x + 4*c) + 4*(a*b^3 - b^4)*d*cos(2*d*x + 2*c) - (a*b^3 - b^4)*d)*cos(6*d*x + 6*c) + 4*(4*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cos(2*d*x + 2*c) - (8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d)*cos(4*d*x + 4*c) - 4*(2*(a*b^3 - b^4)*d*sin(6*d*x + 6*c) + (8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*sin(4*d*x + 4*c) + 2*(a*b^3 - b^4)*d*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*((8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*sin(4*d*x + 4*c) + 2*(a*b^3 - b^4)*d*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))","F",0
214,0,0,0,0.000000," ","integrate(sin(d*x+c)^5/(a-b*sin(d*x+c)^4)^2,x, algorithm=""maxima"")","\frac{4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(d x + c\right) + 4 \, b^{2} \sin\left(2 \, d x + 2 \, c\right) \sin\left(d x + c\right) - b^{2} \cos\left(d x + c\right) - 4 \, {\left(4 \, a b + b^{2}\right)} \sin\left(3 \, d x + 3 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - {\left(b^{2} \cos\left(7 \, d x + 7 \, c\right) + b^{2} \cos\left(d x + c\right) - {\left(4 \, a b + b^{2}\right)} \cos\left(5 \, d x + 5 \, c\right) - {\left(4 \, a b + b^{2}\right)} \cos\left(3 \, d x + 3 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) + {\left(4 \, b^{2} \cos\left(6 \, d x + 6 \, c\right) + 4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) - b^{2} + 2 \, {\left(8 \, a b - 3 \, b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(7 \, d x + 7 \, c\right) + 4 \, {\left(b^{2} \cos\left(d x + c\right) - {\left(4 \, a b + b^{2}\right)} \cos\left(5 \, d x + 5 \, c\right) - {\left(4 \, a b + b^{2}\right)} \cos\left(3 \, d x + 3 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) + {\left(4 \, a b + b^{2} - 2 \, {\left(32 \, a^{2} - 4 \, a b - 3 \, b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(4 \, a b + b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(5 \, d x + 5 \, c\right) - 2 \, {\left({\left(32 \, a^{2} - 4 \, a b - 3 \, b^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) - {\left(8 \, a b - 3 \, b^{2}\right)} \cos\left(d x + c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) + {\left(4 \, a b + b^{2} - 4 \, {\left(4 \, a b + b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(3 \, d x + 3 \, c\right) - {\left({\left(a b^{3} - b^{4}\right)} d \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a b^{3} - b^{4}\right)} d \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{3} b - 112 \, a^{2} b^{2} + 57 \, a b^{3} - 9 \, b^{4}\right)} d \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(a b^{3} - b^{4}\right)} d \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a b^{3} - b^{4}\right)} d \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a b^{3} - b^{4}\right)} d \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{3} b - 112 \, a^{2} b^{2} + 57 \, a b^{3} - 9 \, b^{4}\right)} d \sin\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, {\left(a b^{3} - b^{4}\right)} d \sin\left(2 \, d x + 2 \, c\right)^{2} - 8 \, {\left(a b^{3} - b^{4}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a b^{3} - b^{4}\right)} d - 2 \, {\left(4 \, {\left(a b^{3} - b^{4}\right)} d \cos\left(6 \, d x + 6 \, c\right) + 2 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a b^{3} - b^{4}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(a b^{3} - b^{4}\right)} d\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(2 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a b^{3} - b^{4}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(a b^{3} - b^{4}\right)} d\right)} \cos\left(6 \, d x + 6 \, c\right) + 4 \, {\left(4 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(2 \, {\left(a b^{3} - b^{4}\right)} d \sin\left(6 \, d x + 6 \, c\right) + {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a b^{3} - b^{4}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left({\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a b^{3} - b^{4}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \int \frac{4 \, b^{2} \cos\left(d x + c\right) \sin\left(2 \, d x + 2 \, c\right) - 4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(d x + c\right) + 4 \, {\left(4 \, a b - 11 \, b^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + b^{2} \sin\left(d x + c\right) - {\left(b^{2} \sin\left(7 \, d x + 7 \, c\right) - b^{2} \sin\left(d x + c\right) + {\left(4 \, a b - 11 \, b^{2}\right)} \sin\left(5 \, d x + 5 \, c\right) - {\left(4 \, a b - 11 \, b^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) - 2 \, {\left(2 \, b^{2} \sin\left(6 \, d x + 6 \, c\right) + 2 \, b^{2} \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a b - 3 \, b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \cos\left(7 \, d x + 7 \, c\right) - 4 \, {\left(b^{2} \sin\left(d x + c\right) - {\left(4 \, a b - 11 \, b^{2}\right)} \sin\left(5 \, d x + 5 \, c\right) + {\left(4 \, a b - 11 \, b^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left({\left(32 \, a^{2} - 100 \, a b + 33 \, b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(4 \, a b - 11 \, b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(5 \, d x + 5 \, c\right) - 2 \, {\left({\left(32 \, a^{2} - 100 \, a b + 33 \, b^{2}\right)} \sin\left(3 \, d x + 3 \, c\right) + {\left(8 \, a b - 3 \, b^{2}\right)} \sin\left(d x + c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) + {\left(b^{2} \cos\left(7 \, d x + 7 \, c\right) - b^{2} \cos\left(d x + c\right) + {\left(4 \, a b - 11 \, b^{2}\right)} \cos\left(5 \, d x + 5 \, c\right) - {\left(4 \, a b - 11 \, b^{2}\right)} \cos\left(3 \, d x + 3 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + {\left(4 \, b^{2} \cos\left(6 \, d x + 6 \, c\right) + 4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) - b^{2} + 2 \, {\left(8 \, a b - 3 \, b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \sin\left(7 \, d x + 7 \, c\right) + 4 \, {\left(b^{2} \cos\left(d x + c\right) - {\left(4 \, a b - 11 \, b^{2}\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left(4 \, a b - 11 \, b^{2}\right)} \cos\left(3 \, d x + 3 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) - {\left(4 \, a b - 11 \, b^{2} - 2 \, {\left(32 \, a^{2} - 100 \, a b + 33 \, b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(4 \, a b - 11 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(5 \, d x + 5 \, c\right) + 2 \, {\left({\left(32 \, a^{2} - 100 \, a b + 33 \, b^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(8 \, a b - 3 \, b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) + {\left(4 \, a b - 11 \, b^{2} - 4 \, {\left(4 \, a b - 11 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(3 \, d x + 3 \, c\right)}{a b^{3} - b^{4} + {\left(a b^{3} - b^{4}\right)} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a b^{3} - b^{4}\right)} \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{3} b - 112 \, a^{2} b^{2} + 57 \, a b^{3} - 9 \, b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(a b^{3} - b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a b^{3} - b^{4}\right)} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a b^{3} - b^{4}\right)} \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{3} b - 112 \, a^{2} b^{2} + 57 \, a b^{3} - 9 \, b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, {\left(a b^{3} - b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a b^{3} - b^{4} - 4 \, {\left(a b^{3} - b^{4}\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a b^{3} - b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) - 8 \, {\left(a b^{3} - b^{4} - 2 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a b^{3} - b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4} - 4 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(a b^{3} - b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right) - 4 \, {\left(2 \, {\left(a b^{3} - b^{4}\right)} \sin\left(6 \, d x + 6 \, c\right) + {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a b^{3} - b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left({\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a b^{3} - b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}\,{d x} - {\left(b^{2} \sin\left(7 \, d x + 7 \, c\right) + b^{2} \sin\left(d x + c\right) - {\left(4 \, a b + b^{2}\right)} \sin\left(5 \, d x + 5 \, c\right) - {\left(4 \, a b + b^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 2 \, {\left(2 \, b^{2} \sin\left(6 \, d x + 6 \, c\right) + 2 \, b^{2} \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a b - 3 \, b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(7 \, d x + 7 \, c\right) + 4 \, {\left(b^{2} \sin\left(d x + c\right) - {\left(4 \, a b + b^{2}\right)} \sin\left(5 \, d x + 5 \, c\right) - {\left(4 \, a b + b^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) - 2 \, {\left({\left(32 \, a^{2} - 4 \, a b - 3 \, b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(4 \, a b + b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(5 \, d x + 5 \, c\right) - 2 \, {\left({\left(32 \, a^{2} - 4 \, a b - 3 \, b^{2}\right)} \sin\left(3 \, d x + 3 \, c\right) - {\left(8 \, a b - 3 \, b^{2}\right)} \sin\left(d x + c\right)\right)} \sin\left(4 \, d x + 4 \, c\right)}{2 \, {\left({\left(a b^{3} - b^{4}\right)} d \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a b^{3} - b^{4}\right)} d \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{3} b - 112 \, a^{2} b^{2} + 57 \, a b^{3} - 9 \, b^{4}\right)} d \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(a b^{3} - b^{4}\right)} d \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a b^{3} - b^{4}\right)} d \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a b^{3} - b^{4}\right)} d \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{3} b - 112 \, a^{2} b^{2} + 57 \, a b^{3} - 9 \, b^{4}\right)} d \sin\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, {\left(a b^{3} - b^{4}\right)} d \sin\left(2 \, d x + 2 \, c\right)^{2} - 8 \, {\left(a b^{3} - b^{4}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a b^{3} - b^{4}\right)} d - 2 \, {\left(4 \, {\left(a b^{3} - b^{4}\right)} d \cos\left(6 \, d x + 6 \, c\right) + 2 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a b^{3} - b^{4}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(a b^{3} - b^{4}\right)} d\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(2 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a b^{3} - b^{4}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(a b^{3} - b^{4}\right)} d\right)} \cos\left(6 \, d x + 6 \, c\right) + 4 \, {\left(4 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(2 \, {\left(a b^{3} - b^{4}\right)} d \sin\left(6 \, d x + 6 \, c\right) + {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a b^{3} - b^{4}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left({\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a b^{3} - b^{4}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)}}"," ",0,"1/2*(4*b^2*cos(2*d*x + 2*c)*cos(d*x + c) + 4*b^2*sin(2*d*x + 2*c)*sin(d*x + c) - b^2*cos(d*x + c) - 4*(4*a*b + b^2)*sin(3*d*x + 3*c)*sin(2*d*x + 2*c) - (b^2*cos(7*d*x + 7*c) + b^2*cos(d*x + c) - (4*a*b + b^2)*cos(5*d*x + 5*c) - (4*a*b + b^2)*cos(3*d*x + 3*c))*cos(8*d*x + 8*c) + (4*b^2*cos(6*d*x + 6*c) + 4*b^2*cos(2*d*x + 2*c) - b^2 + 2*(8*a*b - 3*b^2)*cos(4*d*x + 4*c))*cos(7*d*x + 7*c) + 4*(b^2*cos(d*x + c) - (4*a*b + b^2)*cos(5*d*x + 5*c) - (4*a*b + b^2)*cos(3*d*x + 3*c))*cos(6*d*x + 6*c) + (4*a*b + b^2 - 2*(32*a^2 - 4*a*b - 3*b^2)*cos(4*d*x + 4*c) - 4*(4*a*b + b^2)*cos(2*d*x + 2*c))*cos(5*d*x + 5*c) - 2*((32*a^2 - 4*a*b - 3*b^2)*cos(3*d*x + 3*c) - (8*a*b - 3*b^2)*cos(d*x + c))*cos(4*d*x + 4*c) + (4*a*b + b^2 - 4*(4*a*b + b^2)*cos(2*d*x + 2*c))*cos(3*d*x + 3*c) + 2*((a*b^3 - b^4)*d*cos(8*d*x + 8*c)^2 + 16*(a*b^3 - b^4)*d*cos(6*d*x + 6*c)^2 + 4*(64*a^3*b - 112*a^2*b^2 + 57*a*b^3 - 9*b^4)*d*cos(4*d*x + 4*c)^2 + 16*(a*b^3 - b^4)*d*cos(2*d*x + 2*c)^2 + (a*b^3 - b^4)*d*sin(8*d*x + 8*c)^2 + 16*(a*b^3 - b^4)*d*sin(6*d*x + 6*c)^2 + 4*(64*a^3*b - 112*a^2*b^2 + 57*a*b^3 - 9*b^4)*d*sin(4*d*x + 4*c)^2 + 16*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*(a*b^3 - b^4)*d*sin(2*d*x + 2*c)^2 - 8*(a*b^3 - b^4)*d*cos(2*d*x + 2*c) + (a*b^3 - b^4)*d - 2*(4*(a*b^3 - b^4)*d*cos(6*d*x + 6*c) + 2*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cos(4*d*x + 4*c) + 4*(a*b^3 - b^4)*d*cos(2*d*x + 2*c) - (a*b^3 - b^4)*d)*cos(8*d*x + 8*c) + 8*(2*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cos(4*d*x + 4*c) + 4*(a*b^3 - b^4)*d*cos(2*d*x + 2*c) - (a*b^3 - b^4)*d)*cos(6*d*x + 6*c) + 4*(4*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cos(2*d*x + 2*c) - (8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d)*cos(4*d*x + 4*c) - 4*(2*(a*b^3 - b^4)*d*sin(6*d*x + 6*c) + (8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*sin(4*d*x + 4*c) + 2*(a*b^3 - b^4)*d*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*((8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*sin(4*d*x + 4*c) + 2*(a*b^3 - b^4)*d*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*integrate(-1/2*(4*b^2*cos(d*x + c)*sin(2*d*x + 2*c) - 4*b^2*cos(2*d*x + 2*c)*sin(d*x + c) + 4*(4*a*b - 11*b^2)*cos(3*d*x + 3*c)*sin(2*d*x + 2*c) + b^2*sin(d*x + c) - (b^2*sin(7*d*x + 7*c) - b^2*sin(d*x + c) + (4*a*b - 11*b^2)*sin(5*d*x + 5*c) - (4*a*b - 11*b^2)*sin(3*d*x + 3*c))*cos(8*d*x + 8*c) - 2*(2*b^2*sin(6*d*x + 6*c) + 2*b^2*sin(2*d*x + 2*c) + (8*a*b - 3*b^2)*sin(4*d*x + 4*c))*cos(7*d*x + 7*c) - 4*(b^2*sin(d*x + c) - (4*a*b - 11*b^2)*sin(5*d*x + 5*c) + (4*a*b - 11*b^2)*sin(3*d*x + 3*c))*cos(6*d*x + 6*c) - 2*((32*a^2 - 100*a*b + 33*b^2)*sin(4*d*x + 4*c) + 2*(4*a*b - 11*b^2)*sin(2*d*x + 2*c))*cos(5*d*x + 5*c) - 2*((32*a^2 - 100*a*b + 33*b^2)*sin(3*d*x + 3*c) + (8*a*b - 3*b^2)*sin(d*x + c))*cos(4*d*x + 4*c) + (b^2*cos(7*d*x + 7*c) - b^2*cos(d*x + c) + (4*a*b - 11*b^2)*cos(5*d*x + 5*c) - (4*a*b - 11*b^2)*cos(3*d*x + 3*c))*sin(8*d*x + 8*c) + (4*b^2*cos(6*d*x + 6*c) + 4*b^2*cos(2*d*x + 2*c) - b^2 + 2*(8*a*b - 3*b^2)*cos(4*d*x + 4*c))*sin(7*d*x + 7*c) + 4*(b^2*cos(d*x + c) - (4*a*b - 11*b^2)*cos(5*d*x + 5*c) + (4*a*b - 11*b^2)*cos(3*d*x + 3*c))*sin(6*d*x + 6*c) - (4*a*b - 11*b^2 - 2*(32*a^2 - 100*a*b + 33*b^2)*cos(4*d*x + 4*c) - 4*(4*a*b - 11*b^2)*cos(2*d*x + 2*c))*sin(5*d*x + 5*c) + 2*((32*a^2 - 100*a*b + 33*b^2)*cos(3*d*x + 3*c) + (8*a*b - 3*b^2)*cos(d*x + c))*sin(4*d*x + 4*c) + (4*a*b - 11*b^2 - 4*(4*a*b - 11*b^2)*cos(2*d*x + 2*c))*sin(3*d*x + 3*c))/(a*b^3 - b^4 + (a*b^3 - b^4)*cos(8*d*x + 8*c)^2 + 16*(a*b^3 - b^4)*cos(6*d*x + 6*c)^2 + 4*(64*a^3*b - 112*a^2*b^2 + 57*a*b^3 - 9*b^4)*cos(4*d*x + 4*c)^2 + 16*(a*b^3 - b^4)*cos(2*d*x + 2*c)^2 + (a*b^3 - b^4)*sin(8*d*x + 8*c)^2 + 16*(a*b^3 - b^4)*sin(6*d*x + 6*c)^2 + 4*(64*a^3*b - 112*a^2*b^2 + 57*a*b^3 - 9*b^4)*sin(4*d*x + 4*c)^2 + 16*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*(a*b^3 - b^4)*sin(2*d*x + 2*c)^2 + 2*(a*b^3 - b^4 - 4*(a*b^3 - b^4)*cos(6*d*x + 6*c) - 2*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*cos(4*d*x + 4*c) - 4*(a*b^3 - b^4)*cos(2*d*x + 2*c))*cos(8*d*x + 8*c) - 8*(a*b^3 - b^4 - 2*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*cos(4*d*x + 4*c) - 4*(a*b^3 - b^4)*cos(2*d*x + 2*c))*cos(6*d*x + 6*c) - 4*(8*a^2*b^2 - 11*a*b^3 + 3*b^4 - 4*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 8*(a*b^3 - b^4)*cos(2*d*x + 2*c) - 4*(2*(a*b^3 - b^4)*sin(6*d*x + 6*c) + (8*a^2*b^2 - 11*a*b^3 + 3*b^4)*sin(4*d*x + 4*c) + 2*(a*b^3 - b^4)*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*((8*a^2*b^2 - 11*a*b^3 + 3*b^4)*sin(4*d*x + 4*c) + 2*(a*b^3 - b^4)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c)), x) - (b^2*sin(7*d*x + 7*c) + b^2*sin(d*x + c) - (4*a*b + b^2)*sin(5*d*x + 5*c) - (4*a*b + b^2)*sin(3*d*x + 3*c))*sin(8*d*x + 8*c) + 2*(2*b^2*sin(6*d*x + 6*c) + 2*b^2*sin(2*d*x + 2*c) + (8*a*b - 3*b^2)*sin(4*d*x + 4*c))*sin(7*d*x + 7*c) + 4*(b^2*sin(d*x + c) - (4*a*b + b^2)*sin(5*d*x + 5*c) - (4*a*b + b^2)*sin(3*d*x + 3*c))*sin(6*d*x + 6*c) - 2*((32*a^2 - 4*a*b - 3*b^2)*sin(4*d*x + 4*c) + 2*(4*a*b + b^2)*sin(2*d*x + 2*c))*sin(5*d*x + 5*c) - 2*((32*a^2 - 4*a*b - 3*b^2)*sin(3*d*x + 3*c) - (8*a*b - 3*b^2)*sin(d*x + c))*sin(4*d*x + 4*c))/((a*b^3 - b^4)*d*cos(8*d*x + 8*c)^2 + 16*(a*b^3 - b^4)*d*cos(6*d*x + 6*c)^2 + 4*(64*a^3*b - 112*a^2*b^2 + 57*a*b^3 - 9*b^4)*d*cos(4*d*x + 4*c)^2 + 16*(a*b^3 - b^4)*d*cos(2*d*x + 2*c)^2 + (a*b^3 - b^4)*d*sin(8*d*x + 8*c)^2 + 16*(a*b^3 - b^4)*d*sin(6*d*x + 6*c)^2 + 4*(64*a^3*b - 112*a^2*b^2 + 57*a*b^3 - 9*b^4)*d*sin(4*d*x + 4*c)^2 + 16*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*(a*b^3 - b^4)*d*sin(2*d*x + 2*c)^2 - 8*(a*b^3 - b^4)*d*cos(2*d*x + 2*c) + (a*b^3 - b^4)*d - 2*(4*(a*b^3 - b^4)*d*cos(6*d*x + 6*c) + 2*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cos(4*d*x + 4*c) + 4*(a*b^3 - b^4)*d*cos(2*d*x + 2*c) - (a*b^3 - b^4)*d)*cos(8*d*x + 8*c) + 8*(2*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cos(4*d*x + 4*c) + 4*(a*b^3 - b^4)*d*cos(2*d*x + 2*c) - (a*b^3 - b^4)*d)*cos(6*d*x + 6*c) + 4*(4*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cos(2*d*x + 2*c) - (8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d)*cos(4*d*x + 4*c) - 4*(2*(a*b^3 - b^4)*d*sin(6*d*x + 6*c) + (8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*sin(4*d*x + 4*c) + 2*(a*b^3 - b^4)*d*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*((8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*sin(4*d*x + 4*c) + 2*(a*b^3 - b^4)*d*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))","F",0
215,-1,0,0,0.000000," ","integrate(sin(d*x+c)^3/(a-b*sin(d*x+c)^4)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
216,0,0,0,0.000000," ","integrate(sin(d*x+c)/(a-b*sin(d*x+c)^4)^2,x, algorithm=""maxima"")","\frac{4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(d x + c\right) + 4 \, b^{2} \sin\left(2 \, d x + 2 \, c\right) \sin\left(d x + c\right) - b^{2} \cos\left(d x + c\right) - 4 \, {\left(4 \, a b + b^{2}\right)} \sin\left(3 \, d x + 3 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - {\left(b^{2} \cos\left(7 \, d x + 7 \, c\right) + b^{2} \cos\left(d x + c\right) - {\left(4 \, a b + b^{2}\right)} \cos\left(5 \, d x + 5 \, c\right) - {\left(4 \, a b + b^{2}\right)} \cos\left(3 \, d x + 3 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) + {\left(4 \, b^{2} \cos\left(6 \, d x + 6 \, c\right) + 4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) - b^{2} + 2 \, {\left(8 \, a b - 3 \, b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(7 \, d x + 7 \, c\right) + 4 \, {\left(b^{2} \cos\left(d x + c\right) - {\left(4 \, a b + b^{2}\right)} \cos\left(5 \, d x + 5 \, c\right) - {\left(4 \, a b + b^{2}\right)} \cos\left(3 \, d x + 3 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) + {\left(4 \, a b + b^{2} - 2 \, {\left(32 \, a^{2} - 4 \, a b - 3 \, b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(4 \, a b + b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(5 \, d x + 5 \, c\right) - 2 \, {\left({\left(32 \, a^{2} - 4 \, a b - 3 \, b^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) - {\left(8 \, a b - 3 \, b^{2}\right)} \cos\left(d x + c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) + {\left(4 \, a b + b^{2} - 4 \, {\left(4 \, a b + b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(3 \, d x + 3 \, c\right) - {\left({\left(a^{2} b^{2} - a b^{3}\right)} d \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{4} - 112 \, a^{3} b + 57 \, a^{2} b^{2} - 9 \, a b^{3}\right)} d \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{2} b^{2} - a b^{3}\right)} d \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{4} - 112 \, a^{3} b + 57 \, a^{2} b^{2} - 9 \, a b^{3}\right)} d \sin\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(8 \, a^{3} b - 11 \, a^{2} b^{2} + 3 \, a b^{3}\right)} d \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \sin\left(2 \, d x + 2 \, c\right)^{2} - 8 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{2} b^{2} - a b^{3}\right)} d - 2 \, {\left(4 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \cos\left(6 \, d x + 6 \, c\right) + 2 \, {\left(8 \, a^{3} b - 11 \, a^{2} b^{2} + 3 \, a b^{3}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(a^{2} b^{2} - a b^{3}\right)} d\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(2 \, {\left(8 \, a^{3} b - 11 \, a^{2} b^{2} + 3 \, a b^{3}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(a^{2} b^{2} - a b^{3}\right)} d\right)} \cos\left(6 \, d x + 6 \, c\right) + 4 \, {\left(4 \, {\left(8 \, a^{3} b - 11 \, a^{2} b^{2} + 3 \, a b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(8 \, a^{3} b - 11 \, a^{2} b^{2} + 3 \, a b^{3}\right)} d\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(2 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \sin\left(6 \, d x + 6 \, c\right) + {\left(8 \, a^{3} b - 11 \, a^{2} b^{2} + 3 \, a b^{3}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left({\left(8 \, a^{3} b - 11 \, a^{2} b^{2} + 3 \, a b^{3}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \int \frac{4 \, b^{2} \cos\left(d x + c\right) \sin\left(2 \, d x + 2 \, c\right) - 4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(d x + c\right) - 4 \, {\left(12 \, a b - 5 \, b^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + b^{2} \sin\left(d x + c\right) - {\left(b^{2} \sin\left(7 \, d x + 7 \, c\right) - b^{2} \sin\left(d x + c\right) - {\left(12 \, a b - 5 \, b^{2}\right)} \sin\left(5 \, d x + 5 \, c\right) + {\left(12 \, a b - 5 \, b^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) - 2 \, {\left(2 \, b^{2} \sin\left(6 \, d x + 6 \, c\right) + 2 \, b^{2} \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a b - 3 \, b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \cos\left(7 \, d x + 7 \, c\right) - 4 \, {\left(b^{2} \sin\left(d x + c\right) + {\left(12 \, a b - 5 \, b^{2}\right)} \sin\left(5 \, d x + 5 \, c\right) - {\left(12 \, a b - 5 \, b^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) + 2 \, {\left({\left(96 \, a^{2} - 76 \, a b + 15 \, b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(12 \, a b - 5 \, b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(5 \, d x + 5 \, c\right) + 2 \, {\left({\left(96 \, a^{2} - 76 \, a b + 15 \, b^{2}\right)} \sin\left(3 \, d x + 3 \, c\right) - {\left(8 \, a b - 3 \, b^{2}\right)} \sin\left(d x + c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) + {\left(b^{2} \cos\left(7 \, d x + 7 \, c\right) - b^{2} \cos\left(d x + c\right) - {\left(12 \, a b - 5 \, b^{2}\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left(12 \, a b - 5 \, b^{2}\right)} \cos\left(3 \, d x + 3 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + {\left(4 \, b^{2} \cos\left(6 \, d x + 6 \, c\right) + 4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) - b^{2} + 2 \, {\left(8 \, a b - 3 \, b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \sin\left(7 \, d x + 7 \, c\right) + 4 \, {\left(b^{2} \cos\left(d x + c\right) + {\left(12 \, a b - 5 \, b^{2}\right)} \cos\left(5 \, d x + 5 \, c\right) - {\left(12 \, a b - 5 \, b^{2}\right)} \cos\left(3 \, d x + 3 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + {\left(12 \, a b - 5 \, b^{2} - 2 \, {\left(96 \, a^{2} - 76 \, a b + 15 \, b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(12 \, a b - 5 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(5 \, d x + 5 \, c\right) - 2 \, {\left({\left(96 \, a^{2} - 76 \, a b + 15 \, b^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) - {\left(8 \, a b - 3 \, b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) - {\left(12 \, a b - 5 \, b^{2} - 4 \, {\left(12 \, a b - 5 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(3 \, d x + 3 \, c\right)}{a^{2} b^{2} - a b^{3} + {\left(a^{2} b^{2} - a b^{3}\right)} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a^{2} b^{2} - a b^{3}\right)} \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{4} - 112 \, a^{3} b + 57 \, a^{2} b^{2} - 9 \, a b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(a^{2} b^{2} - a b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{2} b^{2} - a b^{3}\right)} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a^{2} b^{2} - a b^{3}\right)} \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{4} - 112 \, a^{3} b + 57 \, a^{2} b^{2} - 9 \, a b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(8 \, a^{3} b - 11 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, {\left(a^{2} b^{2} - a b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{2} b^{2} - a b^{3} - 4 \, {\left(a^{2} b^{2} - a b^{3}\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left(8 \, a^{3} b - 11 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a^{2} b^{2} - a b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) - 8 \, {\left(a^{2} b^{2} - a b^{3} - 2 \, {\left(8 \, a^{3} b - 11 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a^{2} b^{2} - a b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(8 \, a^{3} b - 11 \, a^{2} b^{2} + 3 \, a b^{3} - 4 \, {\left(8 \, a^{3} b - 11 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(a^{2} b^{2} - a b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right) - 4 \, {\left(2 \, {\left(a^{2} b^{2} - a b^{3}\right)} \sin\left(6 \, d x + 6 \, c\right) + {\left(8 \, a^{3} b - 11 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a^{2} b^{2} - a b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left({\left(8 \, a^{3} b - 11 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a^{2} b^{2} - a b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}\,{d x} - {\left(b^{2} \sin\left(7 \, d x + 7 \, c\right) + b^{2} \sin\left(d x + c\right) - {\left(4 \, a b + b^{2}\right)} \sin\left(5 \, d x + 5 \, c\right) - {\left(4 \, a b + b^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 2 \, {\left(2 \, b^{2} \sin\left(6 \, d x + 6 \, c\right) + 2 \, b^{2} \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a b - 3 \, b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(7 \, d x + 7 \, c\right) + 4 \, {\left(b^{2} \sin\left(d x + c\right) - {\left(4 \, a b + b^{2}\right)} \sin\left(5 \, d x + 5 \, c\right) - {\left(4 \, a b + b^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) - 2 \, {\left({\left(32 \, a^{2} - 4 \, a b - 3 \, b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(4 \, a b + b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(5 \, d x + 5 \, c\right) - 2 \, {\left({\left(32 \, a^{2} - 4 \, a b - 3 \, b^{2}\right)} \sin\left(3 \, d x + 3 \, c\right) - {\left(8 \, a b - 3 \, b^{2}\right)} \sin\left(d x + c\right)\right)} \sin\left(4 \, d x + 4 \, c\right)}{2 \, {\left({\left(a^{2} b^{2} - a b^{3}\right)} d \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{4} - 112 \, a^{3} b + 57 \, a^{2} b^{2} - 9 \, a b^{3}\right)} d \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{2} b^{2} - a b^{3}\right)} d \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{4} - 112 \, a^{3} b + 57 \, a^{2} b^{2} - 9 \, a b^{3}\right)} d \sin\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(8 \, a^{3} b - 11 \, a^{2} b^{2} + 3 \, a b^{3}\right)} d \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \sin\left(2 \, d x + 2 \, c\right)^{2} - 8 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{2} b^{2} - a b^{3}\right)} d - 2 \, {\left(4 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \cos\left(6 \, d x + 6 \, c\right) + 2 \, {\left(8 \, a^{3} b - 11 \, a^{2} b^{2} + 3 \, a b^{3}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(a^{2} b^{2} - a b^{3}\right)} d\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(2 \, {\left(8 \, a^{3} b - 11 \, a^{2} b^{2} + 3 \, a b^{3}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(a^{2} b^{2} - a b^{3}\right)} d\right)} \cos\left(6 \, d x + 6 \, c\right) + 4 \, {\left(4 \, {\left(8 \, a^{3} b - 11 \, a^{2} b^{2} + 3 \, a b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(8 \, a^{3} b - 11 \, a^{2} b^{2} + 3 \, a b^{3}\right)} d\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(2 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \sin\left(6 \, d x + 6 \, c\right) + {\left(8 \, a^{3} b - 11 \, a^{2} b^{2} + 3 \, a b^{3}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left({\left(8 \, a^{3} b - 11 \, a^{2} b^{2} + 3 \, a b^{3}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)}}"," ",0,"1/2*(4*b^2*cos(2*d*x + 2*c)*cos(d*x + c) + 4*b^2*sin(2*d*x + 2*c)*sin(d*x + c) - b^2*cos(d*x + c) - 4*(4*a*b + b^2)*sin(3*d*x + 3*c)*sin(2*d*x + 2*c) - (b^2*cos(7*d*x + 7*c) + b^2*cos(d*x + c) - (4*a*b + b^2)*cos(5*d*x + 5*c) - (4*a*b + b^2)*cos(3*d*x + 3*c))*cos(8*d*x + 8*c) + (4*b^2*cos(6*d*x + 6*c) + 4*b^2*cos(2*d*x + 2*c) - b^2 + 2*(8*a*b - 3*b^2)*cos(4*d*x + 4*c))*cos(7*d*x + 7*c) + 4*(b^2*cos(d*x + c) - (4*a*b + b^2)*cos(5*d*x + 5*c) - (4*a*b + b^2)*cos(3*d*x + 3*c))*cos(6*d*x + 6*c) + (4*a*b + b^2 - 2*(32*a^2 - 4*a*b - 3*b^2)*cos(4*d*x + 4*c) - 4*(4*a*b + b^2)*cos(2*d*x + 2*c))*cos(5*d*x + 5*c) - 2*((32*a^2 - 4*a*b - 3*b^2)*cos(3*d*x + 3*c) - (8*a*b - 3*b^2)*cos(d*x + c))*cos(4*d*x + 4*c) + (4*a*b + b^2 - 4*(4*a*b + b^2)*cos(2*d*x + 2*c))*cos(3*d*x + 3*c) + 2*((a^2*b^2 - a*b^3)*d*cos(8*d*x + 8*c)^2 + 16*(a^2*b^2 - a*b^3)*d*cos(6*d*x + 6*c)^2 + 4*(64*a^4 - 112*a^3*b + 57*a^2*b^2 - 9*a*b^3)*d*cos(4*d*x + 4*c)^2 + 16*(a^2*b^2 - a*b^3)*d*cos(2*d*x + 2*c)^2 + (a^2*b^2 - a*b^3)*d*sin(8*d*x + 8*c)^2 + 16*(a^2*b^2 - a*b^3)*d*sin(6*d*x + 6*c)^2 + 4*(64*a^4 - 112*a^3*b + 57*a^2*b^2 - 9*a*b^3)*d*sin(4*d*x + 4*c)^2 + 16*(8*a^3*b - 11*a^2*b^2 + 3*a*b^3)*d*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*(a^2*b^2 - a*b^3)*d*sin(2*d*x + 2*c)^2 - 8*(a^2*b^2 - a*b^3)*d*cos(2*d*x + 2*c) + (a^2*b^2 - a*b^3)*d - 2*(4*(a^2*b^2 - a*b^3)*d*cos(6*d*x + 6*c) + 2*(8*a^3*b - 11*a^2*b^2 + 3*a*b^3)*d*cos(4*d*x + 4*c) + 4*(a^2*b^2 - a*b^3)*d*cos(2*d*x + 2*c) - (a^2*b^2 - a*b^3)*d)*cos(8*d*x + 8*c) + 8*(2*(8*a^3*b - 11*a^2*b^2 + 3*a*b^3)*d*cos(4*d*x + 4*c) + 4*(a^2*b^2 - a*b^3)*d*cos(2*d*x + 2*c) - (a^2*b^2 - a*b^3)*d)*cos(6*d*x + 6*c) + 4*(4*(8*a^3*b - 11*a^2*b^2 + 3*a*b^3)*d*cos(2*d*x + 2*c) - (8*a^3*b - 11*a^2*b^2 + 3*a*b^3)*d)*cos(4*d*x + 4*c) - 4*(2*(a^2*b^2 - a*b^3)*d*sin(6*d*x + 6*c) + (8*a^3*b - 11*a^2*b^2 + 3*a*b^3)*d*sin(4*d*x + 4*c) + 2*(a^2*b^2 - a*b^3)*d*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*((8*a^3*b - 11*a^2*b^2 + 3*a*b^3)*d*sin(4*d*x + 4*c) + 2*(a^2*b^2 - a*b^3)*d*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*integrate(-1/2*(4*b^2*cos(d*x + c)*sin(2*d*x + 2*c) - 4*b^2*cos(2*d*x + 2*c)*sin(d*x + c) - 4*(12*a*b - 5*b^2)*cos(3*d*x + 3*c)*sin(2*d*x + 2*c) + b^2*sin(d*x + c) - (b^2*sin(7*d*x + 7*c) - b^2*sin(d*x + c) - (12*a*b - 5*b^2)*sin(5*d*x + 5*c) + (12*a*b - 5*b^2)*sin(3*d*x + 3*c))*cos(8*d*x + 8*c) - 2*(2*b^2*sin(6*d*x + 6*c) + 2*b^2*sin(2*d*x + 2*c) + (8*a*b - 3*b^2)*sin(4*d*x + 4*c))*cos(7*d*x + 7*c) - 4*(b^2*sin(d*x + c) + (12*a*b - 5*b^2)*sin(5*d*x + 5*c) - (12*a*b - 5*b^2)*sin(3*d*x + 3*c))*cos(6*d*x + 6*c) + 2*((96*a^2 - 76*a*b + 15*b^2)*sin(4*d*x + 4*c) + 2*(12*a*b - 5*b^2)*sin(2*d*x + 2*c))*cos(5*d*x + 5*c) + 2*((96*a^2 - 76*a*b + 15*b^2)*sin(3*d*x + 3*c) - (8*a*b - 3*b^2)*sin(d*x + c))*cos(4*d*x + 4*c) + (b^2*cos(7*d*x + 7*c) - b^2*cos(d*x + c) - (12*a*b - 5*b^2)*cos(5*d*x + 5*c) + (12*a*b - 5*b^2)*cos(3*d*x + 3*c))*sin(8*d*x + 8*c) + (4*b^2*cos(6*d*x + 6*c) + 4*b^2*cos(2*d*x + 2*c) - b^2 + 2*(8*a*b - 3*b^2)*cos(4*d*x + 4*c))*sin(7*d*x + 7*c) + 4*(b^2*cos(d*x + c) + (12*a*b - 5*b^2)*cos(5*d*x + 5*c) - (12*a*b - 5*b^2)*cos(3*d*x + 3*c))*sin(6*d*x + 6*c) + (12*a*b - 5*b^2 - 2*(96*a^2 - 76*a*b + 15*b^2)*cos(4*d*x + 4*c) - 4*(12*a*b - 5*b^2)*cos(2*d*x + 2*c))*sin(5*d*x + 5*c) - 2*((96*a^2 - 76*a*b + 15*b^2)*cos(3*d*x + 3*c) - (8*a*b - 3*b^2)*cos(d*x + c))*sin(4*d*x + 4*c) - (12*a*b - 5*b^2 - 4*(12*a*b - 5*b^2)*cos(2*d*x + 2*c))*sin(3*d*x + 3*c))/(a^2*b^2 - a*b^3 + (a^2*b^2 - a*b^3)*cos(8*d*x + 8*c)^2 + 16*(a^2*b^2 - a*b^3)*cos(6*d*x + 6*c)^2 + 4*(64*a^4 - 112*a^3*b + 57*a^2*b^2 - 9*a*b^3)*cos(4*d*x + 4*c)^2 + 16*(a^2*b^2 - a*b^3)*cos(2*d*x + 2*c)^2 + (a^2*b^2 - a*b^3)*sin(8*d*x + 8*c)^2 + 16*(a^2*b^2 - a*b^3)*sin(6*d*x + 6*c)^2 + 4*(64*a^4 - 112*a^3*b + 57*a^2*b^2 - 9*a*b^3)*sin(4*d*x + 4*c)^2 + 16*(8*a^3*b - 11*a^2*b^2 + 3*a*b^3)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*(a^2*b^2 - a*b^3)*sin(2*d*x + 2*c)^2 + 2*(a^2*b^2 - a*b^3 - 4*(a^2*b^2 - a*b^3)*cos(6*d*x + 6*c) - 2*(8*a^3*b - 11*a^2*b^2 + 3*a*b^3)*cos(4*d*x + 4*c) - 4*(a^2*b^2 - a*b^3)*cos(2*d*x + 2*c))*cos(8*d*x + 8*c) - 8*(a^2*b^2 - a*b^3 - 2*(8*a^3*b - 11*a^2*b^2 + 3*a*b^3)*cos(4*d*x + 4*c) - 4*(a^2*b^2 - a*b^3)*cos(2*d*x + 2*c))*cos(6*d*x + 6*c) - 4*(8*a^3*b - 11*a^2*b^2 + 3*a*b^3 - 4*(8*a^3*b - 11*a^2*b^2 + 3*a*b^3)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 8*(a^2*b^2 - a*b^3)*cos(2*d*x + 2*c) - 4*(2*(a^2*b^2 - a*b^3)*sin(6*d*x + 6*c) + (8*a^3*b - 11*a^2*b^2 + 3*a*b^3)*sin(4*d*x + 4*c) + 2*(a^2*b^2 - a*b^3)*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*((8*a^3*b - 11*a^2*b^2 + 3*a*b^3)*sin(4*d*x + 4*c) + 2*(a^2*b^2 - a*b^3)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c)), x) - (b^2*sin(7*d*x + 7*c) + b^2*sin(d*x + c) - (4*a*b + b^2)*sin(5*d*x + 5*c) - (4*a*b + b^2)*sin(3*d*x + 3*c))*sin(8*d*x + 8*c) + 2*(2*b^2*sin(6*d*x + 6*c) + 2*b^2*sin(2*d*x + 2*c) + (8*a*b - 3*b^2)*sin(4*d*x + 4*c))*sin(7*d*x + 7*c) + 4*(b^2*sin(d*x + c) - (4*a*b + b^2)*sin(5*d*x + 5*c) - (4*a*b + b^2)*sin(3*d*x + 3*c))*sin(6*d*x + 6*c) - 2*((32*a^2 - 4*a*b - 3*b^2)*sin(4*d*x + 4*c) + 2*(4*a*b + b^2)*sin(2*d*x + 2*c))*sin(5*d*x + 5*c) - 2*((32*a^2 - 4*a*b - 3*b^2)*sin(3*d*x + 3*c) - (8*a*b - 3*b^2)*sin(d*x + c))*sin(4*d*x + 4*c))/((a^2*b^2 - a*b^3)*d*cos(8*d*x + 8*c)^2 + 16*(a^2*b^2 - a*b^3)*d*cos(6*d*x + 6*c)^2 + 4*(64*a^4 - 112*a^3*b + 57*a^2*b^2 - 9*a*b^3)*d*cos(4*d*x + 4*c)^2 + 16*(a^2*b^2 - a*b^3)*d*cos(2*d*x + 2*c)^2 + (a^2*b^2 - a*b^3)*d*sin(8*d*x + 8*c)^2 + 16*(a^2*b^2 - a*b^3)*d*sin(6*d*x + 6*c)^2 + 4*(64*a^4 - 112*a^3*b + 57*a^2*b^2 - 9*a*b^3)*d*sin(4*d*x + 4*c)^2 + 16*(8*a^3*b - 11*a^2*b^2 + 3*a*b^3)*d*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*(a^2*b^2 - a*b^3)*d*sin(2*d*x + 2*c)^2 - 8*(a^2*b^2 - a*b^3)*d*cos(2*d*x + 2*c) + (a^2*b^2 - a*b^3)*d - 2*(4*(a^2*b^2 - a*b^3)*d*cos(6*d*x + 6*c) + 2*(8*a^3*b - 11*a^2*b^2 + 3*a*b^3)*d*cos(4*d*x + 4*c) + 4*(a^2*b^2 - a*b^3)*d*cos(2*d*x + 2*c) - (a^2*b^2 - a*b^3)*d)*cos(8*d*x + 8*c) + 8*(2*(8*a^3*b - 11*a^2*b^2 + 3*a*b^3)*d*cos(4*d*x + 4*c) + 4*(a^2*b^2 - a*b^3)*d*cos(2*d*x + 2*c) - (a^2*b^2 - a*b^3)*d)*cos(6*d*x + 6*c) + 4*(4*(8*a^3*b - 11*a^2*b^2 + 3*a*b^3)*d*cos(2*d*x + 2*c) - (8*a^3*b - 11*a^2*b^2 + 3*a*b^3)*d)*cos(4*d*x + 4*c) - 4*(2*(a^2*b^2 - a*b^3)*d*sin(6*d*x + 6*c) + (8*a^3*b - 11*a^2*b^2 + 3*a*b^3)*d*sin(4*d*x + 4*c) + 2*(a^2*b^2 - a*b^3)*d*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*((8*a^3*b - 11*a^2*b^2 + 3*a*b^3)*d*sin(4*d*x + 4*c) + 2*(a^2*b^2 - a*b^3)*d*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))","F",0
217,0,0,0,0.000000," ","integrate(csc(d*x+c)/(a-b*sin(d*x+c)^4)^2,x, algorithm=""maxima"")","\frac{4 \, a b^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(d x + c\right) - 20 \, a b^{2} \sin\left(3 \, d x + 3 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, a b^{2} \sin\left(2 \, d x + 2 \, c\right) \sin\left(d x + c\right) - a b^{2} \cos\left(d x + c\right) - {\left(a b^{2} \cos\left(7 \, d x + 7 \, c\right) - 5 \, a b^{2} \cos\left(5 \, d x + 5 \, c\right) - 5 \, a b^{2} \cos\left(3 \, d x + 3 \, c\right) + a b^{2} \cos\left(d x + c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) + {\left(4 \, a b^{2} \cos\left(6 \, d x + 6 \, c\right) + 4 \, a b^{2} \cos\left(2 \, d x + 2 \, c\right) - a b^{2} + 2 \, {\left(8 \, a^{2} b - 3 \, a b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(7 \, d x + 7 \, c\right) - 4 \, {\left(5 \, a b^{2} \cos\left(5 \, d x + 5 \, c\right) + 5 \, a b^{2} \cos\left(3 \, d x + 3 \, c\right) - a b^{2} \cos\left(d x + c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 5 \, {\left(4 \, a b^{2} \cos\left(2 \, d x + 2 \, c\right) - a b^{2} + 2 \, {\left(8 \, a^{2} b - 3 \, a b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(5 \, d x + 5 \, c\right) - 2 \, {\left(5 \, {\left(8 \, a^{2} b - 3 \, a b^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) - {\left(8 \, a^{2} b - 3 \, a b^{2}\right)} \cos\left(d x + c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 5 \, {\left(4 \, a b^{2} \cos\left(2 \, d x + 2 \, c\right) - a b^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left({\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{5} - 112 \, a^{4} b + 57 \, a^{3} b^{2} - 9 \, a^{2} b^{3}\right)} d \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{5} - 112 \, a^{4} b + 57 \, a^{3} b^{2} - 9 \, a^{2} b^{3}\right)} d \sin\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(8 \, a^{4} b - 11 \, a^{3} b^{2} + 3 \, a^{2} b^{3}\right)} d \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \sin\left(2 \, d x + 2 \, c\right)^{2} - 8 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d - 2 \, {\left(4 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \cos\left(6 \, d x + 6 \, c\right) + 2 \, {\left(8 \, a^{4} b - 11 \, a^{3} b^{2} + 3 \, a^{2} b^{3}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(2 \, {\left(8 \, a^{4} b - 11 \, a^{3} b^{2} + 3 \, a^{2} b^{3}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d\right)} \cos\left(6 \, d x + 6 \, c\right) + 4 \, {\left(4 \, {\left(8 \, a^{4} b - 11 \, a^{3} b^{2} + 3 \, a^{2} b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(8 \, a^{4} b - 11 \, a^{3} b^{2} + 3 \, a^{2} b^{3}\right)} d\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(2 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \sin\left(6 \, d x + 6 \, c\right) + {\left(8 \, a^{4} b - 11 \, a^{3} b^{2} + 3 \, a^{2} b^{3}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left({\left(8 \, a^{4} b - 11 \, a^{3} b^{2} + 3 \, a^{2} b^{3}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \int \frac{4 \, {\left(19 \, a b^{2} - 12 \, b^{3}\right)} \cos\left(3 \, d x + 3 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 4 \, {\left(5 \, a b^{2} - 4 \, b^{3}\right)} \cos\left(d x + c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, {\left(5 \, a b^{2} - 4 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right) \sin\left(d x + c\right) + {\left({\left(5 \, a b^{2} - 4 \, b^{3}\right)} \sin\left(7 \, d x + 7 \, c\right) - {\left(19 \, a b^{2} - 12 \, b^{3}\right)} \sin\left(5 \, d x + 5 \, c\right) + {\left(19 \, a b^{2} - 12 \, b^{3}\right)} \sin\left(3 \, d x + 3 \, c\right) - {\left(5 \, a b^{2} - 4 \, b^{3}\right)} \sin\left(d x + c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) + 2 \, {\left(2 \, {\left(5 \, a b^{2} - 4 \, b^{3}\right)} \sin\left(6 \, d x + 6 \, c\right) + {\left(40 \, a^{2} b - 47 \, a b^{2} + 12 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(5 \, a b^{2} - 4 \, b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(7 \, d x + 7 \, c\right) + 4 \, {\left({\left(19 \, a b^{2} - 12 \, b^{3}\right)} \sin\left(5 \, d x + 5 \, c\right) - {\left(19 \, a b^{2} - 12 \, b^{3}\right)} \sin\left(3 \, d x + 3 \, c\right) + {\left(5 \, a b^{2} - 4 \, b^{3}\right)} \sin\left(d x + c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left({\left(152 \, a^{2} b - 153 \, a b^{2} + 36 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(19 \, a b^{2} - 12 \, b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(5 \, d x + 5 \, c\right) - 2 \, {\left({\left(152 \, a^{2} b - 153 \, a b^{2} + 36 \, b^{3}\right)} \sin\left(3 \, d x + 3 \, c\right) - {\left(40 \, a^{2} b - 47 \, a b^{2} + 12 \, b^{3}\right)} \sin\left(d x + c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - {\left({\left(5 \, a b^{2} - 4 \, b^{3}\right)} \cos\left(7 \, d x + 7 \, c\right) - {\left(19 \, a b^{2} - 12 \, b^{3}\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left(19 \, a b^{2} - 12 \, b^{3}\right)} \cos\left(3 \, d x + 3 \, c\right) - {\left(5 \, a b^{2} - 4 \, b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + {\left(5 \, a b^{2} - 4 \, b^{3} - 4 \, {\left(5 \, a b^{2} - 4 \, b^{3}\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left(40 \, a^{2} b - 47 \, a b^{2} + 12 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(5 \, a b^{2} - 4 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(7 \, d x + 7 \, c\right) - 4 \, {\left({\left(19 \, a b^{2} - 12 \, b^{3}\right)} \cos\left(5 \, d x + 5 \, c\right) - {\left(19 \, a b^{2} - 12 \, b^{3}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(5 \, a b^{2} - 4 \, b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) - {\left(19 \, a b^{2} - 12 \, b^{3} - 2 \, {\left(152 \, a^{2} b - 153 \, a b^{2} + 36 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(19 \, a b^{2} - 12 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(5 \, d x + 5 \, c\right) + 2 \, {\left({\left(152 \, a^{2} b - 153 \, a b^{2} + 36 \, b^{3}\right)} \cos\left(3 \, d x + 3 \, c\right) - {\left(40 \, a^{2} b - 47 \, a b^{2} + 12 \, b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) + {\left(19 \, a b^{2} - 12 \, b^{3} - 4 \, {\left(19 \, a b^{2} - 12 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(3 \, d x + 3 \, c\right) - {\left(5 \, a b^{2} - 4 \, b^{3}\right)} \sin\left(d x + c\right)}{a^{3} b^{2} - a^{2} b^{3} + {\left(a^{3} b^{2} - a^{2} b^{3}\right)} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{5} - 112 \, a^{4} b + 57 \, a^{3} b^{2} - 9 \, a^{2} b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{3} b^{2} - a^{2} b^{3}\right)} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{5} - 112 \, a^{4} b + 57 \, a^{3} b^{2} - 9 \, a^{2} b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(8 \, a^{4} b - 11 \, a^{3} b^{2} + 3 \, a^{2} b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{3} b^{2} - a^{2} b^{3} - 4 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left(8 \, a^{4} b - 11 \, a^{3} b^{2} + 3 \, a^{2} b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) - 8 \, {\left(a^{3} b^{2} - a^{2} b^{3} - 2 \, {\left(8 \, a^{4} b - 11 \, a^{3} b^{2} + 3 \, a^{2} b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(8 \, a^{4} b - 11 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - 4 \, {\left(8 \, a^{4} b - 11 \, a^{3} b^{2} + 3 \, a^{2} b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right) - 4 \, {\left(2 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} \sin\left(6 \, d x + 6 \, c\right) + {\left(8 \, a^{4} b - 11 \, a^{3} b^{2} + 3 \, a^{2} b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left({\left(8 \, a^{4} b - 11 \, a^{3} b^{2} + 3 \, a^{2} b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}\,{d x} - {\left(a b^{2} - b^{3} + {\left(a b^{2} - b^{3}\right)} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a b^{2} - b^{3}\right)} \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{3} - 112 \, a^{2} b + 57 \, a b^{2} - 9 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(a b^{2} - b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a b^{2} - b^{3}\right)} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a b^{2} - b^{3}\right)} \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{3} - 112 \, a^{2} b + 57 \, a b^{2} - 9 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, {\left(a b^{2} - b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a b^{2} - b^{3} - 4 \, {\left(a b^{2} - b^{3}\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a b^{2} - b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) - 8 \, {\left(a b^{2} - b^{3} - 2 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a b^{2} - b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3} - 4 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(a b^{2} - b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right) - 4 \, {\left(2 \, {\left(a b^{2} - b^{3}\right)} \sin\left(6 \, d x + 6 \, c\right) + {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a b^{2} - b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left({\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a b^{2} - b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \log\left(\cos\left(d x\right)^{2} + 2 \, \cos\left(d x\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(d x\right)^{2} - 2 \, \sin\left(d x\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right) + {\left(a b^{2} - b^{3} + {\left(a b^{2} - b^{3}\right)} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a b^{2} - b^{3}\right)} \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{3} - 112 \, a^{2} b + 57 \, a b^{2} - 9 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(a b^{2} - b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a b^{2} - b^{3}\right)} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a b^{2} - b^{3}\right)} \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{3} - 112 \, a^{2} b + 57 \, a b^{2} - 9 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, {\left(a b^{2} - b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a b^{2} - b^{3} - 4 \, {\left(a b^{2} - b^{3}\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a b^{2} - b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) - 8 \, {\left(a b^{2} - b^{3} - 2 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a b^{2} - b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3} - 4 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(a b^{2} - b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right) - 4 \, {\left(2 \, {\left(a b^{2} - b^{3}\right)} \sin\left(6 \, d x + 6 \, c\right) + {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a b^{2} - b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left({\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a b^{2} - b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \log\left(\cos\left(d x\right)^{2} - 2 \, \cos\left(d x\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(d x\right)^{2} + 2 \, \sin\left(d x\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right) - {\left(a b^{2} \sin\left(7 \, d x + 7 \, c\right) - 5 \, a b^{2} \sin\left(5 \, d x + 5 \, c\right) - 5 \, a b^{2} \sin\left(3 \, d x + 3 \, c\right) + a b^{2} \sin\left(d x + c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 2 \, {\left(2 \, a b^{2} \sin\left(6 \, d x + 6 \, c\right) + 2 \, a b^{2} \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a^{2} b - 3 \, a b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(7 \, d x + 7 \, c\right) - 4 \, {\left(5 \, a b^{2} \sin\left(5 \, d x + 5 \, c\right) + 5 \, a b^{2} \sin\left(3 \, d x + 3 \, c\right) - a b^{2} \sin\left(d x + c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) - 10 \, {\left(2 \, a b^{2} \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a^{2} b - 3 \, a b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(5 \, d x + 5 \, c\right) - 2 \, {\left(5 \, {\left(8 \, a^{2} b - 3 \, a b^{2}\right)} \sin\left(3 \, d x + 3 \, c\right) - {\left(8 \, a^{2} b - 3 \, a b^{2}\right)} \sin\left(d x + c\right)\right)} \sin\left(4 \, d x + 4 \, c\right)}{2 \, {\left({\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{5} - 112 \, a^{4} b + 57 \, a^{3} b^{2} - 9 \, a^{2} b^{3}\right)} d \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{5} - 112 \, a^{4} b + 57 \, a^{3} b^{2} - 9 \, a^{2} b^{3}\right)} d \sin\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(8 \, a^{4} b - 11 \, a^{3} b^{2} + 3 \, a^{2} b^{3}\right)} d \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \sin\left(2 \, d x + 2 \, c\right)^{2} - 8 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d - 2 \, {\left(4 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \cos\left(6 \, d x + 6 \, c\right) + 2 \, {\left(8 \, a^{4} b - 11 \, a^{3} b^{2} + 3 \, a^{2} b^{3}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(2 \, {\left(8 \, a^{4} b - 11 \, a^{3} b^{2} + 3 \, a^{2} b^{3}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d\right)} \cos\left(6 \, d x + 6 \, c\right) + 4 \, {\left(4 \, {\left(8 \, a^{4} b - 11 \, a^{3} b^{2} + 3 \, a^{2} b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(8 \, a^{4} b - 11 \, a^{3} b^{2} + 3 \, a^{2} b^{3}\right)} d\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(2 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \sin\left(6 \, d x + 6 \, c\right) + {\left(8 \, a^{4} b - 11 \, a^{3} b^{2} + 3 \, a^{2} b^{3}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left({\left(8 \, a^{4} b - 11 \, a^{3} b^{2} + 3 \, a^{2} b^{3}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)}}"," ",0,"1/2*(4*a*b^2*cos(2*d*x + 2*c)*cos(d*x + c) - 20*a*b^2*sin(3*d*x + 3*c)*sin(2*d*x + 2*c) + 4*a*b^2*sin(2*d*x + 2*c)*sin(d*x + c) - a*b^2*cos(d*x + c) - (a*b^2*cos(7*d*x + 7*c) - 5*a*b^2*cos(5*d*x + 5*c) - 5*a*b^2*cos(3*d*x + 3*c) + a*b^2*cos(d*x + c))*cos(8*d*x + 8*c) + (4*a*b^2*cos(6*d*x + 6*c) + 4*a*b^2*cos(2*d*x + 2*c) - a*b^2 + 2*(8*a^2*b - 3*a*b^2)*cos(4*d*x + 4*c))*cos(7*d*x + 7*c) - 4*(5*a*b^2*cos(5*d*x + 5*c) + 5*a*b^2*cos(3*d*x + 3*c) - a*b^2*cos(d*x + c))*cos(6*d*x + 6*c) - 5*(4*a*b^2*cos(2*d*x + 2*c) - a*b^2 + 2*(8*a^2*b - 3*a*b^2)*cos(4*d*x + 4*c))*cos(5*d*x + 5*c) - 2*(5*(8*a^2*b - 3*a*b^2)*cos(3*d*x + 3*c) - (8*a^2*b - 3*a*b^2)*cos(d*x + c))*cos(4*d*x + 4*c) - 5*(4*a*b^2*cos(2*d*x + 2*c) - a*b^2)*cos(3*d*x + 3*c) - 2*((a^3*b^2 - a^2*b^3)*d*cos(8*d*x + 8*c)^2 + 16*(a^3*b^2 - a^2*b^3)*d*cos(6*d*x + 6*c)^2 + 4*(64*a^5 - 112*a^4*b + 57*a^3*b^2 - 9*a^2*b^3)*d*cos(4*d*x + 4*c)^2 + 16*(a^3*b^2 - a^2*b^3)*d*cos(2*d*x + 2*c)^2 + (a^3*b^2 - a^2*b^3)*d*sin(8*d*x + 8*c)^2 + 16*(a^3*b^2 - a^2*b^3)*d*sin(6*d*x + 6*c)^2 + 4*(64*a^5 - 112*a^4*b + 57*a^3*b^2 - 9*a^2*b^3)*d*sin(4*d*x + 4*c)^2 + 16*(8*a^4*b - 11*a^3*b^2 + 3*a^2*b^3)*d*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*(a^3*b^2 - a^2*b^3)*d*sin(2*d*x + 2*c)^2 - 8*(a^3*b^2 - a^2*b^3)*d*cos(2*d*x + 2*c) + (a^3*b^2 - a^2*b^3)*d - 2*(4*(a^3*b^2 - a^2*b^3)*d*cos(6*d*x + 6*c) + 2*(8*a^4*b - 11*a^3*b^2 + 3*a^2*b^3)*d*cos(4*d*x + 4*c) + 4*(a^3*b^2 - a^2*b^3)*d*cos(2*d*x + 2*c) - (a^3*b^2 - a^2*b^3)*d)*cos(8*d*x + 8*c) + 8*(2*(8*a^4*b - 11*a^3*b^2 + 3*a^2*b^3)*d*cos(4*d*x + 4*c) + 4*(a^3*b^2 - a^2*b^3)*d*cos(2*d*x + 2*c) - (a^3*b^2 - a^2*b^3)*d)*cos(6*d*x + 6*c) + 4*(4*(8*a^4*b - 11*a^3*b^2 + 3*a^2*b^3)*d*cos(2*d*x + 2*c) - (8*a^4*b - 11*a^3*b^2 + 3*a^2*b^3)*d)*cos(4*d*x + 4*c) - 4*(2*(a^3*b^2 - a^2*b^3)*d*sin(6*d*x + 6*c) + (8*a^4*b - 11*a^3*b^2 + 3*a^2*b^3)*d*sin(4*d*x + 4*c) + 2*(a^3*b^2 - a^2*b^3)*d*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*((8*a^4*b - 11*a^3*b^2 + 3*a^2*b^3)*d*sin(4*d*x + 4*c) + 2*(a^3*b^2 - a^2*b^3)*d*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*integrate(-1/2*(4*(19*a*b^2 - 12*b^3)*cos(3*d*x + 3*c)*sin(2*d*x + 2*c) - 4*(5*a*b^2 - 4*b^3)*cos(d*x + c)*sin(2*d*x + 2*c) + 4*(5*a*b^2 - 4*b^3)*cos(2*d*x + 2*c)*sin(d*x + c) + ((5*a*b^2 - 4*b^3)*sin(7*d*x + 7*c) - (19*a*b^2 - 12*b^3)*sin(5*d*x + 5*c) + (19*a*b^2 - 12*b^3)*sin(3*d*x + 3*c) - (5*a*b^2 - 4*b^3)*sin(d*x + c))*cos(8*d*x + 8*c) + 2*(2*(5*a*b^2 - 4*b^3)*sin(6*d*x + 6*c) + (40*a^2*b - 47*a*b^2 + 12*b^3)*sin(4*d*x + 4*c) + 2*(5*a*b^2 - 4*b^3)*sin(2*d*x + 2*c))*cos(7*d*x + 7*c) + 4*((19*a*b^2 - 12*b^3)*sin(5*d*x + 5*c) - (19*a*b^2 - 12*b^3)*sin(3*d*x + 3*c) + (5*a*b^2 - 4*b^3)*sin(d*x + c))*cos(6*d*x + 6*c) - 2*((152*a^2*b - 153*a*b^2 + 36*b^3)*sin(4*d*x + 4*c) + 2*(19*a*b^2 - 12*b^3)*sin(2*d*x + 2*c))*cos(5*d*x + 5*c) - 2*((152*a^2*b - 153*a*b^2 + 36*b^3)*sin(3*d*x + 3*c) - (40*a^2*b - 47*a*b^2 + 12*b^3)*sin(d*x + c))*cos(4*d*x + 4*c) - ((5*a*b^2 - 4*b^3)*cos(7*d*x + 7*c) - (19*a*b^2 - 12*b^3)*cos(5*d*x + 5*c) + (19*a*b^2 - 12*b^3)*cos(3*d*x + 3*c) - (5*a*b^2 - 4*b^3)*cos(d*x + c))*sin(8*d*x + 8*c) + (5*a*b^2 - 4*b^3 - 4*(5*a*b^2 - 4*b^3)*cos(6*d*x + 6*c) - 2*(40*a^2*b - 47*a*b^2 + 12*b^3)*cos(4*d*x + 4*c) - 4*(5*a*b^2 - 4*b^3)*cos(2*d*x + 2*c))*sin(7*d*x + 7*c) - 4*((19*a*b^2 - 12*b^3)*cos(5*d*x + 5*c) - (19*a*b^2 - 12*b^3)*cos(3*d*x + 3*c) + (5*a*b^2 - 4*b^3)*cos(d*x + c))*sin(6*d*x + 6*c) - (19*a*b^2 - 12*b^3 - 2*(152*a^2*b - 153*a*b^2 + 36*b^3)*cos(4*d*x + 4*c) - 4*(19*a*b^2 - 12*b^3)*cos(2*d*x + 2*c))*sin(5*d*x + 5*c) + 2*((152*a^2*b - 153*a*b^2 + 36*b^3)*cos(3*d*x + 3*c) - (40*a^2*b - 47*a*b^2 + 12*b^3)*cos(d*x + c))*sin(4*d*x + 4*c) + (19*a*b^2 - 12*b^3 - 4*(19*a*b^2 - 12*b^3)*cos(2*d*x + 2*c))*sin(3*d*x + 3*c) - (5*a*b^2 - 4*b^3)*sin(d*x + c))/(a^3*b^2 - a^2*b^3 + (a^3*b^2 - a^2*b^3)*cos(8*d*x + 8*c)^2 + 16*(a^3*b^2 - a^2*b^3)*cos(6*d*x + 6*c)^2 + 4*(64*a^5 - 112*a^4*b + 57*a^3*b^2 - 9*a^2*b^3)*cos(4*d*x + 4*c)^2 + 16*(a^3*b^2 - a^2*b^3)*cos(2*d*x + 2*c)^2 + (a^3*b^2 - a^2*b^3)*sin(8*d*x + 8*c)^2 + 16*(a^3*b^2 - a^2*b^3)*sin(6*d*x + 6*c)^2 + 4*(64*a^5 - 112*a^4*b + 57*a^3*b^2 - 9*a^2*b^3)*sin(4*d*x + 4*c)^2 + 16*(8*a^4*b - 11*a^3*b^2 + 3*a^2*b^3)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*(a^3*b^2 - a^2*b^3)*sin(2*d*x + 2*c)^2 + 2*(a^3*b^2 - a^2*b^3 - 4*(a^3*b^2 - a^2*b^3)*cos(6*d*x + 6*c) - 2*(8*a^4*b - 11*a^3*b^2 + 3*a^2*b^3)*cos(4*d*x + 4*c) - 4*(a^3*b^2 - a^2*b^3)*cos(2*d*x + 2*c))*cos(8*d*x + 8*c) - 8*(a^3*b^2 - a^2*b^3 - 2*(8*a^4*b - 11*a^3*b^2 + 3*a^2*b^3)*cos(4*d*x + 4*c) - 4*(a^3*b^2 - a^2*b^3)*cos(2*d*x + 2*c))*cos(6*d*x + 6*c) - 4*(8*a^4*b - 11*a^3*b^2 + 3*a^2*b^3 - 4*(8*a^4*b - 11*a^3*b^2 + 3*a^2*b^3)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 8*(a^3*b^2 - a^2*b^3)*cos(2*d*x + 2*c) - 4*(2*(a^3*b^2 - a^2*b^3)*sin(6*d*x + 6*c) + (8*a^4*b - 11*a^3*b^2 + 3*a^2*b^3)*sin(4*d*x + 4*c) + 2*(a^3*b^2 - a^2*b^3)*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*((8*a^4*b - 11*a^3*b^2 + 3*a^2*b^3)*sin(4*d*x + 4*c) + 2*(a^3*b^2 - a^2*b^3)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c)), x) - (a*b^2 - b^3 + (a*b^2 - b^3)*cos(8*d*x + 8*c)^2 + 16*(a*b^2 - b^3)*cos(6*d*x + 6*c)^2 + 4*(64*a^3 - 112*a^2*b + 57*a*b^2 - 9*b^3)*cos(4*d*x + 4*c)^2 + 16*(a*b^2 - b^3)*cos(2*d*x + 2*c)^2 + (a*b^2 - b^3)*sin(8*d*x + 8*c)^2 + 16*(a*b^2 - b^3)*sin(6*d*x + 6*c)^2 + 4*(64*a^3 - 112*a^2*b + 57*a*b^2 - 9*b^3)*sin(4*d*x + 4*c)^2 + 16*(8*a^2*b - 11*a*b^2 + 3*b^3)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*(a*b^2 - b^3)*sin(2*d*x + 2*c)^2 + 2*(a*b^2 - b^3 - 4*(a*b^2 - b^3)*cos(6*d*x + 6*c) - 2*(8*a^2*b - 11*a*b^2 + 3*b^3)*cos(4*d*x + 4*c) - 4*(a*b^2 - b^3)*cos(2*d*x + 2*c))*cos(8*d*x + 8*c) - 8*(a*b^2 - b^3 - 2*(8*a^2*b - 11*a*b^2 + 3*b^3)*cos(4*d*x + 4*c) - 4*(a*b^2 - b^3)*cos(2*d*x + 2*c))*cos(6*d*x + 6*c) - 4*(8*a^2*b - 11*a*b^2 + 3*b^3 - 4*(8*a^2*b - 11*a*b^2 + 3*b^3)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 8*(a*b^2 - b^3)*cos(2*d*x + 2*c) - 4*(2*(a*b^2 - b^3)*sin(6*d*x + 6*c) + (8*a^2*b - 11*a*b^2 + 3*b^3)*sin(4*d*x + 4*c) + 2*(a*b^2 - b^3)*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*((8*a^2*b - 11*a*b^2 + 3*b^3)*sin(4*d*x + 4*c) + 2*(a*b^2 - b^3)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*log(cos(d*x)^2 + 2*cos(d*x)*cos(c) + cos(c)^2 + sin(d*x)^2 - 2*sin(d*x)*sin(c) + sin(c)^2) + (a*b^2 - b^3 + (a*b^2 - b^3)*cos(8*d*x + 8*c)^2 + 16*(a*b^2 - b^3)*cos(6*d*x + 6*c)^2 + 4*(64*a^3 - 112*a^2*b + 57*a*b^2 - 9*b^3)*cos(4*d*x + 4*c)^2 + 16*(a*b^2 - b^3)*cos(2*d*x + 2*c)^2 + (a*b^2 - b^3)*sin(8*d*x + 8*c)^2 + 16*(a*b^2 - b^3)*sin(6*d*x + 6*c)^2 + 4*(64*a^3 - 112*a^2*b + 57*a*b^2 - 9*b^3)*sin(4*d*x + 4*c)^2 + 16*(8*a^2*b - 11*a*b^2 + 3*b^3)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*(a*b^2 - b^3)*sin(2*d*x + 2*c)^2 + 2*(a*b^2 - b^3 - 4*(a*b^2 - b^3)*cos(6*d*x + 6*c) - 2*(8*a^2*b - 11*a*b^2 + 3*b^3)*cos(4*d*x + 4*c) - 4*(a*b^2 - b^3)*cos(2*d*x + 2*c))*cos(8*d*x + 8*c) - 8*(a*b^2 - b^3 - 2*(8*a^2*b - 11*a*b^2 + 3*b^3)*cos(4*d*x + 4*c) - 4*(a*b^2 - b^3)*cos(2*d*x + 2*c))*cos(6*d*x + 6*c) - 4*(8*a^2*b - 11*a*b^2 + 3*b^3 - 4*(8*a^2*b - 11*a*b^2 + 3*b^3)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 8*(a*b^2 - b^3)*cos(2*d*x + 2*c) - 4*(2*(a*b^2 - b^3)*sin(6*d*x + 6*c) + (8*a^2*b - 11*a*b^2 + 3*b^3)*sin(4*d*x + 4*c) + 2*(a*b^2 - b^3)*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*((8*a^2*b - 11*a*b^2 + 3*b^3)*sin(4*d*x + 4*c) + 2*(a*b^2 - b^3)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*log(cos(d*x)^2 - 2*cos(d*x)*cos(c) + cos(c)^2 + sin(d*x)^2 + 2*sin(d*x)*sin(c) + sin(c)^2) - (a*b^2*sin(7*d*x + 7*c) - 5*a*b^2*sin(5*d*x + 5*c) - 5*a*b^2*sin(3*d*x + 3*c) + a*b^2*sin(d*x + c))*sin(8*d*x + 8*c) + 2*(2*a*b^2*sin(6*d*x + 6*c) + 2*a*b^2*sin(2*d*x + 2*c) + (8*a^2*b - 3*a*b^2)*sin(4*d*x + 4*c))*sin(7*d*x + 7*c) - 4*(5*a*b^2*sin(5*d*x + 5*c) + 5*a*b^2*sin(3*d*x + 3*c) - a*b^2*sin(d*x + c))*sin(6*d*x + 6*c) - 10*(2*a*b^2*sin(2*d*x + 2*c) + (8*a^2*b - 3*a*b^2)*sin(4*d*x + 4*c))*sin(5*d*x + 5*c) - 2*(5*(8*a^2*b - 3*a*b^2)*sin(3*d*x + 3*c) - (8*a^2*b - 3*a*b^2)*sin(d*x + c))*sin(4*d*x + 4*c))/((a^3*b^2 - a^2*b^3)*d*cos(8*d*x + 8*c)^2 + 16*(a^3*b^2 - a^2*b^3)*d*cos(6*d*x + 6*c)^2 + 4*(64*a^5 - 112*a^4*b + 57*a^3*b^2 - 9*a^2*b^3)*d*cos(4*d*x + 4*c)^2 + 16*(a^3*b^2 - a^2*b^3)*d*cos(2*d*x + 2*c)^2 + (a^3*b^2 - a^2*b^3)*d*sin(8*d*x + 8*c)^2 + 16*(a^3*b^2 - a^2*b^3)*d*sin(6*d*x + 6*c)^2 + 4*(64*a^5 - 112*a^4*b + 57*a^3*b^2 - 9*a^2*b^3)*d*sin(4*d*x + 4*c)^2 + 16*(8*a^4*b - 11*a^3*b^2 + 3*a^2*b^3)*d*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*(a^3*b^2 - a^2*b^3)*d*sin(2*d*x + 2*c)^2 - 8*(a^3*b^2 - a^2*b^3)*d*cos(2*d*x + 2*c) + (a^3*b^2 - a^2*b^3)*d - 2*(4*(a^3*b^2 - a^2*b^3)*d*cos(6*d*x + 6*c) + 2*(8*a^4*b - 11*a^3*b^2 + 3*a^2*b^3)*d*cos(4*d*x + 4*c) + 4*(a^3*b^2 - a^2*b^3)*d*cos(2*d*x + 2*c) - (a^3*b^2 - a^2*b^3)*d)*cos(8*d*x + 8*c) + 8*(2*(8*a^4*b - 11*a^3*b^2 + 3*a^2*b^3)*d*cos(4*d*x + 4*c) + 4*(a^3*b^2 - a^2*b^3)*d*cos(2*d*x + 2*c) - (a^3*b^2 - a^2*b^3)*d)*cos(6*d*x + 6*c) + 4*(4*(8*a^4*b - 11*a^3*b^2 + 3*a^2*b^3)*d*cos(2*d*x + 2*c) - (8*a^4*b - 11*a^3*b^2 + 3*a^2*b^3)*d)*cos(4*d*x + 4*c) - 4*(2*(a^3*b^2 - a^2*b^3)*d*sin(6*d*x + 6*c) + (8*a^4*b - 11*a^3*b^2 + 3*a^2*b^3)*d*sin(4*d*x + 4*c) + 2*(a^3*b^2 - a^2*b^3)*d*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*((8*a^4*b - 11*a^3*b^2 + 3*a^2*b^3)*d*sin(4*d*x + 4*c) + 2*(a^3*b^2 - a^2*b^3)*d*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))","F",0
218,-1,0,0,0.000000," ","integrate(sin(d*x+c)^8/(a-b*sin(d*x+c)^4)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
219,0,0,0,0.000000," ","integrate(sin(d*x+c)^6/(a-b*sin(d*x+c)^4)^2,x, algorithm=""maxima"")","\frac{2 \, {\left(16 \, a^{2} + 2 \, a b - 3 \, b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + {\left({\left(2 \, a b - b^{2}\right)} \sin\left(6 \, d x + 6 \, c\right) - {\left(8 \, a b - 3 \, b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) - {\left(2 \, a b + 3 \, b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) + 2 \, {\left({\left(16 \, a^{2} + 2 \, a b - 3 \, b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) + 4 \, {\left(2 \, a b + b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) + 2 \, {\left({\left(a b^{3} - b^{4}\right)} d \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a b^{3} - b^{4}\right)} d \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{3} b - 112 \, a^{2} b^{2} + 57 \, a b^{3} - 9 \, b^{4}\right)} d \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(a b^{3} - b^{4}\right)} d \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a b^{3} - b^{4}\right)} d \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a b^{3} - b^{4}\right)} d \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{3} b - 112 \, a^{2} b^{2} + 57 \, a b^{3} - 9 \, b^{4}\right)} d \sin\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, {\left(a b^{3} - b^{4}\right)} d \sin\left(2 \, d x + 2 \, c\right)^{2} - 8 \, {\left(a b^{3} - b^{4}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a b^{3} - b^{4}\right)} d - 2 \, {\left(4 \, {\left(a b^{3} - b^{4}\right)} d \cos\left(6 \, d x + 6 \, c\right) + 2 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a b^{3} - b^{4}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(a b^{3} - b^{4}\right)} d\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(2 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a b^{3} - b^{4}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(a b^{3} - b^{4}\right)} d\right)} \cos\left(6 \, d x + 6 \, c\right) + 4 \, {\left(4 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(2 \, {\left(a b^{3} - b^{4}\right)} d \sin\left(6 \, d x + 6 \, c\right) + {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a b^{3} - b^{4}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left({\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a b^{3} - b^{4}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \int \frac{4 \, {\left(2 \, a b - 3 \, b^{2}\right)} \cos\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(8 \, a b - 3 \, b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(2 \, a b - 3 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(2 \, a b - 3 \, b^{2}\right)} \sin\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(8 \, a b - 3 \, b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, {\left(16 \, a^{2} - 30 \, a b + 21 \, b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, {\left(2 \, a b - 3 \, b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - {\left(6 \, b^{2} \cos\left(4 \, d x + 4 \, c\right) + {\left(2 \, a b - 3 \, b^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + {\left(2 \, a b - 3 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) - {\left(2 \, a b - 3 \, b^{2} - 2 \, {\left(16 \, a^{2} - 30 \, a b + 21 \, b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(2 \, a b - 3 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left(3 \, b^{2} - {\left(16 \, a^{2} - 30 \, a b + 21 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - {\left(2 \, a b - 3 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) - {\left(6 \, b^{2} \sin\left(4 \, d x + 4 \, c\right) + {\left(2 \, a b - 3 \, b^{2}\right)} \sin\left(6 \, d x + 6 \, c\right) + {\left(2 \, a b - 3 \, b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 2 \, {\left({\left(16 \, a^{2} - 30 \, a b + 21 \, b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) + 4 \, {\left(2 \, a b - 3 \, b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}{a b^{3} - b^{4} + {\left(a b^{3} - b^{4}\right)} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a b^{3} - b^{4}\right)} \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{3} b - 112 \, a^{2} b^{2} + 57 \, a b^{3} - 9 \, b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(a b^{3} - b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a b^{3} - b^{4}\right)} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a b^{3} - b^{4}\right)} \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{3} b - 112 \, a^{2} b^{2} + 57 \, a b^{3} - 9 \, b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, {\left(a b^{3} - b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a b^{3} - b^{4} - 4 \, {\left(a b^{3} - b^{4}\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a b^{3} - b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) - 8 \, {\left(a b^{3} - b^{4} - 2 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a b^{3} - b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4} - 4 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(a b^{3} - b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right) - 4 \, {\left(2 \, {\left(a b^{3} - b^{4}\right)} \sin\left(6 \, d x + 6 \, c\right) + {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a b^{3} - b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left({\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a b^{3} - b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}\,{d x} - {\left(b^{2} + {\left(2 \, a b - b^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) - {\left(8 \, a b - 3 \, b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) - {\left(2 \, a b + 3 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + {\left(2 \, a b + 3 \, b^{2} - 2 \, {\left(16 \, a^{2} + 2 \, a b - 3 \, b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(2 \, a b + b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + {\left(8 \, a b - 3 \, b^{2} - 2 \, {\left(16 \, a^{2} + 2 \, a b - 3 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) - {\left(2 \, a b - b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)}{2 \, {\left({\left(a b^{3} - b^{4}\right)} d \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a b^{3} - b^{4}\right)} d \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{3} b - 112 \, a^{2} b^{2} + 57 \, a b^{3} - 9 \, b^{4}\right)} d \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(a b^{3} - b^{4}\right)} d \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a b^{3} - b^{4}\right)} d \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a b^{3} - b^{4}\right)} d \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{3} b - 112 \, a^{2} b^{2} + 57 \, a b^{3} - 9 \, b^{4}\right)} d \sin\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, {\left(a b^{3} - b^{4}\right)} d \sin\left(2 \, d x + 2 \, c\right)^{2} - 8 \, {\left(a b^{3} - b^{4}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a b^{3} - b^{4}\right)} d - 2 \, {\left(4 \, {\left(a b^{3} - b^{4}\right)} d \cos\left(6 \, d x + 6 \, c\right) + 2 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a b^{3} - b^{4}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(a b^{3} - b^{4}\right)} d\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(2 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a b^{3} - b^{4}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(a b^{3} - b^{4}\right)} d\right)} \cos\left(6 \, d x + 6 \, c\right) + 4 \, {\left(4 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(2 \, {\left(a b^{3} - b^{4}\right)} d \sin\left(6 \, d x + 6 \, c\right) + {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a b^{3} - b^{4}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left({\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a b^{3} - b^{4}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)}}"," ",0,"1/2*(2*(16*a^2 + 2*a*b - 3*b^2)*cos(4*d*x + 4*c)*sin(2*d*x + 2*c) + ((2*a*b - b^2)*sin(6*d*x + 6*c) - (8*a*b - 3*b^2)*sin(4*d*x + 4*c) - (2*a*b + 3*b^2)*sin(2*d*x + 2*c))*cos(8*d*x + 8*c) + 2*((16*a^2 + 2*a*b - 3*b^2)*sin(4*d*x + 4*c) + 4*(2*a*b + b^2)*sin(2*d*x + 2*c))*cos(6*d*x + 6*c) - 2*((a*b^3 - b^4)*d*cos(8*d*x + 8*c)^2 + 16*(a*b^3 - b^4)*d*cos(6*d*x + 6*c)^2 + 4*(64*a^3*b - 112*a^2*b^2 + 57*a*b^3 - 9*b^4)*d*cos(4*d*x + 4*c)^2 + 16*(a*b^3 - b^4)*d*cos(2*d*x + 2*c)^2 + (a*b^3 - b^4)*d*sin(8*d*x + 8*c)^2 + 16*(a*b^3 - b^4)*d*sin(6*d*x + 6*c)^2 + 4*(64*a^3*b - 112*a^2*b^2 + 57*a*b^3 - 9*b^4)*d*sin(4*d*x + 4*c)^2 + 16*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*(a*b^3 - b^4)*d*sin(2*d*x + 2*c)^2 - 8*(a*b^3 - b^4)*d*cos(2*d*x + 2*c) + (a*b^3 - b^4)*d - 2*(4*(a*b^3 - b^4)*d*cos(6*d*x + 6*c) + 2*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cos(4*d*x + 4*c) + 4*(a*b^3 - b^4)*d*cos(2*d*x + 2*c) - (a*b^3 - b^4)*d)*cos(8*d*x + 8*c) + 8*(2*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cos(4*d*x + 4*c) + 4*(a*b^3 - b^4)*d*cos(2*d*x + 2*c) - (a*b^3 - b^4)*d)*cos(6*d*x + 6*c) + 4*(4*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cos(2*d*x + 2*c) - (8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d)*cos(4*d*x + 4*c) - 4*(2*(a*b^3 - b^4)*d*sin(6*d*x + 6*c) + (8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*sin(4*d*x + 4*c) + 2*(a*b^3 - b^4)*d*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*((8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*sin(4*d*x + 4*c) + 2*(a*b^3 - b^4)*d*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*integrate(-(4*(2*a*b - 3*b^2)*cos(6*d*x + 6*c)^2 + 12*(8*a*b - 3*b^2)*cos(4*d*x + 4*c)^2 + 4*(2*a*b - 3*b^2)*cos(2*d*x + 2*c)^2 + 4*(2*a*b - 3*b^2)*sin(6*d*x + 6*c)^2 + 12*(8*a*b - 3*b^2)*sin(4*d*x + 4*c)^2 + 2*(16*a^2 - 30*a*b + 21*b^2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*(2*a*b - 3*b^2)*sin(2*d*x + 2*c)^2 - (6*b^2*cos(4*d*x + 4*c) + (2*a*b - 3*b^2)*cos(6*d*x + 6*c) + (2*a*b - 3*b^2)*cos(2*d*x + 2*c))*cos(8*d*x + 8*c) - (2*a*b - 3*b^2 - 2*(16*a^2 - 30*a*b + 21*b^2)*cos(4*d*x + 4*c) - 8*(2*a*b - 3*b^2)*cos(2*d*x + 2*c))*cos(6*d*x + 6*c) - 2*(3*b^2 - (16*a^2 - 30*a*b + 21*b^2)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - (2*a*b - 3*b^2)*cos(2*d*x + 2*c) - (6*b^2*sin(4*d*x + 4*c) + (2*a*b - 3*b^2)*sin(6*d*x + 6*c) + (2*a*b - 3*b^2)*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 2*((16*a^2 - 30*a*b + 21*b^2)*sin(4*d*x + 4*c) + 4*(2*a*b - 3*b^2)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))/(a*b^3 - b^4 + (a*b^3 - b^4)*cos(8*d*x + 8*c)^2 + 16*(a*b^3 - b^4)*cos(6*d*x + 6*c)^2 + 4*(64*a^3*b - 112*a^2*b^2 + 57*a*b^3 - 9*b^4)*cos(4*d*x + 4*c)^2 + 16*(a*b^3 - b^4)*cos(2*d*x + 2*c)^2 + (a*b^3 - b^4)*sin(8*d*x + 8*c)^2 + 16*(a*b^3 - b^4)*sin(6*d*x + 6*c)^2 + 4*(64*a^3*b - 112*a^2*b^2 + 57*a*b^3 - 9*b^4)*sin(4*d*x + 4*c)^2 + 16*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*(a*b^3 - b^4)*sin(2*d*x + 2*c)^2 + 2*(a*b^3 - b^4 - 4*(a*b^3 - b^4)*cos(6*d*x + 6*c) - 2*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*cos(4*d*x + 4*c) - 4*(a*b^3 - b^4)*cos(2*d*x + 2*c))*cos(8*d*x + 8*c) - 8*(a*b^3 - b^4 - 2*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*cos(4*d*x + 4*c) - 4*(a*b^3 - b^4)*cos(2*d*x + 2*c))*cos(6*d*x + 6*c) - 4*(8*a^2*b^2 - 11*a*b^3 + 3*b^4 - 4*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 8*(a*b^3 - b^4)*cos(2*d*x + 2*c) - 4*(2*(a*b^3 - b^4)*sin(6*d*x + 6*c) + (8*a^2*b^2 - 11*a*b^3 + 3*b^4)*sin(4*d*x + 4*c) + 2*(a*b^3 - b^4)*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*((8*a^2*b^2 - 11*a*b^3 + 3*b^4)*sin(4*d*x + 4*c) + 2*(a*b^3 - b^4)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c)), x) - (b^2 + (2*a*b - b^2)*cos(6*d*x + 6*c) - (8*a*b - 3*b^2)*cos(4*d*x + 4*c) - (2*a*b + 3*b^2)*cos(2*d*x + 2*c))*sin(8*d*x + 8*c) + (2*a*b + 3*b^2 - 2*(16*a^2 + 2*a*b - 3*b^2)*cos(4*d*x + 4*c) - 8*(2*a*b + b^2)*cos(2*d*x + 2*c))*sin(6*d*x + 6*c) + (8*a*b - 3*b^2 - 2*(16*a^2 + 2*a*b - 3*b^2)*cos(2*d*x + 2*c))*sin(4*d*x + 4*c) - (2*a*b - b^2)*sin(2*d*x + 2*c))/((a*b^3 - b^4)*d*cos(8*d*x + 8*c)^2 + 16*(a*b^3 - b^4)*d*cos(6*d*x + 6*c)^2 + 4*(64*a^3*b - 112*a^2*b^2 + 57*a*b^3 - 9*b^4)*d*cos(4*d*x + 4*c)^2 + 16*(a*b^3 - b^4)*d*cos(2*d*x + 2*c)^2 + (a*b^3 - b^4)*d*sin(8*d*x + 8*c)^2 + 16*(a*b^3 - b^4)*d*sin(6*d*x + 6*c)^2 + 4*(64*a^3*b - 112*a^2*b^2 + 57*a*b^3 - 9*b^4)*d*sin(4*d*x + 4*c)^2 + 16*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*(a*b^3 - b^4)*d*sin(2*d*x + 2*c)^2 - 8*(a*b^3 - b^4)*d*cos(2*d*x + 2*c) + (a*b^3 - b^4)*d - 2*(4*(a*b^3 - b^4)*d*cos(6*d*x + 6*c) + 2*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cos(4*d*x + 4*c) + 4*(a*b^3 - b^4)*d*cos(2*d*x + 2*c) - (a*b^3 - b^4)*d)*cos(8*d*x + 8*c) + 8*(2*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cos(4*d*x + 4*c) + 4*(a*b^3 - b^4)*d*cos(2*d*x + 2*c) - (a*b^3 - b^4)*d)*cos(6*d*x + 6*c) + 4*(4*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cos(2*d*x + 2*c) - (8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d)*cos(4*d*x + 4*c) - 4*(2*(a*b^3 - b^4)*d*sin(6*d*x + 6*c) + (8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*sin(4*d*x + 4*c) + 2*(a*b^3 - b^4)*d*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*((8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*sin(4*d*x + 4*c) + 2*(a*b^3 - b^4)*d*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))","F",0
220,-1,0,0,0.000000," ","integrate(sin(d*x+c)^4/(a-b*sin(d*x+c)^4)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
221,0,0,0,0.000000," ","integrate(sin(d*x+c)^2/(a-b*sin(d*x+c)^4)^2,x, algorithm=""maxima"")","\frac{2 \, {\left(16 \, a^{2} + 2 \, a b - 3 \, b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + {\left({\left(2 \, a b - b^{2}\right)} \sin\left(6 \, d x + 6 \, c\right) - {\left(8 \, a b - 3 \, b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) - {\left(2 \, a b + 3 \, b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) + 2 \, {\left({\left(16 \, a^{2} + 2 \, a b - 3 \, b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) + 4 \, {\left(2 \, a b + b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left({\left(a^{2} b^{2} - a b^{3}\right)} d \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{4} - 112 \, a^{3} b + 57 \, a^{2} b^{2} - 9 \, a b^{3}\right)} d \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{2} b^{2} - a b^{3}\right)} d \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{4} - 112 \, a^{3} b + 57 \, a^{2} b^{2} - 9 \, a b^{3}\right)} d \sin\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(8 \, a^{3} b - 11 \, a^{2} b^{2} + 3 \, a b^{3}\right)} d \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \sin\left(2 \, d x + 2 \, c\right)^{2} - 8 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{2} b^{2} - a b^{3}\right)} d - 2 \, {\left(4 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \cos\left(6 \, d x + 6 \, c\right) + 2 \, {\left(8 \, a^{3} b - 11 \, a^{2} b^{2} + 3 \, a b^{3}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(a^{2} b^{2} - a b^{3}\right)} d\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(2 \, {\left(8 \, a^{3} b - 11 \, a^{2} b^{2} + 3 \, a b^{3}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(a^{2} b^{2} - a b^{3}\right)} d\right)} \cos\left(6 \, d x + 6 \, c\right) + 4 \, {\left(4 \, {\left(8 \, a^{3} b - 11 \, a^{2} b^{2} + 3 \, a b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(8 \, a^{3} b - 11 \, a^{2} b^{2} + 3 \, a b^{3}\right)} d\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(2 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \sin\left(6 \, d x + 6 \, c\right) + {\left(8 \, a^{3} b - 11 \, a^{2} b^{2} + 3 \, a b^{3}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left({\left(8 \, a^{3} b - 11 \, a^{2} b^{2} + 3 \, a b^{3}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \int \frac{4 \, {\left(2 \, a b - b^{2}\right)} \cos\left(6 \, d x + 6 \, c\right)^{2} - 4 \, {\left(32 \, a^{2} - 20 \, a b + 3 \, b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(2 \, a b - b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(2 \, a b - b^{2}\right)} \sin\left(6 \, d x + 6 \, c\right)^{2} - 4 \, {\left(32 \, a^{2} - 20 \, a b + 3 \, b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, {\left(16 \, a^{2} - 30 \, a b + 7 \, b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, {\left(2 \, a b - b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - {\left({\left(2 \, a b - b^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left(4 \, a b - b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + {\left(2 \, a b - b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) - {\left(2 \, a b - b^{2} - 2 \, {\left(16 \, a^{2} - 30 \, a b + 7 \, b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(2 \, a b - b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) + 2 \, {\left(4 \, a b - b^{2} + {\left(16 \, a^{2} - 30 \, a b + 7 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - {\left(2 \, a b - b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) - {\left({\left(2 \, a b - b^{2}\right)} \sin\left(6 \, d x + 6 \, c\right) - 2 \, {\left(4 \, a b - b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) + {\left(2 \, a b - b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 2 \, {\left({\left(16 \, a^{2} - 30 \, a b + 7 \, b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) + 4 \, {\left(2 \, a b - b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}{a^{2} b^{2} - a b^{3} + {\left(a^{2} b^{2} - a b^{3}\right)} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a^{2} b^{2} - a b^{3}\right)} \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{4} - 112 \, a^{3} b + 57 \, a^{2} b^{2} - 9 \, a b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(a^{2} b^{2} - a b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{2} b^{2} - a b^{3}\right)} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a^{2} b^{2} - a b^{3}\right)} \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{4} - 112 \, a^{3} b + 57 \, a^{2} b^{2} - 9 \, a b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(8 \, a^{3} b - 11 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, {\left(a^{2} b^{2} - a b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{2} b^{2} - a b^{3} - 4 \, {\left(a^{2} b^{2} - a b^{3}\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left(8 \, a^{3} b - 11 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a^{2} b^{2} - a b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) - 8 \, {\left(a^{2} b^{2} - a b^{3} - 2 \, {\left(8 \, a^{3} b - 11 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a^{2} b^{2} - a b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(8 \, a^{3} b - 11 \, a^{2} b^{2} + 3 \, a b^{3} - 4 \, {\left(8 \, a^{3} b - 11 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(a^{2} b^{2} - a b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right) - 4 \, {\left(2 \, {\left(a^{2} b^{2} - a b^{3}\right)} \sin\left(6 \, d x + 6 \, c\right) + {\left(8 \, a^{3} b - 11 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a^{2} b^{2} - a b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left({\left(8 \, a^{3} b - 11 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a^{2} b^{2} - a b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}\,{d x} - {\left(b^{2} + {\left(2 \, a b - b^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) - {\left(8 \, a b - 3 \, b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) - {\left(2 \, a b + 3 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + {\left(2 \, a b + 3 \, b^{2} - 2 \, {\left(16 \, a^{2} + 2 \, a b - 3 \, b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(2 \, a b + b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + {\left(8 \, a b - 3 \, b^{2} - 2 \, {\left(16 \, a^{2} + 2 \, a b - 3 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) - {\left(2 \, a b - b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)}{2 \, {\left({\left(a^{2} b^{2} - a b^{3}\right)} d \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{4} - 112 \, a^{3} b + 57 \, a^{2} b^{2} - 9 \, a b^{3}\right)} d \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{2} b^{2} - a b^{3}\right)} d \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{4} - 112 \, a^{3} b + 57 \, a^{2} b^{2} - 9 \, a b^{3}\right)} d \sin\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(8 \, a^{3} b - 11 \, a^{2} b^{2} + 3 \, a b^{3}\right)} d \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \sin\left(2 \, d x + 2 \, c\right)^{2} - 8 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{2} b^{2} - a b^{3}\right)} d - 2 \, {\left(4 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \cos\left(6 \, d x + 6 \, c\right) + 2 \, {\left(8 \, a^{3} b - 11 \, a^{2} b^{2} + 3 \, a b^{3}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(a^{2} b^{2} - a b^{3}\right)} d\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(2 \, {\left(8 \, a^{3} b - 11 \, a^{2} b^{2} + 3 \, a b^{3}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(a^{2} b^{2} - a b^{3}\right)} d\right)} \cos\left(6 \, d x + 6 \, c\right) + 4 \, {\left(4 \, {\left(8 \, a^{3} b - 11 \, a^{2} b^{2} + 3 \, a b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(8 \, a^{3} b - 11 \, a^{2} b^{2} + 3 \, a b^{3}\right)} d\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(2 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \sin\left(6 \, d x + 6 \, c\right) + {\left(8 \, a^{3} b - 11 \, a^{2} b^{2} + 3 \, a b^{3}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left({\left(8 \, a^{3} b - 11 \, a^{2} b^{2} + 3 \, a b^{3}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)}}"," ",0,"1/2*(2*(16*a^2 + 2*a*b - 3*b^2)*cos(4*d*x + 4*c)*sin(2*d*x + 2*c) + ((2*a*b - b^2)*sin(6*d*x + 6*c) - (8*a*b - 3*b^2)*sin(4*d*x + 4*c) - (2*a*b + 3*b^2)*sin(2*d*x + 2*c))*cos(8*d*x + 8*c) + 2*((16*a^2 + 2*a*b - 3*b^2)*sin(4*d*x + 4*c) + 4*(2*a*b + b^2)*sin(2*d*x + 2*c))*cos(6*d*x + 6*c) + 2*((a^2*b^2 - a*b^3)*d*cos(8*d*x + 8*c)^2 + 16*(a^2*b^2 - a*b^3)*d*cos(6*d*x + 6*c)^2 + 4*(64*a^4 - 112*a^3*b + 57*a^2*b^2 - 9*a*b^3)*d*cos(4*d*x + 4*c)^2 + 16*(a^2*b^2 - a*b^3)*d*cos(2*d*x + 2*c)^2 + (a^2*b^2 - a*b^3)*d*sin(8*d*x + 8*c)^2 + 16*(a^2*b^2 - a*b^3)*d*sin(6*d*x + 6*c)^2 + 4*(64*a^4 - 112*a^3*b + 57*a^2*b^2 - 9*a*b^3)*d*sin(4*d*x + 4*c)^2 + 16*(8*a^3*b - 11*a^2*b^2 + 3*a*b^3)*d*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*(a^2*b^2 - a*b^3)*d*sin(2*d*x + 2*c)^2 - 8*(a^2*b^2 - a*b^3)*d*cos(2*d*x + 2*c) + (a^2*b^2 - a*b^3)*d - 2*(4*(a^2*b^2 - a*b^3)*d*cos(6*d*x + 6*c) + 2*(8*a^3*b - 11*a^2*b^2 + 3*a*b^3)*d*cos(4*d*x + 4*c) + 4*(a^2*b^2 - a*b^3)*d*cos(2*d*x + 2*c) - (a^2*b^2 - a*b^3)*d)*cos(8*d*x + 8*c) + 8*(2*(8*a^3*b - 11*a^2*b^2 + 3*a*b^3)*d*cos(4*d*x + 4*c) + 4*(a^2*b^2 - a*b^3)*d*cos(2*d*x + 2*c) - (a^2*b^2 - a*b^3)*d)*cos(6*d*x + 6*c) + 4*(4*(8*a^3*b - 11*a^2*b^2 + 3*a*b^3)*d*cos(2*d*x + 2*c) - (8*a^3*b - 11*a^2*b^2 + 3*a*b^3)*d)*cos(4*d*x + 4*c) - 4*(2*(a^2*b^2 - a*b^3)*d*sin(6*d*x + 6*c) + (8*a^3*b - 11*a^2*b^2 + 3*a*b^3)*d*sin(4*d*x + 4*c) + 2*(a^2*b^2 - a*b^3)*d*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*((8*a^3*b - 11*a^2*b^2 + 3*a*b^3)*d*sin(4*d*x + 4*c) + 2*(a^2*b^2 - a*b^3)*d*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*integrate(-(4*(2*a*b - b^2)*cos(6*d*x + 6*c)^2 - 4*(32*a^2 - 20*a*b + 3*b^2)*cos(4*d*x + 4*c)^2 + 4*(2*a*b - b^2)*cos(2*d*x + 2*c)^2 + 4*(2*a*b - b^2)*sin(6*d*x + 6*c)^2 - 4*(32*a^2 - 20*a*b + 3*b^2)*sin(4*d*x + 4*c)^2 + 2*(16*a^2 - 30*a*b + 7*b^2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*(2*a*b - b^2)*sin(2*d*x + 2*c)^2 - ((2*a*b - b^2)*cos(6*d*x + 6*c) - 2*(4*a*b - b^2)*cos(4*d*x + 4*c) + (2*a*b - b^2)*cos(2*d*x + 2*c))*cos(8*d*x + 8*c) - (2*a*b - b^2 - 2*(16*a^2 - 30*a*b + 7*b^2)*cos(4*d*x + 4*c) - 8*(2*a*b - b^2)*cos(2*d*x + 2*c))*cos(6*d*x + 6*c) + 2*(4*a*b - b^2 + (16*a^2 - 30*a*b + 7*b^2)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - (2*a*b - b^2)*cos(2*d*x + 2*c) - ((2*a*b - b^2)*sin(6*d*x + 6*c) - 2*(4*a*b - b^2)*sin(4*d*x + 4*c) + (2*a*b - b^2)*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 2*((16*a^2 - 30*a*b + 7*b^2)*sin(4*d*x + 4*c) + 4*(2*a*b - b^2)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))/(a^2*b^2 - a*b^3 + (a^2*b^2 - a*b^3)*cos(8*d*x + 8*c)^2 + 16*(a^2*b^2 - a*b^3)*cos(6*d*x + 6*c)^2 + 4*(64*a^4 - 112*a^3*b + 57*a^2*b^2 - 9*a*b^3)*cos(4*d*x + 4*c)^2 + 16*(a^2*b^2 - a*b^3)*cos(2*d*x + 2*c)^2 + (a^2*b^2 - a*b^3)*sin(8*d*x + 8*c)^2 + 16*(a^2*b^2 - a*b^3)*sin(6*d*x + 6*c)^2 + 4*(64*a^4 - 112*a^3*b + 57*a^2*b^2 - 9*a*b^3)*sin(4*d*x + 4*c)^2 + 16*(8*a^3*b - 11*a^2*b^2 + 3*a*b^3)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*(a^2*b^2 - a*b^3)*sin(2*d*x + 2*c)^2 + 2*(a^2*b^2 - a*b^3 - 4*(a^2*b^2 - a*b^3)*cos(6*d*x + 6*c) - 2*(8*a^3*b - 11*a^2*b^2 + 3*a*b^3)*cos(4*d*x + 4*c) - 4*(a^2*b^2 - a*b^3)*cos(2*d*x + 2*c))*cos(8*d*x + 8*c) - 8*(a^2*b^2 - a*b^3 - 2*(8*a^3*b - 11*a^2*b^2 + 3*a*b^3)*cos(4*d*x + 4*c) - 4*(a^2*b^2 - a*b^3)*cos(2*d*x + 2*c))*cos(6*d*x + 6*c) - 4*(8*a^3*b - 11*a^2*b^2 + 3*a*b^3 - 4*(8*a^3*b - 11*a^2*b^2 + 3*a*b^3)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 8*(a^2*b^2 - a*b^3)*cos(2*d*x + 2*c) - 4*(2*(a^2*b^2 - a*b^3)*sin(6*d*x + 6*c) + (8*a^3*b - 11*a^2*b^2 + 3*a*b^3)*sin(4*d*x + 4*c) + 2*(a^2*b^2 - a*b^3)*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*((8*a^3*b - 11*a^2*b^2 + 3*a*b^3)*sin(4*d*x + 4*c) + 2*(a^2*b^2 - a*b^3)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c)), x) - (b^2 + (2*a*b - b^2)*cos(6*d*x + 6*c) - (8*a*b - 3*b^2)*cos(4*d*x + 4*c) - (2*a*b + 3*b^2)*cos(2*d*x + 2*c))*sin(8*d*x + 8*c) + (2*a*b + 3*b^2 - 2*(16*a^2 + 2*a*b - 3*b^2)*cos(4*d*x + 4*c) - 8*(2*a*b + b^2)*cos(2*d*x + 2*c))*sin(6*d*x + 6*c) + (8*a*b - 3*b^2 - 2*(16*a^2 + 2*a*b - 3*b^2)*cos(2*d*x + 2*c))*sin(4*d*x + 4*c) - (2*a*b - b^2)*sin(2*d*x + 2*c))/((a^2*b^2 - a*b^3)*d*cos(8*d*x + 8*c)^2 + 16*(a^2*b^2 - a*b^3)*d*cos(6*d*x + 6*c)^2 + 4*(64*a^4 - 112*a^3*b + 57*a^2*b^2 - 9*a*b^3)*d*cos(4*d*x + 4*c)^2 + 16*(a^2*b^2 - a*b^3)*d*cos(2*d*x + 2*c)^2 + (a^2*b^2 - a*b^3)*d*sin(8*d*x + 8*c)^2 + 16*(a^2*b^2 - a*b^3)*d*sin(6*d*x + 6*c)^2 + 4*(64*a^4 - 112*a^3*b + 57*a^2*b^2 - 9*a*b^3)*d*sin(4*d*x + 4*c)^2 + 16*(8*a^3*b - 11*a^2*b^2 + 3*a*b^3)*d*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*(a^2*b^2 - a*b^3)*d*sin(2*d*x + 2*c)^2 - 8*(a^2*b^2 - a*b^3)*d*cos(2*d*x + 2*c) + (a^2*b^2 - a*b^3)*d - 2*(4*(a^2*b^2 - a*b^3)*d*cos(6*d*x + 6*c) + 2*(8*a^3*b - 11*a^2*b^2 + 3*a*b^3)*d*cos(4*d*x + 4*c) + 4*(a^2*b^2 - a*b^3)*d*cos(2*d*x + 2*c) - (a^2*b^2 - a*b^3)*d)*cos(8*d*x + 8*c) + 8*(2*(8*a^3*b - 11*a^2*b^2 + 3*a*b^3)*d*cos(4*d*x + 4*c) + 4*(a^2*b^2 - a*b^3)*d*cos(2*d*x + 2*c) - (a^2*b^2 - a*b^3)*d)*cos(6*d*x + 6*c) + 4*(4*(8*a^3*b - 11*a^2*b^2 + 3*a*b^3)*d*cos(2*d*x + 2*c) - (8*a^3*b - 11*a^2*b^2 + 3*a*b^3)*d)*cos(4*d*x + 4*c) - 4*(2*(a^2*b^2 - a*b^3)*d*sin(6*d*x + 6*c) + (8*a^3*b - 11*a^2*b^2 + 3*a*b^3)*d*sin(4*d*x + 4*c) + 2*(a^2*b^2 - a*b^3)*d*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*((8*a^3*b - 11*a^2*b^2 + 3*a*b^3)*d*sin(4*d*x + 4*c) + 2*(a^2*b^2 - a*b^3)*d*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))","F",0
222,-1,0,0,0.000000," ","integrate(1/(a-b*sin(d*x+c)^4)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
223,0,0,0,0.000000," ","integrate(csc(d*x+c)^2/(a-b*sin(d*x+c)^4)^2,x, algorithm=""maxima"")","\frac{2 \, {\left(48 \, a^{2} b - 5 \, a b^{2} - 25 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + {\left({\left(6 \, a b^{2} - 5 \, b^{3}\right)} \sin\left(8 \, d x + 8 \, c\right) - 2 \, {\left(13 \, a b^{2} - 10 \, b^{3}\right)} \sin\left(6 \, d x + 6 \, c\right) - 2 \, {\left(32 \, a^{2} b - 47 \, a b^{2} + 15 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(7 \, a b^{2} - 10 \, b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(10 \, d x + 10 \, c\right) + {\left(2 \, {\left(48 \, a^{2} b - 5 \, a b^{2} - 25 \, b^{3}\right)} \sin\left(6 \, d x + 6 \, c\right) + 2 \, {\left(112 \, a^{2} b - 165 \, a b^{2} + 50 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) + 5 \, {\left(8 \, a b^{2} - 15 \, b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) + 2 \, {\left(2 \, {\left(256 \, a^{3} - 432 \, a^{2} b + 210 \, a b^{2} - 25 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) + {\left(112 \, a^{2} b - 165 \, a b^{2} + 50 \, b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left({\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \cos\left(10 \, d x + 10 \, c\right)^{2} + 25 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \cos\left(8 \, d x + 8 \, c\right)^{2} + 4 \, {\left(64 \, a^{5} - 144 \, a^{4} b + 105 \, a^{3} b^{2} - 25 \, a^{2} b^{3}\right)} d \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{5} - 144 \, a^{4} b + 105 \, a^{3} b^{2} - 25 \, a^{2} b^{3}\right)} d \cos\left(4 \, d x + 4 \, c\right)^{2} + 25 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \sin\left(10 \, d x + 10 \, c\right)^{2} + 25 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \sin\left(8 \, d x + 8 \, c\right)^{2} + 4 \, {\left(64 \, a^{5} - 144 \, a^{4} b + 105 \, a^{3} b^{2} - 25 \, a^{2} b^{3}\right)} d \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{5} - 144 \, a^{4} b + 105 \, a^{3} b^{2} - 25 \, a^{2} b^{3}\right)} d \sin\left(4 \, d x + 4 \, c\right)^{2} + 20 \, {\left(8 \, a^{4} b - 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} d \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 25 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \sin\left(2 \, d x + 2 \, c\right)^{2} - 10 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d - 2 \, {\left(5 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \cos\left(8 \, d x + 8 \, c\right) + 2 \, {\left(8 \, a^{4} b - 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} d \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left(8 \, a^{4} b - 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} d \cos\left(4 \, d x + 4 \, c\right) - 5 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d\right)} \cos\left(10 \, d x + 10 \, c\right) + 10 \, {\left(2 \, {\left(8 \, a^{4} b - 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} d \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left(8 \, a^{4} b - 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} d \cos\left(4 \, d x + 4 \, c\right) - 5 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d\right)} \cos\left(8 \, d x + 8 \, c\right) - 4 \, {\left(2 \, {\left(64 \, a^{5} - 144 \, a^{4} b + 105 \, a^{3} b^{2} - 25 \, a^{2} b^{3}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 5 \, {\left(8 \, a^{4} b - 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(8 \, a^{4} b - 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} d\right)} \cos\left(6 \, d x + 6 \, c\right) + 4 \, {\left(5 \, {\left(8 \, a^{4} b - 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(8 \, a^{4} b - 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} d\right)} \cos\left(4 \, d x + 4 \, c\right) - 2 \, {\left(5 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \sin\left(8 \, d x + 8 \, c\right) + 2 \, {\left(8 \, a^{4} b - 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} d \sin\left(6 \, d x + 6 \, c\right) - 2 \, {\left(8 \, a^{4} b - 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} d \sin\left(4 \, d x + 4 \, c\right) - 5 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + 10 \, {\left(2 \, {\left(8 \, a^{4} b - 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} d \sin\left(6 \, d x + 6 \, c\right) - 2 \, {\left(8 \, a^{4} b - 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} d \sin\left(4 \, d x + 4 \, c\right) - 5 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) - 4 \, {\left(2 \, {\left(64 \, a^{5} - 144 \, a^{4} b + 105 \, a^{3} b^{2} - 25 \, a^{2} b^{3}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 5 \, {\left(8 \, a^{4} b - 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \int \frac{4 \, {\left(6 \, a b^{2} - 5 \, b^{3}\right)} \cos\left(6 \, d x + 6 \, c\right)^{2} - 4 \, {\left(64 \, a^{2} b - 64 \, a b^{2} + 15 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(6 \, a b^{2} - 5 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(6 \, a b^{2} - 5 \, b^{3}\right)} \sin\left(6 \, d x + 6 \, c\right)^{2} - 4 \, {\left(64 \, a^{2} b - 64 \, a b^{2} + 15 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, {\left(48 \, a^{2} b - 90 \, a b^{2} + 35 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, {\left(6 \, a b^{2} - 5 \, b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - {\left({\left(6 \, a b^{2} - 5 \, b^{3}\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left(8 \, a b^{2} - 5 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right) + {\left(6 \, a b^{2} - 5 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) - {\left(6 \, a b^{2} - 5 \, b^{3} - 2 \, {\left(48 \, a^{2} b - 90 \, a b^{2} + 35 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(6 \, a b^{2} - 5 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) + 2 \, {\left(8 \, a b^{2} - 5 \, b^{3} + {\left(48 \, a^{2} b - 90 \, a b^{2} + 35 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - {\left(6 \, a b^{2} - 5 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right) - {\left({\left(6 \, a b^{2} - 5 \, b^{3}\right)} \sin\left(6 \, d x + 6 \, c\right) - 2 \, {\left(8 \, a b^{2} - 5 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) + {\left(6 \, a b^{2} - 5 \, b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 2 \, {\left({\left(48 \, a^{2} b - 90 \, a b^{2} + 35 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) + 4 \, {\left(6 \, a b^{2} - 5 \, b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}{a^{3} b^{2} - a^{2} b^{3} + {\left(a^{3} b^{2} - a^{2} b^{3}\right)} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{5} - 112 \, a^{4} b + 57 \, a^{3} b^{2} - 9 \, a^{2} b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{3} b^{2} - a^{2} b^{3}\right)} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{5} - 112 \, a^{4} b + 57 \, a^{3} b^{2} - 9 \, a^{2} b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(8 \, a^{4} b - 11 \, a^{3} b^{2} + 3 \, a^{2} b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{3} b^{2} - a^{2} b^{3} - 4 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left(8 \, a^{4} b - 11 \, a^{3} b^{2} + 3 \, a^{2} b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) - 8 \, {\left(a^{3} b^{2} - a^{2} b^{3} - 2 \, {\left(8 \, a^{4} b - 11 \, a^{3} b^{2} + 3 \, a^{2} b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(8 \, a^{4} b - 11 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - 4 \, {\left(8 \, a^{4} b - 11 \, a^{3} b^{2} + 3 \, a^{2} b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right) - 4 \, {\left(2 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} \sin\left(6 \, d x + 6 \, c\right) + {\left(8 \, a^{4} b - 11 \, a^{3} b^{2} + 3 \, a^{2} b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left({\left(8 \, a^{4} b - 11 \, a^{3} b^{2} + 3 \, a^{2} b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}\,{d x} - {\left(4 \, a b^{2} - 5 \, b^{3} + {\left(6 \, a b^{2} - 5 \, b^{3}\right)} \cos\left(8 \, d x + 8 \, c\right) - 2 \, {\left(13 \, a b^{2} - 10 \, b^{3}\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left(32 \, a^{2} b - 47 \, a b^{2} + 15 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right) - 2 \, {\left(7 \, a b^{2} - 10 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + {\left(14 \, a b^{2} - 20 \, b^{3} - 2 \, {\left(48 \, a^{2} b - 5 \, a b^{2} - 25 \, b^{3}\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left(112 \, a^{2} b - 165 \, a b^{2} + 50 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right) - 5 \, {\left(8 \, a b^{2} - 15 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 2 \, {\left(32 \, a^{2} b - 47 \, a b^{2} + 15 \, b^{3} - 2 \, {\left(256 \, a^{3} - 432 \, a^{2} b + 210 \, a b^{2} - 25 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right) - {\left(112 \, a^{2} b - 165 \, a b^{2} + 50 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 2 \, {\left(13 \, a b^{2} - 10 \, b^{3} - {\left(48 \, a^{2} b - 5 \, a b^{2} - 25 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) - {\left(6 \, a b^{2} - 5 \, b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)}{2 \, {\left({\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \cos\left(10 \, d x + 10 \, c\right)^{2} + 25 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \cos\left(8 \, d x + 8 \, c\right)^{2} + 4 \, {\left(64 \, a^{5} - 144 \, a^{4} b + 105 \, a^{3} b^{2} - 25 \, a^{2} b^{3}\right)} d \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{5} - 144 \, a^{4} b + 105 \, a^{3} b^{2} - 25 \, a^{2} b^{3}\right)} d \cos\left(4 \, d x + 4 \, c\right)^{2} + 25 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \sin\left(10 \, d x + 10 \, c\right)^{2} + 25 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \sin\left(8 \, d x + 8 \, c\right)^{2} + 4 \, {\left(64 \, a^{5} - 144 \, a^{4} b + 105 \, a^{3} b^{2} - 25 \, a^{2} b^{3}\right)} d \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{5} - 144 \, a^{4} b + 105 \, a^{3} b^{2} - 25 \, a^{2} b^{3}\right)} d \sin\left(4 \, d x + 4 \, c\right)^{2} + 20 \, {\left(8 \, a^{4} b - 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} d \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 25 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \sin\left(2 \, d x + 2 \, c\right)^{2} - 10 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d - 2 \, {\left(5 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \cos\left(8 \, d x + 8 \, c\right) + 2 \, {\left(8 \, a^{4} b - 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} d \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left(8 \, a^{4} b - 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} d \cos\left(4 \, d x + 4 \, c\right) - 5 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d\right)} \cos\left(10 \, d x + 10 \, c\right) + 10 \, {\left(2 \, {\left(8 \, a^{4} b - 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} d \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left(8 \, a^{4} b - 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} d \cos\left(4 \, d x + 4 \, c\right) - 5 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d\right)} \cos\left(8 \, d x + 8 \, c\right) - 4 \, {\left(2 \, {\left(64 \, a^{5} - 144 \, a^{4} b + 105 \, a^{3} b^{2} - 25 \, a^{2} b^{3}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 5 \, {\left(8 \, a^{4} b - 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(8 \, a^{4} b - 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} d\right)} \cos\left(6 \, d x + 6 \, c\right) + 4 \, {\left(5 \, {\left(8 \, a^{4} b - 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(8 \, a^{4} b - 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} d\right)} \cos\left(4 \, d x + 4 \, c\right) - 2 \, {\left(5 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \sin\left(8 \, d x + 8 \, c\right) + 2 \, {\left(8 \, a^{4} b - 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} d \sin\left(6 \, d x + 6 \, c\right) - 2 \, {\left(8 \, a^{4} b - 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} d \sin\left(4 \, d x + 4 \, c\right) - 5 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + 10 \, {\left(2 \, {\left(8 \, a^{4} b - 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} d \sin\left(6 \, d x + 6 \, c\right) - 2 \, {\left(8 \, a^{4} b - 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} d \sin\left(4 \, d x + 4 \, c\right) - 5 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) - 4 \, {\left(2 \, {\left(64 \, a^{5} - 144 \, a^{4} b + 105 \, a^{3} b^{2} - 25 \, a^{2} b^{3}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 5 \, {\left(8 \, a^{4} b - 13 \, a^{3} b^{2} + 5 \, a^{2} b^{3}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)}}"," ",0,"1/2*(2*(48*a^2*b - 5*a*b^2 - 25*b^3)*cos(4*d*x + 4*c)*sin(2*d*x + 2*c) + ((6*a*b^2 - 5*b^3)*sin(8*d*x + 8*c) - 2*(13*a*b^2 - 10*b^3)*sin(6*d*x + 6*c) - 2*(32*a^2*b - 47*a*b^2 + 15*b^3)*sin(4*d*x + 4*c) - 2*(7*a*b^2 - 10*b^3)*sin(2*d*x + 2*c))*cos(10*d*x + 10*c) + (2*(48*a^2*b - 5*a*b^2 - 25*b^3)*sin(6*d*x + 6*c) + 2*(112*a^2*b - 165*a*b^2 + 50*b^3)*sin(4*d*x + 4*c) + 5*(8*a*b^2 - 15*b^3)*sin(2*d*x + 2*c))*cos(8*d*x + 8*c) + 2*(2*(256*a^3 - 432*a^2*b + 210*a*b^2 - 25*b^3)*sin(4*d*x + 4*c) + (112*a^2*b - 165*a*b^2 + 50*b^3)*sin(2*d*x + 2*c))*cos(6*d*x + 6*c) + 2*((a^3*b^2 - a^2*b^3)*d*cos(10*d*x + 10*c)^2 + 25*(a^3*b^2 - a^2*b^3)*d*cos(8*d*x + 8*c)^2 + 4*(64*a^5 - 144*a^4*b + 105*a^3*b^2 - 25*a^2*b^3)*d*cos(6*d*x + 6*c)^2 + 4*(64*a^5 - 144*a^4*b + 105*a^3*b^2 - 25*a^2*b^3)*d*cos(4*d*x + 4*c)^2 + 25*(a^3*b^2 - a^2*b^3)*d*cos(2*d*x + 2*c)^2 + (a^3*b^2 - a^2*b^3)*d*sin(10*d*x + 10*c)^2 + 25*(a^3*b^2 - a^2*b^3)*d*sin(8*d*x + 8*c)^2 + 4*(64*a^5 - 144*a^4*b + 105*a^3*b^2 - 25*a^2*b^3)*d*sin(6*d*x + 6*c)^2 + 4*(64*a^5 - 144*a^4*b + 105*a^3*b^2 - 25*a^2*b^3)*d*sin(4*d*x + 4*c)^2 + 20*(8*a^4*b - 13*a^3*b^2 + 5*a^2*b^3)*d*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 25*(a^3*b^2 - a^2*b^3)*d*sin(2*d*x + 2*c)^2 - 10*(a^3*b^2 - a^2*b^3)*d*cos(2*d*x + 2*c) + (a^3*b^2 - a^2*b^3)*d - 2*(5*(a^3*b^2 - a^2*b^3)*d*cos(8*d*x + 8*c) + 2*(8*a^4*b - 13*a^3*b^2 + 5*a^2*b^3)*d*cos(6*d*x + 6*c) - 2*(8*a^4*b - 13*a^3*b^2 + 5*a^2*b^3)*d*cos(4*d*x + 4*c) - 5*(a^3*b^2 - a^2*b^3)*d*cos(2*d*x + 2*c) + (a^3*b^2 - a^2*b^3)*d)*cos(10*d*x + 10*c) + 10*(2*(8*a^4*b - 13*a^3*b^2 + 5*a^2*b^3)*d*cos(6*d*x + 6*c) - 2*(8*a^4*b - 13*a^3*b^2 + 5*a^2*b^3)*d*cos(4*d*x + 4*c) - 5*(a^3*b^2 - a^2*b^3)*d*cos(2*d*x + 2*c) + (a^3*b^2 - a^2*b^3)*d)*cos(8*d*x + 8*c) - 4*(2*(64*a^5 - 144*a^4*b + 105*a^3*b^2 - 25*a^2*b^3)*d*cos(4*d*x + 4*c) + 5*(8*a^4*b - 13*a^3*b^2 + 5*a^2*b^3)*d*cos(2*d*x + 2*c) - (8*a^4*b - 13*a^3*b^2 + 5*a^2*b^3)*d)*cos(6*d*x + 6*c) + 4*(5*(8*a^4*b - 13*a^3*b^2 + 5*a^2*b^3)*d*cos(2*d*x + 2*c) - (8*a^4*b - 13*a^3*b^2 + 5*a^2*b^3)*d)*cos(4*d*x + 4*c) - 2*(5*(a^3*b^2 - a^2*b^3)*d*sin(8*d*x + 8*c) + 2*(8*a^4*b - 13*a^3*b^2 + 5*a^2*b^3)*d*sin(6*d*x + 6*c) - 2*(8*a^4*b - 13*a^3*b^2 + 5*a^2*b^3)*d*sin(4*d*x + 4*c) - 5*(a^3*b^2 - a^2*b^3)*d*sin(2*d*x + 2*c))*sin(10*d*x + 10*c) + 10*(2*(8*a^4*b - 13*a^3*b^2 + 5*a^2*b^3)*d*sin(6*d*x + 6*c) - 2*(8*a^4*b - 13*a^3*b^2 + 5*a^2*b^3)*d*sin(4*d*x + 4*c) - 5*(a^3*b^2 - a^2*b^3)*d*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) - 4*(2*(64*a^5 - 144*a^4*b + 105*a^3*b^2 - 25*a^2*b^3)*d*sin(4*d*x + 4*c) + 5*(8*a^4*b - 13*a^3*b^2 + 5*a^2*b^3)*d*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*integrate(-(4*(6*a*b^2 - 5*b^3)*cos(6*d*x + 6*c)^2 - 4*(64*a^2*b - 64*a*b^2 + 15*b^3)*cos(4*d*x + 4*c)^2 + 4*(6*a*b^2 - 5*b^3)*cos(2*d*x + 2*c)^2 + 4*(6*a*b^2 - 5*b^3)*sin(6*d*x + 6*c)^2 - 4*(64*a^2*b - 64*a*b^2 + 15*b^3)*sin(4*d*x + 4*c)^2 + 2*(48*a^2*b - 90*a*b^2 + 35*b^3)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*(6*a*b^2 - 5*b^3)*sin(2*d*x + 2*c)^2 - ((6*a*b^2 - 5*b^3)*cos(6*d*x + 6*c) - 2*(8*a*b^2 - 5*b^3)*cos(4*d*x + 4*c) + (6*a*b^2 - 5*b^3)*cos(2*d*x + 2*c))*cos(8*d*x + 8*c) - (6*a*b^2 - 5*b^3 - 2*(48*a^2*b - 90*a*b^2 + 35*b^3)*cos(4*d*x + 4*c) - 8*(6*a*b^2 - 5*b^3)*cos(2*d*x + 2*c))*cos(6*d*x + 6*c) + 2*(8*a*b^2 - 5*b^3 + (48*a^2*b - 90*a*b^2 + 35*b^3)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - (6*a*b^2 - 5*b^3)*cos(2*d*x + 2*c) - ((6*a*b^2 - 5*b^3)*sin(6*d*x + 6*c) - 2*(8*a*b^2 - 5*b^3)*sin(4*d*x + 4*c) + (6*a*b^2 - 5*b^3)*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 2*((48*a^2*b - 90*a*b^2 + 35*b^3)*sin(4*d*x + 4*c) + 4*(6*a*b^2 - 5*b^3)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))/(a^3*b^2 - a^2*b^3 + (a^3*b^2 - a^2*b^3)*cos(8*d*x + 8*c)^2 + 16*(a^3*b^2 - a^2*b^3)*cos(6*d*x + 6*c)^2 + 4*(64*a^5 - 112*a^4*b + 57*a^3*b^2 - 9*a^2*b^3)*cos(4*d*x + 4*c)^2 + 16*(a^3*b^2 - a^2*b^3)*cos(2*d*x + 2*c)^2 + (a^3*b^2 - a^2*b^3)*sin(8*d*x + 8*c)^2 + 16*(a^3*b^2 - a^2*b^3)*sin(6*d*x + 6*c)^2 + 4*(64*a^5 - 112*a^4*b + 57*a^3*b^2 - 9*a^2*b^3)*sin(4*d*x + 4*c)^2 + 16*(8*a^4*b - 11*a^3*b^2 + 3*a^2*b^3)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*(a^3*b^2 - a^2*b^3)*sin(2*d*x + 2*c)^2 + 2*(a^3*b^2 - a^2*b^3 - 4*(a^3*b^2 - a^2*b^3)*cos(6*d*x + 6*c) - 2*(8*a^4*b - 11*a^3*b^2 + 3*a^2*b^3)*cos(4*d*x + 4*c) - 4*(a^3*b^2 - a^2*b^3)*cos(2*d*x + 2*c))*cos(8*d*x + 8*c) - 8*(a^3*b^2 - a^2*b^3 - 2*(8*a^4*b - 11*a^3*b^2 + 3*a^2*b^3)*cos(4*d*x + 4*c) - 4*(a^3*b^2 - a^2*b^3)*cos(2*d*x + 2*c))*cos(6*d*x + 6*c) - 4*(8*a^4*b - 11*a^3*b^2 + 3*a^2*b^3 - 4*(8*a^4*b - 11*a^3*b^2 + 3*a^2*b^3)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 8*(a^3*b^2 - a^2*b^3)*cos(2*d*x + 2*c) - 4*(2*(a^3*b^2 - a^2*b^3)*sin(6*d*x + 6*c) + (8*a^4*b - 11*a^3*b^2 + 3*a^2*b^3)*sin(4*d*x + 4*c) + 2*(a^3*b^2 - a^2*b^3)*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*((8*a^4*b - 11*a^3*b^2 + 3*a^2*b^3)*sin(4*d*x + 4*c) + 2*(a^3*b^2 - a^2*b^3)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c)), x) - (4*a*b^2 - 5*b^3 + (6*a*b^2 - 5*b^3)*cos(8*d*x + 8*c) - 2*(13*a*b^2 - 10*b^3)*cos(6*d*x + 6*c) - 2*(32*a^2*b - 47*a*b^2 + 15*b^3)*cos(4*d*x + 4*c) - 2*(7*a*b^2 - 10*b^3)*cos(2*d*x + 2*c))*sin(10*d*x + 10*c) + (14*a*b^2 - 20*b^3 - 2*(48*a^2*b - 5*a*b^2 - 25*b^3)*cos(6*d*x + 6*c) - 2*(112*a^2*b - 165*a*b^2 + 50*b^3)*cos(4*d*x + 4*c) - 5*(8*a*b^2 - 15*b^3)*cos(2*d*x + 2*c))*sin(8*d*x + 8*c) + 2*(32*a^2*b - 47*a*b^2 + 15*b^3 - 2*(256*a^3 - 432*a^2*b + 210*a*b^2 - 25*b^3)*cos(4*d*x + 4*c) - (112*a^2*b - 165*a*b^2 + 50*b^3)*cos(2*d*x + 2*c))*sin(6*d*x + 6*c) + 2*(13*a*b^2 - 10*b^3 - (48*a^2*b - 5*a*b^2 - 25*b^3)*cos(2*d*x + 2*c))*sin(4*d*x + 4*c) - (6*a*b^2 - 5*b^3)*sin(2*d*x + 2*c))/((a^3*b^2 - a^2*b^3)*d*cos(10*d*x + 10*c)^2 + 25*(a^3*b^2 - a^2*b^3)*d*cos(8*d*x + 8*c)^2 + 4*(64*a^5 - 144*a^4*b + 105*a^3*b^2 - 25*a^2*b^3)*d*cos(6*d*x + 6*c)^2 + 4*(64*a^5 - 144*a^4*b + 105*a^3*b^2 - 25*a^2*b^3)*d*cos(4*d*x + 4*c)^2 + 25*(a^3*b^2 - a^2*b^3)*d*cos(2*d*x + 2*c)^2 + (a^3*b^2 - a^2*b^3)*d*sin(10*d*x + 10*c)^2 + 25*(a^3*b^2 - a^2*b^3)*d*sin(8*d*x + 8*c)^2 + 4*(64*a^5 - 144*a^4*b + 105*a^3*b^2 - 25*a^2*b^3)*d*sin(6*d*x + 6*c)^2 + 4*(64*a^5 - 144*a^4*b + 105*a^3*b^2 - 25*a^2*b^3)*d*sin(4*d*x + 4*c)^2 + 20*(8*a^4*b - 13*a^3*b^2 + 5*a^2*b^3)*d*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 25*(a^3*b^2 - a^2*b^3)*d*sin(2*d*x + 2*c)^2 - 10*(a^3*b^2 - a^2*b^3)*d*cos(2*d*x + 2*c) + (a^3*b^2 - a^2*b^3)*d - 2*(5*(a^3*b^2 - a^2*b^3)*d*cos(8*d*x + 8*c) + 2*(8*a^4*b - 13*a^3*b^2 + 5*a^2*b^3)*d*cos(6*d*x + 6*c) - 2*(8*a^4*b - 13*a^3*b^2 + 5*a^2*b^3)*d*cos(4*d*x + 4*c) - 5*(a^3*b^2 - a^2*b^3)*d*cos(2*d*x + 2*c) + (a^3*b^2 - a^2*b^3)*d)*cos(10*d*x + 10*c) + 10*(2*(8*a^4*b - 13*a^3*b^2 + 5*a^2*b^3)*d*cos(6*d*x + 6*c) - 2*(8*a^4*b - 13*a^3*b^2 + 5*a^2*b^3)*d*cos(4*d*x + 4*c) - 5*(a^3*b^2 - a^2*b^3)*d*cos(2*d*x + 2*c) + (a^3*b^2 - a^2*b^3)*d)*cos(8*d*x + 8*c) - 4*(2*(64*a^5 - 144*a^4*b + 105*a^3*b^2 - 25*a^2*b^3)*d*cos(4*d*x + 4*c) + 5*(8*a^4*b - 13*a^3*b^2 + 5*a^2*b^3)*d*cos(2*d*x + 2*c) - (8*a^4*b - 13*a^3*b^2 + 5*a^2*b^3)*d)*cos(6*d*x + 6*c) + 4*(5*(8*a^4*b - 13*a^3*b^2 + 5*a^2*b^3)*d*cos(2*d*x + 2*c) - (8*a^4*b - 13*a^3*b^2 + 5*a^2*b^3)*d)*cos(4*d*x + 4*c) - 2*(5*(a^3*b^2 - a^2*b^3)*d*sin(8*d*x + 8*c) + 2*(8*a^4*b - 13*a^3*b^2 + 5*a^2*b^3)*d*sin(6*d*x + 6*c) - 2*(8*a^4*b - 13*a^3*b^2 + 5*a^2*b^3)*d*sin(4*d*x + 4*c) - 5*(a^3*b^2 - a^2*b^3)*d*sin(2*d*x + 2*c))*sin(10*d*x + 10*c) + 10*(2*(8*a^4*b - 13*a^3*b^2 + 5*a^2*b^3)*d*sin(6*d*x + 6*c) - 2*(8*a^4*b - 13*a^3*b^2 + 5*a^2*b^3)*d*sin(4*d*x + 4*c) - 5*(a^3*b^2 - a^2*b^3)*d*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) - 4*(2*(64*a^5 - 144*a^4*b + 105*a^3*b^2 - 25*a^2*b^3)*d*sin(4*d*x + 4*c) + 5*(8*a^4*b - 13*a^3*b^2 + 5*a^2*b^3)*d*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))","F",0
224,-1,0,0,0.000000," ","integrate(sin(d*x+c)^9/(a-b*sin(d*x+c)^4)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
225,-1,0,0,0.000000," ","integrate(sin(d*x+c)^7/(a-b*sin(d*x+c)^4)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
226,-1,0,0,0.000000," ","integrate(sin(d*x+c)^5/(a-b*sin(d*x+c)^4)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
227,-1,0,0,0.000000," ","integrate(sin(d*x+c)^3/(a-b*sin(d*x+c)^4)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
228,-1,0,0,0.000000," ","integrate(sin(d*x+c)/(a-b*sin(d*x+c)^4)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
229,-1,0,0,0.000000," ","integrate(csc(d*x+c)/(a-b*sin(d*x+c)^4)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
230,0,0,0,0.000000," ","integrate(sin(d*x+c)^8/(a-b*sin(d*x+c)^4)^3,x, algorithm=""maxima"")","-\frac{4 \, {\left(72 \, a^{2} b^{2} - 155 \, a b^{3} + 26 \, b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + {\left({\left(a b^{3} - 4 \, b^{4}\right)} \sin\left(14 \, d x + 14 \, c\right) - {\left(32 \, a^{2} b^{2} - 58 \, a b^{3} - b^{4}\right)} \sin\left(12 \, d x + 12 \, c\right) + 3 \, {\left(48 \, a^{2} b^{2} - 73 \, a b^{3} + 20 \, b^{4}\right)} \sin\left(10 \, d x + 10 \, c\right) + {\left(256 \, a^{3} b - 832 \, a^{2} b^{2} + 550 \, a b^{3} - 175 \, b^{4}\right)} \sin\left(8 \, d x + 8 \, c\right) + {\left(112 \, a^{2} b^{2} - 533 \, a b^{3} + 220 \, b^{4}\right)} \sin\left(6 \, d x + 6 \, c\right) - {\left(32 \, a^{2} b^{2} - 158 \, a b^{3} + 141 \, b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right) - {\left(17 \, a b^{3} - 44 \, b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(16 \, d x + 16 \, c\right) + 2 \, {\left(2 \, {\left(72 \, a^{2} b^{2} - 155 \, a b^{3} + 26 \, b^{4}\right)} \sin\left(12 \, d x + 12 \, c\right) - 8 \, {\left(80 \, a^{2} b^{2} - 145 \, a b^{3} + 44 \, b^{4}\right)} \sin\left(10 \, d x + 10 \, c\right) - 3 \, {\left(384 \, a^{3} b - 1312 \, a^{2} b^{2} + 873 \, a b^{3} - 280 \, b^{4}\right)} \sin\left(8 \, d x + 8 \, c\right) - 16 \, {\left(32 \, a^{2} b^{2} - 151 \, a b^{3} + 62 \, b^{4}\right)} \sin\left(6 \, d x + 6 \, c\right) + 2 \, {\left(72 \, a^{2} b^{2} - 355 \, a b^{3} + 310 \, b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right) + 24 \, {\left(3 \, a b^{3} - 8 \, b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(14 \, d x + 14 \, c\right) - 2 \, {\left(2 \, {\left(128 \, a^{3} b - 456 \, a^{2} b^{2} + 1233 \, a b^{3} - 434 \, b^{4}\right)} \sin\left(10 \, d x + 10 \, c\right) - {\left(6400 \, a^{3} b - 13888 \, a^{2} b^{2} + 8566 \, a b^{3} - 2485 \, b^{4}\right)} \sin\left(8 \, d x + 8 \, c\right) - 2 \, {\left(128 \, a^{3} b + 2744 \, a^{2} b^{2} - 4711 \, a b^{3} + 1554 \, b^{4}\right)} \sin\left(6 \, d x + 6 \, c\right) + 4 \, {\left(400 \, a^{2} b^{2} - 918 \, a b^{3} + 497 \, b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(72 \, a^{2} b^{2} - 355 \, a b^{3} + 310 \, b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(12 \, d x + 12 \, c\right) - 2 \, {\left({\left(2048 \, a^{4} + 18560 \, a^{3} b - 24752 \, a^{2} b^{2} + 13175 \, a b^{3} - 2800 \, b^{4}\right)} \sin\left(8 \, d x + 8 \, c\right) + 8 \, {\left(256 \, a^{3} b + 2400 \, a^{2} b^{2} - 2379 \, a b^{3} + 560 \, b^{4}\right)} \sin\left(6 \, d x + 6 \, c\right) - 2 \, {\left(128 \, a^{3} b + 2744 \, a^{2} b^{2} - 4711 \, a b^{3} + 1554 \, b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right) + 16 \, {\left(32 \, a^{2} b^{2} - 151 \, a b^{3} + 62 \, b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(10 \, d x + 10 \, c\right) - 2 \, {\left({\left(2048 \, a^{4} + 18560 \, a^{3} b - 24752 \, a^{2} b^{2} + 13175 \, a b^{3} - 2800 \, b^{4}\right)} \sin\left(6 \, d x + 6 \, c\right) - {\left(6400 \, a^{3} b - 13888 \, a^{2} b^{2} + 8566 \, a b^{3} - 2485 \, b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right) + 3 \, {\left(384 \, a^{3} b - 1312 \, a^{2} b^{2} + 873 \, a b^{3} - 280 \, b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) - 4 \, {\left({\left(128 \, a^{3} b - 456 \, a^{2} b^{2} + 1233 \, a b^{3} - 434 \, b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right) + 4 \, {\left(80 \, a^{2} b^{2} - 145 \, a b^{3} + 44 \, b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left({\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d \cos\left(16 \, d x + 16 \, c\right)^{2} + 64 \, {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d \cos\left(14 \, d x + 14 \, c\right)^{2} + 16 \, {\left(64 \, a^{4} b^{3} - 240 \, a^{3} b^{4} + 337 \, a^{2} b^{5} - 210 \, a b^{6} + 49 \, b^{7}\right)} d \cos\left(12 \, d x + 12 \, c\right)^{2} + 64 \, {\left(256 \, a^{4} b^{3} - 736 \, a^{3} b^{4} + 753 \, a^{2} b^{5} - 322 \, a b^{6} + 49 \, b^{7}\right)} d \cos\left(10 \, d x + 10 \, c\right)^{2} + 4 \, {\left(16384 \, a^{6} b - 57344 \, a^{5} b^{2} + 83712 \, a^{4} b^{3} - 67648 \, a^{3} b^{4} + 32841 \, a^{2} b^{5} - 9170 \, a b^{6} + 1225 \, b^{7}\right)} d \cos\left(8 \, d x + 8 \, c\right)^{2} + 64 \, {\left(256 \, a^{4} b^{3} - 736 \, a^{3} b^{4} + 753 \, a^{2} b^{5} - 322 \, a b^{6} + 49 \, b^{7}\right)} d \cos\left(6 \, d x + 6 \, c\right)^{2} + 16 \, {\left(64 \, a^{4} b^{3} - 240 \, a^{3} b^{4} + 337 \, a^{2} b^{5} - 210 \, a b^{6} + 49 \, b^{7}\right)} d \cos\left(4 \, d x + 4 \, c\right)^{2} + 64 \, {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d \sin\left(16 \, d x + 16 \, c\right)^{2} + 64 \, {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d \sin\left(14 \, d x + 14 \, c\right)^{2} + 16 \, {\left(64 \, a^{4} b^{3} - 240 \, a^{3} b^{4} + 337 \, a^{2} b^{5} - 210 \, a b^{6} + 49 \, b^{7}\right)} d \sin\left(12 \, d x + 12 \, c\right)^{2} + 64 \, {\left(256 \, a^{4} b^{3} - 736 \, a^{3} b^{4} + 753 \, a^{2} b^{5} - 322 \, a b^{6} + 49 \, b^{7}\right)} d \sin\left(10 \, d x + 10 \, c\right)^{2} + 4 \, {\left(16384 \, a^{6} b - 57344 \, a^{5} b^{2} + 83712 \, a^{4} b^{3} - 67648 \, a^{3} b^{4} + 32841 \, a^{2} b^{5} - 9170 \, a b^{6} + 1225 \, b^{7}\right)} d \sin\left(8 \, d x + 8 \, c\right)^{2} + 64 \, {\left(256 \, a^{4} b^{3} - 736 \, a^{3} b^{4} + 753 \, a^{2} b^{5} - 322 \, a b^{6} + 49 \, b^{7}\right)} d \sin\left(6 \, d x + 6 \, c\right)^{2} + 16 \, {\left(64 \, a^{4} b^{3} - 240 \, a^{3} b^{4} + 337 \, a^{2} b^{5} - 210 \, a b^{6} + 49 \, b^{7}\right)} d \sin\left(4 \, d x + 4 \, c\right)^{2} + 64 \, {\left(8 \, a^{3} b^{4} - 23 \, a^{2} b^{5} + 22 \, a b^{6} - 7 \, b^{7}\right)} d \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 64 \, {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d \sin\left(2 \, d x + 2 \, c\right)^{2} - 16 \, {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d - 2 \, {\left(8 \, {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d \cos\left(14 \, d x + 14 \, c\right) + 4 \, {\left(8 \, a^{3} b^{4} - 23 \, a^{2} b^{5} + 22 \, a b^{6} - 7 \, b^{7}\right)} d \cos\left(12 \, d x + 12 \, c\right) - 8 \, {\left(16 \, a^{3} b^{4} - 39 \, a^{2} b^{5} + 30 \, a b^{6} - 7 \, b^{7}\right)} d \cos\left(10 \, d x + 10 \, c\right) - 2 \, {\left(128 \, a^{4} b^{3} - 352 \, a^{3} b^{4} + 355 \, a^{2} b^{5} - 166 \, a b^{6} + 35 \, b^{7}\right)} d \cos\left(8 \, d x + 8 \, c\right) - 8 \, {\left(16 \, a^{3} b^{4} - 39 \, a^{2} b^{5} + 30 \, a b^{6} - 7 \, b^{7}\right)} d \cos\left(6 \, d x + 6 \, c\right) + 4 \, {\left(8 \, a^{3} b^{4} - 23 \, a^{2} b^{5} + 22 \, a b^{6} - 7 \, b^{7}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d\right)} \cos\left(16 \, d x + 16 \, c\right) + 16 \, {\left(4 \, {\left(8 \, a^{3} b^{4} - 23 \, a^{2} b^{5} + 22 \, a b^{6} - 7 \, b^{7}\right)} d \cos\left(12 \, d x + 12 \, c\right) - 8 \, {\left(16 \, a^{3} b^{4} - 39 \, a^{2} b^{5} + 30 \, a b^{6} - 7 \, b^{7}\right)} d \cos\left(10 \, d x + 10 \, c\right) - 2 \, {\left(128 \, a^{4} b^{3} - 352 \, a^{3} b^{4} + 355 \, a^{2} b^{5} - 166 \, a b^{6} + 35 \, b^{7}\right)} d \cos\left(8 \, d x + 8 \, c\right) - 8 \, {\left(16 \, a^{3} b^{4} - 39 \, a^{2} b^{5} + 30 \, a b^{6} - 7 \, b^{7}\right)} d \cos\left(6 \, d x + 6 \, c\right) + 4 \, {\left(8 \, a^{3} b^{4} - 23 \, a^{2} b^{5} + 22 \, a b^{6} - 7 \, b^{7}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d\right)} \cos\left(14 \, d x + 14 \, c\right) - 8 \, {\left(8 \, {\left(128 \, a^{4} b^{3} - 424 \, a^{3} b^{4} + 513 \, a^{2} b^{5} - 266 \, a b^{6} + 49 \, b^{7}\right)} d \cos\left(10 \, d x + 10 \, c\right) + 2 \, {\left(1024 \, a^{5} b^{2} - 3712 \, a^{4} b^{3} + 5304 \, a^{3} b^{4} - 3813 \, a^{2} b^{5} + 1442 \, a b^{6} - 245 \, b^{7}\right)} d \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(128 \, a^{4} b^{3} - 424 \, a^{3} b^{4} + 513 \, a^{2} b^{5} - 266 \, a b^{6} + 49 \, b^{7}\right)} d \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(64 \, a^{4} b^{3} - 240 \, a^{3} b^{4} + 337 \, a^{2} b^{5} - 210 \, a b^{6} + 49 \, b^{7}\right)} d \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(8 \, a^{3} b^{4} - 23 \, a^{2} b^{5} + 22 \, a b^{6} - 7 \, b^{7}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(8 \, a^{3} b^{4} - 23 \, a^{2} b^{5} + 22 \, a b^{6} - 7 \, b^{7}\right)} d\right)} \cos\left(12 \, d x + 12 \, c\right) + 16 \, {\left(2 \, {\left(2048 \, a^{5} b^{2} - 6528 \, a^{4} b^{3} + 8144 \, a^{3} b^{4} - 5141 \, a^{2} b^{5} + 1722 \, a b^{6} - 245 \, b^{7}\right)} d \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(256 \, a^{4} b^{3} - 736 \, a^{3} b^{4} + 753 \, a^{2} b^{5} - 322 \, a b^{6} + 49 \, b^{7}\right)} d \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(128 \, a^{4} b^{3} - 424 \, a^{3} b^{4} + 513 \, a^{2} b^{5} - 266 \, a b^{6} + 49 \, b^{7}\right)} d \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(16 \, a^{3} b^{4} - 39 \, a^{2} b^{5} + 30 \, a b^{6} - 7 \, b^{7}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(16 \, a^{3} b^{4} - 39 \, a^{2} b^{5} + 30 \, a b^{6} - 7 \, b^{7}\right)} d\right)} \cos\left(10 \, d x + 10 \, c\right) + 4 \, {\left(8 \, {\left(2048 \, a^{5} b^{2} - 6528 \, a^{4} b^{3} + 8144 \, a^{3} b^{4} - 5141 \, a^{2} b^{5} + 1722 \, a b^{6} - 245 \, b^{7}\right)} d \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(1024 \, a^{5} b^{2} - 3712 \, a^{4} b^{3} + 5304 \, a^{3} b^{4} - 3813 \, a^{2} b^{5} + 1442 \, a b^{6} - 245 \, b^{7}\right)} d \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(128 \, a^{4} b^{3} - 352 \, a^{3} b^{4} + 355 \, a^{2} b^{5} - 166 \, a b^{6} + 35 \, b^{7}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(128 \, a^{4} b^{3} - 352 \, a^{3} b^{4} + 355 \, a^{2} b^{5} - 166 \, a b^{6} + 35 \, b^{7}\right)} d\right)} \cos\left(8 \, d x + 8 \, c\right) - 16 \, {\left(4 \, {\left(128 \, a^{4} b^{3} - 424 \, a^{3} b^{4} + 513 \, a^{2} b^{5} - 266 \, a b^{6} + 49 \, b^{7}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(16 \, a^{3} b^{4} - 39 \, a^{2} b^{5} + 30 \, a b^{6} - 7 \, b^{7}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(16 \, a^{3} b^{4} - 39 \, a^{2} b^{5} + 30 \, a b^{6} - 7 \, b^{7}\right)} d\right)} \cos\left(6 \, d x + 6 \, c\right) + 8 \, {\left(8 \, {\left(8 \, a^{3} b^{4} - 23 \, a^{2} b^{5} + 22 \, a b^{6} - 7 \, b^{7}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(8 \, a^{3} b^{4} - 23 \, a^{2} b^{5} + 22 \, a b^{6} - 7 \, b^{7}\right)} d\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(4 \, {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d \sin\left(14 \, d x + 14 \, c\right) + 2 \, {\left(8 \, a^{3} b^{4} - 23 \, a^{2} b^{5} + 22 \, a b^{6} - 7 \, b^{7}\right)} d \sin\left(12 \, d x + 12 \, c\right) - 4 \, {\left(16 \, a^{3} b^{4} - 39 \, a^{2} b^{5} + 30 \, a b^{6} - 7 \, b^{7}\right)} d \sin\left(10 \, d x + 10 \, c\right) - {\left(128 \, a^{4} b^{3} - 352 \, a^{3} b^{4} + 355 \, a^{2} b^{5} - 166 \, a b^{6} + 35 \, b^{7}\right)} d \sin\left(8 \, d x + 8 \, c\right) - 4 \, {\left(16 \, a^{3} b^{4} - 39 \, a^{2} b^{5} + 30 \, a b^{6} - 7 \, b^{7}\right)} d \sin\left(6 \, d x + 6 \, c\right) + 2 \, {\left(8 \, a^{3} b^{4} - 23 \, a^{2} b^{5} + 22 \, a b^{6} - 7 \, b^{7}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(16 \, d x + 16 \, c\right) + 32 \, {\left(2 \, {\left(8 \, a^{3} b^{4} - 23 \, a^{2} b^{5} + 22 \, a b^{6} - 7 \, b^{7}\right)} d \sin\left(12 \, d x + 12 \, c\right) - 4 \, {\left(16 \, a^{3} b^{4} - 39 \, a^{2} b^{5} + 30 \, a b^{6} - 7 \, b^{7}\right)} d \sin\left(10 \, d x + 10 \, c\right) - {\left(128 \, a^{4} b^{3} - 352 \, a^{3} b^{4} + 355 \, a^{2} b^{5} - 166 \, a b^{6} + 35 \, b^{7}\right)} d \sin\left(8 \, d x + 8 \, c\right) - 4 \, {\left(16 \, a^{3} b^{4} - 39 \, a^{2} b^{5} + 30 \, a b^{6} - 7 \, b^{7}\right)} d \sin\left(6 \, d x + 6 \, c\right) + 2 \, {\left(8 \, a^{3} b^{4} - 23 \, a^{2} b^{5} + 22 \, a b^{6} - 7 \, b^{7}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(14 \, d x + 14 \, c\right) - 16 \, {\left(4 \, {\left(128 \, a^{4} b^{3} - 424 \, a^{3} b^{4} + 513 \, a^{2} b^{5} - 266 \, a b^{6} + 49 \, b^{7}\right)} d \sin\left(10 \, d x + 10 \, c\right) + {\left(1024 \, a^{5} b^{2} - 3712 \, a^{4} b^{3} + 5304 \, a^{3} b^{4} - 3813 \, a^{2} b^{5} + 1442 \, a b^{6} - 245 \, b^{7}\right)} d \sin\left(8 \, d x + 8 \, c\right) + 4 \, {\left(128 \, a^{4} b^{3} - 424 \, a^{3} b^{4} + 513 \, a^{2} b^{5} - 266 \, a b^{6} + 49 \, b^{7}\right)} d \sin\left(6 \, d x + 6 \, c\right) - 2 \, {\left(64 \, a^{4} b^{3} - 240 \, a^{3} b^{4} + 337 \, a^{2} b^{5} - 210 \, a b^{6} + 49 \, b^{7}\right)} d \sin\left(4 \, d x + 4 \, c\right) - 4 \, {\left(8 \, a^{3} b^{4} - 23 \, a^{2} b^{5} + 22 \, a b^{6} - 7 \, b^{7}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(12 \, d x + 12 \, c\right) + 32 \, {\left({\left(2048 \, a^{5} b^{2} - 6528 \, a^{4} b^{3} + 8144 \, a^{3} b^{4} - 5141 \, a^{2} b^{5} + 1722 \, a b^{6} - 245 \, b^{7}\right)} d \sin\left(8 \, d x + 8 \, c\right) + 4 \, {\left(256 \, a^{4} b^{3} - 736 \, a^{3} b^{4} + 753 \, a^{2} b^{5} - 322 \, a b^{6} + 49 \, b^{7}\right)} d \sin\left(6 \, d x + 6 \, c\right) - 2 \, {\left(128 \, a^{4} b^{3} - 424 \, a^{3} b^{4} + 513 \, a^{2} b^{5} - 266 \, a b^{6} + 49 \, b^{7}\right)} d \sin\left(4 \, d x + 4 \, c\right) - 4 \, {\left(16 \, a^{3} b^{4} - 39 \, a^{2} b^{5} + 30 \, a b^{6} - 7 \, b^{7}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + 16 \, {\left(2 \, {\left(2048 \, a^{5} b^{2} - 6528 \, a^{4} b^{3} + 8144 \, a^{3} b^{4} - 5141 \, a^{2} b^{5} + 1722 \, a b^{6} - 245 \, b^{7}\right)} d \sin\left(6 \, d x + 6 \, c\right) - {\left(1024 \, a^{5} b^{2} - 3712 \, a^{4} b^{3} + 5304 \, a^{3} b^{4} - 3813 \, a^{2} b^{5} + 1442 \, a b^{6} - 245 \, b^{7}\right)} d \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(128 \, a^{4} b^{3} - 352 \, a^{3} b^{4} + 355 \, a^{2} b^{5} - 166 \, a b^{6} + 35 \, b^{7}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) - 64 \, {\left({\left(128 \, a^{4} b^{3} - 424 \, a^{3} b^{4} + 513 \, a^{2} b^{5} - 266 \, a b^{6} + 49 \, b^{7}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(16 \, a^{3} b^{4} - 39 \, a^{2} b^{5} + 30 \, a b^{6} - 7 \, b^{7}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \int \frac{4 \, {\left(a b - 4 \, b^{2}\right)} \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, {\left(8 \, a b - 3 \, b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a b - 4 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(a b - 4 \, b^{2}\right)} \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, {\left(8 \, a b - 3 \, b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, {\left(8 \, a^{2} - 35 \, a b + 48 \, b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, {\left(a b - 4 \, b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - {\left(18 \, b^{2} \cos\left(4 \, d x + 4 \, c\right) + {\left(a b - 4 \, b^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + {\left(a b - 4 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) - {\left(a b - 4 \, b^{2} - 2 \, {\left(8 \, a^{2} - 35 \, a b + 48 \, b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(a b - 4 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left(9 \, b^{2} - {\left(8 \, a^{2} - 35 \, a b + 48 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - {\left(a b - 4 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) - {\left(18 \, b^{2} \sin\left(4 \, d x + 4 \, c\right) + {\left(a b - 4 \, b^{2}\right)} \sin\left(6 \, d x + 6 \, c\right) + {\left(a b - 4 \, b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 2 \, {\left({\left(8 \, a^{2} - 35 \, a b + 48 \, b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a b - 4 \, b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}{a^{2} b^{3} - 2 \, a b^{4} + b^{5} + {\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{4} b - 176 \, a^{3} b^{2} + 169 \, a^{2} b^{3} - 66 \, a b^{4} + 9 \, b^{5}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{4} b - 176 \, a^{3} b^{2} + 169 \, a^{2} b^{3} - 66 \, a b^{4} + 9 \, b^{5}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(8 \, a^{3} b^{2} - 19 \, a^{2} b^{3} + 14 \, a b^{4} - 3 \, b^{5}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, {\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5} - 4 \, {\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left(8 \, a^{3} b^{2} - 19 \, a^{2} b^{3} + 14 \, a b^{4} - 3 \, b^{5}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) - 8 \, {\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5} - 2 \, {\left(8 \, a^{3} b^{2} - 19 \, a^{2} b^{3} + 14 \, a b^{4} - 3 \, b^{5}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(8 \, a^{3} b^{2} - 19 \, a^{2} b^{3} + 14 \, a b^{4} - 3 \, b^{5} - 4 \, {\left(8 \, a^{3} b^{2} - 19 \, a^{2} b^{3} + 14 \, a b^{4} - 3 \, b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right) - 4 \, {\left(2 \, {\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} \sin\left(6 \, d x + 6 \, c\right) + {\left(8 \, a^{3} b^{2} - 19 \, a^{2} b^{3} + 14 \, a b^{4} - 3 \, b^{5}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left({\left(8 \, a^{3} b^{2} - 19 \, a^{2} b^{3} + 14 \, a b^{4} - 3 \, b^{5}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}\,{d x} - {\left(2 \, a b^{3} - 5 \, b^{4} + {\left(a b^{3} - 4 \, b^{4}\right)} \cos\left(14 \, d x + 14 \, c\right) - {\left(32 \, a^{2} b^{2} - 58 \, a b^{3} - b^{4}\right)} \cos\left(12 \, d x + 12 \, c\right) + 3 \, {\left(48 \, a^{2} b^{2} - 73 \, a b^{3} + 20 \, b^{4}\right)} \cos\left(10 \, d x + 10 \, c\right) + {\left(256 \, a^{3} b - 832 \, a^{2} b^{2} + 550 \, a b^{3} - 175 \, b^{4}\right)} \cos\left(8 \, d x + 8 \, c\right) + {\left(112 \, a^{2} b^{2} - 533 \, a b^{3} + 220 \, b^{4}\right)} \cos\left(6 \, d x + 6 \, c\right) - {\left(32 \, a^{2} b^{2} - 158 \, a b^{3} + 141 \, b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right) - {\left(17 \, a b^{3} - 44 \, b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(16 \, d x + 16 \, c\right) + {\left(17 \, a b^{3} - 44 \, b^{4} - 4 \, {\left(72 \, a^{2} b^{2} - 155 \, a b^{3} + 26 \, b^{4}\right)} \cos\left(12 \, d x + 12 \, c\right) + 16 \, {\left(80 \, a^{2} b^{2} - 145 \, a b^{3} + 44 \, b^{4}\right)} \cos\left(10 \, d x + 10 \, c\right) + 6 \, {\left(384 \, a^{3} b - 1312 \, a^{2} b^{2} + 873 \, a b^{3} - 280 \, b^{4}\right)} \cos\left(8 \, d x + 8 \, c\right) + 32 \, {\left(32 \, a^{2} b^{2} - 151 \, a b^{3} + 62 \, b^{4}\right)} \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(72 \, a^{2} b^{2} - 355 \, a b^{3} + 310 \, b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right) - 48 \, {\left(3 \, a b^{3} - 8 \, b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(14 \, d x + 14 \, c\right) + {\left(32 \, a^{2} b^{2} - 158 \, a b^{3} + 141 \, b^{4} + 4 \, {\left(128 \, a^{3} b - 456 \, a^{2} b^{2} + 1233 \, a b^{3} - 434 \, b^{4}\right)} \cos\left(10 \, d x + 10 \, c\right) - 2 \, {\left(6400 \, a^{3} b - 13888 \, a^{2} b^{2} + 8566 \, a b^{3} - 2485 \, b^{4}\right)} \cos\left(8 \, d x + 8 \, c\right) - 4 \, {\left(128 \, a^{3} b + 2744 \, a^{2} b^{2} - 4711 \, a b^{3} + 1554 \, b^{4}\right)} \cos\left(6 \, d x + 6 \, c\right) + 8 \, {\left(400 \, a^{2} b^{2} - 918 \, a b^{3} + 497 \, b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(72 \, a^{2} b^{2} - 355 \, a b^{3} + 310 \, b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(12 \, d x + 12 \, c\right) - {\left(112 \, a^{2} b^{2} - 533 \, a b^{3} + 220 \, b^{4} - 2 \, {\left(2048 \, a^{4} + 18560 \, a^{3} b - 24752 \, a^{2} b^{2} + 13175 \, a b^{3} - 2800 \, b^{4}\right)} \cos\left(8 \, d x + 8 \, c\right) - 16 \, {\left(256 \, a^{3} b + 2400 \, a^{2} b^{2} - 2379 \, a b^{3} + 560 \, b^{4}\right)} \cos\left(6 \, d x + 6 \, c\right) + 4 \, {\left(128 \, a^{3} b + 2744 \, a^{2} b^{2} - 4711 \, a b^{3} + 1554 \, b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right) - 32 \, {\left(32 \, a^{2} b^{2} - 151 \, a b^{3} + 62 \, b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) - {\left(256 \, a^{3} b - 832 \, a^{2} b^{2} + 550 \, a b^{3} - 175 \, b^{4} - 2 \, {\left(2048 \, a^{4} + 18560 \, a^{3} b - 24752 \, a^{2} b^{2} + 13175 \, a b^{3} - 2800 \, b^{4}\right)} \cos\left(6 \, d x + 6 \, c\right) + 2 \, {\left(6400 \, a^{3} b - 13888 \, a^{2} b^{2} + 8566 \, a b^{3} - 2485 \, b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right) - 6 \, {\left(384 \, a^{3} b - 1312 \, a^{2} b^{2} + 873 \, a b^{3} - 280 \, b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) - {\left(144 \, a^{2} b^{2} - 219 \, a b^{3} + 60 \, b^{4} - 4 \, {\left(128 \, a^{3} b - 456 \, a^{2} b^{2} + 1233 \, a b^{3} - 434 \, b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right) - 16 \, {\left(80 \, a^{2} b^{2} - 145 \, a b^{3} + 44 \, b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + {\left(32 \, a^{2} b^{2} - 58 \, a b^{3} - b^{4} - 4 \, {\left(72 \, a^{2} b^{2} - 155 \, a b^{3} + 26 \, b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) - {\left(a b^{3} - 4 \, b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)}{8 \, {\left({\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d \cos\left(16 \, d x + 16 \, c\right)^{2} + 64 \, {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d \cos\left(14 \, d x + 14 \, c\right)^{2} + 16 \, {\left(64 \, a^{4} b^{3} - 240 \, a^{3} b^{4} + 337 \, a^{2} b^{5} - 210 \, a b^{6} + 49 \, b^{7}\right)} d \cos\left(12 \, d x + 12 \, c\right)^{2} + 64 \, {\left(256 \, a^{4} b^{3} - 736 \, a^{3} b^{4} + 753 \, a^{2} b^{5} - 322 \, a b^{6} + 49 \, b^{7}\right)} d \cos\left(10 \, d x + 10 \, c\right)^{2} + 4 \, {\left(16384 \, a^{6} b - 57344 \, a^{5} b^{2} + 83712 \, a^{4} b^{3} - 67648 \, a^{3} b^{4} + 32841 \, a^{2} b^{5} - 9170 \, a b^{6} + 1225 \, b^{7}\right)} d \cos\left(8 \, d x + 8 \, c\right)^{2} + 64 \, {\left(256 \, a^{4} b^{3} - 736 \, a^{3} b^{4} + 753 \, a^{2} b^{5} - 322 \, a b^{6} + 49 \, b^{7}\right)} d \cos\left(6 \, d x + 6 \, c\right)^{2} + 16 \, {\left(64 \, a^{4} b^{3} - 240 \, a^{3} b^{4} + 337 \, a^{2} b^{5} - 210 \, a b^{6} + 49 \, b^{7}\right)} d \cos\left(4 \, d x + 4 \, c\right)^{2} + 64 \, {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d \sin\left(16 \, d x + 16 \, c\right)^{2} + 64 \, {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d \sin\left(14 \, d x + 14 \, c\right)^{2} + 16 \, {\left(64 \, a^{4} b^{3} - 240 \, a^{3} b^{4} + 337 \, a^{2} b^{5} - 210 \, a b^{6} + 49 \, b^{7}\right)} d \sin\left(12 \, d x + 12 \, c\right)^{2} + 64 \, {\left(256 \, a^{4} b^{3} - 736 \, a^{3} b^{4} + 753 \, a^{2} b^{5} - 322 \, a b^{6} + 49 \, b^{7}\right)} d \sin\left(10 \, d x + 10 \, c\right)^{2} + 4 \, {\left(16384 \, a^{6} b - 57344 \, a^{5} b^{2} + 83712 \, a^{4} b^{3} - 67648 \, a^{3} b^{4} + 32841 \, a^{2} b^{5} - 9170 \, a b^{6} + 1225 \, b^{7}\right)} d \sin\left(8 \, d x + 8 \, c\right)^{2} + 64 \, {\left(256 \, a^{4} b^{3} - 736 \, a^{3} b^{4} + 753 \, a^{2} b^{5} - 322 \, a b^{6} + 49 \, b^{7}\right)} d \sin\left(6 \, d x + 6 \, c\right)^{2} + 16 \, {\left(64 \, a^{4} b^{3} - 240 \, a^{3} b^{4} + 337 \, a^{2} b^{5} - 210 \, a b^{6} + 49 \, b^{7}\right)} d \sin\left(4 \, d x + 4 \, c\right)^{2} + 64 \, {\left(8 \, a^{3} b^{4} - 23 \, a^{2} b^{5} + 22 \, a b^{6} - 7 \, b^{7}\right)} d \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 64 \, {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d \sin\left(2 \, d x + 2 \, c\right)^{2} - 16 \, {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d - 2 \, {\left(8 \, {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d \cos\left(14 \, d x + 14 \, c\right) + 4 \, {\left(8 \, a^{3} b^{4} - 23 \, a^{2} b^{5} + 22 \, a b^{6} - 7 \, b^{7}\right)} d \cos\left(12 \, d x + 12 \, c\right) - 8 \, {\left(16 \, a^{3} b^{4} - 39 \, a^{2} b^{5} + 30 \, a b^{6} - 7 \, b^{7}\right)} d \cos\left(10 \, d x + 10 \, c\right) - 2 \, {\left(128 \, a^{4} b^{3} - 352 \, a^{3} b^{4} + 355 \, a^{2} b^{5} - 166 \, a b^{6} + 35 \, b^{7}\right)} d \cos\left(8 \, d x + 8 \, c\right) - 8 \, {\left(16 \, a^{3} b^{4} - 39 \, a^{2} b^{5} + 30 \, a b^{6} - 7 \, b^{7}\right)} d \cos\left(6 \, d x + 6 \, c\right) + 4 \, {\left(8 \, a^{3} b^{4} - 23 \, a^{2} b^{5} + 22 \, a b^{6} - 7 \, b^{7}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d\right)} \cos\left(16 \, d x + 16 \, c\right) + 16 \, {\left(4 \, {\left(8 \, a^{3} b^{4} - 23 \, a^{2} b^{5} + 22 \, a b^{6} - 7 \, b^{7}\right)} d \cos\left(12 \, d x + 12 \, c\right) - 8 \, {\left(16 \, a^{3} b^{4} - 39 \, a^{2} b^{5} + 30 \, a b^{6} - 7 \, b^{7}\right)} d \cos\left(10 \, d x + 10 \, c\right) - 2 \, {\left(128 \, a^{4} b^{3} - 352 \, a^{3} b^{4} + 355 \, a^{2} b^{5} - 166 \, a b^{6} + 35 \, b^{7}\right)} d \cos\left(8 \, d x + 8 \, c\right) - 8 \, {\left(16 \, a^{3} b^{4} - 39 \, a^{2} b^{5} + 30 \, a b^{6} - 7 \, b^{7}\right)} d \cos\left(6 \, d x + 6 \, c\right) + 4 \, {\left(8 \, a^{3} b^{4} - 23 \, a^{2} b^{5} + 22 \, a b^{6} - 7 \, b^{7}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d\right)} \cos\left(14 \, d x + 14 \, c\right) - 8 \, {\left(8 \, {\left(128 \, a^{4} b^{3} - 424 \, a^{3} b^{4} + 513 \, a^{2} b^{5} - 266 \, a b^{6} + 49 \, b^{7}\right)} d \cos\left(10 \, d x + 10 \, c\right) + 2 \, {\left(1024 \, a^{5} b^{2} - 3712 \, a^{4} b^{3} + 5304 \, a^{3} b^{4} - 3813 \, a^{2} b^{5} + 1442 \, a b^{6} - 245 \, b^{7}\right)} d \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(128 \, a^{4} b^{3} - 424 \, a^{3} b^{4} + 513 \, a^{2} b^{5} - 266 \, a b^{6} + 49 \, b^{7}\right)} d \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(64 \, a^{4} b^{3} - 240 \, a^{3} b^{4} + 337 \, a^{2} b^{5} - 210 \, a b^{6} + 49 \, b^{7}\right)} d \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(8 \, a^{3} b^{4} - 23 \, a^{2} b^{5} + 22 \, a b^{6} - 7 \, b^{7}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(8 \, a^{3} b^{4} - 23 \, a^{2} b^{5} + 22 \, a b^{6} - 7 \, b^{7}\right)} d\right)} \cos\left(12 \, d x + 12 \, c\right) + 16 \, {\left(2 \, {\left(2048 \, a^{5} b^{2} - 6528 \, a^{4} b^{3} + 8144 \, a^{3} b^{4} - 5141 \, a^{2} b^{5} + 1722 \, a b^{6} - 245 \, b^{7}\right)} d \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(256 \, a^{4} b^{3} - 736 \, a^{3} b^{4} + 753 \, a^{2} b^{5} - 322 \, a b^{6} + 49 \, b^{7}\right)} d \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(128 \, a^{4} b^{3} - 424 \, a^{3} b^{4} + 513 \, a^{2} b^{5} - 266 \, a b^{6} + 49 \, b^{7}\right)} d \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(16 \, a^{3} b^{4} - 39 \, a^{2} b^{5} + 30 \, a b^{6} - 7 \, b^{7}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(16 \, a^{3} b^{4} - 39 \, a^{2} b^{5} + 30 \, a b^{6} - 7 \, b^{7}\right)} d\right)} \cos\left(10 \, d x + 10 \, c\right) + 4 \, {\left(8 \, {\left(2048 \, a^{5} b^{2} - 6528 \, a^{4} b^{3} + 8144 \, a^{3} b^{4} - 5141 \, a^{2} b^{5} + 1722 \, a b^{6} - 245 \, b^{7}\right)} d \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(1024 \, a^{5} b^{2} - 3712 \, a^{4} b^{3} + 5304 \, a^{3} b^{4} - 3813 \, a^{2} b^{5} + 1442 \, a b^{6} - 245 \, b^{7}\right)} d \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(128 \, a^{4} b^{3} - 352 \, a^{3} b^{4} + 355 \, a^{2} b^{5} - 166 \, a b^{6} + 35 \, b^{7}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(128 \, a^{4} b^{3} - 352 \, a^{3} b^{4} + 355 \, a^{2} b^{5} - 166 \, a b^{6} + 35 \, b^{7}\right)} d\right)} \cos\left(8 \, d x + 8 \, c\right) - 16 \, {\left(4 \, {\left(128 \, a^{4} b^{3} - 424 \, a^{3} b^{4} + 513 \, a^{2} b^{5} - 266 \, a b^{6} + 49 \, b^{7}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(16 \, a^{3} b^{4} - 39 \, a^{2} b^{5} + 30 \, a b^{6} - 7 \, b^{7}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(16 \, a^{3} b^{4} - 39 \, a^{2} b^{5} + 30 \, a b^{6} - 7 \, b^{7}\right)} d\right)} \cos\left(6 \, d x + 6 \, c\right) + 8 \, {\left(8 \, {\left(8 \, a^{3} b^{4} - 23 \, a^{2} b^{5} + 22 \, a b^{6} - 7 \, b^{7}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(8 \, a^{3} b^{4} - 23 \, a^{2} b^{5} + 22 \, a b^{6} - 7 \, b^{7}\right)} d\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(4 \, {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d \sin\left(14 \, d x + 14 \, c\right) + 2 \, {\left(8 \, a^{3} b^{4} - 23 \, a^{2} b^{5} + 22 \, a b^{6} - 7 \, b^{7}\right)} d \sin\left(12 \, d x + 12 \, c\right) - 4 \, {\left(16 \, a^{3} b^{4} - 39 \, a^{2} b^{5} + 30 \, a b^{6} - 7 \, b^{7}\right)} d \sin\left(10 \, d x + 10 \, c\right) - {\left(128 \, a^{4} b^{3} - 352 \, a^{3} b^{4} + 355 \, a^{2} b^{5} - 166 \, a b^{6} + 35 \, b^{7}\right)} d \sin\left(8 \, d x + 8 \, c\right) - 4 \, {\left(16 \, a^{3} b^{4} - 39 \, a^{2} b^{5} + 30 \, a b^{6} - 7 \, b^{7}\right)} d \sin\left(6 \, d x + 6 \, c\right) + 2 \, {\left(8 \, a^{3} b^{4} - 23 \, a^{2} b^{5} + 22 \, a b^{6} - 7 \, b^{7}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(16 \, d x + 16 \, c\right) + 32 \, {\left(2 \, {\left(8 \, a^{3} b^{4} - 23 \, a^{2} b^{5} + 22 \, a b^{6} - 7 \, b^{7}\right)} d \sin\left(12 \, d x + 12 \, c\right) - 4 \, {\left(16 \, a^{3} b^{4} - 39 \, a^{2} b^{5} + 30 \, a b^{6} - 7 \, b^{7}\right)} d \sin\left(10 \, d x + 10 \, c\right) - {\left(128 \, a^{4} b^{3} - 352 \, a^{3} b^{4} + 355 \, a^{2} b^{5} - 166 \, a b^{6} + 35 \, b^{7}\right)} d \sin\left(8 \, d x + 8 \, c\right) - 4 \, {\left(16 \, a^{3} b^{4} - 39 \, a^{2} b^{5} + 30 \, a b^{6} - 7 \, b^{7}\right)} d \sin\left(6 \, d x + 6 \, c\right) + 2 \, {\left(8 \, a^{3} b^{4} - 23 \, a^{2} b^{5} + 22 \, a b^{6} - 7 \, b^{7}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(14 \, d x + 14 \, c\right) - 16 \, {\left(4 \, {\left(128 \, a^{4} b^{3} - 424 \, a^{3} b^{4} + 513 \, a^{2} b^{5} - 266 \, a b^{6} + 49 \, b^{7}\right)} d \sin\left(10 \, d x + 10 \, c\right) + {\left(1024 \, a^{5} b^{2} - 3712 \, a^{4} b^{3} + 5304 \, a^{3} b^{4} - 3813 \, a^{2} b^{5} + 1442 \, a b^{6} - 245 \, b^{7}\right)} d \sin\left(8 \, d x + 8 \, c\right) + 4 \, {\left(128 \, a^{4} b^{3} - 424 \, a^{3} b^{4} + 513 \, a^{2} b^{5} - 266 \, a b^{6} + 49 \, b^{7}\right)} d \sin\left(6 \, d x + 6 \, c\right) - 2 \, {\left(64 \, a^{4} b^{3} - 240 \, a^{3} b^{4} + 337 \, a^{2} b^{5} - 210 \, a b^{6} + 49 \, b^{7}\right)} d \sin\left(4 \, d x + 4 \, c\right) - 4 \, {\left(8 \, a^{3} b^{4} - 23 \, a^{2} b^{5} + 22 \, a b^{6} - 7 \, b^{7}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(12 \, d x + 12 \, c\right) + 32 \, {\left({\left(2048 \, a^{5} b^{2} - 6528 \, a^{4} b^{3} + 8144 \, a^{3} b^{4} - 5141 \, a^{2} b^{5} + 1722 \, a b^{6} - 245 \, b^{7}\right)} d \sin\left(8 \, d x + 8 \, c\right) + 4 \, {\left(256 \, a^{4} b^{3} - 736 \, a^{3} b^{4} + 753 \, a^{2} b^{5} - 322 \, a b^{6} + 49 \, b^{7}\right)} d \sin\left(6 \, d x + 6 \, c\right) - 2 \, {\left(128 \, a^{4} b^{3} - 424 \, a^{3} b^{4} + 513 \, a^{2} b^{5} - 266 \, a b^{6} + 49 \, b^{7}\right)} d \sin\left(4 \, d x + 4 \, c\right) - 4 \, {\left(16 \, a^{3} b^{4} - 39 \, a^{2} b^{5} + 30 \, a b^{6} - 7 \, b^{7}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + 16 \, {\left(2 \, {\left(2048 \, a^{5} b^{2} - 6528 \, a^{4} b^{3} + 8144 \, a^{3} b^{4} - 5141 \, a^{2} b^{5} + 1722 \, a b^{6} - 245 \, b^{7}\right)} d \sin\left(6 \, d x + 6 \, c\right) - {\left(1024 \, a^{5} b^{2} - 3712 \, a^{4} b^{3} + 5304 \, a^{3} b^{4} - 3813 \, a^{2} b^{5} + 1442 \, a b^{6} - 245 \, b^{7}\right)} d \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(128 \, a^{4} b^{3} - 352 \, a^{3} b^{4} + 355 \, a^{2} b^{5} - 166 \, a b^{6} + 35 \, b^{7}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) - 64 \, {\left({\left(128 \, a^{4} b^{3} - 424 \, a^{3} b^{4} + 513 \, a^{2} b^{5} - 266 \, a b^{6} + 49 \, b^{7}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(16 \, a^{3} b^{4} - 39 \, a^{2} b^{5} + 30 \, a b^{6} - 7 \, b^{7}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)}}"," ",0,"-1/8*(4*(72*a^2*b^2 - 155*a*b^3 + 26*b^4)*cos(4*d*x + 4*c)*sin(2*d*x + 2*c) + ((a*b^3 - 4*b^4)*sin(14*d*x + 14*c) - (32*a^2*b^2 - 58*a*b^3 - b^4)*sin(12*d*x + 12*c) + 3*(48*a^2*b^2 - 73*a*b^3 + 20*b^4)*sin(10*d*x + 10*c) + (256*a^3*b - 832*a^2*b^2 + 550*a*b^3 - 175*b^4)*sin(8*d*x + 8*c) + (112*a^2*b^2 - 533*a*b^3 + 220*b^4)*sin(6*d*x + 6*c) - (32*a^2*b^2 - 158*a*b^3 + 141*b^4)*sin(4*d*x + 4*c) - (17*a*b^3 - 44*b^4)*sin(2*d*x + 2*c))*cos(16*d*x + 16*c) + 2*(2*(72*a^2*b^2 - 155*a*b^3 + 26*b^4)*sin(12*d*x + 12*c) - 8*(80*a^2*b^2 - 145*a*b^3 + 44*b^4)*sin(10*d*x + 10*c) - 3*(384*a^3*b - 1312*a^2*b^2 + 873*a*b^3 - 280*b^4)*sin(8*d*x + 8*c) - 16*(32*a^2*b^2 - 151*a*b^3 + 62*b^4)*sin(6*d*x + 6*c) + 2*(72*a^2*b^2 - 355*a*b^3 + 310*b^4)*sin(4*d*x + 4*c) + 24*(3*a*b^3 - 8*b^4)*sin(2*d*x + 2*c))*cos(14*d*x + 14*c) - 2*(2*(128*a^3*b - 456*a^2*b^2 + 1233*a*b^3 - 434*b^4)*sin(10*d*x + 10*c) - (6400*a^3*b - 13888*a^2*b^2 + 8566*a*b^3 - 2485*b^4)*sin(8*d*x + 8*c) - 2*(128*a^3*b + 2744*a^2*b^2 - 4711*a*b^3 + 1554*b^4)*sin(6*d*x + 6*c) + 4*(400*a^2*b^2 - 918*a*b^3 + 497*b^4)*sin(4*d*x + 4*c) - 2*(72*a^2*b^2 - 355*a*b^3 + 310*b^4)*sin(2*d*x + 2*c))*cos(12*d*x + 12*c) - 2*((2048*a^4 + 18560*a^3*b - 24752*a^2*b^2 + 13175*a*b^3 - 2800*b^4)*sin(8*d*x + 8*c) + 8*(256*a^3*b + 2400*a^2*b^2 - 2379*a*b^3 + 560*b^4)*sin(6*d*x + 6*c) - 2*(128*a^3*b + 2744*a^2*b^2 - 4711*a*b^3 + 1554*b^4)*sin(4*d*x + 4*c) + 16*(32*a^2*b^2 - 151*a*b^3 + 62*b^4)*sin(2*d*x + 2*c))*cos(10*d*x + 10*c) - 2*((2048*a^4 + 18560*a^3*b - 24752*a^2*b^2 + 13175*a*b^3 - 2800*b^4)*sin(6*d*x + 6*c) - (6400*a^3*b - 13888*a^2*b^2 + 8566*a*b^3 - 2485*b^4)*sin(4*d*x + 4*c) + 3*(384*a^3*b - 1312*a^2*b^2 + 873*a*b^3 - 280*b^4)*sin(2*d*x + 2*c))*cos(8*d*x + 8*c) - 4*((128*a^3*b - 456*a^2*b^2 + 1233*a*b^3 - 434*b^4)*sin(4*d*x + 4*c) + 4*(80*a^2*b^2 - 145*a*b^3 + 44*b^4)*sin(2*d*x + 2*c))*cos(6*d*x + 6*c) - 8*((a^2*b^5 - 2*a*b^6 + b^7)*d*cos(16*d*x + 16*c)^2 + 64*(a^2*b^5 - 2*a*b^6 + b^7)*d*cos(14*d*x + 14*c)^2 + 16*(64*a^4*b^3 - 240*a^3*b^4 + 337*a^2*b^5 - 210*a*b^6 + 49*b^7)*d*cos(12*d*x + 12*c)^2 + 64*(256*a^4*b^3 - 736*a^3*b^4 + 753*a^2*b^5 - 322*a*b^6 + 49*b^7)*d*cos(10*d*x + 10*c)^2 + 4*(16384*a^6*b - 57344*a^5*b^2 + 83712*a^4*b^3 - 67648*a^3*b^4 + 32841*a^2*b^5 - 9170*a*b^6 + 1225*b^7)*d*cos(8*d*x + 8*c)^2 + 64*(256*a^4*b^3 - 736*a^3*b^4 + 753*a^2*b^5 - 322*a*b^6 + 49*b^7)*d*cos(6*d*x + 6*c)^2 + 16*(64*a^4*b^3 - 240*a^3*b^4 + 337*a^2*b^5 - 210*a*b^6 + 49*b^7)*d*cos(4*d*x + 4*c)^2 + 64*(a^2*b^5 - 2*a*b^6 + b^7)*d*cos(2*d*x + 2*c)^2 + (a^2*b^5 - 2*a*b^6 + b^7)*d*sin(16*d*x + 16*c)^2 + 64*(a^2*b^5 - 2*a*b^6 + b^7)*d*sin(14*d*x + 14*c)^2 + 16*(64*a^4*b^3 - 240*a^3*b^4 + 337*a^2*b^5 - 210*a*b^6 + 49*b^7)*d*sin(12*d*x + 12*c)^2 + 64*(256*a^4*b^3 - 736*a^3*b^4 + 753*a^2*b^5 - 322*a*b^6 + 49*b^7)*d*sin(10*d*x + 10*c)^2 + 4*(16384*a^6*b - 57344*a^5*b^2 + 83712*a^4*b^3 - 67648*a^3*b^4 + 32841*a^2*b^5 - 9170*a*b^6 + 1225*b^7)*d*sin(8*d*x + 8*c)^2 + 64*(256*a^4*b^3 - 736*a^3*b^4 + 753*a^2*b^5 - 322*a*b^6 + 49*b^7)*d*sin(6*d*x + 6*c)^2 + 16*(64*a^4*b^3 - 240*a^3*b^4 + 337*a^2*b^5 - 210*a*b^6 + 49*b^7)*d*sin(4*d*x + 4*c)^2 + 64*(8*a^3*b^4 - 23*a^2*b^5 + 22*a*b^6 - 7*b^7)*d*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 64*(a^2*b^5 - 2*a*b^6 + b^7)*d*sin(2*d*x + 2*c)^2 - 16*(a^2*b^5 - 2*a*b^6 + b^7)*d*cos(2*d*x + 2*c) + (a^2*b^5 - 2*a*b^6 + b^7)*d - 2*(8*(a^2*b^5 - 2*a*b^6 + b^7)*d*cos(14*d*x + 14*c) + 4*(8*a^3*b^4 - 23*a^2*b^5 + 22*a*b^6 - 7*b^7)*d*cos(12*d*x + 12*c) - 8*(16*a^3*b^4 - 39*a^2*b^5 + 30*a*b^6 - 7*b^7)*d*cos(10*d*x + 10*c) - 2*(128*a^4*b^3 - 352*a^3*b^4 + 355*a^2*b^5 - 166*a*b^6 + 35*b^7)*d*cos(8*d*x + 8*c) - 8*(16*a^3*b^4 - 39*a^2*b^5 + 30*a*b^6 - 7*b^7)*d*cos(6*d*x + 6*c) + 4*(8*a^3*b^4 - 23*a^2*b^5 + 22*a*b^6 - 7*b^7)*d*cos(4*d*x + 4*c) + 8*(a^2*b^5 - 2*a*b^6 + b^7)*d*cos(2*d*x + 2*c) - (a^2*b^5 - 2*a*b^6 + b^7)*d)*cos(16*d*x + 16*c) + 16*(4*(8*a^3*b^4 - 23*a^2*b^5 + 22*a*b^6 - 7*b^7)*d*cos(12*d*x + 12*c) - 8*(16*a^3*b^4 - 39*a^2*b^5 + 30*a*b^6 - 7*b^7)*d*cos(10*d*x + 10*c) - 2*(128*a^4*b^3 - 352*a^3*b^4 + 355*a^2*b^5 - 166*a*b^6 + 35*b^7)*d*cos(8*d*x + 8*c) - 8*(16*a^3*b^4 - 39*a^2*b^5 + 30*a*b^6 - 7*b^7)*d*cos(6*d*x + 6*c) + 4*(8*a^3*b^4 - 23*a^2*b^5 + 22*a*b^6 - 7*b^7)*d*cos(4*d*x + 4*c) + 8*(a^2*b^5 - 2*a*b^6 + b^7)*d*cos(2*d*x + 2*c) - (a^2*b^5 - 2*a*b^6 + b^7)*d)*cos(14*d*x + 14*c) - 8*(8*(128*a^4*b^3 - 424*a^3*b^4 + 513*a^2*b^5 - 266*a*b^6 + 49*b^7)*d*cos(10*d*x + 10*c) + 2*(1024*a^5*b^2 - 3712*a^4*b^3 + 5304*a^3*b^4 - 3813*a^2*b^5 + 1442*a*b^6 - 245*b^7)*d*cos(8*d*x + 8*c) + 8*(128*a^4*b^3 - 424*a^3*b^4 + 513*a^2*b^5 - 266*a*b^6 + 49*b^7)*d*cos(6*d*x + 6*c) - 4*(64*a^4*b^3 - 240*a^3*b^4 + 337*a^2*b^5 - 210*a*b^6 + 49*b^7)*d*cos(4*d*x + 4*c) - 8*(8*a^3*b^4 - 23*a^2*b^5 + 22*a*b^6 - 7*b^7)*d*cos(2*d*x + 2*c) + (8*a^3*b^4 - 23*a^2*b^5 + 22*a*b^6 - 7*b^7)*d)*cos(12*d*x + 12*c) + 16*(2*(2048*a^5*b^2 - 6528*a^4*b^3 + 8144*a^3*b^4 - 5141*a^2*b^5 + 1722*a*b^6 - 245*b^7)*d*cos(8*d*x + 8*c) + 8*(256*a^4*b^3 - 736*a^3*b^4 + 753*a^2*b^5 - 322*a*b^6 + 49*b^7)*d*cos(6*d*x + 6*c) - 4*(128*a^4*b^3 - 424*a^3*b^4 + 513*a^2*b^5 - 266*a*b^6 + 49*b^7)*d*cos(4*d*x + 4*c) - 8*(16*a^3*b^4 - 39*a^2*b^5 + 30*a*b^6 - 7*b^7)*d*cos(2*d*x + 2*c) + (16*a^3*b^4 - 39*a^2*b^5 + 30*a*b^6 - 7*b^7)*d)*cos(10*d*x + 10*c) + 4*(8*(2048*a^5*b^2 - 6528*a^4*b^3 + 8144*a^3*b^4 - 5141*a^2*b^5 + 1722*a*b^6 - 245*b^7)*d*cos(6*d*x + 6*c) - 4*(1024*a^5*b^2 - 3712*a^4*b^3 + 5304*a^3*b^4 - 3813*a^2*b^5 + 1442*a*b^6 - 245*b^7)*d*cos(4*d*x + 4*c) - 8*(128*a^4*b^3 - 352*a^3*b^4 + 355*a^2*b^5 - 166*a*b^6 + 35*b^7)*d*cos(2*d*x + 2*c) + (128*a^4*b^3 - 352*a^3*b^4 + 355*a^2*b^5 - 166*a*b^6 + 35*b^7)*d)*cos(8*d*x + 8*c) - 16*(4*(128*a^4*b^3 - 424*a^3*b^4 + 513*a^2*b^5 - 266*a*b^6 + 49*b^7)*d*cos(4*d*x + 4*c) + 8*(16*a^3*b^4 - 39*a^2*b^5 + 30*a*b^6 - 7*b^7)*d*cos(2*d*x + 2*c) - (16*a^3*b^4 - 39*a^2*b^5 + 30*a*b^6 - 7*b^7)*d)*cos(6*d*x + 6*c) + 8*(8*(8*a^3*b^4 - 23*a^2*b^5 + 22*a*b^6 - 7*b^7)*d*cos(2*d*x + 2*c) - (8*a^3*b^4 - 23*a^2*b^5 + 22*a*b^6 - 7*b^7)*d)*cos(4*d*x + 4*c) - 4*(4*(a^2*b^5 - 2*a*b^6 + b^7)*d*sin(14*d*x + 14*c) + 2*(8*a^3*b^4 - 23*a^2*b^5 + 22*a*b^6 - 7*b^7)*d*sin(12*d*x + 12*c) - 4*(16*a^3*b^4 - 39*a^2*b^5 + 30*a*b^6 - 7*b^7)*d*sin(10*d*x + 10*c) - (128*a^4*b^3 - 352*a^3*b^4 + 355*a^2*b^5 - 166*a*b^6 + 35*b^7)*d*sin(8*d*x + 8*c) - 4*(16*a^3*b^4 - 39*a^2*b^5 + 30*a*b^6 - 7*b^7)*d*sin(6*d*x + 6*c) + 2*(8*a^3*b^4 - 23*a^2*b^5 + 22*a*b^6 - 7*b^7)*d*sin(4*d*x + 4*c) + 4*(a^2*b^5 - 2*a*b^6 + b^7)*d*sin(2*d*x + 2*c))*sin(16*d*x + 16*c) + 32*(2*(8*a^3*b^4 - 23*a^2*b^5 + 22*a*b^6 - 7*b^7)*d*sin(12*d*x + 12*c) - 4*(16*a^3*b^4 - 39*a^2*b^5 + 30*a*b^6 - 7*b^7)*d*sin(10*d*x + 10*c) - (128*a^4*b^3 - 352*a^3*b^4 + 355*a^2*b^5 - 166*a*b^6 + 35*b^7)*d*sin(8*d*x + 8*c) - 4*(16*a^3*b^4 - 39*a^2*b^5 + 30*a*b^6 - 7*b^7)*d*sin(6*d*x + 6*c) + 2*(8*a^3*b^4 - 23*a^2*b^5 + 22*a*b^6 - 7*b^7)*d*sin(4*d*x + 4*c) + 4*(a^2*b^5 - 2*a*b^6 + b^7)*d*sin(2*d*x + 2*c))*sin(14*d*x + 14*c) - 16*(4*(128*a^4*b^3 - 424*a^3*b^4 + 513*a^2*b^5 - 266*a*b^6 + 49*b^7)*d*sin(10*d*x + 10*c) + (1024*a^5*b^2 - 3712*a^4*b^3 + 5304*a^3*b^4 - 3813*a^2*b^5 + 1442*a*b^6 - 245*b^7)*d*sin(8*d*x + 8*c) + 4*(128*a^4*b^3 - 424*a^3*b^4 + 513*a^2*b^5 - 266*a*b^6 + 49*b^7)*d*sin(6*d*x + 6*c) - 2*(64*a^4*b^3 - 240*a^3*b^4 + 337*a^2*b^5 - 210*a*b^6 + 49*b^7)*d*sin(4*d*x + 4*c) - 4*(8*a^3*b^4 - 23*a^2*b^5 + 22*a*b^6 - 7*b^7)*d*sin(2*d*x + 2*c))*sin(12*d*x + 12*c) + 32*((2048*a^5*b^2 - 6528*a^4*b^3 + 8144*a^3*b^4 - 5141*a^2*b^5 + 1722*a*b^6 - 245*b^7)*d*sin(8*d*x + 8*c) + 4*(256*a^4*b^3 - 736*a^3*b^4 + 753*a^2*b^5 - 322*a*b^6 + 49*b^7)*d*sin(6*d*x + 6*c) - 2*(128*a^4*b^3 - 424*a^3*b^4 + 513*a^2*b^5 - 266*a*b^6 + 49*b^7)*d*sin(4*d*x + 4*c) - 4*(16*a^3*b^4 - 39*a^2*b^5 + 30*a*b^6 - 7*b^7)*d*sin(2*d*x + 2*c))*sin(10*d*x + 10*c) + 16*(2*(2048*a^5*b^2 - 6528*a^4*b^3 + 8144*a^3*b^4 - 5141*a^2*b^5 + 1722*a*b^6 - 245*b^7)*d*sin(6*d*x + 6*c) - (1024*a^5*b^2 - 3712*a^4*b^3 + 5304*a^3*b^4 - 3813*a^2*b^5 + 1442*a*b^6 - 245*b^7)*d*sin(4*d*x + 4*c) - 2*(128*a^4*b^3 - 352*a^3*b^4 + 355*a^2*b^5 - 166*a*b^6 + 35*b^7)*d*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) - 64*((128*a^4*b^3 - 424*a^3*b^4 + 513*a^2*b^5 - 266*a*b^6 + 49*b^7)*d*sin(4*d*x + 4*c) + 2*(16*a^3*b^4 - 39*a^2*b^5 + 30*a*b^6 - 7*b^7)*d*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*integrate(1/4*(4*(a*b - 4*b^2)*cos(6*d*x + 6*c)^2 + 36*(8*a*b - 3*b^2)*cos(4*d*x + 4*c)^2 + 4*(a*b - 4*b^2)*cos(2*d*x + 2*c)^2 + 4*(a*b - 4*b^2)*sin(6*d*x + 6*c)^2 + 36*(8*a*b - 3*b^2)*sin(4*d*x + 4*c)^2 + 2*(8*a^2 - 35*a*b + 48*b^2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*(a*b - 4*b^2)*sin(2*d*x + 2*c)^2 - (18*b^2*cos(4*d*x + 4*c) + (a*b - 4*b^2)*cos(6*d*x + 6*c) + (a*b - 4*b^2)*cos(2*d*x + 2*c))*cos(8*d*x + 8*c) - (a*b - 4*b^2 - 2*(8*a^2 - 35*a*b + 48*b^2)*cos(4*d*x + 4*c) - 8*(a*b - 4*b^2)*cos(2*d*x + 2*c))*cos(6*d*x + 6*c) - 2*(9*b^2 - (8*a^2 - 35*a*b + 48*b^2)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - (a*b - 4*b^2)*cos(2*d*x + 2*c) - (18*b^2*sin(4*d*x + 4*c) + (a*b - 4*b^2)*sin(6*d*x + 6*c) + (a*b - 4*b^2)*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 2*((8*a^2 - 35*a*b + 48*b^2)*sin(4*d*x + 4*c) + 4*(a*b - 4*b^2)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))/(a^2*b^3 - 2*a*b^4 + b^5 + (a^2*b^3 - 2*a*b^4 + b^5)*cos(8*d*x + 8*c)^2 + 16*(a^2*b^3 - 2*a*b^4 + b^5)*cos(6*d*x + 6*c)^2 + 4*(64*a^4*b - 176*a^3*b^2 + 169*a^2*b^3 - 66*a*b^4 + 9*b^5)*cos(4*d*x + 4*c)^2 + 16*(a^2*b^3 - 2*a*b^4 + b^5)*cos(2*d*x + 2*c)^2 + (a^2*b^3 - 2*a*b^4 + b^5)*sin(8*d*x + 8*c)^2 + 16*(a^2*b^3 - 2*a*b^4 + b^5)*sin(6*d*x + 6*c)^2 + 4*(64*a^4*b - 176*a^3*b^2 + 169*a^2*b^3 - 66*a*b^4 + 9*b^5)*sin(4*d*x + 4*c)^2 + 16*(8*a^3*b^2 - 19*a^2*b^3 + 14*a*b^4 - 3*b^5)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*(a^2*b^3 - 2*a*b^4 + b^5)*sin(2*d*x + 2*c)^2 + 2*(a^2*b^3 - 2*a*b^4 + b^5 - 4*(a^2*b^3 - 2*a*b^4 + b^5)*cos(6*d*x + 6*c) - 2*(8*a^3*b^2 - 19*a^2*b^3 + 14*a*b^4 - 3*b^5)*cos(4*d*x + 4*c) - 4*(a^2*b^3 - 2*a*b^4 + b^5)*cos(2*d*x + 2*c))*cos(8*d*x + 8*c) - 8*(a^2*b^3 - 2*a*b^4 + b^5 - 2*(8*a^3*b^2 - 19*a^2*b^3 + 14*a*b^4 - 3*b^5)*cos(4*d*x + 4*c) - 4*(a^2*b^3 - 2*a*b^4 + b^5)*cos(2*d*x + 2*c))*cos(6*d*x + 6*c) - 4*(8*a^3*b^2 - 19*a^2*b^3 + 14*a*b^4 - 3*b^5 - 4*(8*a^3*b^2 - 19*a^2*b^3 + 14*a*b^4 - 3*b^5)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 8*(a^2*b^3 - 2*a*b^4 + b^5)*cos(2*d*x + 2*c) - 4*(2*(a^2*b^3 - 2*a*b^4 + b^5)*sin(6*d*x + 6*c) + (8*a^3*b^2 - 19*a^2*b^3 + 14*a*b^4 - 3*b^5)*sin(4*d*x + 4*c) + 2*(a^2*b^3 - 2*a*b^4 + b^5)*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*((8*a^3*b^2 - 19*a^2*b^3 + 14*a*b^4 - 3*b^5)*sin(4*d*x + 4*c) + 2*(a^2*b^3 - 2*a*b^4 + b^5)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c)), x) - (2*a*b^3 - 5*b^4 + (a*b^3 - 4*b^4)*cos(14*d*x + 14*c) - (32*a^2*b^2 - 58*a*b^3 - b^4)*cos(12*d*x + 12*c) + 3*(48*a^2*b^2 - 73*a*b^3 + 20*b^4)*cos(10*d*x + 10*c) + (256*a^3*b - 832*a^2*b^2 + 550*a*b^3 - 175*b^4)*cos(8*d*x + 8*c) + (112*a^2*b^2 - 533*a*b^3 + 220*b^4)*cos(6*d*x + 6*c) - (32*a^2*b^2 - 158*a*b^3 + 141*b^4)*cos(4*d*x + 4*c) - (17*a*b^3 - 44*b^4)*cos(2*d*x + 2*c))*sin(16*d*x + 16*c) + (17*a*b^3 - 44*b^4 - 4*(72*a^2*b^2 - 155*a*b^3 + 26*b^4)*cos(12*d*x + 12*c) + 16*(80*a^2*b^2 - 145*a*b^3 + 44*b^4)*cos(10*d*x + 10*c) + 6*(384*a^3*b - 1312*a^2*b^2 + 873*a*b^3 - 280*b^4)*cos(8*d*x + 8*c) + 32*(32*a^2*b^2 - 151*a*b^3 + 62*b^4)*cos(6*d*x + 6*c) - 4*(72*a^2*b^2 - 355*a*b^3 + 310*b^4)*cos(4*d*x + 4*c) - 48*(3*a*b^3 - 8*b^4)*cos(2*d*x + 2*c))*sin(14*d*x + 14*c) + (32*a^2*b^2 - 158*a*b^3 + 141*b^4 + 4*(128*a^3*b - 456*a^2*b^2 + 1233*a*b^3 - 434*b^4)*cos(10*d*x + 10*c) - 2*(6400*a^3*b - 13888*a^2*b^2 + 8566*a*b^3 - 2485*b^4)*cos(8*d*x + 8*c) - 4*(128*a^3*b + 2744*a^2*b^2 - 4711*a*b^3 + 1554*b^4)*cos(6*d*x + 6*c) + 8*(400*a^2*b^2 - 918*a*b^3 + 497*b^4)*cos(4*d*x + 4*c) - 4*(72*a^2*b^2 - 355*a*b^3 + 310*b^4)*cos(2*d*x + 2*c))*sin(12*d*x + 12*c) - (112*a^2*b^2 - 533*a*b^3 + 220*b^4 - 2*(2048*a^4 + 18560*a^3*b - 24752*a^2*b^2 + 13175*a*b^3 - 2800*b^4)*cos(8*d*x + 8*c) - 16*(256*a^3*b + 2400*a^2*b^2 - 2379*a*b^3 + 560*b^4)*cos(6*d*x + 6*c) + 4*(128*a^3*b + 2744*a^2*b^2 - 4711*a*b^3 + 1554*b^4)*cos(4*d*x + 4*c) - 32*(32*a^2*b^2 - 151*a*b^3 + 62*b^4)*cos(2*d*x + 2*c))*sin(10*d*x + 10*c) - (256*a^3*b - 832*a^2*b^2 + 550*a*b^3 - 175*b^4 - 2*(2048*a^4 + 18560*a^3*b - 24752*a^2*b^2 + 13175*a*b^3 - 2800*b^4)*cos(6*d*x + 6*c) + 2*(6400*a^3*b - 13888*a^2*b^2 + 8566*a*b^3 - 2485*b^4)*cos(4*d*x + 4*c) - 6*(384*a^3*b - 1312*a^2*b^2 + 873*a*b^3 - 280*b^4)*cos(2*d*x + 2*c))*sin(8*d*x + 8*c) - (144*a^2*b^2 - 219*a*b^3 + 60*b^4 - 4*(128*a^3*b - 456*a^2*b^2 + 1233*a*b^3 - 434*b^4)*cos(4*d*x + 4*c) - 16*(80*a^2*b^2 - 145*a*b^3 + 44*b^4)*cos(2*d*x + 2*c))*sin(6*d*x + 6*c) + (32*a^2*b^2 - 58*a*b^3 - b^4 - 4*(72*a^2*b^2 - 155*a*b^3 + 26*b^4)*cos(2*d*x + 2*c))*sin(4*d*x + 4*c) - (a*b^3 - 4*b^4)*sin(2*d*x + 2*c))/((a^2*b^5 - 2*a*b^6 + b^7)*d*cos(16*d*x + 16*c)^2 + 64*(a^2*b^5 - 2*a*b^6 + b^7)*d*cos(14*d*x + 14*c)^2 + 16*(64*a^4*b^3 - 240*a^3*b^4 + 337*a^2*b^5 - 210*a*b^6 + 49*b^7)*d*cos(12*d*x + 12*c)^2 + 64*(256*a^4*b^3 - 736*a^3*b^4 + 753*a^2*b^5 - 322*a*b^6 + 49*b^7)*d*cos(10*d*x + 10*c)^2 + 4*(16384*a^6*b - 57344*a^5*b^2 + 83712*a^4*b^3 - 67648*a^3*b^4 + 32841*a^2*b^5 - 9170*a*b^6 + 1225*b^7)*d*cos(8*d*x + 8*c)^2 + 64*(256*a^4*b^3 - 736*a^3*b^4 + 753*a^2*b^5 - 322*a*b^6 + 49*b^7)*d*cos(6*d*x + 6*c)^2 + 16*(64*a^4*b^3 - 240*a^3*b^4 + 337*a^2*b^5 - 210*a*b^6 + 49*b^7)*d*cos(4*d*x + 4*c)^2 + 64*(a^2*b^5 - 2*a*b^6 + b^7)*d*cos(2*d*x + 2*c)^2 + (a^2*b^5 - 2*a*b^6 + b^7)*d*sin(16*d*x + 16*c)^2 + 64*(a^2*b^5 - 2*a*b^6 + b^7)*d*sin(14*d*x + 14*c)^2 + 16*(64*a^4*b^3 - 240*a^3*b^4 + 337*a^2*b^5 - 210*a*b^6 + 49*b^7)*d*sin(12*d*x + 12*c)^2 + 64*(256*a^4*b^3 - 736*a^3*b^4 + 753*a^2*b^5 - 322*a*b^6 + 49*b^7)*d*sin(10*d*x + 10*c)^2 + 4*(16384*a^6*b - 57344*a^5*b^2 + 83712*a^4*b^3 - 67648*a^3*b^4 + 32841*a^2*b^5 - 9170*a*b^6 + 1225*b^7)*d*sin(8*d*x + 8*c)^2 + 64*(256*a^4*b^3 - 736*a^3*b^4 + 753*a^2*b^5 - 322*a*b^6 + 49*b^7)*d*sin(6*d*x + 6*c)^2 + 16*(64*a^4*b^3 - 240*a^3*b^4 + 337*a^2*b^5 - 210*a*b^6 + 49*b^7)*d*sin(4*d*x + 4*c)^2 + 64*(8*a^3*b^4 - 23*a^2*b^5 + 22*a*b^6 - 7*b^7)*d*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 64*(a^2*b^5 - 2*a*b^6 + b^7)*d*sin(2*d*x + 2*c)^2 - 16*(a^2*b^5 - 2*a*b^6 + b^7)*d*cos(2*d*x + 2*c) + (a^2*b^5 - 2*a*b^6 + b^7)*d - 2*(8*(a^2*b^5 - 2*a*b^6 + b^7)*d*cos(14*d*x + 14*c) + 4*(8*a^3*b^4 - 23*a^2*b^5 + 22*a*b^6 - 7*b^7)*d*cos(12*d*x + 12*c) - 8*(16*a^3*b^4 - 39*a^2*b^5 + 30*a*b^6 - 7*b^7)*d*cos(10*d*x + 10*c) - 2*(128*a^4*b^3 - 352*a^3*b^4 + 355*a^2*b^5 - 166*a*b^6 + 35*b^7)*d*cos(8*d*x + 8*c) - 8*(16*a^3*b^4 - 39*a^2*b^5 + 30*a*b^6 - 7*b^7)*d*cos(6*d*x + 6*c) + 4*(8*a^3*b^4 - 23*a^2*b^5 + 22*a*b^6 - 7*b^7)*d*cos(4*d*x + 4*c) + 8*(a^2*b^5 - 2*a*b^6 + b^7)*d*cos(2*d*x + 2*c) - (a^2*b^5 - 2*a*b^6 + b^7)*d)*cos(16*d*x + 16*c) + 16*(4*(8*a^3*b^4 - 23*a^2*b^5 + 22*a*b^6 - 7*b^7)*d*cos(12*d*x + 12*c) - 8*(16*a^3*b^4 - 39*a^2*b^5 + 30*a*b^6 - 7*b^7)*d*cos(10*d*x + 10*c) - 2*(128*a^4*b^3 - 352*a^3*b^4 + 355*a^2*b^5 - 166*a*b^6 + 35*b^7)*d*cos(8*d*x + 8*c) - 8*(16*a^3*b^4 - 39*a^2*b^5 + 30*a*b^6 - 7*b^7)*d*cos(6*d*x + 6*c) + 4*(8*a^3*b^4 - 23*a^2*b^5 + 22*a*b^6 - 7*b^7)*d*cos(4*d*x + 4*c) + 8*(a^2*b^5 - 2*a*b^6 + b^7)*d*cos(2*d*x + 2*c) - (a^2*b^5 - 2*a*b^6 + b^7)*d)*cos(14*d*x + 14*c) - 8*(8*(128*a^4*b^3 - 424*a^3*b^4 + 513*a^2*b^5 - 266*a*b^6 + 49*b^7)*d*cos(10*d*x + 10*c) + 2*(1024*a^5*b^2 - 3712*a^4*b^3 + 5304*a^3*b^4 - 3813*a^2*b^5 + 1442*a*b^6 - 245*b^7)*d*cos(8*d*x + 8*c) + 8*(128*a^4*b^3 - 424*a^3*b^4 + 513*a^2*b^5 - 266*a*b^6 + 49*b^7)*d*cos(6*d*x + 6*c) - 4*(64*a^4*b^3 - 240*a^3*b^4 + 337*a^2*b^5 - 210*a*b^6 + 49*b^7)*d*cos(4*d*x + 4*c) - 8*(8*a^3*b^4 - 23*a^2*b^5 + 22*a*b^6 - 7*b^7)*d*cos(2*d*x + 2*c) + (8*a^3*b^4 - 23*a^2*b^5 + 22*a*b^6 - 7*b^7)*d)*cos(12*d*x + 12*c) + 16*(2*(2048*a^5*b^2 - 6528*a^4*b^3 + 8144*a^3*b^4 - 5141*a^2*b^5 + 1722*a*b^6 - 245*b^7)*d*cos(8*d*x + 8*c) + 8*(256*a^4*b^3 - 736*a^3*b^4 + 753*a^2*b^5 - 322*a*b^6 + 49*b^7)*d*cos(6*d*x + 6*c) - 4*(128*a^4*b^3 - 424*a^3*b^4 + 513*a^2*b^5 - 266*a*b^6 + 49*b^7)*d*cos(4*d*x + 4*c) - 8*(16*a^3*b^4 - 39*a^2*b^5 + 30*a*b^6 - 7*b^7)*d*cos(2*d*x + 2*c) + (16*a^3*b^4 - 39*a^2*b^5 + 30*a*b^6 - 7*b^7)*d)*cos(10*d*x + 10*c) + 4*(8*(2048*a^5*b^2 - 6528*a^4*b^3 + 8144*a^3*b^4 - 5141*a^2*b^5 + 1722*a*b^6 - 245*b^7)*d*cos(6*d*x + 6*c) - 4*(1024*a^5*b^2 - 3712*a^4*b^3 + 5304*a^3*b^4 - 3813*a^2*b^5 + 1442*a*b^6 - 245*b^7)*d*cos(4*d*x + 4*c) - 8*(128*a^4*b^3 - 352*a^3*b^4 + 355*a^2*b^5 - 166*a*b^6 + 35*b^7)*d*cos(2*d*x + 2*c) + (128*a^4*b^3 - 352*a^3*b^4 + 355*a^2*b^5 - 166*a*b^6 + 35*b^7)*d)*cos(8*d*x + 8*c) - 16*(4*(128*a^4*b^3 - 424*a^3*b^4 + 513*a^2*b^5 - 266*a*b^6 + 49*b^7)*d*cos(4*d*x + 4*c) + 8*(16*a^3*b^4 - 39*a^2*b^5 + 30*a*b^6 - 7*b^7)*d*cos(2*d*x + 2*c) - (16*a^3*b^4 - 39*a^2*b^5 + 30*a*b^6 - 7*b^7)*d)*cos(6*d*x + 6*c) + 8*(8*(8*a^3*b^4 - 23*a^2*b^5 + 22*a*b^6 - 7*b^7)*d*cos(2*d*x + 2*c) - (8*a^3*b^4 - 23*a^2*b^5 + 22*a*b^6 - 7*b^7)*d)*cos(4*d*x + 4*c) - 4*(4*(a^2*b^5 - 2*a*b^6 + b^7)*d*sin(14*d*x + 14*c) + 2*(8*a^3*b^4 - 23*a^2*b^5 + 22*a*b^6 - 7*b^7)*d*sin(12*d*x + 12*c) - 4*(16*a^3*b^4 - 39*a^2*b^5 + 30*a*b^6 - 7*b^7)*d*sin(10*d*x + 10*c) - (128*a^4*b^3 - 352*a^3*b^4 + 355*a^2*b^5 - 166*a*b^6 + 35*b^7)*d*sin(8*d*x + 8*c) - 4*(16*a^3*b^4 - 39*a^2*b^5 + 30*a*b^6 - 7*b^7)*d*sin(6*d*x + 6*c) + 2*(8*a^3*b^4 - 23*a^2*b^5 + 22*a*b^6 - 7*b^7)*d*sin(4*d*x + 4*c) + 4*(a^2*b^5 - 2*a*b^6 + b^7)*d*sin(2*d*x + 2*c))*sin(16*d*x + 16*c) + 32*(2*(8*a^3*b^4 - 23*a^2*b^5 + 22*a*b^6 - 7*b^7)*d*sin(12*d*x + 12*c) - 4*(16*a^3*b^4 - 39*a^2*b^5 + 30*a*b^6 - 7*b^7)*d*sin(10*d*x + 10*c) - (128*a^4*b^3 - 352*a^3*b^4 + 355*a^2*b^5 - 166*a*b^6 + 35*b^7)*d*sin(8*d*x + 8*c) - 4*(16*a^3*b^4 - 39*a^2*b^5 + 30*a*b^6 - 7*b^7)*d*sin(6*d*x + 6*c) + 2*(8*a^3*b^4 - 23*a^2*b^5 + 22*a*b^6 - 7*b^7)*d*sin(4*d*x + 4*c) + 4*(a^2*b^5 - 2*a*b^6 + b^7)*d*sin(2*d*x + 2*c))*sin(14*d*x + 14*c) - 16*(4*(128*a^4*b^3 - 424*a^3*b^4 + 513*a^2*b^5 - 266*a*b^6 + 49*b^7)*d*sin(10*d*x + 10*c) + (1024*a^5*b^2 - 3712*a^4*b^3 + 5304*a^3*b^4 - 3813*a^2*b^5 + 1442*a*b^6 - 245*b^7)*d*sin(8*d*x + 8*c) + 4*(128*a^4*b^3 - 424*a^3*b^4 + 513*a^2*b^5 - 266*a*b^6 + 49*b^7)*d*sin(6*d*x + 6*c) - 2*(64*a^4*b^3 - 240*a^3*b^4 + 337*a^2*b^5 - 210*a*b^6 + 49*b^7)*d*sin(4*d*x + 4*c) - 4*(8*a^3*b^4 - 23*a^2*b^5 + 22*a*b^6 - 7*b^7)*d*sin(2*d*x + 2*c))*sin(12*d*x + 12*c) + 32*((2048*a^5*b^2 - 6528*a^4*b^3 + 8144*a^3*b^4 - 5141*a^2*b^5 + 1722*a*b^6 - 245*b^7)*d*sin(8*d*x + 8*c) + 4*(256*a^4*b^3 - 736*a^3*b^4 + 753*a^2*b^5 - 322*a*b^6 + 49*b^7)*d*sin(6*d*x + 6*c) - 2*(128*a^4*b^3 - 424*a^3*b^4 + 513*a^2*b^5 - 266*a*b^6 + 49*b^7)*d*sin(4*d*x + 4*c) - 4*(16*a^3*b^4 - 39*a^2*b^5 + 30*a*b^6 - 7*b^7)*d*sin(2*d*x + 2*c))*sin(10*d*x + 10*c) + 16*(2*(2048*a^5*b^2 - 6528*a^4*b^3 + 8144*a^3*b^4 - 5141*a^2*b^5 + 1722*a*b^6 - 245*b^7)*d*sin(6*d*x + 6*c) - (1024*a^5*b^2 - 3712*a^4*b^3 + 5304*a^3*b^4 - 3813*a^2*b^5 + 1442*a*b^6 - 245*b^7)*d*sin(4*d*x + 4*c) - 2*(128*a^4*b^3 - 352*a^3*b^4 + 355*a^2*b^5 - 166*a*b^6 + 35*b^7)*d*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) - 64*((128*a^4*b^3 - 424*a^3*b^4 + 513*a^2*b^5 - 266*a*b^6 + 49*b^7)*d*sin(4*d*x + 4*c) + 2*(16*a^3*b^4 - 39*a^2*b^5 + 30*a*b^6 - 7*b^7)*d*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))","F",0
231,0,0,0,0.000000," ","integrate(sin(d*x+c)^6/(a-b*sin(d*x+c)^4)^3,x, algorithm=""maxima"")","-\frac{4 \, {\left(32 \, a^{3} b^{2} - 84 \, a^{2} b^{3} - 83 \, a b^{4} + 21 \, b^{5}\right)} \cos\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + {\left({\left(4 \, a^{2} b^{3} - 13 \, a b^{4} + 3 \, b^{5}\right)} \sin\left(14 \, d x + 14 \, c\right) - 3 \, {\left(8 \, a^{2} b^{3} - 33 \, a b^{4} + 7 \, b^{5}\right)} \sin\left(12 \, d x + 12 \, c\right) + {\left(64 \, a^{3} b^{2} + 68 \, a^{2} b^{3} - 225 \, a b^{4} + 63 \, b^{5}\right)} \sin\left(10 \, d x + 10 \, c\right) - 3 \, {\left(128 \, a^{3} b^{2} + 32 \, a^{2} b^{3} - 61 \, a b^{4} + 35 \, b^{5}\right)} \sin\left(8 \, d x + 8 \, c\right) - {\left(64 \, a^{3} b^{2} + 452 \, a^{2} b^{3} - 9 \, a b^{4} - 105 \, b^{5}\right)} \sin\left(6 \, d x + 6 \, c\right) + 3 \, {\left(40 \, a^{2} b^{3} - 29 \, a b^{4} - 21 \, b^{5}\right)} \sin\left(4 \, d x + 4 \, c\right) - {\left(4 \, a^{2} b^{3} - 37 \, a b^{4} - 21 \, b^{5}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(16 \, d x + 16 \, c\right) + 2 \, {\left(2 \, {\left(32 \, a^{3} b^{2} - 84 \, a^{2} b^{3} - 83 \, a b^{4} + 21 \, b^{5}\right)} \sin\left(12 \, d x + 12 \, c\right) - 8 \, {\left(64 \, a^{3} b^{2} - 84 \, a^{2} b^{3} - 43 \, a b^{4} + 21 \, b^{5}\right)} \sin\left(10 \, d x + 10 \, c\right) - {\left(512 \, a^{4} b - 3584 \, a^{3} b^{2} + 1388 \, a^{2} b^{3} - 11 \, a b^{4} - 315 \, b^{5}\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(172 \, a^{2} b^{3} - 37 \, a b^{4} - 21 \, b^{5}\right)} \sin\left(6 \, d x + 6 \, c\right) + 2 \, {\left(32 \, a^{3} b^{2} - 372 \, a^{2} b^{3} + 289 \, a b^{4} + 105 \, b^{5}\right)} \sin\left(4 \, d x + 4 \, c\right) + 8 \, {\left(4 \, a^{2} b^{3} - 25 \, a b^{4} - 9 \, b^{5}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(14 \, d x + 14 \, c\right) - 2 \, {\left(2 \, {\left(512 \, a^{4} b - 672 \, a^{3} b^{2} + 1228 \, a^{2} b^{3} + 21 \, a b^{4} - 147 \, b^{5}\right)} \sin\left(10 \, d x + 10 \, c\right) - 3 \, {\left(3072 \, a^{4} b - 6272 \, a^{3} b^{2} + 2920 \, a^{2} b^{3} - 413 \, a b^{4} - 245 \, b^{5}\right)} \sin\left(8 \, d x + 8 \, c\right) - 2 \, {\left(512 \, a^{4} b + 3936 \, a^{3} b^{2} - 6740 \, a^{2} b^{3} + 1281 \, a b^{4} + 441 \, b^{5}\right)} \sin\left(6 \, d x + 6 \, c\right) + 12 \, {\left(192 \, a^{3} b^{2} - 416 \, a^{2} b^{3} + 161 \, a b^{4} + 49 \, b^{5}\right)} \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(32 \, a^{3} b^{2} - 372 \, a^{2} b^{3} + 289 \, a b^{4} + 105 \, b^{5}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(12 \, d x + 12 \, c\right) - 2 \, {\left({\left(8192 \, a^{5} + 27136 \, a^{4} b - 37696 \, a^{3} b^{2} + 17644 \, a^{2} b^{3} - 2079 \, a b^{4} - 735 \, b^{5}\right)} \sin\left(8 \, d x + 8 \, c\right) + 8 \, {\left(1024 \, a^{4} b + 3712 \, a^{3} b^{2} - 3692 \, a^{2} b^{3} + 483 \, a b^{4} + 147 \, b^{5}\right)} \sin\left(6 \, d x + 6 \, c\right) - 2 \, {\left(512 \, a^{4} b + 3936 \, a^{3} b^{2} - 6740 \, a^{2} b^{3} + 1281 \, a b^{4} + 441 \, b^{5}\right)} \sin\left(4 \, d x + 4 \, c\right) - 16 \, {\left(172 \, a^{2} b^{3} - 37 \, a b^{4} - 21 \, b^{5}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(10 \, d x + 10 \, c\right) - 2 \, {\left({\left(8192 \, a^{5} + 27136 \, a^{4} b - 37696 \, a^{3} b^{2} + 17644 \, a^{2} b^{3} - 2079 \, a b^{4} - 735 \, b^{5}\right)} \sin\left(6 \, d x + 6 \, c\right) - 3 \, {\left(3072 \, a^{4} b - 6272 \, a^{3} b^{2} + 2920 \, a^{2} b^{3} - 413 \, a b^{4} - 245 \, b^{5}\right)} \sin\left(4 \, d x + 4 \, c\right) + {\left(512 \, a^{4} b - 3584 \, a^{3} b^{2} + 1388 \, a^{2} b^{3} - 11 \, a b^{4} - 315 \, b^{5}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) - 4 \, {\left({\left(512 \, a^{4} b - 672 \, a^{3} b^{2} + 1228 \, a^{2} b^{3} + 21 \, a b^{4} - 147 \, b^{5}\right)} \sin\left(4 \, d x + 4 \, c\right) + 4 \, {\left(64 \, a^{3} b^{2} - 84 \, a^{2} b^{3} - 43 \, a b^{4} + 21 \, b^{5}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left({\left(a^{3} b^{5} - 2 \, a^{2} b^{6} + a b^{7}\right)} d \cos\left(16 \, d x + 16 \, c\right)^{2} + 64 \, {\left(a^{3} b^{5} - 2 \, a^{2} b^{6} + a b^{7}\right)} d \cos\left(14 \, d x + 14 \, c\right)^{2} + 16 \, {\left(64 \, a^{5} b^{3} - 240 \, a^{4} b^{4} + 337 \, a^{3} b^{5} - 210 \, a^{2} b^{6} + 49 \, a b^{7}\right)} d \cos\left(12 \, d x + 12 \, c\right)^{2} + 64 \, {\left(256 \, a^{5} b^{3} - 736 \, a^{4} b^{4} + 753 \, a^{3} b^{5} - 322 \, a^{2} b^{6} + 49 \, a b^{7}\right)} d \cos\left(10 \, d x + 10 \, c\right)^{2} + 4 \, {\left(16384 \, a^{7} b - 57344 \, a^{6} b^{2} + 83712 \, a^{5} b^{3} - 67648 \, a^{4} b^{4} + 32841 \, a^{3} b^{5} - 9170 \, a^{2} b^{6} + 1225 \, a b^{7}\right)} d \cos\left(8 \, d x + 8 \, c\right)^{2} + 64 \, {\left(256 \, a^{5} b^{3} - 736 \, a^{4} b^{4} + 753 \, a^{3} b^{5} - 322 \, a^{2} b^{6} + 49 \, a b^{7}\right)} d \cos\left(6 \, d x + 6 \, c\right)^{2} + 16 \, {\left(64 \, a^{5} b^{3} - 240 \, a^{4} b^{4} + 337 \, a^{3} b^{5} - 210 \, a^{2} b^{6} + 49 \, a b^{7}\right)} d \cos\left(4 \, d x + 4 \, c\right)^{2} + 64 \, {\left(a^{3} b^{5} - 2 \, a^{2} b^{6} + a b^{7}\right)} d \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{3} b^{5} - 2 \, a^{2} b^{6} + a b^{7}\right)} d \sin\left(16 \, d x + 16 \, c\right)^{2} + 64 \, {\left(a^{3} b^{5} - 2 \, a^{2} b^{6} + a b^{7}\right)} d \sin\left(14 \, d x + 14 \, c\right)^{2} + 16 \, {\left(64 \, a^{5} b^{3} - 240 \, a^{4} b^{4} + 337 \, a^{3} b^{5} - 210 \, a^{2} b^{6} + 49 \, a b^{7}\right)} d \sin\left(12 \, d x + 12 \, c\right)^{2} + 64 \, {\left(256 \, a^{5} b^{3} - 736 \, a^{4} b^{4} + 753 \, a^{3} b^{5} - 322 \, a^{2} b^{6} + 49 \, a b^{7}\right)} d \sin\left(10 \, d x + 10 \, c\right)^{2} + 4 \, {\left(16384 \, a^{7} b - 57344 \, a^{6} b^{2} + 83712 \, a^{5} b^{3} - 67648 \, a^{4} b^{4} + 32841 \, a^{3} b^{5} - 9170 \, a^{2} b^{6} + 1225 \, a b^{7}\right)} d \sin\left(8 \, d x + 8 \, c\right)^{2} + 64 \, {\left(256 \, a^{5} b^{3} - 736 \, a^{4} b^{4} + 753 \, a^{3} b^{5} - 322 \, a^{2} b^{6} + 49 \, a b^{7}\right)} d \sin\left(6 \, d x + 6 \, c\right)^{2} + 16 \, {\left(64 \, a^{5} b^{3} - 240 \, a^{4} b^{4} + 337 \, a^{3} b^{5} - 210 \, a^{2} b^{6} + 49 \, a b^{7}\right)} d \sin\left(4 \, d x + 4 \, c\right)^{2} + 64 \, {\left(8 \, a^{4} b^{4} - 23 \, a^{3} b^{5} + 22 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 64 \, {\left(a^{3} b^{5} - 2 \, a^{2} b^{6} + a b^{7}\right)} d \sin\left(2 \, d x + 2 \, c\right)^{2} - 16 \, {\left(a^{3} b^{5} - 2 \, a^{2} b^{6} + a b^{7}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{3} b^{5} - 2 \, a^{2} b^{6} + a b^{7}\right)} d - 2 \, {\left(8 \, {\left(a^{3} b^{5} - 2 \, a^{2} b^{6} + a b^{7}\right)} d \cos\left(14 \, d x + 14 \, c\right) + 4 \, {\left(8 \, a^{4} b^{4} - 23 \, a^{3} b^{5} + 22 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \cos\left(12 \, d x + 12 \, c\right) - 8 \, {\left(16 \, a^{4} b^{4} - 39 \, a^{3} b^{5} + 30 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \cos\left(10 \, d x + 10 \, c\right) - 2 \, {\left(128 \, a^{5} b^{3} - 352 \, a^{4} b^{4} + 355 \, a^{3} b^{5} - 166 \, a^{2} b^{6} + 35 \, a b^{7}\right)} d \cos\left(8 \, d x + 8 \, c\right) - 8 \, {\left(16 \, a^{4} b^{4} - 39 \, a^{3} b^{5} + 30 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \cos\left(6 \, d x + 6 \, c\right) + 4 \, {\left(8 \, a^{4} b^{4} - 23 \, a^{3} b^{5} + 22 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(a^{3} b^{5} - 2 \, a^{2} b^{6} + a b^{7}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(a^{3} b^{5} - 2 \, a^{2} b^{6} + a b^{7}\right)} d\right)} \cos\left(16 \, d x + 16 \, c\right) + 16 \, {\left(4 \, {\left(8 \, a^{4} b^{4} - 23 \, a^{3} b^{5} + 22 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \cos\left(12 \, d x + 12 \, c\right) - 8 \, {\left(16 \, a^{4} b^{4} - 39 \, a^{3} b^{5} + 30 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \cos\left(10 \, d x + 10 \, c\right) - 2 \, {\left(128 \, a^{5} b^{3} - 352 \, a^{4} b^{4} + 355 \, a^{3} b^{5} - 166 \, a^{2} b^{6} + 35 \, a b^{7}\right)} d \cos\left(8 \, d x + 8 \, c\right) - 8 \, {\left(16 \, a^{4} b^{4} - 39 \, a^{3} b^{5} + 30 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \cos\left(6 \, d x + 6 \, c\right) + 4 \, {\left(8 \, a^{4} b^{4} - 23 \, a^{3} b^{5} + 22 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(a^{3} b^{5} - 2 \, a^{2} b^{6} + a b^{7}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(a^{3} b^{5} - 2 \, a^{2} b^{6} + a b^{7}\right)} d\right)} \cos\left(14 \, d x + 14 \, c\right) - 8 \, {\left(8 \, {\left(128 \, a^{5} b^{3} - 424 \, a^{4} b^{4} + 513 \, a^{3} b^{5} - 266 \, a^{2} b^{6} + 49 \, a b^{7}\right)} d \cos\left(10 \, d x + 10 \, c\right) + 2 \, {\left(1024 \, a^{6} b^{2} - 3712 \, a^{5} b^{3} + 5304 \, a^{4} b^{4} - 3813 \, a^{3} b^{5} + 1442 \, a^{2} b^{6} - 245 \, a b^{7}\right)} d \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(128 \, a^{5} b^{3} - 424 \, a^{4} b^{4} + 513 \, a^{3} b^{5} - 266 \, a^{2} b^{6} + 49 \, a b^{7}\right)} d \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(64 \, a^{5} b^{3} - 240 \, a^{4} b^{4} + 337 \, a^{3} b^{5} - 210 \, a^{2} b^{6} + 49 \, a b^{7}\right)} d \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(8 \, a^{4} b^{4} - 23 \, a^{3} b^{5} + 22 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(8 \, a^{4} b^{4} - 23 \, a^{3} b^{5} + 22 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d\right)} \cos\left(12 \, d x + 12 \, c\right) + 16 \, {\left(2 \, {\left(2048 \, a^{6} b^{2} - 6528 \, a^{5} b^{3} + 8144 \, a^{4} b^{4} - 5141 \, a^{3} b^{5} + 1722 \, a^{2} b^{6} - 245 \, a b^{7}\right)} d \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(256 \, a^{5} b^{3} - 736 \, a^{4} b^{4} + 753 \, a^{3} b^{5} - 322 \, a^{2} b^{6} + 49 \, a b^{7}\right)} d \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(128 \, a^{5} b^{3} - 424 \, a^{4} b^{4} + 513 \, a^{3} b^{5} - 266 \, a^{2} b^{6} + 49 \, a b^{7}\right)} d \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(16 \, a^{4} b^{4} - 39 \, a^{3} b^{5} + 30 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(16 \, a^{4} b^{4} - 39 \, a^{3} b^{5} + 30 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d\right)} \cos\left(10 \, d x + 10 \, c\right) + 4 \, {\left(8 \, {\left(2048 \, a^{6} b^{2} - 6528 \, a^{5} b^{3} + 8144 \, a^{4} b^{4} - 5141 \, a^{3} b^{5} + 1722 \, a^{2} b^{6} - 245 \, a b^{7}\right)} d \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(1024 \, a^{6} b^{2} - 3712 \, a^{5} b^{3} + 5304 \, a^{4} b^{4} - 3813 \, a^{3} b^{5} + 1442 \, a^{2} b^{6} - 245 \, a b^{7}\right)} d \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(128 \, a^{5} b^{3} - 352 \, a^{4} b^{4} + 355 \, a^{3} b^{5} - 166 \, a^{2} b^{6} + 35 \, a b^{7}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(128 \, a^{5} b^{3} - 352 \, a^{4} b^{4} + 355 \, a^{3} b^{5} - 166 \, a^{2} b^{6} + 35 \, a b^{7}\right)} d\right)} \cos\left(8 \, d x + 8 \, c\right) - 16 \, {\left(4 \, {\left(128 \, a^{5} b^{3} - 424 \, a^{4} b^{4} + 513 \, a^{3} b^{5} - 266 \, a^{2} b^{6} + 49 \, a b^{7}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(16 \, a^{4} b^{4} - 39 \, a^{3} b^{5} + 30 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(16 \, a^{4} b^{4} - 39 \, a^{3} b^{5} + 30 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d\right)} \cos\left(6 \, d x + 6 \, c\right) + 8 \, {\left(8 \, {\left(8 \, a^{4} b^{4} - 23 \, a^{3} b^{5} + 22 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(8 \, a^{4} b^{4} - 23 \, a^{3} b^{5} + 22 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(4 \, {\left(a^{3} b^{5} - 2 \, a^{2} b^{6} + a b^{7}\right)} d \sin\left(14 \, d x + 14 \, c\right) + 2 \, {\left(8 \, a^{4} b^{4} - 23 \, a^{3} b^{5} + 22 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \sin\left(12 \, d x + 12 \, c\right) - 4 \, {\left(16 \, a^{4} b^{4} - 39 \, a^{3} b^{5} + 30 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \sin\left(10 \, d x + 10 \, c\right) - {\left(128 \, a^{5} b^{3} - 352 \, a^{4} b^{4} + 355 \, a^{3} b^{5} - 166 \, a^{2} b^{6} + 35 \, a b^{7}\right)} d \sin\left(8 \, d x + 8 \, c\right) - 4 \, {\left(16 \, a^{4} b^{4} - 39 \, a^{3} b^{5} + 30 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \sin\left(6 \, d x + 6 \, c\right) + 2 \, {\left(8 \, a^{4} b^{4} - 23 \, a^{3} b^{5} + 22 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a^{3} b^{5} - 2 \, a^{2} b^{6} + a b^{7}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(16 \, d x + 16 \, c\right) + 32 \, {\left(2 \, {\left(8 \, a^{4} b^{4} - 23 \, a^{3} b^{5} + 22 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \sin\left(12 \, d x + 12 \, c\right) - 4 \, {\left(16 \, a^{4} b^{4} - 39 \, a^{3} b^{5} + 30 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \sin\left(10 \, d x + 10 \, c\right) - {\left(128 \, a^{5} b^{3} - 352 \, a^{4} b^{4} + 355 \, a^{3} b^{5} - 166 \, a^{2} b^{6} + 35 \, a b^{7}\right)} d \sin\left(8 \, d x + 8 \, c\right) - 4 \, {\left(16 \, a^{4} b^{4} - 39 \, a^{3} b^{5} + 30 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \sin\left(6 \, d x + 6 \, c\right) + 2 \, {\left(8 \, a^{4} b^{4} - 23 \, a^{3} b^{5} + 22 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a^{3} b^{5} - 2 \, a^{2} b^{6} + a b^{7}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(14 \, d x + 14 \, c\right) - 16 \, {\left(4 \, {\left(128 \, a^{5} b^{3} - 424 \, a^{4} b^{4} + 513 \, a^{3} b^{5} - 266 \, a^{2} b^{6} + 49 \, a b^{7}\right)} d \sin\left(10 \, d x + 10 \, c\right) + {\left(1024 \, a^{6} b^{2} - 3712 \, a^{5} b^{3} + 5304 \, a^{4} b^{4} - 3813 \, a^{3} b^{5} + 1442 \, a^{2} b^{6} - 245 \, a b^{7}\right)} d \sin\left(8 \, d x + 8 \, c\right) + 4 \, {\left(128 \, a^{5} b^{3} - 424 \, a^{4} b^{4} + 513 \, a^{3} b^{5} - 266 \, a^{2} b^{6} + 49 \, a b^{7}\right)} d \sin\left(6 \, d x + 6 \, c\right) - 2 \, {\left(64 \, a^{5} b^{3} - 240 \, a^{4} b^{4} + 337 \, a^{3} b^{5} - 210 \, a^{2} b^{6} + 49 \, a b^{7}\right)} d \sin\left(4 \, d x + 4 \, c\right) - 4 \, {\left(8 \, a^{4} b^{4} - 23 \, a^{3} b^{5} + 22 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(12 \, d x + 12 \, c\right) + 32 \, {\left({\left(2048 \, a^{6} b^{2} - 6528 \, a^{5} b^{3} + 8144 \, a^{4} b^{4} - 5141 \, a^{3} b^{5} + 1722 \, a^{2} b^{6} - 245 \, a b^{7}\right)} d \sin\left(8 \, d x + 8 \, c\right) + 4 \, {\left(256 \, a^{5} b^{3} - 736 \, a^{4} b^{4} + 753 \, a^{3} b^{5} - 322 \, a^{2} b^{6} + 49 \, a b^{7}\right)} d \sin\left(6 \, d x + 6 \, c\right) - 2 \, {\left(128 \, a^{5} b^{3} - 424 \, a^{4} b^{4} + 513 \, a^{3} b^{5} - 266 \, a^{2} b^{6} + 49 \, a b^{7}\right)} d \sin\left(4 \, d x + 4 \, c\right) - 4 \, {\left(16 \, a^{4} b^{4} - 39 \, a^{3} b^{5} + 30 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + 16 \, {\left(2 \, {\left(2048 \, a^{6} b^{2} - 6528 \, a^{5} b^{3} + 8144 \, a^{4} b^{4} - 5141 \, a^{3} b^{5} + 1722 \, a^{2} b^{6} - 245 \, a b^{7}\right)} d \sin\left(6 \, d x + 6 \, c\right) - {\left(1024 \, a^{6} b^{2} - 3712 \, a^{5} b^{3} + 5304 \, a^{4} b^{4} - 3813 \, a^{3} b^{5} + 1442 \, a^{2} b^{6} - 245 \, a b^{7}\right)} d \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(128 \, a^{5} b^{3} - 352 \, a^{4} b^{4} + 355 \, a^{3} b^{5} - 166 \, a^{2} b^{6} + 35 \, a b^{7}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) - 64 \, {\left({\left(128 \, a^{5} b^{3} - 424 \, a^{4} b^{4} + 513 \, a^{3} b^{5} - 266 \, a^{2} b^{6} + 49 \, a b^{7}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(16 \, a^{4} b^{4} - 39 \, a^{3} b^{5} + 30 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \int \frac{4 \, {\left(4 \, a^{2} b - 13 \, a b^{2} + 3 \, b^{3}\right)} \cos\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(56 \, a^{2} b - 29 \, a b^{2} + 3 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(4 \, a^{2} b - 13 \, a b^{2} + 3 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(4 \, a^{2} b - 13 \, a b^{2} + 3 \, b^{3}\right)} \sin\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(56 \, a^{2} b - 29 \, a b^{2} + 3 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, {\left(32 \, a^{3} - 116 \, a^{2} b + 147 \, a b^{2} - 21 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, {\left(4 \, a^{2} b - 13 \, a b^{2} + 3 \, b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - {\left({\left(4 \, a^{2} b - 13 \, a b^{2} + 3 \, b^{3}\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(7 \, a b^{2} - b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right) + {\left(4 \, a^{2} b - 13 \, a b^{2} + 3 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) - {\left(4 \, a^{2} b - 13 \, a b^{2} + 3 \, b^{3} - 2 \, {\left(32 \, a^{3} - 116 \, a^{2} b + 147 \, a b^{2} - 21 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(4 \, a^{2} b - 13 \, a b^{2} + 3 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left(21 \, a b^{2} - 3 \, b^{3} - {\left(32 \, a^{3} - 116 \, a^{2} b + 147 \, a b^{2} - 21 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - {\left(4 \, a^{2} b - 13 \, a b^{2} + 3 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right) - {\left({\left(4 \, a^{2} b - 13 \, a b^{2} + 3 \, b^{3}\right)} \sin\left(6 \, d x + 6 \, c\right) + 6 \, {\left(7 \, a b^{2} - b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) + {\left(4 \, a^{2} b - 13 \, a b^{2} + 3 \, b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 2 \, {\left({\left(32 \, a^{3} - 116 \, a^{2} b + 147 \, a b^{2} - 21 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) + 4 \, {\left(4 \, a^{2} b - 13 \, a b^{2} + 3 \, b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}{a^{3} b^{3} - 2 \, a^{2} b^{4} + a b^{5} + {\left(a^{3} b^{3} - 2 \, a^{2} b^{4} + a b^{5}\right)} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a^{3} b^{3} - 2 \, a^{2} b^{4} + a b^{5}\right)} \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{5} b - 176 \, a^{4} b^{2} + 169 \, a^{3} b^{3} - 66 \, a^{2} b^{4} + 9 \, a b^{5}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(a^{3} b^{3} - 2 \, a^{2} b^{4} + a b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{3} b^{3} - 2 \, a^{2} b^{4} + a b^{5}\right)} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a^{3} b^{3} - 2 \, a^{2} b^{4} + a b^{5}\right)} \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{5} b - 176 \, a^{4} b^{2} + 169 \, a^{3} b^{3} - 66 \, a^{2} b^{4} + 9 \, a b^{5}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(8 \, a^{4} b^{2} - 19 \, a^{3} b^{3} + 14 \, a^{2} b^{4} - 3 \, a b^{5}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, {\left(a^{3} b^{3} - 2 \, a^{2} b^{4} + a b^{5}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{3} b^{3} - 2 \, a^{2} b^{4} + a b^{5} - 4 \, {\left(a^{3} b^{3} - 2 \, a^{2} b^{4} + a b^{5}\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left(8 \, a^{4} b^{2} - 19 \, a^{3} b^{3} + 14 \, a^{2} b^{4} - 3 \, a b^{5}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a^{3} b^{3} - 2 \, a^{2} b^{4} + a b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) - 8 \, {\left(a^{3} b^{3} - 2 \, a^{2} b^{4} + a b^{5} - 2 \, {\left(8 \, a^{4} b^{2} - 19 \, a^{3} b^{3} + 14 \, a^{2} b^{4} - 3 \, a b^{5}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a^{3} b^{3} - 2 \, a^{2} b^{4} + a b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(8 \, a^{4} b^{2} - 19 \, a^{3} b^{3} + 14 \, a^{2} b^{4} - 3 \, a b^{5} - 4 \, {\left(8 \, a^{4} b^{2} - 19 \, a^{3} b^{3} + 14 \, a^{2} b^{4} - 3 \, a b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(a^{3} b^{3} - 2 \, a^{2} b^{4} + a b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right) - 4 \, {\left(2 \, {\left(a^{3} b^{3} - 2 \, a^{2} b^{4} + a b^{5}\right)} \sin\left(6 \, d x + 6 \, c\right) + {\left(8 \, a^{4} b^{2} - 19 \, a^{3} b^{3} + 14 \, a^{2} b^{4} - 3 \, a b^{5}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a^{3} b^{3} - 2 \, a^{2} b^{4} + a b^{5}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left({\left(8 \, a^{4} b^{2} - 19 \, a^{3} b^{3} + 14 \, a^{2} b^{4} - 3 \, a b^{5}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a^{3} b^{3} - 2 \, a^{2} b^{4} + a b^{5}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}\,{d x} + {\left(3 \, a b^{4} + 3 \, b^{5} - {\left(4 \, a^{2} b^{3} - 13 \, a b^{4} + 3 \, b^{5}\right)} \cos\left(14 \, d x + 14 \, c\right) + 3 \, {\left(8 \, a^{2} b^{3} - 33 \, a b^{4} + 7 \, b^{5}\right)} \cos\left(12 \, d x + 12 \, c\right) - {\left(64 \, a^{3} b^{2} + 68 \, a^{2} b^{3} - 225 \, a b^{4} + 63 \, b^{5}\right)} \cos\left(10 \, d x + 10 \, c\right) + 3 \, {\left(128 \, a^{3} b^{2} + 32 \, a^{2} b^{3} - 61 \, a b^{4} + 35 \, b^{5}\right)} \cos\left(8 \, d x + 8 \, c\right) + {\left(64 \, a^{3} b^{2} + 452 \, a^{2} b^{3} - 9 \, a b^{4} - 105 \, b^{5}\right)} \cos\left(6 \, d x + 6 \, c\right) - 3 \, {\left(40 \, a^{2} b^{3} - 29 \, a b^{4} - 21 \, b^{5}\right)} \cos\left(4 \, d x + 4 \, c\right) + {\left(4 \, a^{2} b^{3} - 37 \, a b^{4} - 21 \, b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(16 \, d x + 16 \, c\right) + {\left(4 \, a^{2} b^{3} - 37 \, a b^{4} - 21 \, b^{5} - 4 \, {\left(32 \, a^{3} b^{2} - 84 \, a^{2} b^{3} - 83 \, a b^{4} + 21 \, b^{5}\right)} \cos\left(12 \, d x + 12 \, c\right) + 16 \, {\left(64 \, a^{3} b^{2} - 84 \, a^{2} b^{3} - 43 \, a b^{4} + 21 \, b^{5}\right)} \cos\left(10 \, d x + 10 \, c\right) + 2 \, {\left(512 \, a^{4} b - 3584 \, a^{3} b^{2} + 1388 \, a^{2} b^{3} - 11 \, a b^{4} - 315 \, b^{5}\right)} \cos\left(8 \, d x + 8 \, c\right) - 32 \, {\left(172 \, a^{2} b^{3} - 37 \, a b^{4} - 21 \, b^{5}\right)} \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(32 \, a^{3} b^{2} - 372 \, a^{2} b^{3} + 289 \, a b^{4} + 105 \, b^{5}\right)} \cos\left(4 \, d x + 4 \, c\right) - 16 \, {\left(4 \, a^{2} b^{3} - 25 \, a b^{4} - 9 \, b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(14 \, d x + 14 \, c\right) - {\left(120 \, a^{2} b^{3} - 87 \, a b^{4} - 63 \, b^{5} - 4 \, {\left(512 \, a^{4} b - 672 \, a^{3} b^{2} + 1228 \, a^{2} b^{3} + 21 \, a b^{4} - 147 \, b^{5}\right)} \cos\left(10 \, d x + 10 \, c\right) + 6 \, {\left(3072 \, a^{4} b - 6272 \, a^{3} b^{2} + 2920 \, a^{2} b^{3} - 413 \, a b^{4} - 245 \, b^{5}\right)} \cos\left(8 \, d x + 8 \, c\right) + 4 \, {\left(512 \, a^{4} b + 3936 \, a^{3} b^{2} - 6740 \, a^{2} b^{3} + 1281 \, a b^{4} + 441 \, b^{5}\right)} \cos\left(6 \, d x + 6 \, c\right) - 24 \, {\left(192 \, a^{3} b^{2} - 416 \, a^{2} b^{3} + 161 \, a b^{4} + 49 \, b^{5}\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(32 \, a^{3} b^{2} - 372 \, a^{2} b^{3} + 289 \, a b^{4} + 105 \, b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(12 \, d x + 12 \, c\right) + {\left(64 \, a^{3} b^{2} + 452 \, a^{2} b^{3} - 9 \, a b^{4} - 105 \, b^{5} + 2 \, {\left(8192 \, a^{5} + 27136 \, a^{4} b - 37696 \, a^{3} b^{2} + 17644 \, a^{2} b^{3} - 2079 \, a b^{4} - 735 \, b^{5}\right)} \cos\left(8 \, d x + 8 \, c\right) + 16 \, {\left(1024 \, a^{4} b + 3712 \, a^{3} b^{2} - 3692 \, a^{2} b^{3} + 483 \, a b^{4} + 147 \, b^{5}\right)} \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(512 \, a^{4} b + 3936 \, a^{3} b^{2} - 6740 \, a^{2} b^{3} + 1281 \, a b^{4} + 441 \, b^{5}\right)} \cos\left(4 \, d x + 4 \, c\right) - 32 \, {\left(172 \, a^{2} b^{3} - 37 \, a b^{4} - 21 \, b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + {\left(384 \, a^{3} b^{2} + 96 \, a^{2} b^{3} - 183 \, a b^{4} + 105 \, b^{5} + 2 \, {\left(8192 \, a^{5} + 27136 \, a^{4} b - 37696 \, a^{3} b^{2} + 17644 \, a^{2} b^{3} - 2079 \, a b^{4} - 735 \, b^{5}\right)} \cos\left(6 \, d x + 6 \, c\right) - 6 \, {\left(3072 \, a^{4} b - 6272 \, a^{3} b^{2} + 2920 \, a^{2} b^{3} - 413 \, a b^{4} - 245 \, b^{5}\right)} \cos\left(4 \, d x + 4 \, c\right) + 2 \, {\left(512 \, a^{4} b - 3584 \, a^{3} b^{2} + 1388 \, a^{2} b^{3} - 11 \, a b^{4} - 315 \, b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) - {\left(64 \, a^{3} b^{2} + 68 \, a^{2} b^{3} - 225 \, a b^{4} + 63 \, b^{5} - 4 \, {\left(512 \, a^{4} b - 672 \, a^{3} b^{2} + 1228 \, a^{2} b^{3} + 21 \, a b^{4} - 147 \, b^{5}\right)} \cos\left(4 \, d x + 4 \, c\right) - 16 \, {\left(64 \, a^{3} b^{2} - 84 \, a^{2} b^{3} - 43 \, a b^{4} + 21 \, b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + {\left(24 \, a^{2} b^{3} - 99 \, a b^{4} + 21 \, b^{5} - 4 \, {\left(32 \, a^{3} b^{2} - 84 \, a^{2} b^{3} - 83 \, a b^{4} + 21 \, b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) - {\left(4 \, a^{2} b^{3} - 13 \, a b^{4} + 3 \, b^{5}\right)} \sin\left(2 \, d x + 2 \, c\right)}{16 \, {\left({\left(a^{3} b^{5} - 2 \, a^{2} b^{6} + a b^{7}\right)} d \cos\left(16 \, d x + 16 \, c\right)^{2} + 64 \, {\left(a^{3} b^{5} - 2 \, a^{2} b^{6} + a b^{7}\right)} d \cos\left(14 \, d x + 14 \, c\right)^{2} + 16 \, {\left(64 \, a^{5} b^{3} - 240 \, a^{4} b^{4} + 337 \, a^{3} b^{5} - 210 \, a^{2} b^{6} + 49 \, a b^{7}\right)} d \cos\left(12 \, d x + 12 \, c\right)^{2} + 64 \, {\left(256 \, a^{5} b^{3} - 736 \, a^{4} b^{4} + 753 \, a^{3} b^{5} - 322 \, a^{2} b^{6} + 49 \, a b^{7}\right)} d \cos\left(10 \, d x + 10 \, c\right)^{2} + 4 \, {\left(16384 \, a^{7} b - 57344 \, a^{6} b^{2} + 83712 \, a^{5} b^{3} - 67648 \, a^{4} b^{4} + 32841 \, a^{3} b^{5} - 9170 \, a^{2} b^{6} + 1225 \, a b^{7}\right)} d \cos\left(8 \, d x + 8 \, c\right)^{2} + 64 \, {\left(256 \, a^{5} b^{3} - 736 \, a^{4} b^{4} + 753 \, a^{3} b^{5} - 322 \, a^{2} b^{6} + 49 \, a b^{7}\right)} d \cos\left(6 \, d x + 6 \, c\right)^{2} + 16 \, {\left(64 \, a^{5} b^{3} - 240 \, a^{4} b^{4} + 337 \, a^{3} b^{5} - 210 \, a^{2} b^{6} + 49 \, a b^{7}\right)} d \cos\left(4 \, d x + 4 \, c\right)^{2} + 64 \, {\left(a^{3} b^{5} - 2 \, a^{2} b^{6} + a b^{7}\right)} d \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{3} b^{5} - 2 \, a^{2} b^{6} + a b^{7}\right)} d \sin\left(16 \, d x + 16 \, c\right)^{2} + 64 \, {\left(a^{3} b^{5} - 2 \, a^{2} b^{6} + a b^{7}\right)} d \sin\left(14 \, d x + 14 \, c\right)^{2} + 16 \, {\left(64 \, a^{5} b^{3} - 240 \, a^{4} b^{4} + 337 \, a^{3} b^{5} - 210 \, a^{2} b^{6} + 49 \, a b^{7}\right)} d \sin\left(12 \, d x + 12 \, c\right)^{2} + 64 \, {\left(256 \, a^{5} b^{3} - 736 \, a^{4} b^{4} + 753 \, a^{3} b^{5} - 322 \, a^{2} b^{6} + 49 \, a b^{7}\right)} d \sin\left(10 \, d x + 10 \, c\right)^{2} + 4 \, {\left(16384 \, a^{7} b - 57344 \, a^{6} b^{2} + 83712 \, a^{5} b^{3} - 67648 \, a^{4} b^{4} + 32841 \, a^{3} b^{5} - 9170 \, a^{2} b^{6} + 1225 \, a b^{7}\right)} d \sin\left(8 \, d x + 8 \, c\right)^{2} + 64 \, {\left(256 \, a^{5} b^{3} - 736 \, a^{4} b^{4} + 753 \, a^{3} b^{5} - 322 \, a^{2} b^{6} + 49 \, a b^{7}\right)} d \sin\left(6 \, d x + 6 \, c\right)^{2} + 16 \, {\left(64 \, a^{5} b^{3} - 240 \, a^{4} b^{4} + 337 \, a^{3} b^{5} - 210 \, a^{2} b^{6} + 49 \, a b^{7}\right)} d \sin\left(4 \, d x + 4 \, c\right)^{2} + 64 \, {\left(8 \, a^{4} b^{4} - 23 \, a^{3} b^{5} + 22 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 64 \, {\left(a^{3} b^{5} - 2 \, a^{2} b^{6} + a b^{7}\right)} d \sin\left(2 \, d x + 2 \, c\right)^{2} - 16 \, {\left(a^{3} b^{5} - 2 \, a^{2} b^{6} + a b^{7}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{3} b^{5} - 2 \, a^{2} b^{6} + a b^{7}\right)} d - 2 \, {\left(8 \, {\left(a^{3} b^{5} - 2 \, a^{2} b^{6} + a b^{7}\right)} d \cos\left(14 \, d x + 14 \, c\right) + 4 \, {\left(8 \, a^{4} b^{4} - 23 \, a^{3} b^{5} + 22 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \cos\left(12 \, d x + 12 \, c\right) - 8 \, {\left(16 \, a^{4} b^{4} - 39 \, a^{3} b^{5} + 30 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \cos\left(10 \, d x + 10 \, c\right) - 2 \, {\left(128 \, a^{5} b^{3} - 352 \, a^{4} b^{4} + 355 \, a^{3} b^{5} - 166 \, a^{2} b^{6} + 35 \, a b^{7}\right)} d \cos\left(8 \, d x + 8 \, c\right) - 8 \, {\left(16 \, a^{4} b^{4} - 39 \, a^{3} b^{5} + 30 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \cos\left(6 \, d x + 6 \, c\right) + 4 \, {\left(8 \, a^{4} b^{4} - 23 \, a^{3} b^{5} + 22 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(a^{3} b^{5} - 2 \, a^{2} b^{6} + a b^{7}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(a^{3} b^{5} - 2 \, a^{2} b^{6} + a b^{7}\right)} d\right)} \cos\left(16 \, d x + 16 \, c\right) + 16 \, {\left(4 \, {\left(8 \, a^{4} b^{4} - 23 \, a^{3} b^{5} + 22 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \cos\left(12 \, d x + 12 \, c\right) - 8 \, {\left(16 \, a^{4} b^{4} - 39 \, a^{3} b^{5} + 30 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \cos\left(10 \, d x + 10 \, c\right) - 2 \, {\left(128 \, a^{5} b^{3} - 352 \, a^{4} b^{4} + 355 \, a^{3} b^{5} - 166 \, a^{2} b^{6} + 35 \, a b^{7}\right)} d \cos\left(8 \, d x + 8 \, c\right) - 8 \, {\left(16 \, a^{4} b^{4} - 39 \, a^{3} b^{5} + 30 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \cos\left(6 \, d x + 6 \, c\right) + 4 \, {\left(8 \, a^{4} b^{4} - 23 \, a^{3} b^{5} + 22 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(a^{3} b^{5} - 2 \, a^{2} b^{6} + a b^{7}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(a^{3} b^{5} - 2 \, a^{2} b^{6} + a b^{7}\right)} d\right)} \cos\left(14 \, d x + 14 \, c\right) - 8 \, {\left(8 \, {\left(128 \, a^{5} b^{3} - 424 \, a^{4} b^{4} + 513 \, a^{3} b^{5} - 266 \, a^{2} b^{6} + 49 \, a b^{7}\right)} d \cos\left(10 \, d x + 10 \, c\right) + 2 \, {\left(1024 \, a^{6} b^{2} - 3712 \, a^{5} b^{3} + 5304 \, a^{4} b^{4} - 3813 \, a^{3} b^{5} + 1442 \, a^{2} b^{6} - 245 \, a b^{7}\right)} d \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(128 \, a^{5} b^{3} - 424 \, a^{4} b^{4} + 513 \, a^{3} b^{5} - 266 \, a^{2} b^{6} + 49 \, a b^{7}\right)} d \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(64 \, a^{5} b^{3} - 240 \, a^{4} b^{4} + 337 \, a^{3} b^{5} - 210 \, a^{2} b^{6} + 49 \, a b^{7}\right)} d \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(8 \, a^{4} b^{4} - 23 \, a^{3} b^{5} + 22 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(8 \, a^{4} b^{4} - 23 \, a^{3} b^{5} + 22 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d\right)} \cos\left(12 \, d x + 12 \, c\right) + 16 \, {\left(2 \, {\left(2048 \, a^{6} b^{2} - 6528 \, a^{5} b^{3} + 8144 \, a^{4} b^{4} - 5141 \, a^{3} b^{5} + 1722 \, a^{2} b^{6} - 245 \, a b^{7}\right)} d \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(256 \, a^{5} b^{3} - 736 \, a^{4} b^{4} + 753 \, a^{3} b^{5} - 322 \, a^{2} b^{6} + 49 \, a b^{7}\right)} d \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(128 \, a^{5} b^{3} - 424 \, a^{4} b^{4} + 513 \, a^{3} b^{5} - 266 \, a^{2} b^{6} + 49 \, a b^{7}\right)} d \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(16 \, a^{4} b^{4} - 39 \, a^{3} b^{5} + 30 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(16 \, a^{4} b^{4} - 39 \, a^{3} b^{5} + 30 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d\right)} \cos\left(10 \, d x + 10 \, c\right) + 4 \, {\left(8 \, {\left(2048 \, a^{6} b^{2} - 6528 \, a^{5} b^{3} + 8144 \, a^{4} b^{4} - 5141 \, a^{3} b^{5} + 1722 \, a^{2} b^{6} - 245 \, a b^{7}\right)} d \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(1024 \, a^{6} b^{2} - 3712 \, a^{5} b^{3} + 5304 \, a^{4} b^{4} - 3813 \, a^{3} b^{5} + 1442 \, a^{2} b^{6} - 245 \, a b^{7}\right)} d \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(128 \, a^{5} b^{3} - 352 \, a^{4} b^{4} + 355 \, a^{3} b^{5} - 166 \, a^{2} b^{6} + 35 \, a b^{7}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(128 \, a^{5} b^{3} - 352 \, a^{4} b^{4} + 355 \, a^{3} b^{5} - 166 \, a^{2} b^{6} + 35 \, a b^{7}\right)} d\right)} \cos\left(8 \, d x + 8 \, c\right) - 16 \, {\left(4 \, {\left(128 \, a^{5} b^{3} - 424 \, a^{4} b^{4} + 513 \, a^{3} b^{5} - 266 \, a^{2} b^{6} + 49 \, a b^{7}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(16 \, a^{4} b^{4} - 39 \, a^{3} b^{5} + 30 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(16 \, a^{4} b^{4} - 39 \, a^{3} b^{5} + 30 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d\right)} \cos\left(6 \, d x + 6 \, c\right) + 8 \, {\left(8 \, {\left(8 \, a^{4} b^{4} - 23 \, a^{3} b^{5} + 22 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(8 \, a^{4} b^{4} - 23 \, a^{3} b^{5} + 22 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(4 \, {\left(a^{3} b^{5} - 2 \, a^{2} b^{6} + a b^{7}\right)} d \sin\left(14 \, d x + 14 \, c\right) + 2 \, {\left(8 \, a^{4} b^{4} - 23 \, a^{3} b^{5} + 22 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \sin\left(12 \, d x + 12 \, c\right) - 4 \, {\left(16 \, a^{4} b^{4} - 39 \, a^{3} b^{5} + 30 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \sin\left(10 \, d x + 10 \, c\right) - {\left(128 \, a^{5} b^{3} - 352 \, a^{4} b^{4} + 355 \, a^{3} b^{5} - 166 \, a^{2} b^{6} + 35 \, a b^{7}\right)} d \sin\left(8 \, d x + 8 \, c\right) - 4 \, {\left(16 \, a^{4} b^{4} - 39 \, a^{3} b^{5} + 30 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \sin\left(6 \, d x + 6 \, c\right) + 2 \, {\left(8 \, a^{4} b^{4} - 23 \, a^{3} b^{5} + 22 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a^{3} b^{5} - 2 \, a^{2} b^{6} + a b^{7}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(16 \, d x + 16 \, c\right) + 32 \, {\left(2 \, {\left(8 \, a^{4} b^{4} - 23 \, a^{3} b^{5} + 22 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \sin\left(12 \, d x + 12 \, c\right) - 4 \, {\left(16 \, a^{4} b^{4} - 39 \, a^{3} b^{5} + 30 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \sin\left(10 \, d x + 10 \, c\right) - {\left(128 \, a^{5} b^{3} - 352 \, a^{4} b^{4} + 355 \, a^{3} b^{5} - 166 \, a^{2} b^{6} + 35 \, a b^{7}\right)} d \sin\left(8 \, d x + 8 \, c\right) - 4 \, {\left(16 \, a^{4} b^{4} - 39 \, a^{3} b^{5} + 30 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \sin\left(6 \, d x + 6 \, c\right) + 2 \, {\left(8 \, a^{4} b^{4} - 23 \, a^{3} b^{5} + 22 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a^{3} b^{5} - 2 \, a^{2} b^{6} + a b^{7}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(14 \, d x + 14 \, c\right) - 16 \, {\left(4 \, {\left(128 \, a^{5} b^{3} - 424 \, a^{4} b^{4} + 513 \, a^{3} b^{5} - 266 \, a^{2} b^{6} + 49 \, a b^{7}\right)} d \sin\left(10 \, d x + 10 \, c\right) + {\left(1024 \, a^{6} b^{2} - 3712 \, a^{5} b^{3} + 5304 \, a^{4} b^{4} - 3813 \, a^{3} b^{5} + 1442 \, a^{2} b^{6} - 245 \, a b^{7}\right)} d \sin\left(8 \, d x + 8 \, c\right) + 4 \, {\left(128 \, a^{5} b^{3} - 424 \, a^{4} b^{4} + 513 \, a^{3} b^{5} - 266 \, a^{2} b^{6} + 49 \, a b^{7}\right)} d \sin\left(6 \, d x + 6 \, c\right) - 2 \, {\left(64 \, a^{5} b^{3} - 240 \, a^{4} b^{4} + 337 \, a^{3} b^{5} - 210 \, a^{2} b^{6} + 49 \, a b^{7}\right)} d \sin\left(4 \, d x + 4 \, c\right) - 4 \, {\left(8 \, a^{4} b^{4} - 23 \, a^{3} b^{5} + 22 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(12 \, d x + 12 \, c\right) + 32 \, {\left({\left(2048 \, a^{6} b^{2} - 6528 \, a^{5} b^{3} + 8144 \, a^{4} b^{4} - 5141 \, a^{3} b^{5} + 1722 \, a^{2} b^{6} - 245 \, a b^{7}\right)} d \sin\left(8 \, d x + 8 \, c\right) + 4 \, {\left(256 \, a^{5} b^{3} - 736 \, a^{4} b^{4} + 753 \, a^{3} b^{5} - 322 \, a^{2} b^{6} + 49 \, a b^{7}\right)} d \sin\left(6 \, d x + 6 \, c\right) - 2 \, {\left(128 \, a^{5} b^{3} - 424 \, a^{4} b^{4} + 513 \, a^{3} b^{5} - 266 \, a^{2} b^{6} + 49 \, a b^{7}\right)} d \sin\left(4 \, d x + 4 \, c\right) - 4 \, {\left(16 \, a^{4} b^{4} - 39 \, a^{3} b^{5} + 30 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + 16 \, {\left(2 \, {\left(2048 \, a^{6} b^{2} - 6528 \, a^{5} b^{3} + 8144 \, a^{4} b^{4} - 5141 \, a^{3} b^{5} + 1722 \, a^{2} b^{6} - 245 \, a b^{7}\right)} d \sin\left(6 \, d x + 6 \, c\right) - {\left(1024 \, a^{6} b^{2} - 3712 \, a^{5} b^{3} + 5304 \, a^{4} b^{4} - 3813 \, a^{3} b^{5} + 1442 \, a^{2} b^{6} - 245 \, a b^{7}\right)} d \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(128 \, a^{5} b^{3} - 352 \, a^{4} b^{4} + 355 \, a^{3} b^{5} - 166 \, a^{2} b^{6} + 35 \, a b^{7}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) - 64 \, {\left({\left(128 \, a^{5} b^{3} - 424 \, a^{4} b^{4} + 513 \, a^{3} b^{5} - 266 \, a^{2} b^{6} + 49 \, a b^{7}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(16 \, a^{4} b^{4} - 39 \, a^{3} b^{5} + 30 \, a^{2} b^{6} - 7 \, a b^{7}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)}}"," ",0,"-1/16*(4*(32*a^3*b^2 - 84*a^2*b^3 - 83*a*b^4 + 21*b^5)*cos(4*d*x + 4*c)*sin(2*d*x + 2*c) + ((4*a^2*b^3 - 13*a*b^4 + 3*b^5)*sin(14*d*x + 14*c) - 3*(8*a^2*b^3 - 33*a*b^4 + 7*b^5)*sin(12*d*x + 12*c) + (64*a^3*b^2 + 68*a^2*b^3 - 225*a*b^4 + 63*b^5)*sin(10*d*x + 10*c) - 3*(128*a^3*b^2 + 32*a^2*b^3 - 61*a*b^4 + 35*b^5)*sin(8*d*x + 8*c) - (64*a^3*b^2 + 452*a^2*b^3 - 9*a*b^4 - 105*b^5)*sin(6*d*x + 6*c) + 3*(40*a^2*b^3 - 29*a*b^4 - 21*b^5)*sin(4*d*x + 4*c) - (4*a^2*b^3 - 37*a*b^4 - 21*b^5)*sin(2*d*x + 2*c))*cos(16*d*x + 16*c) + 2*(2*(32*a^3*b^2 - 84*a^2*b^3 - 83*a*b^4 + 21*b^5)*sin(12*d*x + 12*c) - 8*(64*a^3*b^2 - 84*a^2*b^3 - 43*a*b^4 + 21*b^5)*sin(10*d*x + 10*c) - (512*a^4*b - 3584*a^3*b^2 + 1388*a^2*b^3 - 11*a*b^4 - 315*b^5)*sin(8*d*x + 8*c) + 16*(172*a^2*b^3 - 37*a*b^4 - 21*b^5)*sin(6*d*x + 6*c) + 2*(32*a^3*b^2 - 372*a^2*b^3 + 289*a*b^4 + 105*b^5)*sin(4*d*x + 4*c) + 8*(4*a^2*b^3 - 25*a*b^4 - 9*b^5)*sin(2*d*x + 2*c))*cos(14*d*x + 14*c) - 2*(2*(512*a^4*b - 672*a^3*b^2 + 1228*a^2*b^3 + 21*a*b^4 - 147*b^5)*sin(10*d*x + 10*c) - 3*(3072*a^4*b - 6272*a^3*b^2 + 2920*a^2*b^3 - 413*a*b^4 - 245*b^5)*sin(8*d*x + 8*c) - 2*(512*a^4*b + 3936*a^3*b^2 - 6740*a^2*b^3 + 1281*a*b^4 + 441*b^5)*sin(6*d*x + 6*c) + 12*(192*a^3*b^2 - 416*a^2*b^3 + 161*a*b^4 + 49*b^5)*sin(4*d*x + 4*c) - 2*(32*a^3*b^2 - 372*a^2*b^3 + 289*a*b^4 + 105*b^5)*sin(2*d*x + 2*c))*cos(12*d*x + 12*c) - 2*((8192*a^5 + 27136*a^4*b - 37696*a^3*b^2 + 17644*a^2*b^3 - 2079*a*b^4 - 735*b^5)*sin(8*d*x + 8*c) + 8*(1024*a^4*b + 3712*a^3*b^2 - 3692*a^2*b^3 + 483*a*b^4 + 147*b^5)*sin(6*d*x + 6*c) - 2*(512*a^4*b + 3936*a^3*b^2 - 6740*a^2*b^3 + 1281*a*b^4 + 441*b^5)*sin(4*d*x + 4*c) - 16*(172*a^2*b^3 - 37*a*b^4 - 21*b^5)*sin(2*d*x + 2*c))*cos(10*d*x + 10*c) - 2*((8192*a^5 + 27136*a^4*b - 37696*a^3*b^2 + 17644*a^2*b^3 - 2079*a*b^4 - 735*b^5)*sin(6*d*x + 6*c) - 3*(3072*a^4*b - 6272*a^3*b^2 + 2920*a^2*b^3 - 413*a*b^4 - 245*b^5)*sin(4*d*x + 4*c) + (512*a^4*b - 3584*a^3*b^2 + 1388*a^2*b^3 - 11*a*b^4 - 315*b^5)*sin(2*d*x + 2*c))*cos(8*d*x + 8*c) - 4*((512*a^4*b - 672*a^3*b^2 + 1228*a^2*b^3 + 21*a*b^4 - 147*b^5)*sin(4*d*x + 4*c) + 4*(64*a^3*b^2 - 84*a^2*b^3 - 43*a*b^4 + 21*b^5)*sin(2*d*x + 2*c))*cos(6*d*x + 6*c) + 16*((a^3*b^5 - 2*a^2*b^6 + a*b^7)*d*cos(16*d*x + 16*c)^2 + 64*(a^3*b^5 - 2*a^2*b^6 + a*b^7)*d*cos(14*d*x + 14*c)^2 + 16*(64*a^5*b^3 - 240*a^4*b^4 + 337*a^3*b^5 - 210*a^2*b^6 + 49*a*b^7)*d*cos(12*d*x + 12*c)^2 + 64*(256*a^5*b^3 - 736*a^4*b^4 + 753*a^3*b^5 - 322*a^2*b^6 + 49*a*b^7)*d*cos(10*d*x + 10*c)^2 + 4*(16384*a^7*b - 57344*a^6*b^2 + 83712*a^5*b^3 - 67648*a^4*b^4 + 32841*a^3*b^5 - 9170*a^2*b^6 + 1225*a*b^7)*d*cos(8*d*x + 8*c)^2 + 64*(256*a^5*b^3 - 736*a^4*b^4 + 753*a^3*b^5 - 322*a^2*b^6 + 49*a*b^7)*d*cos(6*d*x + 6*c)^2 + 16*(64*a^5*b^3 - 240*a^4*b^4 + 337*a^3*b^5 - 210*a^2*b^6 + 49*a*b^7)*d*cos(4*d*x + 4*c)^2 + 64*(a^3*b^5 - 2*a^2*b^6 + a*b^7)*d*cos(2*d*x + 2*c)^2 + (a^3*b^5 - 2*a^2*b^6 + a*b^7)*d*sin(16*d*x + 16*c)^2 + 64*(a^3*b^5 - 2*a^2*b^6 + a*b^7)*d*sin(14*d*x + 14*c)^2 + 16*(64*a^5*b^3 - 240*a^4*b^4 + 337*a^3*b^5 - 210*a^2*b^6 + 49*a*b^7)*d*sin(12*d*x + 12*c)^2 + 64*(256*a^5*b^3 - 736*a^4*b^4 + 753*a^3*b^5 - 322*a^2*b^6 + 49*a*b^7)*d*sin(10*d*x + 10*c)^2 + 4*(16384*a^7*b - 57344*a^6*b^2 + 83712*a^5*b^3 - 67648*a^4*b^4 + 32841*a^3*b^5 - 9170*a^2*b^6 + 1225*a*b^7)*d*sin(8*d*x + 8*c)^2 + 64*(256*a^5*b^3 - 736*a^4*b^4 + 753*a^3*b^5 - 322*a^2*b^6 + 49*a*b^7)*d*sin(6*d*x + 6*c)^2 + 16*(64*a^5*b^3 - 240*a^4*b^4 + 337*a^3*b^5 - 210*a^2*b^6 + 49*a*b^7)*d*sin(4*d*x + 4*c)^2 + 64*(8*a^4*b^4 - 23*a^3*b^5 + 22*a^2*b^6 - 7*a*b^7)*d*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 64*(a^3*b^5 - 2*a^2*b^6 + a*b^7)*d*sin(2*d*x + 2*c)^2 - 16*(a^3*b^5 - 2*a^2*b^6 + a*b^7)*d*cos(2*d*x + 2*c) + (a^3*b^5 - 2*a^2*b^6 + a*b^7)*d - 2*(8*(a^3*b^5 - 2*a^2*b^6 + a*b^7)*d*cos(14*d*x + 14*c) + 4*(8*a^4*b^4 - 23*a^3*b^5 + 22*a^2*b^6 - 7*a*b^7)*d*cos(12*d*x + 12*c) - 8*(16*a^4*b^4 - 39*a^3*b^5 + 30*a^2*b^6 - 7*a*b^7)*d*cos(10*d*x + 10*c) - 2*(128*a^5*b^3 - 352*a^4*b^4 + 355*a^3*b^5 - 166*a^2*b^6 + 35*a*b^7)*d*cos(8*d*x + 8*c) - 8*(16*a^4*b^4 - 39*a^3*b^5 + 30*a^2*b^6 - 7*a*b^7)*d*cos(6*d*x + 6*c) + 4*(8*a^4*b^4 - 23*a^3*b^5 + 22*a^2*b^6 - 7*a*b^7)*d*cos(4*d*x + 4*c) + 8*(a^3*b^5 - 2*a^2*b^6 + a*b^7)*d*cos(2*d*x + 2*c) - (a^3*b^5 - 2*a^2*b^6 + a*b^7)*d)*cos(16*d*x + 16*c) + 16*(4*(8*a^4*b^4 - 23*a^3*b^5 + 22*a^2*b^6 - 7*a*b^7)*d*cos(12*d*x + 12*c) - 8*(16*a^4*b^4 - 39*a^3*b^5 + 30*a^2*b^6 - 7*a*b^7)*d*cos(10*d*x + 10*c) - 2*(128*a^5*b^3 - 352*a^4*b^4 + 355*a^3*b^5 - 166*a^2*b^6 + 35*a*b^7)*d*cos(8*d*x + 8*c) - 8*(16*a^4*b^4 - 39*a^3*b^5 + 30*a^2*b^6 - 7*a*b^7)*d*cos(6*d*x + 6*c) + 4*(8*a^4*b^4 - 23*a^3*b^5 + 22*a^2*b^6 - 7*a*b^7)*d*cos(4*d*x + 4*c) + 8*(a^3*b^5 - 2*a^2*b^6 + a*b^7)*d*cos(2*d*x + 2*c) - (a^3*b^5 - 2*a^2*b^6 + a*b^7)*d)*cos(14*d*x + 14*c) - 8*(8*(128*a^5*b^3 - 424*a^4*b^4 + 513*a^3*b^5 - 266*a^2*b^6 + 49*a*b^7)*d*cos(10*d*x + 10*c) + 2*(1024*a^6*b^2 - 3712*a^5*b^3 + 5304*a^4*b^4 - 3813*a^3*b^5 + 1442*a^2*b^6 - 245*a*b^7)*d*cos(8*d*x + 8*c) + 8*(128*a^5*b^3 - 424*a^4*b^4 + 513*a^3*b^5 - 266*a^2*b^6 + 49*a*b^7)*d*cos(6*d*x + 6*c) - 4*(64*a^5*b^3 - 240*a^4*b^4 + 337*a^3*b^5 - 210*a^2*b^6 + 49*a*b^7)*d*cos(4*d*x + 4*c) - 8*(8*a^4*b^4 - 23*a^3*b^5 + 22*a^2*b^6 - 7*a*b^7)*d*cos(2*d*x + 2*c) + (8*a^4*b^4 - 23*a^3*b^5 + 22*a^2*b^6 - 7*a*b^7)*d)*cos(12*d*x + 12*c) + 16*(2*(2048*a^6*b^2 - 6528*a^5*b^3 + 8144*a^4*b^4 - 5141*a^3*b^5 + 1722*a^2*b^6 - 245*a*b^7)*d*cos(8*d*x + 8*c) + 8*(256*a^5*b^3 - 736*a^4*b^4 + 753*a^3*b^5 - 322*a^2*b^6 + 49*a*b^7)*d*cos(6*d*x + 6*c) - 4*(128*a^5*b^3 - 424*a^4*b^4 + 513*a^3*b^5 - 266*a^2*b^6 + 49*a*b^7)*d*cos(4*d*x + 4*c) - 8*(16*a^4*b^4 - 39*a^3*b^5 + 30*a^2*b^6 - 7*a*b^7)*d*cos(2*d*x + 2*c) + (16*a^4*b^4 - 39*a^3*b^5 + 30*a^2*b^6 - 7*a*b^7)*d)*cos(10*d*x + 10*c) + 4*(8*(2048*a^6*b^2 - 6528*a^5*b^3 + 8144*a^4*b^4 - 5141*a^3*b^5 + 1722*a^2*b^6 - 245*a*b^7)*d*cos(6*d*x + 6*c) - 4*(1024*a^6*b^2 - 3712*a^5*b^3 + 5304*a^4*b^4 - 3813*a^3*b^5 + 1442*a^2*b^6 - 245*a*b^7)*d*cos(4*d*x + 4*c) - 8*(128*a^5*b^3 - 352*a^4*b^4 + 355*a^3*b^5 - 166*a^2*b^6 + 35*a*b^7)*d*cos(2*d*x + 2*c) + (128*a^5*b^3 - 352*a^4*b^4 + 355*a^3*b^5 - 166*a^2*b^6 + 35*a*b^7)*d)*cos(8*d*x + 8*c) - 16*(4*(128*a^5*b^3 - 424*a^4*b^4 + 513*a^3*b^5 - 266*a^2*b^6 + 49*a*b^7)*d*cos(4*d*x + 4*c) + 8*(16*a^4*b^4 - 39*a^3*b^5 + 30*a^2*b^6 - 7*a*b^7)*d*cos(2*d*x + 2*c) - (16*a^4*b^4 - 39*a^3*b^5 + 30*a^2*b^6 - 7*a*b^7)*d)*cos(6*d*x + 6*c) + 8*(8*(8*a^4*b^4 - 23*a^3*b^5 + 22*a^2*b^6 - 7*a*b^7)*d*cos(2*d*x + 2*c) - (8*a^4*b^4 - 23*a^3*b^5 + 22*a^2*b^6 - 7*a*b^7)*d)*cos(4*d*x + 4*c) - 4*(4*(a^3*b^5 - 2*a^2*b^6 + a*b^7)*d*sin(14*d*x + 14*c) + 2*(8*a^4*b^4 - 23*a^3*b^5 + 22*a^2*b^6 - 7*a*b^7)*d*sin(12*d*x + 12*c) - 4*(16*a^4*b^4 - 39*a^3*b^5 + 30*a^2*b^6 - 7*a*b^7)*d*sin(10*d*x + 10*c) - (128*a^5*b^3 - 352*a^4*b^4 + 355*a^3*b^5 - 166*a^2*b^6 + 35*a*b^7)*d*sin(8*d*x + 8*c) - 4*(16*a^4*b^4 - 39*a^3*b^5 + 30*a^2*b^6 - 7*a*b^7)*d*sin(6*d*x + 6*c) + 2*(8*a^4*b^4 - 23*a^3*b^5 + 22*a^2*b^6 - 7*a*b^7)*d*sin(4*d*x + 4*c) + 4*(a^3*b^5 - 2*a^2*b^6 + a*b^7)*d*sin(2*d*x + 2*c))*sin(16*d*x + 16*c) + 32*(2*(8*a^4*b^4 - 23*a^3*b^5 + 22*a^2*b^6 - 7*a*b^7)*d*sin(12*d*x + 12*c) - 4*(16*a^4*b^4 - 39*a^3*b^5 + 30*a^2*b^6 - 7*a*b^7)*d*sin(10*d*x + 10*c) - (128*a^5*b^3 - 352*a^4*b^4 + 355*a^3*b^5 - 166*a^2*b^6 + 35*a*b^7)*d*sin(8*d*x + 8*c) - 4*(16*a^4*b^4 - 39*a^3*b^5 + 30*a^2*b^6 - 7*a*b^7)*d*sin(6*d*x + 6*c) + 2*(8*a^4*b^4 - 23*a^3*b^5 + 22*a^2*b^6 - 7*a*b^7)*d*sin(4*d*x + 4*c) + 4*(a^3*b^5 - 2*a^2*b^6 + a*b^7)*d*sin(2*d*x + 2*c))*sin(14*d*x + 14*c) - 16*(4*(128*a^5*b^3 - 424*a^4*b^4 + 513*a^3*b^5 - 266*a^2*b^6 + 49*a*b^7)*d*sin(10*d*x + 10*c) + (1024*a^6*b^2 - 3712*a^5*b^3 + 5304*a^4*b^4 - 3813*a^3*b^5 + 1442*a^2*b^6 - 245*a*b^7)*d*sin(8*d*x + 8*c) + 4*(128*a^5*b^3 - 424*a^4*b^4 + 513*a^3*b^5 - 266*a^2*b^6 + 49*a*b^7)*d*sin(6*d*x + 6*c) - 2*(64*a^5*b^3 - 240*a^4*b^4 + 337*a^3*b^5 - 210*a^2*b^6 + 49*a*b^7)*d*sin(4*d*x + 4*c) - 4*(8*a^4*b^4 - 23*a^3*b^5 + 22*a^2*b^6 - 7*a*b^7)*d*sin(2*d*x + 2*c))*sin(12*d*x + 12*c) + 32*((2048*a^6*b^2 - 6528*a^5*b^3 + 8144*a^4*b^4 - 5141*a^3*b^5 + 1722*a^2*b^6 - 245*a*b^7)*d*sin(8*d*x + 8*c) + 4*(256*a^5*b^3 - 736*a^4*b^4 + 753*a^3*b^5 - 322*a^2*b^6 + 49*a*b^7)*d*sin(6*d*x + 6*c) - 2*(128*a^5*b^3 - 424*a^4*b^4 + 513*a^3*b^5 - 266*a^2*b^6 + 49*a*b^7)*d*sin(4*d*x + 4*c) - 4*(16*a^4*b^4 - 39*a^3*b^5 + 30*a^2*b^6 - 7*a*b^7)*d*sin(2*d*x + 2*c))*sin(10*d*x + 10*c) + 16*(2*(2048*a^6*b^2 - 6528*a^5*b^3 + 8144*a^4*b^4 - 5141*a^3*b^5 + 1722*a^2*b^6 - 245*a*b^7)*d*sin(6*d*x + 6*c) - (1024*a^6*b^2 - 3712*a^5*b^3 + 5304*a^4*b^4 - 3813*a^3*b^5 + 1442*a^2*b^6 - 245*a*b^7)*d*sin(4*d*x + 4*c) - 2*(128*a^5*b^3 - 352*a^4*b^4 + 355*a^3*b^5 - 166*a^2*b^6 + 35*a*b^7)*d*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) - 64*((128*a^5*b^3 - 424*a^4*b^4 + 513*a^3*b^5 - 266*a^2*b^6 + 49*a*b^7)*d*sin(4*d*x + 4*c) + 2*(16*a^4*b^4 - 39*a^3*b^5 + 30*a^2*b^6 - 7*a*b^7)*d*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*integrate(-1/8*(4*(4*a^2*b - 13*a*b^2 + 3*b^3)*cos(6*d*x + 6*c)^2 + 12*(56*a^2*b - 29*a*b^2 + 3*b^3)*cos(4*d*x + 4*c)^2 + 4*(4*a^2*b - 13*a*b^2 + 3*b^3)*cos(2*d*x + 2*c)^2 + 4*(4*a^2*b - 13*a*b^2 + 3*b^3)*sin(6*d*x + 6*c)^2 + 12*(56*a^2*b - 29*a*b^2 + 3*b^3)*sin(4*d*x + 4*c)^2 + 2*(32*a^3 - 116*a^2*b + 147*a*b^2 - 21*b^3)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*(4*a^2*b - 13*a*b^2 + 3*b^3)*sin(2*d*x + 2*c)^2 - ((4*a^2*b - 13*a*b^2 + 3*b^3)*cos(6*d*x + 6*c) + 6*(7*a*b^2 - b^3)*cos(4*d*x + 4*c) + (4*a^2*b - 13*a*b^2 + 3*b^3)*cos(2*d*x + 2*c))*cos(8*d*x + 8*c) - (4*a^2*b - 13*a*b^2 + 3*b^3 - 2*(32*a^3 - 116*a^2*b + 147*a*b^2 - 21*b^3)*cos(4*d*x + 4*c) - 8*(4*a^2*b - 13*a*b^2 + 3*b^3)*cos(2*d*x + 2*c))*cos(6*d*x + 6*c) - 2*(21*a*b^2 - 3*b^3 - (32*a^3 - 116*a^2*b + 147*a*b^2 - 21*b^3)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - (4*a^2*b - 13*a*b^2 + 3*b^3)*cos(2*d*x + 2*c) - ((4*a^2*b - 13*a*b^2 + 3*b^3)*sin(6*d*x + 6*c) + 6*(7*a*b^2 - b^3)*sin(4*d*x + 4*c) + (4*a^2*b - 13*a*b^2 + 3*b^3)*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 2*((32*a^3 - 116*a^2*b + 147*a*b^2 - 21*b^3)*sin(4*d*x + 4*c) + 4*(4*a^2*b - 13*a*b^2 + 3*b^3)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))/(a^3*b^3 - 2*a^2*b^4 + a*b^5 + (a^3*b^3 - 2*a^2*b^4 + a*b^5)*cos(8*d*x + 8*c)^2 + 16*(a^3*b^3 - 2*a^2*b^4 + a*b^5)*cos(6*d*x + 6*c)^2 + 4*(64*a^5*b - 176*a^4*b^2 + 169*a^3*b^3 - 66*a^2*b^4 + 9*a*b^5)*cos(4*d*x + 4*c)^2 + 16*(a^3*b^3 - 2*a^2*b^4 + a*b^5)*cos(2*d*x + 2*c)^2 + (a^3*b^3 - 2*a^2*b^4 + a*b^5)*sin(8*d*x + 8*c)^2 + 16*(a^3*b^3 - 2*a^2*b^4 + a*b^5)*sin(6*d*x + 6*c)^2 + 4*(64*a^5*b - 176*a^4*b^2 + 169*a^3*b^3 - 66*a^2*b^4 + 9*a*b^5)*sin(4*d*x + 4*c)^2 + 16*(8*a^4*b^2 - 19*a^3*b^3 + 14*a^2*b^4 - 3*a*b^5)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*(a^3*b^3 - 2*a^2*b^4 + a*b^5)*sin(2*d*x + 2*c)^2 + 2*(a^3*b^3 - 2*a^2*b^4 + a*b^5 - 4*(a^3*b^3 - 2*a^2*b^4 + a*b^5)*cos(6*d*x + 6*c) - 2*(8*a^4*b^2 - 19*a^3*b^3 + 14*a^2*b^4 - 3*a*b^5)*cos(4*d*x + 4*c) - 4*(a^3*b^3 - 2*a^2*b^4 + a*b^5)*cos(2*d*x + 2*c))*cos(8*d*x + 8*c) - 8*(a^3*b^3 - 2*a^2*b^4 + a*b^5 - 2*(8*a^4*b^2 - 19*a^3*b^3 + 14*a^2*b^4 - 3*a*b^5)*cos(4*d*x + 4*c) - 4*(a^3*b^3 - 2*a^2*b^4 + a*b^5)*cos(2*d*x + 2*c))*cos(6*d*x + 6*c) - 4*(8*a^4*b^2 - 19*a^3*b^3 + 14*a^2*b^4 - 3*a*b^5 - 4*(8*a^4*b^2 - 19*a^3*b^3 + 14*a^2*b^4 - 3*a*b^5)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 8*(a^3*b^3 - 2*a^2*b^4 + a*b^5)*cos(2*d*x + 2*c) - 4*(2*(a^3*b^3 - 2*a^2*b^4 + a*b^5)*sin(6*d*x + 6*c) + (8*a^4*b^2 - 19*a^3*b^3 + 14*a^2*b^4 - 3*a*b^5)*sin(4*d*x + 4*c) + 2*(a^3*b^3 - 2*a^2*b^4 + a*b^5)*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*((8*a^4*b^2 - 19*a^3*b^3 + 14*a^2*b^4 - 3*a*b^5)*sin(4*d*x + 4*c) + 2*(a^3*b^3 - 2*a^2*b^4 + a*b^5)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c)), x) + (3*a*b^4 + 3*b^5 - (4*a^2*b^3 - 13*a*b^4 + 3*b^5)*cos(14*d*x + 14*c) + 3*(8*a^2*b^3 - 33*a*b^4 + 7*b^5)*cos(12*d*x + 12*c) - (64*a^3*b^2 + 68*a^2*b^3 - 225*a*b^4 + 63*b^5)*cos(10*d*x + 10*c) + 3*(128*a^3*b^2 + 32*a^2*b^3 - 61*a*b^4 + 35*b^5)*cos(8*d*x + 8*c) + (64*a^3*b^2 + 452*a^2*b^3 - 9*a*b^4 - 105*b^5)*cos(6*d*x + 6*c) - 3*(40*a^2*b^3 - 29*a*b^4 - 21*b^5)*cos(4*d*x + 4*c) + (4*a^2*b^3 - 37*a*b^4 - 21*b^5)*cos(2*d*x + 2*c))*sin(16*d*x + 16*c) + (4*a^2*b^3 - 37*a*b^4 - 21*b^5 - 4*(32*a^3*b^2 - 84*a^2*b^3 - 83*a*b^4 + 21*b^5)*cos(12*d*x + 12*c) + 16*(64*a^3*b^2 - 84*a^2*b^3 - 43*a*b^4 + 21*b^5)*cos(10*d*x + 10*c) + 2*(512*a^4*b - 3584*a^3*b^2 + 1388*a^2*b^3 - 11*a*b^4 - 315*b^5)*cos(8*d*x + 8*c) - 32*(172*a^2*b^3 - 37*a*b^4 - 21*b^5)*cos(6*d*x + 6*c) - 4*(32*a^3*b^2 - 372*a^2*b^3 + 289*a*b^4 + 105*b^5)*cos(4*d*x + 4*c) - 16*(4*a^2*b^3 - 25*a*b^4 - 9*b^5)*cos(2*d*x + 2*c))*sin(14*d*x + 14*c) - (120*a^2*b^3 - 87*a*b^4 - 63*b^5 - 4*(512*a^4*b - 672*a^3*b^2 + 1228*a^2*b^3 + 21*a*b^4 - 147*b^5)*cos(10*d*x + 10*c) + 6*(3072*a^4*b - 6272*a^3*b^2 + 2920*a^2*b^3 - 413*a*b^4 - 245*b^5)*cos(8*d*x + 8*c) + 4*(512*a^4*b + 3936*a^3*b^2 - 6740*a^2*b^3 + 1281*a*b^4 + 441*b^5)*cos(6*d*x + 6*c) - 24*(192*a^3*b^2 - 416*a^2*b^3 + 161*a*b^4 + 49*b^5)*cos(4*d*x + 4*c) + 4*(32*a^3*b^2 - 372*a^2*b^3 + 289*a*b^4 + 105*b^5)*cos(2*d*x + 2*c))*sin(12*d*x + 12*c) + (64*a^3*b^2 + 452*a^2*b^3 - 9*a*b^4 - 105*b^5 + 2*(8192*a^5 + 27136*a^4*b - 37696*a^3*b^2 + 17644*a^2*b^3 - 2079*a*b^4 - 735*b^5)*cos(8*d*x + 8*c) + 16*(1024*a^4*b + 3712*a^3*b^2 - 3692*a^2*b^3 + 483*a*b^4 + 147*b^5)*cos(6*d*x + 6*c) - 4*(512*a^4*b + 3936*a^3*b^2 - 6740*a^2*b^3 + 1281*a*b^4 + 441*b^5)*cos(4*d*x + 4*c) - 32*(172*a^2*b^3 - 37*a*b^4 - 21*b^5)*cos(2*d*x + 2*c))*sin(10*d*x + 10*c) + (384*a^3*b^2 + 96*a^2*b^3 - 183*a*b^4 + 105*b^5 + 2*(8192*a^5 + 27136*a^4*b - 37696*a^3*b^2 + 17644*a^2*b^3 - 2079*a*b^4 - 735*b^5)*cos(6*d*x + 6*c) - 6*(3072*a^4*b - 6272*a^3*b^2 + 2920*a^2*b^3 - 413*a*b^4 - 245*b^5)*cos(4*d*x + 4*c) + 2*(512*a^4*b - 3584*a^3*b^2 + 1388*a^2*b^3 - 11*a*b^4 - 315*b^5)*cos(2*d*x + 2*c))*sin(8*d*x + 8*c) - (64*a^3*b^2 + 68*a^2*b^3 - 225*a*b^4 + 63*b^5 - 4*(512*a^4*b - 672*a^3*b^2 + 1228*a^2*b^3 + 21*a*b^4 - 147*b^5)*cos(4*d*x + 4*c) - 16*(64*a^3*b^2 - 84*a^2*b^3 - 43*a*b^4 + 21*b^5)*cos(2*d*x + 2*c))*sin(6*d*x + 6*c) + (24*a^2*b^3 - 99*a*b^4 + 21*b^5 - 4*(32*a^3*b^2 - 84*a^2*b^3 - 83*a*b^4 + 21*b^5)*cos(2*d*x + 2*c))*sin(4*d*x + 4*c) - (4*a^2*b^3 - 13*a*b^4 + 3*b^5)*sin(2*d*x + 2*c))/((a^3*b^5 - 2*a^2*b^6 + a*b^7)*d*cos(16*d*x + 16*c)^2 + 64*(a^3*b^5 - 2*a^2*b^6 + a*b^7)*d*cos(14*d*x + 14*c)^2 + 16*(64*a^5*b^3 - 240*a^4*b^4 + 337*a^3*b^5 - 210*a^2*b^6 + 49*a*b^7)*d*cos(12*d*x + 12*c)^2 + 64*(256*a^5*b^3 - 736*a^4*b^4 + 753*a^3*b^5 - 322*a^2*b^6 + 49*a*b^7)*d*cos(10*d*x + 10*c)^2 + 4*(16384*a^7*b - 57344*a^6*b^2 + 83712*a^5*b^3 - 67648*a^4*b^4 + 32841*a^3*b^5 - 9170*a^2*b^6 + 1225*a*b^7)*d*cos(8*d*x + 8*c)^2 + 64*(256*a^5*b^3 - 736*a^4*b^4 + 753*a^3*b^5 - 322*a^2*b^6 + 49*a*b^7)*d*cos(6*d*x + 6*c)^2 + 16*(64*a^5*b^3 - 240*a^4*b^4 + 337*a^3*b^5 - 210*a^2*b^6 + 49*a*b^7)*d*cos(4*d*x + 4*c)^2 + 64*(a^3*b^5 - 2*a^2*b^6 + a*b^7)*d*cos(2*d*x + 2*c)^2 + (a^3*b^5 - 2*a^2*b^6 + a*b^7)*d*sin(16*d*x + 16*c)^2 + 64*(a^3*b^5 - 2*a^2*b^6 + a*b^7)*d*sin(14*d*x + 14*c)^2 + 16*(64*a^5*b^3 - 240*a^4*b^4 + 337*a^3*b^5 - 210*a^2*b^6 + 49*a*b^7)*d*sin(12*d*x + 12*c)^2 + 64*(256*a^5*b^3 - 736*a^4*b^4 + 753*a^3*b^5 - 322*a^2*b^6 + 49*a*b^7)*d*sin(10*d*x + 10*c)^2 + 4*(16384*a^7*b - 57344*a^6*b^2 + 83712*a^5*b^3 - 67648*a^4*b^4 + 32841*a^3*b^5 - 9170*a^2*b^6 + 1225*a*b^7)*d*sin(8*d*x + 8*c)^2 + 64*(256*a^5*b^3 - 736*a^4*b^4 + 753*a^3*b^5 - 322*a^2*b^6 + 49*a*b^7)*d*sin(6*d*x + 6*c)^2 + 16*(64*a^5*b^3 - 240*a^4*b^4 + 337*a^3*b^5 - 210*a^2*b^6 + 49*a*b^7)*d*sin(4*d*x + 4*c)^2 + 64*(8*a^4*b^4 - 23*a^3*b^5 + 22*a^2*b^6 - 7*a*b^7)*d*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 64*(a^3*b^5 - 2*a^2*b^6 + a*b^7)*d*sin(2*d*x + 2*c)^2 - 16*(a^3*b^5 - 2*a^2*b^6 + a*b^7)*d*cos(2*d*x + 2*c) + (a^3*b^5 - 2*a^2*b^6 + a*b^7)*d - 2*(8*(a^3*b^5 - 2*a^2*b^6 + a*b^7)*d*cos(14*d*x + 14*c) + 4*(8*a^4*b^4 - 23*a^3*b^5 + 22*a^2*b^6 - 7*a*b^7)*d*cos(12*d*x + 12*c) - 8*(16*a^4*b^4 - 39*a^3*b^5 + 30*a^2*b^6 - 7*a*b^7)*d*cos(10*d*x + 10*c) - 2*(128*a^5*b^3 - 352*a^4*b^4 + 355*a^3*b^5 - 166*a^2*b^6 + 35*a*b^7)*d*cos(8*d*x + 8*c) - 8*(16*a^4*b^4 - 39*a^3*b^5 + 30*a^2*b^6 - 7*a*b^7)*d*cos(6*d*x + 6*c) + 4*(8*a^4*b^4 - 23*a^3*b^5 + 22*a^2*b^6 - 7*a*b^7)*d*cos(4*d*x + 4*c) + 8*(a^3*b^5 - 2*a^2*b^6 + a*b^7)*d*cos(2*d*x + 2*c) - (a^3*b^5 - 2*a^2*b^6 + a*b^7)*d)*cos(16*d*x + 16*c) + 16*(4*(8*a^4*b^4 - 23*a^3*b^5 + 22*a^2*b^6 - 7*a*b^7)*d*cos(12*d*x + 12*c) - 8*(16*a^4*b^4 - 39*a^3*b^5 + 30*a^2*b^6 - 7*a*b^7)*d*cos(10*d*x + 10*c) - 2*(128*a^5*b^3 - 352*a^4*b^4 + 355*a^3*b^5 - 166*a^2*b^6 + 35*a*b^7)*d*cos(8*d*x + 8*c) - 8*(16*a^4*b^4 - 39*a^3*b^5 + 30*a^2*b^6 - 7*a*b^7)*d*cos(6*d*x + 6*c) + 4*(8*a^4*b^4 - 23*a^3*b^5 + 22*a^2*b^6 - 7*a*b^7)*d*cos(4*d*x + 4*c) + 8*(a^3*b^5 - 2*a^2*b^6 + a*b^7)*d*cos(2*d*x + 2*c) - (a^3*b^5 - 2*a^2*b^6 + a*b^7)*d)*cos(14*d*x + 14*c) - 8*(8*(128*a^5*b^3 - 424*a^4*b^4 + 513*a^3*b^5 - 266*a^2*b^6 + 49*a*b^7)*d*cos(10*d*x + 10*c) + 2*(1024*a^6*b^2 - 3712*a^5*b^3 + 5304*a^4*b^4 - 3813*a^3*b^5 + 1442*a^2*b^6 - 245*a*b^7)*d*cos(8*d*x + 8*c) + 8*(128*a^5*b^3 - 424*a^4*b^4 + 513*a^3*b^5 - 266*a^2*b^6 + 49*a*b^7)*d*cos(6*d*x + 6*c) - 4*(64*a^5*b^3 - 240*a^4*b^4 + 337*a^3*b^5 - 210*a^2*b^6 + 49*a*b^7)*d*cos(4*d*x + 4*c) - 8*(8*a^4*b^4 - 23*a^3*b^5 + 22*a^2*b^6 - 7*a*b^7)*d*cos(2*d*x + 2*c) + (8*a^4*b^4 - 23*a^3*b^5 + 22*a^2*b^6 - 7*a*b^7)*d)*cos(12*d*x + 12*c) + 16*(2*(2048*a^6*b^2 - 6528*a^5*b^3 + 8144*a^4*b^4 - 5141*a^3*b^5 + 1722*a^2*b^6 - 245*a*b^7)*d*cos(8*d*x + 8*c) + 8*(256*a^5*b^3 - 736*a^4*b^4 + 753*a^3*b^5 - 322*a^2*b^6 + 49*a*b^7)*d*cos(6*d*x + 6*c) - 4*(128*a^5*b^3 - 424*a^4*b^4 + 513*a^3*b^5 - 266*a^2*b^6 + 49*a*b^7)*d*cos(4*d*x + 4*c) - 8*(16*a^4*b^4 - 39*a^3*b^5 + 30*a^2*b^6 - 7*a*b^7)*d*cos(2*d*x + 2*c) + (16*a^4*b^4 - 39*a^3*b^5 + 30*a^2*b^6 - 7*a*b^7)*d)*cos(10*d*x + 10*c) + 4*(8*(2048*a^6*b^2 - 6528*a^5*b^3 + 8144*a^4*b^4 - 5141*a^3*b^5 + 1722*a^2*b^6 - 245*a*b^7)*d*cos(6*d*x + 6*c) - 4*(1024*a^6*b^2 - 3712*a^5*b^3 + 5304*a^4*b^4 - 3813*a^3*b^5 + 1442*a^2*b^6 - 245*a*b^7)*d*cos(4*d*x + 4*c) - 8*(128*a^5*b^3 - 352*a^4*b^4 + 355*a^3*b^5 - 166*a^2*b^6 + 35*a*b^7)*d*cos(2*d*x + 2*c) + (128*a^5*b^3 - 352*a^4*b^4 + 355*a^3*b^5 - 166*a^2*b^6 + 35*a*b^7)*d)*cos(8*d*x + 8*c) - 16*(4*(128*a^5*b^3 - 424*a^4*b^4 + 513*a^3*b^5 - 266*a^2*b^6 + 49*a*b^7)*d*cos(4*d*x + 4*c) + 8*(16*a^4*b^4 - 39*a^3*b^5 + 30*a^2*b^6 - 7*a*b^7)*d*cos(2*d*x + 2*c) - (16*a^4*b^4 - 39*a^3*b^5 + 30*a^2*b^6 - 7*a*b^7)*d)*cos(6*d*x + 6*c) + 8*(8*(8*a^4*b^4 - 23*a^3*b^5 + 22*a^2*b^6 - 7*a*b^7)*d*cos(2*d*x + 2*c) - (8*a^4*b^4 - 23*a^3*b^5 + 22*a^2*b^6 - 7*a*b^7)*d)*cos(4*d*x + 4*c) - 4*(4*(a^3*b^5 - 2*a^2*b^6 + a*b^7)*d*sin(14*d*x + 14*c) + 2*(8*a^4*b^4 - 23*a^3*b^5 + 22*a^2*b^6 - 7*a*b^7)*d*sin(12*d*x + 12*c) - 4*(16*a^4*b^4 - 39*a^3*b^5 + 30*a^2*b^6 - 7*a*b^7)*d*sin(10*d*x + 10*c) - (128*a^5*b^3 - 352*a^4*b^4 + 355*a^3*b^5 - 166*a^2*b^6 + 35*a*b^7)*d*sin(8*d*x + 8*c) - 4*(16*a^4*b^4 - 39*a^3*b^5 + 30*a^2*b^6 - 7*a*b^7)*d*sin(6*d*x + 6*c) + 2*(8*a^4*b^4 - 23*a^3*b^5 + 22*a^2*b^6 - 7*a*b^7)*d*sin(4*d*x + 4*c) + 4*(a^3*b^5 - 2*a^2*b^6 + a*b^7)*d*sin(2*d*x + 2*c))*sin(16*d*x + 16*c) + 32*(2*(8*a^4*b^4 - 23*a^3*b^5 + 22*a^2*b^6 - 7*a*b^7)*d*sin(12*d*x + 12*c) - 4*(16*a^4*b^4 - 39*a^3*b^5 + 30*a^2*b^6 - 7*a*b^7)*d*sin(10*d*x + 10*c) - (128*a^5*b^3 - 352*a^4*b^4 + 355*a^3*b^5 - 166*a^2*b^6 + 35*a*b^7)*d*sin(8*d*x + 8*c) - 4*(16*a^4*b^4 - 39*a^3*b^5 + 30*a^2*b^6 - 7*a*b^7)*d*sin(6*d*x + 6*c) + 2*(8*a^4*b^4 - 23*a^3*b^5 + 22*a^2*b^6 - 7*a*b^7)*d*sin(4*d*x + 4*c) + 4*(a^3*b^5 - 2*a^2*b^6 + a*b^7)*d*sin(2*d*x + 2*c))*sin(14*d*x + 14*c) - 16*(4*(128*a^5*b^3 - 424*a^4*b^4 + 513*a^3*b^5 - 266*a^2*b^6 + 49*a*b^7)*d*sin(10*d*x + 10*c) + (1024*a^6*b^2 - 3712*a^5*b^3 + 5304*a^4*b^4 - 3813*a^3*b^5 + 1442*a^2*b^6 - 245*a*b^7)*d*sin(8*d*x + 8*c) + 4*(128*a^5*b^3 - 424*a^4*b^4 + 513*a^3*b^5 - 266*a^2*b^6 + 49*a*b^7)*d*sin(6*d*x + 6*c) - 2*(64*a^5*b^3 - 240*a^4*b^4 + 337*a^3*b^5 - 210*a^2*b^6 + 49*a*b^7)*d*sin(4*d*x + 4*c) - 4*(8*a^4*b^4 - 23*a^3*b^5 + 22*a^2*b^6 - 7*a*b^7)*d*sin(2*d*x + 2*c))*sin(12*d*x + 12*c) + 32*((2048*a^6*b^2 - 6528*a^5*b^3 + 8144*a^4*b^4 - 5141*a^3*b^5 + 1722*a^2*b^6 - 245*a*b^7)*d*sin(8*d*x + 8*c) + 4*(256*a^5*b^3 - 736*a^4*b^4 + 753*a^3*b^5 - 322*a^2*b^6 + 49*a*b^7)*d*sin(6*d*x + 6*c) - 2*(128*a^5*b^3 - 424*a^4*b^4 + 513*a^3*b^5 - 266*a^2*b^6 + 49*a*b^7)*d*sin(4*d*x + 4*c) - 4*(16*a^4*b^4 - 39*a^3*b^5 + 30*a^2*b^6 - 7*a*b^7)*d*sin(2*d*x + 2*c))*sin(10*d*x + 10*c) + 16*(2*(2048*a^6*b^2 - 6528*a^5*b^3 + 8144*a^4*b^4 - 5141*a^3*b^5 + 1722*a^2*b^6 - 245*a*b^7)*d*sin(6*d*x + 6*c) - (1024*a^6*b^2 - 3712*a^5*b^3 + 5304*a^4*b^4 - 3813*a^3*b^5 + 1442*a^2*b^6 - 245*a*b^7)*d*sin(4*d*x + 4*c) - 2*(128*a^5*b^3 - 352*a^4*b^4 + 355*a^3*b^5 - 166*a^2*b^6 + 35*a*b^7)*d*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) - 64*((128*a^5*b^3 - 424*a^4*b^4 + 513*a^3*b^5 - 266*a^2*b^6 + 49*a*b^7)*d*sin(4*d*x + 4*c) + 2*(16*a^4*b^4 - 39*a^3*b^5 + 30*a^2*b^6 - 7*a*b^7)*d*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))","F",0
232,0,0,0,0.000000," ","integrate(sin(d*x+c)^4/(a-b*sin(d*x+c)^4)^3,x, algorithm=""maxima"")","-\frac{3 \, a b^{3} \sin\left(2 \, d x + 2 \, c\right) - 12 \, {\left(8 \, a^{2} b^{2} + 13 \, a b^{3} - 2 \, b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - {\left(3 \, a b^{3} \sin\left(14 \, d x + 14 \, c\right) - 3 \, {\left(10 \, a b^{3} - b^{4}\right)} \sin\left(12 \, d x + 12 \, c\right) - {\left(80 \, a^{2} b^{2} - 111 \, a b^{3} + 16 \, b^{4}\right)} \sin\left(10 \, d x + 10 \, c\right) + {\left(256 \, a^{3} b - 64 \, a^{2} b^{2} - 26 \, a b^{3} + 35 \, b^{4}\right)} \sin\left(8 \, d x + 8 \, c\right) + {\left(336 \, a^{2} b^{2} - 95 \, a b^{3} - 40 \, b^{4}\right)} \sin\left(6 \, d x + 6 \, c\right) - {\left(64 \, a^{2} b^{2} - 54 \, a b^{3} - 25 \, b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right) - {\left(19 \, a b^{3} + 8 \, b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(16 \, d x + 16 \, c\right) - 2 \, {\left(6 \, {\left(8 \, a^{2} b^{2} + 13 \, a b^{3} - 2 \, b^{4}\right)} \sin\left(12 \, d x + 12 \, c\right) + 8 \, {\left(16 \, a^{2} b^{2} - 45 \, a b^{3} + 8 \, b^{4}\right)} \sin\left(10 \, d x + 10 \, c\right) - {\left(1408 \, a^{3} b - 544 \, a^{2} b^{2} + a b^{3} + 140 \, b^{4}\right)} \sin\left(8 \, d x + 8 \, c\right) - 16 \, {\left(96 \, a^{2} b^{2} - 29 \, a b^{3} - 10 \, b^{4}\right)} \sin\left(6 \, d x + 6 \, c\right) + 2 \, {\left(152 \, a^{2} b^{2} - 129 \, a b^{3} - 50 \, b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right) + 8 \, {\left(11 \, a b^{3} + 4 \, b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(14 \, d x + 14 \, c\right) - 2 \, {\left(2 \, {\left(640 \, a^{3} b - 488 \, a^{2} b^{2} + 389 \, a b^{3} - 70 \, b^{4}\right)} \sin\left(10 \, d x + 10 \, c\right) - {\left(4096 \, a^{4} - 8448 \, a^{3} b + 3744 \, a^{2} b^{2} - 414 \, a b^{3} - 385 \, b^{4}\right)} \sin\left(8 \, d x + 8 \, c\right) - 2 \, {\left(2688 \, a^{3} b - 4072 \, a^{2} b^{2} + 861 \, a b^{3} + 238 \, b^{4}\right)} \sin\left(6 \, d x + 6 \, c\right) + 4 \, {\left(256 \, a^{3} b - 560 \, a^{2} b^{2} + 206 \, a b^{3} + 77 \, b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(152 \, a^{2} b^{2} - 129 \, a b^{3} - 50 \, b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(12 \, d x + 12 \, c\right) - 2 \, {\left({\left(26624 \, a^{4} - 33152 \, a^{3} b + 15632 \, a^{2} b^{2} - 2453 \, a b^{3} - 420 \, b^{4}\right)} \sin\left(8 \, d x + 8 \, c\right) + 8 \, {\left(3328 \, a^{3} b - 3104 \, a^{2} b^{2} + 529 \, a b^{3} + 84 \, b^{4}\right)} \sin\left(6 \, d x + 6 \, c\right) - 2 \, {\left(2688 \, a^{3} b - 4072 \, a^{2} b^{2} + 861 \, a b^{3} + 238 \, b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right) - 16 \, {\left(96 \, a^{2} b^{2} - 29 \, a b^{3} - 10 \, b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(10 \, d x + 10 \, c\right) - 2 \, {\left({\left(26624 \, a^{4} - 33152 \, a^{3} b + 15632 \, a^{2} b^{2} - 2453 \, a b^{3} - 420 \, b^{4}\right)} \sin\left(6 \, d x + 6 \, c\right) - {\left(4096 \, a^{4} - 8448 \, a^{3} b + 3744 \, a^{2} b^{2} - 414 \, a b^{3} - 385 \, b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right) - {\left(1408 \, a^{3} b - 544 \, a^{2} b^{2} + a b^{3} + 140 \, b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) - 4 \, {\left({\left(640 \, a^{3} b - 488 \, a^{2} b^{2} + 389 \, a b^{3} - 70 \, b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right) + 4 \, {\left(16 \, a^{2} b^{2} - 45 \, a b^{3} + 8 \, b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left({\left(a^{3} b^{4} - 2 \, a^{2} b^{5} + a b^{6}\right)} d \cos\left(16 \, d x + 16 \, c\right)^{2} + 64 \, {\left(a^{3} b^{4} - 2 \, a^{2} b^{5} + a b^{6}\right)} d \cos\left(14 \, d x + 14 \, c\right)^{2} + 16 \, {\left(64 \, a^{5} b^{2} - 240 \, a^{4} b^{3} + 337 \, a^{3} b^{4} - 210 \, a^{2} b^{5} + 49 \, a b^{6}\right)} d \cos\left(12 \, d x + 12 \, c\right)^{2} + 64 \, {\left(256 \, a^{5} b^{2} - 736 \, a^{4} b^{3} + 753 \, a^{3} b^{4} - 322 \, a^{2} b^{5} + 49 \, a b^{6}\right)} d \cos\left(10 \, d x + 10 \, c\right)^{2} + 4 \, {\left(16384 \, a^{7} - 57344 \, a^{6} b + 83712 \, a^{5} b^{2} - 67648 \, a^{4} b^{3} + 32841 \, a^{3} b^{4} - 9170 \, a^{2} b^{5} + 1225 \, a b^{6}\right)} d \cos\left(8 \, d x + 8 \, c\right)^{2} + 64 \, {\left(256 \, a^{5} b^{2} - 736 \, a^{4} b^{3} + 753 \, a^{3} b^{4} - 322 \, a^{2} b^{5} + 49 \, a b^{6}\right)} d \cos\left(6 \, d x + 6 \, c\right)^{2} + 16 \, {\left(64 \, a^{5} b^{2} - 240 \, a^{4} b^{3} + 337 \, a^{3} b^{4} - 210 \, a^{2} b^{5} + 49 \, a b^{6}\right)} d \cos\left(4 \, d x + 4 \, c\right)^{2} + 64 \, {\left(a^{3} b^{4} - 2 \, a^{2} b^{5} + a b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{3} b^{4} - 2 \, a^{2} b^{5} + a b^{6}\right)} d \sin\left(16 \, d x + 16 \, c\right)^{2} + 64 \, {\left(a^{3} b^{4} - 2 \, a^{2} b^{5} + a b^{6}\right)} d \sin\left(14 \, d x + 14 \, c\right)^{2} + 16 \, {\left(64 \, a^{5} b^{2} - 240 \, a^{4} b^{3} + 337 \, a^{3} b^{4} - 210 \, a^{2} b^{5} + 49 \, a b^{6}\right)} d \sin\left(12 \, d x + 12 \, c\right)^{2} + 64 \, {\left(256 \, a^{5} b^{2} - 736 \, a^{4} b^{3} + 753 \, a^{3} b^{4} - 322 \, a^{2} b^{5} + 49 \, a b^{6}\right)} d \sin\left(10 \, d x + 10 \, c\right)^{2} + 4 \, {\left(16384 \, a^{7} - 57344 \, a^{6} b + 83712 \, a^{5} b^{2} - 67648 \, a^{4} b^{3} + 32841 \, a^{3} b^{4} - 9170 \, a^{2} b^{5} + 1225 \, a b^{6}\right)} d \sin\left(8 \, d x + 8 \, c\right)^{2} + 64 \, {\left(256 \, a^{5} b^{2} - 736 \, a^{4} b^{3} + 753 \, a^{3} b^{4} - 322 \, a^{2} b^{5} + 49 \, a b^{6}\right)} d \sin\left(6 \, d x + 6 \, c\right)^{2} + 16 \, {\left(64 \, a^{5} b^{2} - 240 \, a^{4} b^{3} + 337 \, a^{3} b^{4} - 210 \, a^{2} b^{5} + 49 \, a b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right)^{2} + 64 \, {\left(8 \, a^{4} b^{3} - 23 \, a^{3} b^{4} + 22 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 64 \, {\left(a^{3} b^{4} - 2 \, a^{2} b^{5} + a b^{6}\right)} d \sin\left(2 \, d x + 2 \, c\right)^{2} - 16 \, {\left(a^{3} b^{4} - 2 \, a^{2} b^{5} + a b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{3} b^{4} - 2 \, a^{2} b^{5} + a b^{6}\right)} d - 2 \, {\left(8 \, {\left(a^{3} b^{4} - 2 \, a^{2} b^{5} + a b^{6}\right)} d \cos\left(14 \, d x + 14 \, c\right) + 4 \, {\left(8 \, a^{4} b^{3} - 23 \, a^{3} b^{4} + 22 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \cos\left(12 \, d x + 12 \, c\right) - 8 \, {\left(16 \, a^{4} b^{3} - 39 \, a^{3} b^{4} + 30 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \cos\left(10 \, d x + 10 \, c\right) - 2 \, {\left(128 \, a^{5} b^{2} - 352 \, a^{4} b^{3} + 355 \, a^{3} b^{4} - 166 \, a^{2} b^{5} + 35 \, a b^{6}\right)} d \cos\left(8 \, d x + 8 \, c\right) - 8 \, {\left(16 \, a^{4} b^{3} - 39 \, a^{3} b^{4} + 30 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \cos\left(6 \, d x + 6 \, c\right) + 4 \, {\left(8 \, a^{4} b^{3} - 23 \, a^{3} b^{4} + 22 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(a^{3} b^{4} - 2 \, a^{2} b^{5} + a b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(a^{3} b^{4} - 2 \, a^{2} b^{5} + a b^{6}\right)} d\right)} \cos\left(16 \, d x + 16 \, c\right) + 16 \, {\left(4 \, {\left(8 \, a^{4} b^{3} - 23 \, a^{3} b^{4} + 22 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \cos\left(12 \, d x + 12 \, c\right) - 8 \, {\left(16 \, a^{4} b^{3} - 39 \, a^{3} b^{4} + 30 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \cos\left(10 \, d x + 10 \, c\right) - 2 \, {\left(128 \, a^{5} b^{2} - 352 \, a^{4} b^{3} + 355 \, a^{3} b^{4} - 166 \, a^{2} b^{5} + 35 \, a b^{6}\right)} d \cos\left(8 \, d x + 8 \, c\right) - 8 \, {\left(16 \, a^{4} b^{3} - 39 \, a^{3} b^{4} + 30 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \cos\left(6 \, d x + 6 \, c\right) + 4 \, {\left(8 \, a^{4} b^{3} - 23 \, a^{3} b^{4} + 22 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(a^{3} b^{4} - 2 \, a^{2} b^{5} + a b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(a^{3} b^{4} - 2 \, a^{2} b^{5} + a b^{6}\right)} d\right)} \cos\left(14 \, d x + 14 \, c\right) - 8 \, {\left(8 \, {\left(128 \, a^{5} b^{2} - 424 \, a^{4} b^{3} + 513 \, a^{3} b^{4} - 266 \, a^{2} b^{5} + 49 \, a b^{6}\right)} d \cos\left(10 \, d x + 10 \, c\right) + 2 \, {\left(1024 \, a^{6} b - 3712 \, a^{5} b^{2} + 5304 \, a^{4} b^{3} - 3813 \, a^{3} b^{4} + 1442 \, a^{2} b^{5} - 245 \, a b^{6}\right)} d \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(128 \, a^{5} b^{2} - 424 \, a^{4} b^{3} + 513 \, a^{3} b^{4} - 266 \, a^{2} b^{5} + 49 \, a b^{6}\right)} d \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(64 \, a^{5} b^{2} - 240 \, a^{4} b^{3} + 337 \, a^{3} b^{4} - 210 \, a^{2} b^{5} + 49 \, a b^{6}\right)} d \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(8 \, a^{4} b^{3} - 23 \, a^{3} b^{4} + 22 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(8 \, a^{4} b^{3} - 23 \, a^{3} b^{4} + 22 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d\right)} \cos\left(12 \, d x + 12 \, c\right) + 16 \, {\left(2 \, {\left(2048 \, a^{6} b - 6528 \, a^{5} b^{2} + 8144 \, a^{4} b^{3} - 5141 \, a^{3} b^{4} + 1722 \, a^{2} b^{5} - 245 \, a b^{6}\right)} d \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(256 \, a^{5} b^{2} - 736 \, a^{4} b^{3} + 753 \, a^{3} b^{4} - 322 \, a^{2} b^{5} + 49 \, a b^{6}\right)} d \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(128 \, a^{5} b^{2} - 424 \, a^{4} b^{3} + 513 \, a^{3} b^{4} - 266 \, a^{2} b^{5} + 49 \, a b^{6}\right)} d \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(16 \, a^{4} b^{3} - 39 \, a^{3} b^{4} + 30 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(16 \, a^{4} b^{3} - 39 \, a^{3} b^{4} + 30 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d\right)} \cos\left(10 \, d x + 10 \, c\right) + 4 \, {\left(8 \, {\left(2048 \, a^{6} b - 6528 \, a^{5} b^{2} + 8144 \, a^{4} b^{3} - 5141 \, a^{3} b^{4} + 1722 \, a^{2} b^{5} - 245 \, a b^{6}\right)} d \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(1024 \, a^{6} b - 3712 \, a^{5} b^{2} + 5304 \, a^{4} b^{3} - 3813 \, a^{3} b^{4} + 1442 \, a^{2} b^{5} - 245 \, a b^{6}\right)} d \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(128 \, a^{5} b^{2} - 352 \, a^{4} b^{3} + 355 \, a^{3} b^{4} - 166 \, a^{2} b^{5} + 35 \, a b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(128 \, a^{5} b^{2} - 352 \, a^{4} b^{3} + 355 \, a^{3} b^{4} - 166 \, a^{2} b^{5} + 35 \, a b^{6}\right)} d\right)} \cos\left(8 \, d x + 8 \, c\right) - 16 \, {\left(4 \, {\left(128 \, a^{5} b^{2} - 424 \, a^{4} b^{3} + 513 \, a^{3} b^{4} - 266 \, a^{2} b^{5} + 49 \, a b^{6}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(16 \, a^{4} b^{3} - 39 \, a^{3} b^{4} + 30 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(16 \, a^{4} b^{3} - 39 \, a^{3} b^{4} + 30 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d\right)} \cos\left(6 \, d x + 6 \, c\right) + 8 \, {\left(8 \, {\left(8 \, a^{4} b^{3} - 23 \, a^{3} b^{4} + 22 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(8 \, a^{4} b^{3} - 23 \, a^{3} b^{4} + 22 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(4 \, {\left(a^{3} b^{4} - 2 \, a^{2} b^{5} + a b^{6}\right)} d \sin\left(14 \, d x + 14 \, c\right) + 2 \, {\left(8 \, a^{4} b^{3} - 23 \, a^{3} b^{4} + 22 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \sin\left(12 \, d x + 12 \, c\right) - 4 \, {\left(16 \, a^{4} b^{3} - 39 \, a^{3} b^{4} + 30 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \sin\left(10 \, d x + 10 \, c\right) - {\left(128 \, a^{5} b^{2} - 352 \, a^{4} b^{3} + 355 \, a^{3} b^{4} - 166 \, a^{2} b^{5} + 35 \, a b^{6}\right)} d \sin\left(8 \, d x + 8 \, c\right) - 4 \, {\left(16 \, a^{4} b^{3} - 39 \, a^{3} b^{4} + 30 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \sin\left(6 \, d x + 6 \, c\right) + 2 \, {\left(8 \, a^{4} b^{3} - 23 \, a^{3} b^{4} + 22 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a^{3} b^{4} - 2 \, a^{2} b^{5} + a b^{6}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(16 \, d x + 16 \, c\right) + 32 \, {\left(2 \, {\left(8 \, a^{4} b^{3} - 23 \, a^{3} b^{4} + 22 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \sin\left(12 \, d x + 12 \, c\right) - 4 \, {\left(16 \, a^{4} b^{3} - 39 \, a^{3} b^{4} + 30 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \sin\left(10 \, d x + 10 \, c\right) - {\left(128 \, a^{5} b^{2} - 352 \, a^{4} b^{3} + 355 \, a^{3} b^{4} - 166 \, a^{2} b^{5} + 35 \, a b^{6}\right)} d \sin\left(8 \, d x + 8 \, c\right) - 4 \, {\left(16 \, a^{4} b^{3} - 39 \, a^{3} b^{4} + 30 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \sin\left(6 \, d x + 6 \, c\right) + 2 \, {\left(8 \, a^{4} b^{3} - 23 \, a^{3} b^{4} + 22 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a^{3} b^{4} - 2 \, a^{2} b^{5} + a b^{6}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(14 \, d x + 14 \, c\right) - 16 \, {\left(4 \, {\left(128 \, a^{5} b^{2} - 424 \, a^{4} b^{3} + 513 \, a^{3} b^{4} - 266 \, a^{2} b^{5} + 49 \, a b^{6}\right)} d \sin\left(10 \, d x + 10 \, c\right) + {\left(1024 \, a^{6} b - 3712 \, a^{5} b^{2} + 5304 \, a^{4} b^{3} - 3813 \, a^{3} b^{4} + 1442 \, a^{2} b^{5} - 245 \, a b^{6}\right)} d \sin\left(8 \, d x + 8 \, c\right) + 4 \, {\left(128 \, a^{5} b^{2} - 424 \, a^{4} b^{3} + 513 \, a^{3} b^{4} - 266 \, a^{2} b^{5} + 49 \, a b^{6}\right)} d \sin\left(6 \, d x + 6 \, c\right) - 2 \, {\left(64 \, a^{5} b^{2} - 240 \, a^{4} b^{3} + 337 \, a^{3} b^{4} - 210 \, a^{2} b^{5} + 49 \, a b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right) - 4 \, {\left(8 \, a^{4} b^{3} - 23 \, a^{3} b^{4} + 22 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(12 \, d x + 12 \, c\right) + 32 \, {\left({\left(2048 \, a^{6} b - 6528 \, a^{5} b^{2} + 8144 \, a^{4} b^{3} - 5141 \, a^{3} b^{4} + 1722 \, a^{2} b^{5} - 245 \, a b^{6}\right)} d \sin\left(8 \, d x + 8 \, c\right) + 4 \, {\left(256 \, a^{5} b^{2} - 736 \, a^{4} b^{3} + 753 \, a^{3} b^{4} - 322 \, a^{2} b^{5} + 49 \, a b^{6}\right)} d \sin\left(6 \, d x + 6 \, c\right) - 2 \, {\left(128 \, a^{5} b^{2} - 424 \, a^{4} b^{3} + 513 \, a^{3} b^{4} - 266 \, a^{2} b^{5} + 49 \, a b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right) - 4 \, {\left(16 \, a^{4} b^{3} - 39 \, a^{3} b^{4} + 30 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + 16 \, {\left(2 \, {\left(2048 \, a^{6} b - 6528 \, a^{5} b^{2} + 8144 \, a^{4} b^{3} - 5141 \, a^{3} b^{4} + 1722 \, a^{2} b^{5} - 245 \, a b^{6}\right)} d \sin\left(6 \, d x + 6 \, c\right) - {\left(1024 \, a^{6} b - 3712 \, a^{5} b^{2} + 5304 \, a^{4} b^{3} - 3813 \, a^{3} b^{4} + 1442 \, a^{2} b^{5} - 245 \, a b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(128 \, a^{5} b^{2} - 352 \, a^{4} b^{3} + 355 \, a^{3} b^{4} - 166 \, a^{2} b^{5} + 35 \, a b^{6}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) - 64 \, {\left({\left(128 \, a^{5} b^{2} - 424 \, a^{4} b^{3} + 513 \, a^{3} b^{4} - 266 \, a^{2} b^{5} + 49 \, a b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(16 \, a^{4} b^{3} - 39 \, a^{3} b^{4} + 30 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \int \frac{4 \, a b \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, a b \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, a b \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, a b \sin\left(2 \, d x + 2 \, c\right)^{2} - 4 \, {\left(32 \, a^{2} - 20 \, a b + 3 \, b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} - a b \cos\left(2 \, d x + 2 \, c\right) - 4 \, {\left(32 \, a^{2} - 20 \, a b + 3 \, b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, {\left(8 \, a^{2} - 19 \, a b + 4 \, b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - {\left(a b \cos\left(6 \, d x + 6 \, c\right) + a b \cos\left(2 \, d x + 2 \, c\right) - 2 \, {\left(4 \, a b - b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) + {\left(8 \, a b \cos\left(2 \, d x + 2 \, c\right) - a b + 2 \, {\left(8 \, a^{2} - 19 \, a b + 4 \, b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) + 2 \, {\left(4 \, a b - b^{2} + {\left(8 \, a^{2} - 19 \, a b + 4 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - {\left(a b \sin\left(6 \, d x + 6 \, c\right) + a b \sin\left(2 \, d x + 2 \, c\right) - 2 \, {\left(4 \, a b - b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 2 \, {\left(4 \, a b \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a^{2} - 19 \, a b + 4 \, b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}{a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4} + {\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4}\right)} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4}\right)} \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{5} - 176 \, a^{4} b + 169 \, a^{3} b^{2} - 66 \, a^{2} b^{3} + 9 \, a b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4}\right)} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4}\right)} \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{5} - 176 \, a^{4} b + 169 \, a^{3} b^{2} - 66 \, a^{2} b^{3} + 9 \, a b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(8 \, a^{4} b - 19 \, a^{3} b^{2} + 14 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, {\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4} - 4 \, {\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4}\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left(8 \, a^{4} b - 19 \, a^{3} b^{2} + 14 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) - 8 \, {\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4} - 2 \, {\left(8 \, a^{4} b - 19 \, a^{3} b^{2} + 14 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(8 \, a^{4} b - 19 \, a^{3} b^{2} + 14 \, a^{2} b^{3} - 3 \, a b^{4} - 4 \, {\left(8 \, a^{4} b - 19 \, a^{3} b^{2} + 14 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right) - 4 \, {\left(2 \, {\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4}\right)} \sin\left(6 \, d x + 6 \, c\right) + {\left(8 \, a^{4} b - 19 \, a^{3} b^{2} + 14 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left({\left(8 \, a^{4} b - 19 \, a^{3} b^{2} + 14 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}\,{d x} + {\left(3 \, a b^{3} \cos\left(14 \, d x + 14 \, c\right) + 2 \, a b^{3} + b^{4} - 3 \, {\left(10 \, a b^{3} - b^{4}\right)} \cos\left(12 \, d x + 12 \, c\right) - {\left(80 \, a^{2} b^{2} - 111 \, a b^{3} + 16 \, b^{4}\right)} \cos\left(10 \, d x + 10 \, c\right) + {\left(256 \, a^{3} b - 64 \, a^{2} b^{2} - 26 \, a b^{3} + 35 \, b^{4}\right)} \cos\left(8 \, d x + 8 \, c\right) + {\left(336 \, a^{2} b^{2} - 95 \, a b^{3} - 40 \, b^{4}\right)} \cos\left(6 \, d x + 6 \, c\right) - {\left(64 \, a^{2} b^{2} - 54 \, a b^{3} - 25 \, b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right) - {\left(19 \, a b^{3} + 8 \, b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(16 \, d x + 16 \, c\right) - {\left(19 \, a b^{3} + 8 \, b^{4} - 12 \, {\left(8 \, a^{2} b^{2} + 13 \, a b^{3} - 2 \, b^{4}\right)} \cos\left(12 \, d x + 12 \, c\right) - 16 \, {\left(16 \, a^{2} b^{2} - 45 \, a b^{3} + 8 \, b^{4}\right)} \cos\left(10 \, d x + 10 \, c\right) + 2 \, {\left(1408 \, a^{3} b - 544 \, a^{2} b^{2} + a b^{3} + 140 \, b^{4}\right)} \cos\left(8 \, d x + 8 \, c\right) + 32 \, {\left(96 \, a^{2} b^{2} - 29 \, a b^{3} - 10 \, b^{4}\right)} \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(152 \, a^{2} b^{2} - 129 \, a b^{3} - 50 \, b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right) - 16 \, {\left(11 \, a b^{3} + 4 \, b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(14 \, d x + 14 \, c\right) - {\left(64 \, a^{2} b^{2} - 54 \, a b^{3} - 25 \, b^{4} - 4 \, {\left(640 \, a^{3} b - 488 \, a^{2} b^{2} + 389 \, a b^{3} - 70 \, b^{4}\right)} \cos\left(10 \, d x + 10 \, c\right) + 2 \, {\left(4096 \, a^{4} - 8448 \, a^{3} b + 3744 \, a^{2} b^{2} - 414 \, a b^{3} - 385 \, b^{4}\right)} \cos\left(8 \, d x + 8 \, c\right) + 4 \, {\left(2688 \, a^{3} b - 4072 \, a^{2} b^{2} + 861 \, a b^{3} + 238 \, b^{4}\right)} \cos\left(6 \, d x + 6 \, c\right) - 8 \, {\left(256 \, a^{3} b - 560 \, a^{2} b^{2} + 206 \, a b^{3} + 77 \, b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(152 \, a^{2} b^{2} - 129 \, a b^{3} - 50 \, b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(12 \, d x + 12 \, c\right) + {\left(336 \, a^{2} b^{2} - 95 \, a b^{3} - 40 \, b^{4} + 2 \, {\left(26624 \, a^{4} - 33152 \, a^{3} b + 15632 \, a^{2} b^{2} - 2453 \, a b^{3} - 420 \, b^{4}\right)} \cos\left(8 \, d x + 8 \, c\right) + 16 \, {\left(3328 \, a^{3} b - 3104 \, a^{2} b^{2} + 529 \, a b^{3} + 84 \, b^{4}\right)} \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(2688 \, a^{3} b - 4072 \, a^{2} b^{2} + 861 \, a b^{3} + 238 \, b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right) - 32 \, {\left(96 \, a^{2} b^{2} - 29 \, a b^{3} - 10 \, b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + {\left(256 \, a^{3} b - 64 \, a^{2} b^{2} - 26 \, a b^{3} + 35 \, b^{4} + 2 \, {\left(26624 \, a^{4} - 33152 \, a^{3} b + 15632 \, a^{2} b^{2} - 2453 \, a b^{3} - 420 \, b^{4}\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left(4096 \, a^{4} - 8448 \, a^{3} b + 3744 \, a^{2} b^{2} - 414 \, a b^{3} - 385 \, b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right) - 2 \, {\left(1408 \, a^{3} b - 544 \, a^{2} b^{2} + a b^{3} + 140 \, b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) - {\left(80 \, a^{2} b^{2} - 111 \, a b^{3} + 16 \, b^{4} - 4 \, {\left(640 \, a^{3} b - 488 \, a^{2} b^{2} + 389 \, a b^{3} - 70 \, b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right) - 16 \, {\left(16 \, a^{2} b^{2} - 45 \, a b^{3} + 8 \, b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) - 3 \, {\left(10 \, a b^{3} - b^{4} - 4 \, {\left(8 \, a^{2} b^{2} + 13 \, a b^{3} - 2 \, b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(4 \, d x + 4 \, c\right)}{8 \, {\left({\left(a^{3} b^{4} - 2 \, a^{2} b^{5} + a b^{6}\right)} d \cos\left(16 \, d x + 16 \, c\right)^{2} + 64 \, {\left(a^{3} b^{4} - 2 \, a^{2} b^{5} + a b^{6}\right)} d \cos\left(14 \, d x + 14 \, c\right)^{2} + 16 \, {\left(64 \, a^{5} b^{2} - 240 \, a^{4} b^{3} + 337 \, a^{3} b^{4} - 210 \, a^{2} b^{5} + 49 \, a b^{6}\right)} d \cos\left(12 \, d x + 12 \, c\right)^{2} + 64 \, {\left(256 \, a^{5} b^{2} - 736 \, a^{4} b^{3} + 753 \, a^{3} b^{4} - 322 \, a^{2} b^{5} + 49 \, a b^{6}\right)} d \cos\left(10 \, d x + 10 \, c\right)^{2} + 4 \, {\left(16384 \, a^{7} - 57344 \, a^{6} b + 83712 \, a^{5} b^{2} - 67648 \, a^{4} b^{3} + 32841 \, a^{3} b^{4} - 9170 \, a^{2} b^{5} + 1225 \, a b^{6}\right)} d \cos\left(8 \, d x + 8 \, c\right)^{2} + 64 \, {\left(256 \, a^{5} b^{2} - 736 \, a^{4} b^{3} + 753 \, a^{3} b^{4} - 322 \, a^{2} b^{5} + 49 \, a b^{6}\right)} d \cos\left(6 \, d x + 6 \, c\right)^{2} + 16 \, {\left(64 \, a^{5} b^{2} - 240 \, a^{4} b^{3} + 337 \, a^{3} b^{4} - 210 \, a^{2} b^{5} + 49 \, a b^{6}\right)} d \cos\left(4 \, d x + 4 \, c\right)^{2} + 64 \, {\left(a^{3} b^{4} - 2 \, a^{2} b^{5} + a b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{3} b^{4} - 2 \, a^{2} b^{5} + a b^{6}\right)} d \sin\left(16 \, d x + 16 \, c\right)^{2} + 64 \, {\left(a^{3} b^{4} - 2 \, a^{2} b^{5} + a b^{6}\right)} d \sin\left(14 \, d x + 14 \, c\right)^{2} + 16 \, {\left(64 \, a^{5} b^{2} - 240 \, a^{4} b^{3} + 337 \, a^{3} b^{4} - 210 \, a^{2} b^{5} + 49 \, a b^{6}\right)} d \sin\left(12 \, d x + 12 \, c\right)^{2} + 64 \, {\left(256 \, a^{5} b^{2} - 736 \, a^{4} b^{3} + 753 \, a^{3} b^{4} - 322 \, a^{2} b^{5} + 49 \, a b^{6}\right)} d \sin\left(10 \, d x + 10 \, c\right)^{2} + 4 \, {\left(16384 \, a^{7} - 57344 \, a^{6} b + 83712 \, a^{5} b^{2} - 67648 \, a^{4} b^{3} + 32841 \, a^{3} b^{4} - 9170 \, a^{2} b^{5} + 1225 \, a b^{6}\right)} d \sin\left(8 \, d x + 8 \, c\right)^{2} + 64 \, {\left(256 \, a^{5} b^{2} - 736 \, a^{4} b^{3} + 753 \, a^{3} b^{4} - 322 \, a^{2} b^{5} + 49 \, a b^{6}\right)} d \sin\left(6 \, d x + 6 \, c\right)^{2} + 16 \, {\left(64 \, a^{5} b^{2} - 240 \, a^{4} b^{3} + 337 \, a^{3} b^{4} - 210 \, a^{2} b^{5} + 49 \, a b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right)^{2} + 64 \, {\left(8 \, a^{4} b^{3} - 23 \, a^{3} b^{4} + 22 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 64 \, {\left(a^{3} b^{4} - 2 \, a^{2} b^{5} + a b^{6}\right)} d \sin\left(2 \, d x + 2 \, c\right)^{2} - 16 \, {\left(a^{3} b^{4} - 2 \, a^{2} b^{5} + a b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{3} b^{4} - 2 \, a^{2} b^{5} + a b^{6}\right)} d - 2 \, {\left(8 \, {\left(a^{3} b^{4} - 2 \, a^{2} b^{5} + a b^{6}\right)} d \cos\left(14 \, d x + 14 \, c\right) + 4 \, {\left(8 \, a^{4} b^{3} - 23 \, a^{3} b^{4} + 22 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \cos\left(12 \, d x + 12 \, c\right) - 8 \, {\left(16 \, a^{4} b^{3} - 39 \, a^{3} b^{4} + 30 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \cos\left(10 \, d x + 10 \, c\right) - 2 \, {\left(128 \, a^{5} b^{2} - 352 \, a^{4} b^{3} + 355 \, a^{3} b^{4} - 166 \, a^{2} b^{5} + 35 \, a b^{6}\right)} d \cos\left(8 \, d x + 8 \, c\right) - 8 \, {\left(16 \, a^{4} b^{3} - 39 \, a^{3} b^{4} + 30 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \cos\left(6 \, d x + 6 \, c\right) + 4 \, {\left(8 \, a^{4} b^{3} - 23 \, a^{3} b^{4} + 22 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(a^{3} b^{4} - 2 \, a^{2} b^{5} + a b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(a^{3} b^{4} - 2 \, a^{2} b^{5} + a b^{6}\right)} d\right)} \cos\left(16 \, d x + 16 \, c\right) + 16 \, {\left(4 \, {\left(8 \, a^{4} b^{3} - 23 \, a^{3} b^{4} + 22 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \cos\left(12 \, d x + 12 \, c\right) - 8 \, {\left(16 \, a^{4} b^{3} - 39 \, a^{3} b^{4} + 30 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \cos\left(10 \, d x + 10 \, c\right) - 2 \, {\left(128 \, a^{5} b^{2} - 352 \, a^{4} b^{3} + 355 \, a^{3} b^{4} - 166 \, a^{2} b^{5} + 35 \, a b^{6}\right)} d \cos\left(8 \, d x + 8 \, c\right) - 8 \, {\left(16 \, a^{4} b^{3} - 39 \, a^{3} b^{4} + 30 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \cos\left(6 \, d x + 6 \, c\right) + 4 \, {\left(8 \, a^{4} b^{3} - 23 \, a^{3} b^{4} + 22 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(a^{3} b^{4} - 2 \, a^{2} b^{5} + a b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(a^{3} b^{4} - 2 \, a^{2} b^{5} + a b^{6}\right)} d\right)} \cos\left(14 \, d x + 14 \, c\right) - 8 \, {\left(8 \, {\left(128 \, a^{5} b^{2} - 424 \, a^{4} b^{3} + 513 \, a^{3} b^{4} - 266 \, a^{2} b^{5} + 49 \, a b^{6}\right)} d \cos\left(10 \, d x + 10 \, c\right) + 2 \, {\left(1024 \, a^{6} b - 3712 \, a^{5} b^{2} + 5304 \, a^{4} b^{3} - 3813 \, a^{3} b^{4} + 1442 \, a^{2} b^{5} - 245 \, a b^{6}\right)} d \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(128 \, a^{5} b^{2} - 424 \, a^{4} b^{3} + 513 \, a^{3} b^{4} - 266 \, a^{2} b^{5} + 49 \, a b^{6}\right)} d \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(64 \, a^{5} b^{2} - 240 \, a^{4} b^{3} + 337 \, a^{3} b^{4} - 210 \, a^{2} b^{5} + 49 \, a b^{6}\right)} d \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(8 \, a^{4} b^{3} - 23 \, a^{3} b^{4} + 22 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(8 \, a^{4} b^{3} - 23 \, a^{3} b^{4} + 22 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d\right)} \cos\left(12 \, d x + 12 \, c\right) + 16 \, {\left(2 \, {\left(2048 \, a^{6} b - 6528 \, a^{5} b^{2} + 8144 \, a^{4} b^{3} - 5141 \, a^{3} b^{4} + 1722 \, a^{2} b^{5} - 245 \, a b^{6}\right)} d \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(256 \, a^{5} b^{2} - 736 \, a^{4} b^{3} + 753 \, a^{3} b^{4} - 322 \, a^{2} b^{5} + 49 \, a b^{6}\right)} d \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(128 \, a^{5} b^{2} - 424 \, a^{4} b^{3} + 513 \, a^{3} b^{4} - 266 \, a^{2} b^{5} + 49 \, a b^{6}\right)} d \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(16 \, a^{4} b^{3} - 39 \, a^{3} b^{4} + 30 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(16 \, a^{4} b^{3} - 39 \, a^{3} b^{4} + 30 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d\right)} \cos\left(10 \, d x + 10 \, c\right) + 4 \, {\left(8 \, {\left(2048 \, a^{6} b - 6528 \, a^{5} b^{2} + 8144 \, a^{4} b^{3} - 5141 \, a^{3} b^{4} + 1722 \, a^{2} b^{5} - 245 \, a b^{6}\right)} d \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(1024 \, a^{6} b - 3712 \, a^{5} b^{2} + 5304 \, a^{4} b^{3} - 3813 \, a^{3} b^{4} + 1442 \, a^{2} b^{5} - 245 \, a b^{6}\right)} d \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(128 \, a^{5} b^{2} - 352 \, a^{4} b^{3} + 355 \, a^{3} b^{4} - 166 \, a^{2} b^{5} + 35 \, a b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(128 \, a^{5} b^{2} - 352 \, a^{4} b^{3} + 355 \, a^{3} b^{4} - 166 \, a^{2} b^{5} + 35 \, a b^{6}\right)} d\right)} \cos\left(8 \, d x + 8 \, c\right) - 16 \, {\left(4 \, {\left(128 \, a^{5} b^{2} - 424 \, a^{4} b^{3} + 513 \, a^{3} b^{4} - 266 \, a^{2} b^{5} + 49 \, a b^{6}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(16 \, a^{4} b^{3} - 39 \, a^{3} b^{4} + 30 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(16 \, a^{4} b^{3} - 39 \, a^{3} b^{4} + 30 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d\right)} \cos\left(6 \, d x + 6 \, c\right) + 8 \, {\left(8 \, {\left(8 \, a^{4} b^{3} - 23 \, a^{3} b^{4} + 22 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(8 \, a^{4} b^{3} - 23 \, a^{3} b^{4} + 22 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(4 \, {\left(a^{3} b^{4} - 2 \, a^{2} b^{5} + a b^{6}\right)} d \sin\left(14 \, d x + 14 \, c\right) + 2 \, {\left(8 \, a^{4} b^{3} - 23 \, a^{3} b^{4} + 22 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \sin\left(12 \, d x + 12 \, c\right) - 4 \, {\left(16 \, a^{4} b^{3} - 39 \, a^{3} b^{4} + 30 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \sin\left(10 \, d x + 10 \, c\right) - {\left(128 \, a^{5} b^{2} - 352 \, a^{4} b^{3} + 355 \, a^{3} b^{4} - 166 \, a^{2} b^{5} + 35 \, a b^{6}\right)} d \sin\left(8 \, d x + 8 \, c\right) - 4 \, {\left(16 \, a^{4} b^{3} - 39 \, a^{3} b^{4} + 30 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \sin\left(6 \, d x + 6 \, c\right) + 2 \, {\left(8 \, a^{4} b^{3} - 23 \, a^{3} b^{4} + 22 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a^{3} b^{4} - 2 \, a^{2} b^{5} + a b^{6}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(16 \, d x + 16 \, c\right) + 32 \, {\left(2 \, {\left(8 \, a^{4} b^{3} - 23 \, a^{3} b^{4} + 22 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \sin\left(12 \, d x + 12 \, c\right) - 4 \, {\left(16 \, a^{4} b^{3} - 39 \, a^{3} b^{4} + 30 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \sin\left(10 \, d x + 10 \, c\right) - {\left(128 \, a^{5} b^{2} - 352 \, a^{4} b^{3} + 355 \, a^{3} b^{4} - 166 \, a^{2} b^{5} + 35 \, a b^{6}\right)} d \sin\left(8 \, d x + 8 \, c\right) - 4 \, {\left(16 \, a^{4} b^{3} - 39 \, a^{3} b^{4} + 30 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \sin\left(6 \, d x + 6 \, c\right) + 2 \, {\left(8 \, a^{4} b^{3} - 23 \, a^{3} b^{4} + 22 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a^{3} b^{4} - 2 \, a^{2} b^{5} + a b^{6}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(14 \, d x + 14 \, c\right) - 16 \, {\left(4 \, {\left(128 \, a^{5} b^{2} - 424 \, a^{4} b^{3} + 513 \, a^{3} b^{4} - 266 \, a^{2} b^{5} + 49 \, a b^{6}\right)} d \sin\left(10 \, d x + 10 \, c\right) + {\left(1024 \, a^{6} b - 3712 \, a^{5} b^{2} + 5304 \, a^{4} b^{3} - 3813 \, a^{3} b^{4} + 1442 \, a^{2} b^{5} - 245 \, a b^{6}\right)} d \sin\left(8 \, d x + 8 \, c\right) + 4 \, {\left(128 \, a^{5} b^{2} - 424 \, a^{4} b^{3} + 513 \, a^{3} b^{4} - 266 \, a^{2} b^{5} + 49 \, a b^{6}\right)} d \sin\left(6 \, d x + 6 \, c\right) - 2 \, {\left(64 \, a^{5} b^{2} - 240 \, a^{4} b^{3} + 337 \, a^{3} b^{4} - 210 \, a^{2} b^{5} + 49 \, a b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right) - 4 \, {\left(8 \, a^{4} b^{3} - 23 \, a^{3} b^{4} + 22 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(12 \, d x + 12 \, c\right) + 32 \, {\left({\left(2048 \, a^{6} b - 6528 \, a^{5} b^{2} + 8144 \, a^{4} b^{3} - 5141 \, a^{3} b^{4} + 1722 \, a^{2} b^{5} - 245 \, a b^{6}\right)} d \sin\left(8 \, d x + 8 \, c\right) + 4 \, {\left(256 \, a^{5} b^{2} - 736 \, a^{4} b^{3} + 753 \, a^{3} b^{4} - 322 \, a^{2} b^{5} + 49 \, a b^{6}\right)} d \sin\left(6 \, d x + 6 \, c\right) - 2 \, {\left(128 \, a^{5} b^{2} - 424 \, a^{4} b^{3} + 513 \, a^{3} b^{4} - 266 \, a^{2} b^{5} + 49 \, a b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right) - 4 \, {\left(16 \, a^{4} b^{3} - 39 \, a^{3} b^{4} + 30 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + 16 \, {\left(2 \, {\left(2048 \, a^{6} b - 6528 \, a^{5} b^{2} + 8144 \, a^{4} b^{3} - 5141 \, a^{3} b^{4} + 1722 \, a^{2} b^{5} - 245 \, a b^{6}\right)} d \sin\left(6 \, d x + 6 \, c\right) - {\left(1024 \, a^{6} b - 3712 \, a^{5} b^{2} + 5304 \, a^{4} b^{3} - 3813 \, a^{3} b^{4} + 1442 \, a^{2} b^{5} - 245 \, a b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(128 \, a^{5} b^{2} - 352 \, a^{4} b^{3} + 355 \, a^{3} b^{4} - 166 \, a^{2} b^{5} + 35 \, a b^{6}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) - 64 \, {\left({\left(128 \, a^{5} b^{2} - 424 \, a^{4} b^{3} + 513 \, a^{3} b^{4} - 266 \, a^{2} b^{5} + 49 \, a b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(16 \, a^{4} b^{3} - 39 \, a^{3} b^{4} + 30 \, a^{2} b^{5} - 7 \, a b^{6}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)}}"," ",0,"-1/8*(3*a*b^3*sin(2*d*x + 2*c) - 12*(8*a^2*b^2 + 13*a*b^3 - 2*b^4)*cos(4*d*x + 4*c)*sin(2*d*x + 2*c) - (3*a*b^3*sin(14*d*x + 14*c) - 3*(10*a*b^3 - b^4)*sin(12*d*x + 12*c) - (80*a^2*b^2 - 111*a*b^3 + 16*b^4)*sin(10*d*x + 10*c) + (256*a^3*b - 64*a^2*b^2 - 26*a*b^3 + 35*b^4)*sin(8*d*x + 8*c) + (336*a^2*b^2 - 95*a*b^3 - 40*b^4)*sin(6*d*x + 6*c) - (64*a^2*b^2 - 54*a*b^3 - 25*b^4)*sin(4*d*x + 4*c) - (19*a*b^3 + 8*b^4)*sin(2*d*x + 2*c))*cos(16*d*x + 16*c) - 2*(6*(8*a^2*b^2 + 13*a*b^3 - 2*b^4)*sin(12*d*x + 12*c) + 8*(16*a^2*b^2 - 45*a*b^3 + 8*b^4)*sin(10*d*x + 10*c) - (1408*a^3*b - 544*a^2*b^2 + a*b^3 + 140*b^4)*sin(8*d*x + 8*c) - 16*(96*a^2*b^2 - 29*a*b^3 - 10*b^4)*sin(6*d*x + 6*c) + 2*(152*a^2*b^2 - 129*a*b^3 - 50*b^4)*sin(4*d*x + 4*c) + 8*(11*a*b^3 + 4*b^4)*sin(2*d*x + 2*c))*cos(14*d*x + 14*c) - 2*(2*(640*a^3*b - 488*a^2*b^2 + 389*a*b^3 - 70*b^4)*sin(10*d*x + 10*c) - (4096*a^4 - 8448*a^3*b + 3744*a^2*b^2 - 414*a*b^3 - 385*b^4)*sin(8*d*x + 8*c) - 2*(2688*a^3*b - 4072*a^2*b^2 + 861*a*b^3 + 238*b^4)*sin(6*d*x + 6*c) + 4*(256*a^3*b - 560*a^2*b^2 + 206*a*b^3 + 77*b^4)*sin(4*d*x + 4*c) + 2*(152*a^2*b^2 - 129*a*b^3 - 50*b^4)*sin(2*d*x + 2*c))*cos(12*d*x + 12*c) - 2*((26624*a^4 - 33152*a^3*b + 15632*a^2*b^2 - 2453*a*b^3 - 420*b^4)*sin(8*d*x + 8*c) + 8*(3328*a^3*b - 3104*a^2*b^2 + 529*a*b^3 + 84*b^4)*sin(6*d*x + 6*c) - 2*(2688*a^3*b - 4072*a^2*b^2 + 861*a*b^3 + 238*b^4)*sin(4*d*x + 4*c) - 16*(96*a^2*b^2 - 29*a*b^3 - 10*b^4)*sin(2*d*x + 2*c))*cos(10*d*x + 10*c) - 2*((26624*a^4 - 33152*a^3*b + 15632*a^2*b^2 - 2453*a*b^3 - 420*b^4)*sin(6*d*x + 6*c) - (4096*a^4 - 8448*a^3*b + 3744*a^2*b^2 - 414*a*b^3 - 385*b^4)*sin(4*d*x + 4*c) - (1408*a^3*b - 544*a^2*b^2 + a*b^3 + 140*b^4)*sin(2*d*x + 2*c))*cos(8*d*x + 8*c) - 4*((640*a^3*b - 488*a^2*b^2 + 389*a*b^3 - 70*b^4)*sin(4*d*x + 4*c) + 4*(16*a^2*b^2 - 45*a*b^3 + 8*b^4)*sin(2*d*x + 2*c))*cos(6*d*x + 6*c) - 8*((a^3*b^4 - 2*a^2*b^5 + a*b^6)*d*cos(16*d*x + 16*c)^2 + 64*(a^3*b^4 - 2*a^2*b^5 + a*b^6)*d*cos(14*d*x + 14*c)^2 + 16*(64*a^5*b^2 - 240*a^4*b^3 + 337*a^3*b^4 - 210*a^2*b^5 + 49*a*b^6)*d*cos(12*d*x + 12*c)^2 + 64*(256*a^5*b^2 - 736*a^4*b^3 + 753*a^3*b^4 - 322*a^2*b^5 + 49*a*b^6)*d*cos(10*d*x + 10*c)^2 + 4*(16384*a^7 - 57344*a^6*b + 83712*a^5*b^2 - 67648*a^4*b^3 + 32841*a^3*b^4 - 9170*a^2*b^5 + 1225*a*b^6)*d*cos(8*d*x + 8*c)^2 + 64*(256*a^5*b^2 - 736*a^4*b^3 + 753*a^3*b^4 - 322*a^2*b^5 + 49*a*b^6)*d*cos(6*d*x + 6*c)^2 + 16*(64*a^5*b^2 - 240*a^4*b^3 + 337*a^3*b^4 - 210*a^2*b^5 + 49*a*b^6)*d*cos(4*d*x + 4*c)^2 + 64*(a^3*b^4 - 2*a^2*b^5 + a*b^6)*d*cos(2*d*x + 2*c)^2 + (a^3*b^4 - 2*a^2*b^5 + a*b^6)*d*sin(16*d*x + 16*c)^2 + 64*(a^3*b^4 - 2*a^2*b^5 + a*b^6)*d*sin(14*d*x + 14*c)^2 + 16*(64*a^5*b^2 - 240*a^4*b^3 + 337*a^3*b^4 - 210*a^2*b^5 + 49*a*b^6)*d*sin(12*d*x + 12*c)^2 + 64*(256*a^5*b^2 - 736*a^4*b^3 + 753*a^3*b^4 - 322*a^2*b^5 + 49*a*b^6)*d*sin(10*d*x + 10*c)^2 + 4*(16384*a^7 - 57344*a^6*b + 83712*a^5*b^2 - 67648*a^4*b^3 + 32841*a^3*b^4 - 9170*a^2*b^5 + 1225*a*b^6)*d*sin(8*d*x + 8*c)^2 + 64*(256*a^5*b^2 - 736*a^4*b^3 + 753*a^3*b^4 - 322*a^2*b^5 + 49*a*b^6)*d*sin(6*d*x + 6*c)^2 + 16*(64*a^5*b^2 - 240*a^4*b^3 + 337*a^3*b^4 - 210*a^2*b^5 + 49*a*b^6)*d*sin(4*d*x + 4*c)^2 + 64*(8*a^4*b^3 - 23*a^3*b^4 + 22*a^2*b^5 - 7*a*b^6)*d*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 64*(a^3*b^4 - 2*a^2*b^5 + a*b^6)*d*sin(2*d*x + 2*c)^2 - 16*(a^3*b^4 - 2*a^2*b^5 + a*b^6)*d*cos(2*d*x + 2*c) + (a^3*b^4 - 2*a^2*b^5 + a*b^6)*d - 2*(8*(a^3*b^4 - 2*a^2*b^5 + a*b^6)*d*cos(14*d*x + 14*c) + 4*(8*a^4*b^3 - 23*a^3*b^4 + 22*a^2*b^5 - 7*a*b^6)*d*cos(12*d*x + 12*c) - 8*(16*a^4*b^3 - 39*a^3*b^4 + 30*a^2*b^5 - 7*a*b^6)*d*cos(10*d*x + 10*c) - 2*(128*a^5*b^2 - 352*a^4*b^3 + 355*a^3*b^4 - 166*a^2*b^5 + 35*a*b^6)*d*cos(8*d*x + 8*c) - 8*(16*a^4*b^3 - 39*a^3*b^4 + 30*a^2*b^5 - 7*a*b^6)*d*cos(6*d*x + 6*c) + 4*(8*a^4*b^3 - 23*a^3*b^4 + 22*a^2*b^5 - 7*a*b^6)*d*cos(4*d*x + 4*c) + 8*(a^3*b^4 - 2*a^2*b^5 + a*b^6)*d*cos(2*d*x + 2*c) - (a^3*b^4 - 2*a^2*b^5 + a*b^6)*d)*cos(16*d*x + 16*c) + 16*(4*(8*a^4*b^3 - 23*a^3*b^4 + 22*a^2*b^5 - 7*a*b^6)*d*cos(12*d*x + 12*c) - 8*(16*a^4*b^3 - 39*a^3*b^4 + 30*a^2*b^5 - 7*a*b^6)*d*cos(10*d*x + 10*c) - 2*(128*a^5*b^2 - 352*a^4*b^3 + 355*a^3*b^4 - 166*a^2*b^5 + 35*a*b^6)*d*cos(8*d*x + 8*c) - 8*(16*a^4*b^3 - 39*a^3*b^4 + 30*a^2*b^5 - 7*a*b^6)*d*cos(6*d*x + 6*c) + 4*(8*a^4*b^3 - 23*a^3*b^4 + 22*a^2*b^5 - 7*a*b^6)*d*cos(4*d*x + 4*c) + 8*(a^3*b^4 - 2*a^2*b^5 + a*b^6)*d*cos(2*d*x + 2*c) - (a^3*b^4 - 2*a^2*b^5 + a*b^6)*d)*cos(14*d*x + 14*c) - 8*(8*(128*a^5*b^2 - 424*a^4*b^3 + 513*a^3*b^4 - 266*a^2*b^5 + 49*a*b^6)*d*cos(10*d*x + 10*c) + 2*(1024*a^6*b - 3712*a^5*b^2 + 5304*a^4*b^3 - 3813*a^3*b^4 + 1442*a^2*b^5 - 245*a*b^6)*d*cos(8*d*x + 8*c) + 8*(128*a^5*b^2 - 424*a^4*b^3 + 513*a^3*b^4 - 266*a^2*b^5 + 49*a*b^6)*d*cos(6*d*x + 6*c) - 4*(64*a^5*b^2 - 240*a^4*b^3 + 337*a^3*b^4 - 210*a^2*b^5 + 49*a*b^6)*d*cos(4*d*x + 4*c) - 8*(8*a^4*b^3 - 23*a^3*b^4 + 22*a^2*b^5 - 7*a*b^6)*d*cos(2*d*x + 2*c) + (8*a^4*b^3 - 23*a^3*b^4 + 22*a^2*b^5 - 7*a*b^6)*d)*cos(12*d*x + 12*c) + 16*(2*(2048*a^6*b - 6528*a^5*b^2 + 8144*a^4*b^3 - 5141*a^3*b^4 + 1722*a^2*b^5 - 245*a*b^6)*d*cos(8*d*x + 8*c) + 8*(256*a^5*b^2 - 736*a^4*b^3 + 753*a^3*b^4 - 322*a^2*b^5 + 49*a*b^6)*d*cos(6*d*x + 6*c) - 4*(128*a^5*b^2 - 424*a^4*b^3 + 513*a^3*b^4 - 266*a^2*b^5 + 49*a*b^6)*d*cos(4*d*x + 4*c) - 8*(16*a^4*b^3 - 39*a^3*b^4 + 30*a^2*b^5 - 7*a*b^6)*d*cos(2*d*x + 2*c) + (16*a^4*b^3 - 39*a^3*b^4 + 30*a^2*b^5 - 7*a*b^6)*d)*cos(10*d*x + 10*c) + 4*(8*(2048*a^6*b - 6528*a^5*b^2 + 8144*a^4*b^3 - 5141*a^3*b^4 + 1722*a^2*b^5 - 245*a*b^6)*d*cos(6*d*x + 6*c) - 4*(1024*a^6*b - 3712*a^5*b^2 + 5304*a^4*b^3 - 3813*a^3*b^4 + 1442*a^2*b^5 - 245*a*b^6)*d*cos(4*d*x + 4*c) - 8*(128*a^5*b^2 - 352*a^4*b^3 + 355*a^3*b^4 - 166*a^2*b^5 + 35*a*b^6)*d*cos(2*d*x + 2*c) + (128*a^5*b^2 - 352*a^4*b^3 + 355*a^3*b^4 - 166*a^2*b^5 + 35*a*b^6)*d)*cos(8*d*x + 8*c) - 16*(4*(128*a^5*b^2 - 424*a^4*b^3 + 513*a^3*b^4 - 266*a^2*b^5 + 49*a*b^6)*d*cos(4*d*x + 4*c) + 8*(16*a^4*b^3 - 39*a^3*b^4 + 30*a^2*b^5 - 7*a*b^6)*d*cos(2*d*x + 2*c) - (16*a^4*b^3 - 39*a^3*b^4 + 30*a^2*b^5 - 7*a*b^6)*d)*cos(6*d*x + 6*c) + 8*(8*(8*a^4*b^3 - 23*a^3*b^4 + 22*a^2*b^5 - 7*a*b^6)*d*cos(2*d*x + 2*c) - (8*a^4*b^3 - 23*a^3*b^4 + 22*a^2*b^5 - 7*a*b^6)*d)*cos(4*d*x + 4*c) - 4*(4*(a^3*b^4 - 2*a^2*b^5 + a*b^6)*d*sin(14*d*x + 14*c) + 2*(8*a^4*b^3 - 23*a^3*b^4 + 22*a^2*b^5 - 7*a*b^6)*d*sin(12*d*x + 12*c) - 4*(16*a^4*b^3 - 39*a^3*b^4 + 30*a^2*b^5 - 7*a*b^6)*d*sin(10*d*x + 10*c) - (128*a^5*b^2 - 352*a^4*b^3 + 355*a^3*b^4 - 166*a^2*b^5 + 35*a*b^6)*d*sin(8*d*x + 8*c) - 4*(16*a^4*b^3 - 39*a^3*b^4 + 30*a^2*b^5 - 7*a*b^6)*d*sin(6*d*x + 6*c) + 2*(8*a^4*b^3 - 23*a^3*b^4 + 22*a^2*b^5 - 7*a*b^6)*d*sin(4*d*x + 4*c) + 4*(a^3*b^4 - 2*a^2*b^5 + a*b^6)*d*sin(2*d*x + 2*c))*sin(16*d*x + 16*c) + 32*(2*(8*a^4*b^3 - 23*a^3*b^4 + 22*a^2*b^5 - 7*a*b^6)*d*sin(12*d*x + 12*c) - 4*(16*a^4*b^3 - 39*a^3*b^4 + 30*a^2*b^5 - 7*a*b^6)*d*sin(10*d*x + 10*c) - (128*a^5*b^2 - 352*a^4*b^3 + 355*a^3*b^4 - 166*a^2*b^5 + 35*a*b^6)*d*sin(8*d*x + 8*c) - 4*(16*a^4*b^3 - 39*a^3*b^4 + 30*a^2*b^5 - 7*a*b^6)*d*sin(6*d*x + 6*c) + 2*(8*a^4*b^3 - 23*a^3*b^4 + 22*a^2*b^5 - 7*a*b^6)*d*sin(4*d*x + 4*c) + 4*(a^3*b^4 - 2*a^2*b^5 + a*b^6)*d*sin(2*d*x + 2*c))*sin(14*d*x + 14*c) - 16*(4*(128*a^5*b^2 - 424*a^4*b^3 + 513*a^3*b^4 - 266*a^2*b^5 + 49*a*b^6)*d*sin(10*d*x + 10*c) + (1024*a^6*b - 3712*a^5*b^2 + 5304*a^4*b^3 - 3813*a^3*b^4 + 1442*a^2*b^5 - 245*a*b^6)*d*sin(8*d*x + 8*c) + 4*(128*a^5*b^2 - 424*a^4*b^3 + 513*a^3*b^4 - 266*a^2*b^5 + 49*a*b^6)*d*sin(6*d*x + 6*c) - 2*(64*a^5*b^2 - 240*a^4*b^3 + 337*a^3*b^4 - 210*a^2*b^5 + 49*a*b^6)*d*sin(4*d*x + 4*c) - 4*(8*a^4*b^3 - 23*a^3*b^4 + 22*a^2*b^5 - 7*a*b^6)*d*sin(2*d*x + 2*c))*sin(12*d*x + 12*c) + 32*((2048*a^6*b - 6528*a^5*b^2 + 8144*a^4*b^3 - 5141*a^3*b^4 + 1722*a^2*b^5 - 245*a*b^6)*d*sin(8*d*x + 8*c) + 4*(256*a^5*b^2 - 736*a^4*b^3 + 753*a^3*b^4 - 322*a^2*b^5 + 49*a*b^6)*d*sin(6*d*x + 6*c) - 2*(128*a^5*b^2 - 424*a^4*b^3 + 513*a^3*b^4 - 266*a^2*b^5 + 49*a*b^6)*d*sin(4*d*x + 4*c) - 4*(16*a^4*b^3 - 39*a^3*b^4 + 30*a^2*b^5 - 7*a*b^6)*d*sin(2*d*x + 2*c))*sin(10*d*x + 10*c) + 16*(2*(2048*a^6*b - 6528*a^5*b^2 + 8144*a^4*b^3 - 5141*a^3*b^4 + 1722*a^2*b^5 - 245*a*b^6)*d*sin(6*d*x + 6*c) - (1024*a^6*b - 3712*a^5*b^2 + 5304*a^4*b^3 - 3813*a^3*b^4 + 1442*a^2*b^5 - 245*a*b^6)*d*sin(4*d*x + 4*c) - 2*(128*a^5*b^2 - 352*a^4*b^3 + 355*a^3*b^4 - 166*a^2*b^5 + 35*a*b^6)*d*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) - 64*((128*a^5*b^2 - 424*a^4*b^3 + 513*a^3*b^4 - 266*a^2*b^5 + 49*a*b^6)*d*sin(4*d*x + 4*c) + 2*(16*a^4*b^3 - 39*a^3*b^4 + 30*a^2*b^5 - 7*a*b^6)*d*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*integrate(-3/4*(4*a*b*cos(6*d*x + 6*c)^2 + 4*a*b*cos(2*d*x + 2*c)^2 + 4*a*b*sin(6*d*x + 6*c)^2 + 4*a*b*sin(2*d*x + 2*c)^2 - 4*(32*a^2 - 20*a*b + 3*b^2)*cos(4*d*x + 4*c)^2 - a*b*cos(2*d*x + 2*c) - 4*(32*a^2 - 20*a*b + 3*b^2)*sin(4*d*x + 4*c)^2 + 2*(8*a^2 - 19*a*b + 4*b^2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) - (a*b*cos(6*d*x + 6*c) + a*b*cos(2*d*x + 2*c) - 2*(4*a*b - b^2)*cos(4*d*x + 4*c))*cos(8*d*x + 8*c) + (8*a*b*cos(2*d*x + 2*c) - a*b + 2*(8*a^2 - 19*a*b + 4*b^2)*cos(4*d*x + 4*c))*cos(6*d*x + 6*c) + 2*(4*a*b - b^2 + (8*a^2 - 19*a*b + 4*b^2)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - (a*b*sin(6*d*x + 6*c) + a*b*sin(2*d*x + 2*c) - 2*(4*a*b - b^2)*sin(4*d*x + 4*c))*sin(8*d*x + 8*c) + 2*(4*a*b*sin(2*d*x + 2*c) + (8*a^2 - 19*a*b + 4*b^2)*sin(4*d*x + 4*c))*sin(6*d*x + 6*c))/(a^3*b^2 - 2*a^2*b^3 + a*b^4 + (a^3*b^2 - 2*a^2*b^3 + a*b^4)*cos(8*d*x + 8*c)^2 + 16*(a^3*b^2 - 2*a^2*b^3 + a*b^4)*cos(6*d*x + 6*c)^2 + 4*(64*a^5 - 176*a^4*b + 169*a^3*b^2 - 66*a^2*b^3 + 9*a*b^4)*cos(4*d*x + 4*c)^2 + 16*(a^3*b^2 - 2*a^2*b^3 + a*b^4)*cos(2*d*x + 2*c)^2 + (a^3*b^2 - 2*a^2*b^3 + a*b^4)*sin(8*d*x + 8*c)^2 + 16*(a^3*b^2 - 2*a^2*b^3 + a*b^4)*sin(6*d*x + 6*c)^2 + 4*(64*a^5 - 176*a^4*b + 169*a^3*b^2 - 66*a^2*b^3 + 9*a*b^4)*sin(4*d*x + 4*c)^2 + 16*(8*a^4*b - 19*a^3*b^2 + 14*a^2*b^3 - 3*a*b^4)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*(a^3*b^2 - 2*a^2*b^3 + a*b^4)*sin(2*d*x + 2*c)^2 + 2*(a^3*b^2 - 2*a^2*b^3 + a*b^4 - 4*(a^3*b^2 - 2*a^2*b^3 + a*b^4)*cos(6*d*x + 6*c) - 2*(8*a^4*b - 19*a^3*b^2 + 14*a^2*b^3 - 3*a*b^4)*cos(4*d*x + 4*c) - 4*(a^3*b^2 - 2*a^2*b^3 + a*b^4)*cos(2*d*x + 2*c))*cos(8*d*x + 8*c) - 8*(a^3*b^2 - 2*a^2*b^3 + a*b^4 - 2*(8*a^4*b - 19*a^3*b^2 + 14*a^2*b^3 - 3*a*b^4)*cos(4*d*x + 4*c) - 4*(a^3*b^2 - 2*a^2*b^3 + a*b^4)*cos(2*d*x + 2*c))*cos(6*d*x + 6*c) - 4*(8*a^4*b - 19*a^3*b^2 + 14*a^2*b^3 - 3*a*b^4 - 4*(8*a^4*b - 19*a^3*b^2 + 14*a^2*b^3 - 3*a*b^4)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 8*(a^3*b^2 - 2*a^2*b^3 + a*b^4)*cos(2*d*x + 2*c) - 4*(2*(a^3*b^2 - 2*a^2*b^3 + a*b^4)*sin(6*d*x + 6*c) + (8*a^4*b - 19*a^3*b^2 + 14*a^2*b^3 - 3*a*b^4)*sin(4*d*x + 4*c) + 2*(a^3*b^2 - 2*a^2*b^3 + a*b^4)*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*((8*a^4*b - 19*a^3*b^2 + 14*a^2*b^3 - 3*a*b^4)*sin(4*d*x + 4*c) + 2*(a^3*b^2 - 2*a^2*b^3 + a*b^4)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c)), x) + (3*a*b^3*cos(14*d*x + 14*c) + 2*a*b^3 + b^4 - 3*(10*a*b^3 - b^4)*cos(12*d*x + 12*c) - (80*a^2*b^2 - 111*a*b^3 + 16*b^4)*cos(10*d*x + 10*c) + (256*a^3*b - 64*a^2*b^2 - 26*a*b^3 + 35*b^4)*cos(8*d*x + 8*c) + (336*a^2*b^2 - 95*a*b^3 - 40*b^4)*cos(6*d*x + 6*c) - (64*a^2*b^2 - 54*a*b^3 - 25*b^4)*cos(4*d*x + 4*c) - (19*a*b^3 + 8*b^4)*cos(2*d*x + 2*c))*sin(16*d*x + 16*c) - (19*a*b^3 + 8*b^4 - 12*(8*a^2*b^2 + 13*a*b^3 - 2*b^4)*cos(12*d*x + 12*c) - 16*(16*a^2*b^2 - 45*a*b^3 + 8*b^4)*cos(10*d*x + 10*c) + 2*(1408*a^3*b - 544*a^2*b^2 + a*b^3 + 140*b^4)*cos(8*d*x + 8*c) + 32*(96*a^2*b^2 - 29*a*b^3 - 10*b^4)*cos(6*d*x + 6*c) - 4*(152*a^2*b^2 - 129*a*b^3 - 50*b^4)*cos(4*d*x + 4*c) - 16*(11*a*b^3 + 4*b^4)*cos(2*d*x + 2*c))*sin(14*d*x + 14*c) - (64*a^2*b^2 - 54*a*b^3 - 25*b^4 - 4*(640*a^3*b - 488*a^2*b^2 + 389*a*b^3 - 70*b^4)*cos(10*d*x + 10*c) + 2*(4096*a^4 - 8448*a^3*b + 3744*a^2*b^2 - 414*a*b^3 - 385*b^4)*cos(8*d*x + 8*c) + 4*(2688*a^3*b - 4072*a^2*b^2 + 861*a*b^3 + 238*b^4)*cos(6*d*x + 6*c) - 8*(256*a^3*b - 560*a^2*b^2 + 206*a*b^3 + 77*b^4)*cos(4*d*x + 4*c) - 4*(152*a^2*b^2 - 129*a*b^3 - 50*b^4)*cos(2*d*x + 2*c))*sin(12*d*x + 12*c) + (336*a^2*b^2 - 95*a*b^3 - 40*b^4 + 2*(26624*a^4 - 33152*a^3*b + 15632*a^2*b^2 - 2453*a*b^3 - 420*b^4)*cos(8*d*x + 8*c) + 16*(3328*a^3*b - 3104*a^2*b^2 + 529*a*b^3 + 84*b^4)*cos(6*d*x + 6*c) - 4*(2688*a^3*b - 4072*a^2*b^2 + 861*a*b^3 + 238*b^4)*cos(4*d*x + 4*c) - 32*(96*a^2*b^2 - 29*a*b^3 - 10*b^4)*cos(2*d*x + 2*c))*sin(10*d*x + 10*c) + (256*a^3*b - 64*a^2*b^2 - 26*a*b^3 + 35*b^4 + 2*(26624*a^4 - 33152*a^3*b + 15632*a^2*b^2 - 2453*a*b^3 - 420*b^4)*cos(6*d*x + 6*c) - 2*(4096*a^4 - 8448*a^3*b + 3744*a^2*b^2 - 414*a*b^3 - 385*b^4)*cos(4*d*x + 4*c) - 2*(1408*a^3*b - 544*a^2*b^2 + a*b^3 + 140*b^4)*cos(2*d*x + 2*c))*sin(8*d*x + 8*c) - (80*a^2*b^2 - 111*a*b^3 + 16*b^4 - 4*(640*a^3*b - 488*a^2*b^2 + 389*a*b^3 - 70*b^4)*cos(4*d*x + 4*c) - 16*(16*a^2*b^2 - 45*a*b^3 + 8*b^4)*cos(2*d*x + 2*c))*sin(6*d*x + 6*c) - 3*(10*a*b^3 - b^4 - 4*(8*a^2*b^2 + 13*a*b^3 - 2*b^4)*cos(2*d*x + 2*c))*sin(4*d*x + 4*c))/((a^3*b^4 - 2*a^2*b^5 + a*b^6)*d*cos(16*d*x + 16*c)^2 + 64*(a^3*b^4 - 2*a^2*b^5 + a*b^6)*d*cos(14*d*x + 14*c)^2 + 16*(64*a^5*b^2 - 240*a^4*b^3 + 337*a^3*b^4 - 210*a^2*b^5 + 49*a*b^6)*d*cos(12*d*x + 12*c)^2 + 64*(256*a^5*b^2 - 736*a^4*b^3 + 753*a^3*b^4 - 322*a^2*b^5 + 49*a*b^6)*d*cos(10*d*x + 10*c)^2 + 4*(16384*a^7 - 57344*a^6*b + 83712*a^5*b^2 - 67648*a^4*b^3 + 32841*a^3*b^4 - 9170*a^2*b^5 + 1225*a*b^6)*d*cos(8*d*x + 8*c)^2 + 64*(256*a^5*b^2 - 736*a^4*b^3 + 753*a^3*b^4 - 322*a^2*b^5 + 49*a*b^6)*d*cos(6*d*x + 6*c)^2 + 16*(64*a^5*b^2 - 240*a^4*b^3 + 337*a^3*b^4 - 210*a^2*b^5 + 49*a*b^6)*d*cos(4*d*x + 4*c)^2 + 64*(a^3*b^4 - 2*a^2*b^5 + a*b^6)*d*cos(2*d*x + 2*c)^2 + (a^3*b^4 - 2*a^2*b^5 + a*b^6)*d*sin(16*d*x + 16*c)^2 + 64*(a^3*b^4 - 2*a^2*b^5 + a*b^6)*d*sin(14*d*x + 14*c)^2 + 16*(64*a^5*b^2 - 240*a^4*b^3 + 337*a^3*b^4 - 210*a^2*b^5 + 49*a*b^6)*d*sin(12*d*x + 12*c)^2 + 64*(256*a^5*b^2 - 736*a^4*b^3 + 753*a^3*b^4 - 322*a^2*b^5 + 49*a*b^6)*d*sin(10*d*x + 10*c)^2 + 4*(16384*a^7 - 57344*a^6*b + 83712*a^5*b^2 - 67648*a^4*b^3 + 32841*a^3*b^4 - 9170*a^2*b^5 + 1225*a*b^6)*d*sin(8*d*x + 8*c)^2 + 64*(256*a^5*b^2 - 736*a^4*b^3 + 753*a^3*b^4 - 322*a^2*b^5 + 49*a*b^6)*d*sin(6*d*x + 6*c)^2 + 16*(64*a^5*b^2 - 240*a^4*b^3 + 337*a^3*b^4 - 210*a^2*b^5 + 49*a*b^6)*d*sin(4*d*x + 4*c)^2 + 64*(8*a^4*b^3 - 23*a^3*b^4 + 22*a^2*b^5 - 7*a*b^6)*d*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 64*(a^3*b^4 - 2*a^2*b^5 + a*b^6)*d*sin(2*d*x + 2*c)^2 - 16*(a^3*b^4 - 2*a^2*b^5 + a*b^6)*d*cos(2*d*x + 2*c) + (a^3*b^4 - 2*a^2*b^5 + a*b^6)*d - 2*(8*(a^3*b^4 - 2*a^2*b^5 + a*b^6)*d*cos(14*d*x + 14*c) + 4*(8*a^4*b^3 - 23*a^3*b^4 + 22*a^2*b^5 - 7*a*b^6)*d*cos(12*d*x + 12*c) - 8*(16*a^4*b^3 - 39*a^3*b^4 + 30*a^2*b^5 - 7*a*b^6)*d*cos(10*d*x + 10*c) - 2*(128*a^5*b^2 - 352*a^4*b^3 + 355*a^3*b^4 - 166*a^2*b^5 + 35*a*b^6)*d*cos(8*d*x + 8*c) - 8*(16*a^4*b^3 - 39*a^3*b^4 + 30*a^2*b^5 - 7*a*b^6)*d*cos(6*d*x + 6*c) + 4*(8*a^4*b^3 - 23*a^3*b^4 + 22*a^2*b^5 - 7*a*b^6)*d*cos(4*d*x + 4*c) + 8*(a^3*b^4 - 2*a^2*b^5 + a*b^6)*d*cos(2*d*x + 2*c) - (a^3*b^4 - 2*a^2*b^5 + a*b^6)*d)*cos(16*d*x + 16*c) + 16*(4*(8*a^4*b^3 - 23*a^3*b^4 + 22*a^2*b^5 - 7*a*b^6)*d*cos(12*d*x + 12*c) - 8*(16*a^4*b^3 - 39*a^3*b^4 + 30*a^2*b^5 - 7*a*b^6)*d*cos(10*d*x + 10*c) - 2*(128*a^5*b^2 - 352*a^4*b^3 + 355*a^3*b^4 - 166*a^2*b^5 + 35*a*b^6)*d*cos(8*d*x + 8*c) - 8*(16*a^4*b^3 - 39*a^3*b^4 + 30*a^2*b^5 - 7*a*b^6)*d*cos(6*d*x + 6*c) + 4*(8*a^4*b^3 - 23*a^3*b^4 + 22*a^2*b^5 - 7*a*b^6)*d*cos(4*d*x + 4*c) + 8*(a^3*b^4 - 2*a^2*b^5 + a*b^6)*d*cos(2*d*x + 2*c) - (a^3*b^4 - 2*a^2*b^5 + a*b^6)*d)*cos(14*d*x + 14*c) - 8*(8*(128*a^5*b^2 - 424*a^4*b^3 + 513*a^3*b^4 - 266*a^2*b^5 + 49*a*b^6)*d*cos(10*d*x + 10*c) + 2*(1024*a^6*b - 3712*a^5*b^2 + 5304*a^4*b^3 - 3813*a^3*b^4 + 1442*a^2*b^5 - 245*a*b^6)*d*cos(8*d*x + 8*c) + 8*(128*a^5*b^2 - 424*a^4*b^3 + 513*a^3*b^4 - 266*a^2*b^5 + 49*a*b^6)*d*cos(6*d*x + 6*c) - 4*(64*a^5*b^2 - 240*a^4*b^3 + 337*a^3*b^4 - 210*a^2*b^5 + 49*a*b^6)*d*cos(4*d*x + 4*c) - 8*(8*a^4*b^3 - 23*a^3*b^4 + 22*a^2*b^5 - 7*a*b^6)*d*cos(2*d*x + 2*c) + (8*a^4*b^3 - 23*a^3*b^4 + 22*a^2*b^5 - 7*a*b^6)*d)*cos(12*d*x + 12*c) + 16*(2*(2048*a^6*b - 6528*a^5*b^2 + 8144*a^4*b^3 - 5141*a^3*b^4 + 1722*a^2*b^5 - 245*a*b^6)*d*cos(8*d*x + 8*c) + 8*(256*a^5*b^2 - 736*a^4*b^3 + 753*a^3*b^4 - 322*a^2*b^5 + 49*a*b^6)*d*cos(6*d*x + 6*c) - 4*(128*a^5*b^2 - 424*a^4*b^3 + 513*a^3*b^4 - 266*a^2*b^5 + 49*a*b^6)*d*cos(4*d*x + 4*c) - 8*(16*a^4*b^3 - 39*a^3*b^4 + 30*a^2*b^5 - 7*a*b^6)*d*cos(2*d*x + 2*c) + (16*a^4*b^3 - 39*a^3*b^4 + 30*a^2*b^5 - 7*a*b^6)*d)*cos(10*d*x + 10*c) + 4*(8*(2048*a^6*b - 6528*a^5*b^2 + 8144*a^4*b^3 - 5141*a^3*b^4 + 1722*a^2*b^5 - 245*a*b^6)*d*cos(6*d*x + 6*c) - 4*(1024*a^6*b - 3712*a^5*b^2 + 5304*a^4*b^3 - 3813*a^3*b^4 + 1442*a^2*b^5 - 245*a*b^6)*d*cos(4*d*x + 4*c) - 8*(128*a^5*b^2 - 352*a^4*b^3 + 355*a^3*b^4 - 166*a^2*b^5 + 35*a*b^6)*d*cos(2*d*x + 2*c) + (128*a^5*b^2 - 352*a^4*b^3 + 355*a^3*b^4 - 166*a^2*b^5 + 35*a*b^6)*d)*cos(8*d*x + 8*c) - 16*(4*(128*a^5*b^2 - 424*a^4*b^3 + 513*a^3*b^4 - 266*a^2*b^5 + 49*a*b^6)*d*cos(4*d*x + 4*c) + 8*(16*a^4*b^3 - 39*a^3*b^4 + 30*a^2*b^5 - 7*a*b^6)*d*cos(2*d*x + 2*c) - (16*a^4*b^3 - 39*a^3*b^4 + 30*a^2*b^5 - 7*a*b^6)*d)*cos(6*d*x + 6*c) + 8*(8*(8*a^4*b^3 - 23*a^3*b^4 + 22*a^2*b^5 - 7*a*b^6)*d*cos(2*d*x + 2*c) - (8*a^4*b^3 - 23*a^3*b^4 + 22*a^2*b^5 - 7*a*b^6)*d)*cos(4*d*x + 4*c) - 4*(4*(a^3*b^4 - 2*a^2*b^5 + a*b^6)*d*sin(14*d*x + 14*c) + 2*(8*a^4*b^3 - 23*a^3*b^4 + 22*a^2*b^5 - 7*a*b^6)*d*sin(12*d*x + 12*c) - 4*(16*a^4*b^3 - 39*a^3*b^4 + 30*a^2*b^5 - 7*a*b^6)*d*sin(10*d*x + 10*c) - (128*a^5*b^2 - 352*a^4*b^3 + 355*a^3*b^4 - 166*a^2*b^5 + 35*a*b^6)*d*sin(8*d*x + 8*c) - 4*(16*a^4*b^3 - 39*a^3*b^4 + 30*a^2*b^5 - 7*a*b^6)*d*sin(6*d*x + 6*c) + 2*(8*a^4*b^3 - 23*a^3*b^4 + 22*a^2*b^5 - 7*a*b^6)*d*sin(4*d*x + 4*c) + 4*(a^3*b^4 - 2*a^2*b^5 + a*b^6)*d*sin(2*d*x + 2*c))*sin(16*d*x + 16*c) + 32*(2*(8*a^4*b^3 - 23*a^3*b^4 + 22*a^2*b^5 - 7*a*b^6)*d*sin(12*d*x + 12*c) - 4*(16*a^4*b^3 - 39*a^3*b^4 + 30*a^2*b^5 - 7*a*b^6)*d*sin(10*d*x + 10*c) - (128*a^5*b^2 - 352*a^4*b^3 + 355*a^3*b^4 - 166*a^2*b^5 + 35*a*b^6)*d*sin(8*d*x + 8*c) - 4*(16*a^4*b^3 - 39*a^3*b^4 + 30*a^2*b^5 - 7*a*b^6)*d*sin(6*d*x + 6*c) + 2*(8*a^4*b^3 - 23*a^3*b^4 + 22*a^2*b^5 - 7*a*b^6)*d*sin(4*d*x + 4*c) + 4*(a^3*b^4 - 2*a^2*b^5 + a*b^6)*d*sin(2*d*x + 2*c))*sin(14*d*x + 14*c) - 16*(4*(128*a^5*b^2 - 424*a^4*b^3 + 513*a^3*b^4 - 266*a^2*b^5 + 49*a*b^6)*d*sin(10*d*x + 10*c) + (1024*a^6*b - 3712*a^5*b^2 + 5304*a^4*b^3 - 3813*a^3*b^4 + 1442*a^2*b^5 - 245*a*b^6)*d*sin(8*d*x + 8*c) + 4*(128*a^5*b^2 - 424*a^4*b^3 + 513*a^3*b^4 - 266*a^2*b^5 + 49*a*b^6)*d*sin(6*d*x + 6*c) - 2*(64*a^5*b^2 - 240*a^4*b^3 + 337*a^3*b^4 - 210*a^2*b^5 + 49*a*b^6)*d*sin(4*d*x + 4*c) - 4*(8*a^4*b^3 - 23*a^3*b^4 + 22*a^2*b^5 - 7*a*b^6)*d*sin(2*d*x + 2*c))*sin(12*d*x + 12*c) + 32*((2048*a^6*b - 6528*a^5*b^2 + 8144*a^4*b^3 - 5141*a^3*b^4 + 1722*a^2*b^5 - 245*a*b^6)*d*sin(8*d*x + 8*c) + 4*(256*a^5*b^2 - 736*a^4*b^3 + 753*a^3*b^4 - 322*a^2*b^5 + 49*a*b^6)*d*sin(6*d*x + 6*c) - 2*(128*a^5*b^2 - 424*a^4*b^3 + 513*a^3*b^4 - 266*a^2*b^5 + 49*a*b^6)*d*sin(4*d*x + 4*c) - 4*(16*a^4*b^3 - 39*a^3*b^4 + 30*a^2*b^5 - 7*a*b^6)*d*sin(2*d*x + 2*c))*sin(10*d*x + 10*c) + 16*(2*(2048*a^6*b - 6528*a^5*b^2 + 8144*a^4*b^3 - 5141*a^3*b^4 + 1722*a^2*b^5 - 245*a*b^6)*d*sin(6*d*x + 6*c) - (1024*a^6*b - 3712*a^5*b^2 + 5304*a^4*b^3 - 3813*a^3*b^4 + 1442*a^2*b^5 - 245*a*b^6)*d*sin(4*d*x + 4*c) - 2*(128*a^5*b^2 - 352*a^4*b^3 + 355*a^3*b^4 - 166*a^2*b^5 + 35*a*b^6)*d*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) - 64*((128*a^5*b^2 - 424*a^4*b^3 + 513*a^3*b^4 - 266*a^2*b^5 + 49*a*b^6)*d*sin(4*d*x + 4*c) + 2*(16*a^4*b^3 - 39*a^3*b^4 + 30*a^2*b^5 - 7*a*b^6)*d*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))","F",0
233,0,0,0,0.000000," ","integrate(sin(d*x+c)^2/(a-b*sin(d*x+c)^4)^3,x, algorithm=""maxima"")","\frac{4 \, {\left(96 \, a^{3} b^{2} + 36 \, a^{2} b^{3} - 53 \, a b^{4} + 35 \, b^{5}\right)} \cos\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + {\left({\left(12 \, a^{2} b^{3} - 11 \, a b^{4} + 5 \, b^{5}\right)} \sin\left(14 \, d x + 14 \, c\right) - {\left(104 \, a^{2} b^{3} - 85 \, a b^{4} + 35 \, b^{5}\right)} \sin\left(12 \, d x + 12 \, c\right) - {\left(320 \, a^{3} b^{2} - 652 \, a^{2} b^{3} + 407 \, a b^{4} - 105 \, b^{5}\right)} \sin\left(10 \, d x + 10 \, c\right) + {\left(1408 \, a^{3} b^{2} - 1696 \, a^{2} b^{3} + 865 \, a b^{4} - 175 \, b^{5}\right)} \sin\left(8 \, d x + 8 \, c\right) + {\left(320 \, a^{3} b^{2} + 756 \, a^{2} b^{3} - 849 \, a b^{4} + 175 \, b^{5}\right)} \sin\left(6 \, d x + 6 \, c\right) - {\left(248 \, a^{2} b^{3} - 383 \, a b^{4} + 105 \, b^{5}\right)} \sin\left(4 \, d x + 4 \, c\right) - {\left(12 \, a^{2} b^{3} + 77 \, a b^{4} - 35 \, b^{5}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(16 \, d x + 16 \, c\right) + 2 \, {\left(2 \, {\left(96 \, a^{3} b^{2} + 36 \, a^{2} b^{3} - 53 \, a b^{4} + 35 \, b^{5}\right)} \sin\left(12 \, d x + 12 \, c\right) + 8 \, {\left(64 \, a^{3} b^{2} - 196 \, a^{2} b^{3} + 125 \, a b^{4} - 35 \, b^{5}\right)} \sin\left(10 \, d x + 10 \, c\right) - 3 \, {\left(512 \, a^{4} b + 1024 \, a^{3} b^{2} - 1556 \, a^{2} b^{3} + 865 \, a b^{4} - 175 \, b^{5}\right)} \sin\left(8 \, d x + 8 \, c\right) - 16 \, {\left(128 \, a^{3} b^{2} + 124 \, a^{2} b^{3} - 173 \, a b^{4} + 35 \, b^{5}\right)} \sin\left(6 \, d x + 6 \, c\right) + 2 \, {\left(96 \, a^{3} b^{2} + 324 \, a^{2} b^{3} - 649 \, a b^{4} + 175 \, b^{5}\right)} \sin\left(4 \, d x + 4 \, c\right) + 24 \, {\left(4 \, a^{2} b^{3} + 11 \, a b^{4} - 5 \, b^{5}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(14 \, d x + 14 \, c\right) + 2 \, {\left(2 \, {\left(2560 \, a^{4} b - 4128 \, a^{3} b^{2} + 3644 \, a^{2} b^{3} - 1379 \, a b^{4} + 245 \, b^{5}\right)} \sin\left(10 \, d x + 10 \, c\right) - {\left(9216 \, a^{4} b - 25984 \, a^{3} b^{2} + 21304 \, a^{2} b^{3} - 8575 \, a b^{4} + 1225 \, b^{5}\right)} \sin\left(8 \, d x + 8 \, c\right) - 2 \, {\left(2560 \, a^{4} b + 480 \, a^{3} b^{2} - 7908 \, a^{2} b^{3} + 5033 \, a b^{4} - 735 \, b^{5}\right)} \sin\left(6 \, d x + 6 \, c\right) + 4 \, {\left(576 \, a^{3} b^{2} - 1696 \, a^{2} b^{3} + 1323 \, a b^{4} - 245 \, b^{5}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(96 \, a^{3} b^{2} + 324 \, a^{2} b^{3} - 649 \, a b^{4} + 175 \, b^{5}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(12 \, d x + 12 \, c\right) + 2 \, {\left({\left(40960 \, a^{5} - 24064 \, a^{4} b - 22080 \, a^{3} b^{2} + 27516 \, a^{2} b^{3} - 11095 \, a b^{4} + 1225 \, b^{5}\right)} \sin\left(8 \, d x + 8 \, c\right) + 8 \, {\left(5120 \, a^{4} b - 1408 \, a^{3} b^{2} - 3900 \, a^{2} b^{3} + 2107 \, a b^{4} - 245 \, b^{5}\right)} \sin\left(6 \, d x + 6 \, c\right) - 2 \, {\left(2560 \, a^{4} b + 480 \, a^{3} b^{2} - 7908 \, a^{2} b^{3} + 5033 \, a b^{4} - 735 \, b^{5}\right)} \sin\left(4 \, d x + 4 \, c\right) - 16 \, {\left(128 \, a^{3} b^{2} + 124 \, a^{2} b^{3} - 173 \, a b^{4} + 35 \, b^{5}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(10 \, d x + 10 \, c\right) + 2 \, {\left({\left(40960 \, a^{5} - 24064 \, a^{4} b - 22080 \, a^{3} b^{2} + 27516 \, a^{2} b^{3} - 11095 \, a b^{4} + 1225 \, b^{5}\right)} \sin\left(6 \, d x + 6 \, c\right) - {\left(9216 \, a^{4} b - 25984 \, a^{3} b^{2} + 21304 \, a^{2} b^{3} - 8575 \, a b^{4} + 1225 \, b^{5}\right)} \sin\left(4 \, d x + 4 \, c\right) - 3 \, {\left(512 \, a^{4} b + 1024 \, a^{3} b^{2} - 1556 \, a^{2} b^{3} + 865 \, a b^{4} - 175 \, b^{5}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) + 4 \, {\left({\left(2560 \, a^{4} b - 4128 \, a^{3} b^{2} + 3644 \, a^{2} b^{3} - 1379 \, a b^{4} + 245 \, b^{5}\right)} \sin\left(4 \, d x + 4 \, c\right) + 4 \, {\left(64 \, a^{3} b^{2} - 196 \, a^{2} b^{3} + 125 \, a b^{4} - 35 \, b^{5}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left({\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cos\left(16 \, d x + 16 \, c\right)^{2} + 64 \, {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cos\left(14 \, d x + 14 \, c\right)^{2} + 16 \, {\left(64 \, a^{6} b^{2} - 240 \, a^{5} b^{3} + 337 \, a^{4} b^{4} - 210 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \cos\left(12 \, d x + 12 \, c\right)^{2} + 64 \, {\left(256 \, a^{6} b^{2} - 736 \, a^{5} b^{3} + 753 \, a^{4} b^{4} - 322 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \cos\left(10 \, d x + 10 \, c\right)^{2} + 4 \, {\left(16384 \, a^{8} - 57344 \, a^{7} b + 83712 \, a^{6} b^{2} - 67648 \, a^{5} b^{3} + 32841 \, a^{4} b^{4} - 9170 \, a^{3} b^{5} + 1225 \, a^{2} b^{6}\right)} d \cos\left(8 \, d x + 8 \, c\right)^{2} + 64 \, {\left(256 \, a^{6} b^{2} - 736 \, a^{5} b^{3} + 753 \, a^{4} b^{4} - 322 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \cos\left(6 \, d x + 6 \, c\right)^{2} + 16 \, {\left(64 \, a^{6} b^{2} - 240 \, a^{5} b^{3} + 337 \, a^{4} b^{4} - 210 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \cos\left(4 \, d x + 4 \, c\right)^{2} + 64 \, {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \sin\left(16 \, d x + 16 \, c\right)^{2} + 64 \, {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \sin\left(14 \, d x + 14 \, c\right)^{2} + 16 \, {\left(64 \, a^{6} b^{2} - 240 \, a^{5} b^{3} + 337 \, a^{4} b^{4} - 210 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \sin\left(12 \, d x + 12 \, c\right)^{2} + 64 \, {\left(256 \, a^{6} b^{2} - 736 \, a^{5} b^{3} + 753 \, a^{4} b^{4} - 322 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \sin\left(10 \, d x + 10 \, c\right)^{2} + 4 \, {\left(16384 \, a^{8} - 57344 \, a^{7} b + 83712 \, a^{6} b^{2} - 67648 \, a^{5} b^{3} + 32841 \, a^{4} b^{4} - 9170 \, a^{3} b^{5} + 1225 \, a^{2} b^{6}\right)} d \sin\left(8 \, d x + 8 \, c\right)^{2} + 64 \, {\left(256 \, a^{6} b^{2} - 736 \, a^{5} b^{3} + 753 \, a^{4} b^{4} - 322 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \sin\left(6 \, d x + 6 \, c\right)^{2} + 16 \, {\left(64 \, a^{6} b^{2} - 240 \, a^{5} b^{3} + 337 \, a^{4} b^{4} - 210 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right)^{2} + 64 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 64 \, {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \sin\left(2 \, d x + 2 \, c\right)^{2} - 16 \, {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d - 2 \, {\left(8 \, {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cos\left(14 \, d x + 14 \, c\right) + 4 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(12 \, d x + 12 \, c\right) - 8 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(10 \, d x + 10 \, c\right) - 2 \, {\left(128 \, a^{6} b^{2} - 352 \, a^{5} b^{3} + 355 \, a^{4} b^{4} - 166 \, a^{3} b^{5} + 35 \, a^{2} b^{6}\right)} d \cos\left(8 \, d x + 8 \, c\right) - 8 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(6 \, d x + 6 \, c\right) + 4 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d\right)} \cos\left(16 \, d x + 16 \, c\right) + 16 \, {\left(4 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(12 \, d x + 12 \, c\right) - 8 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(10 \, d x + 10 \, c\right) - 2 \, {\left(128 \, a^{6} b^{2} - 352 \, a^{5} b^{3} + 355 \, a^{4} b^{4} - 166 \, a^{3} b^{5} + 35 \, a^{2} b^{6}\right)} d \cos\left(8 \, d x + 8 \, c\right) - 8 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(6 \, d x + 6 \, c\right) + 4 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d\right)} \cos\left(14 \, d x + 14 \, c\right) - 8 \, {\left(8 \, {\left(128 \, a^{6} b^{2} - 424 \, a^{5} b^{3} + 513 \, a^{4} b^{4} - 266 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \cos\left(10 \, d x + 10 \, c\right) + 2 \, {\left(1024 \, a^{7} b - 3712 \, a^{6} b^{2} + 5304 \, a^{5} b^{3} - 3813 \, a^{4} b^{4} + 1442 \, a^{3} b^{5} - 245 \, a^{2} b^{6}\right)} d \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(128 \, a^{6} b^{2} - 424 \, a^{5} b^{3} + 513 \, a^{4} b^{4} - 266 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(64 \, a^{6} b^{2} - 240 \, a^{5} b^{3} + 337 \, a^{4} b^{4} - 210 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d\right)} \cos\left(12 \, d x + 12 \, c\right) + 16 \, {\left(2 \, {\left(2048 \, a^{7} b - 6528 \, a^{6} b^{2} + 8144 \, a^{5} b^{3} - 5141 \, a^{4} b^{4} + 1722 \, a^{3} b^{5} - 245 \, a^{2} b^{6}\right)} d \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(256 \, a^{6} b^{2} - 736 \, a^{5} b^{3} + 753 \, a^{4} b^{4} - 322 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(128 \, a^{6} b^{2} - 424 \, a^{5} b^{3} + 513 \, a^{4} b^{4} - 266 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d\right)} \cos\left(10 \, d x + 10 \, c\right) + 4 \, {\left(8 \, {\left(2048 \, a^{7} b - 6528 \, a^{6} b^{2} + 8144 \, a^{5} b^{3} - 5141 \, a^{4} b^{4} + 1722 \, a^{3} b^{5} - 245 \, a^{2} b^{6}\right)} d \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(1024 \, a^{7} b - 3712 \, a^{6} b^{2} + 5304 \, a^{5} b^{3} - 3813 \, a^{4} b^{4} + 1442 \, a^{3} b^{5} - 245 \, a^{2} b^{6}\right)} d \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(128 \, a^{6} b^{2} - 352 \, a^{5} b^{3} + 355 \, a^{4} b^{4} - 166 \, a^{3} b^{5} + 35 \, a^{2} b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(128 \, a^{6} b^{2} - 352 \, a^{5} b^{3} + 355 \, a^{4} b^{4} - 166 \, a^{3} b^{5} + 35 \, a^{2} b^{6}\right)} d\right)} \cos\left(8 \, d x + 8 \, c\right) - 16 \, {\left(4 \, {\left(128 \, a^{6} b^{2} - 424 \, a^{5} b^{3} + 513 \, a^{4} b^{4} - 266 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d\right)} \cos\left(6 \, d x + 6 \, c\right) + 8 \, {\left(8 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(4 \, {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \sin\left(14 \, d x + 14 \, c\right) + 2 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(12 \, d x + 12 \, c\right) - 4 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(10 \, d x + 10 \, c\right) - {\left(128 \, a^{6} b^{2} - 352 \, a^{5} b^{3} + 355 \, a^{4} b^{4} - 166 \, a^{3} b^{5} + 35 \, a^{2} b^{6}\right)} d \sin\left(8 \, d x + 8 \, c\right) - 4 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(6 \, d x + 6 \, c\right) + 2 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(16 \, d x + 16 \, c\right) + 32 \, {\left(2 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(12 \, d x + 12 \, c\right) - 4 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(10 \, d x + 10 \, c\right) - {\left(128 \, a^{6} b^{2} - 352 \, a^{5} b^{3} + 355 \, a^{4} b^{4} - 166 \, a^{3} b^{5} + 35 \, a^{2} b^{6}\right)} d \sin\left(8 \, d x + 8 \, c\right) - 4 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(6 \, d x + 6 \, c\right) + 2 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(14 \, d x + 14 \, c\right) - 16 \, {\left(4 \, {\left(128 \, a^{6} b^{2} - 424 \, a^{5} b^{3} + 513 \, a^{4} b^{4} - 266 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \sin\left(10 \, d x + 10 \, c\right) + {\left(1024 \, a^{7} b - 3712 \, a^{6} b^{2} + 5304 \, a^{5} b^{3} - 3813 \, a^{4} b^{4} + 1442 \, a^{3} b^{5} - 245 \, a^{2} b^{6}\right)} d \sin\left(8 \, d x + 8 \, c\right) + 4 \, {\left(128 \, a^{6} b^{2} - 424 \, a^{5} b^{3} + 513 \, a^{4} b^{4} - 266 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \sin\left(6 \, d x + 6 \, c\right) - 2 \, {\left(64 \, a^{6} b^{2} - 240 \, a^{5} b^{3} + 337 \, a^{4} b^{4} - 210 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right) - 4 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(12 \, d x + 12 \, c\right) + 32 \, {\left({\left(2048 \, a^{7} b - 6528 \, a^{6} b^{2} + 8144 \, a^{5} b^{3} - 5141 \, a^{4} b^{4} + 1722 \, a^{3} b^{5} - 245 \, a^{2} b^{6}\right)} d \sin\left(8 \, d x + 8 \, c\right) + 4 \, {\left(256 \, a^{6} b^{2} - 736 \, a^{5} b^{3} + 753 \, a^{4} b^{4} - 322 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \sin\left(6 \, d x + 6 \, c\right) - 2 \, {\left(128 \, a^{6} b^{2} - 424 \, a^{5} b^{3} + 513 \, a^{4} b^{4} - 266 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right) - 4 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + 16 \, {\left(2 \, {\left(2048 \, a^{7} b - 6528 \, a^{6} b^{2} + 8144 \, a^{5} b^{3} - 5141 \, a^{4} b^{4} + 1722 \, a^{3} b^{5} - 245 \, a^{2} b^{6}\right)} d \sin\left(6 \, d x + 6 \, c\right) - {\left(1024 \, a^{7} b - 3712 \, a^{6} b^{2} + 5304 \, a^{5} b^{3} - 3813 \, a^{4} b^{4} + 1442 \, a^{3} b^{5} - 245 \, a^{2} b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(128 \, a^{6} b^{2} - 352 \, a^{5} b^{3} + 355 \, a^{4} b^{4} - 166 \, a^{3} b^{5} + 35 \, a^{2} b^{6}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) - 64 \, {\left({\left(128 \, a^{6} b^{2} - 424 \, a^{5} b^{3} + 513 \, a^{4} b^{4} - 266 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \int \frac{4 \, {\left(12 \, a^{2} b - 11 \, a b^{2} + 5 \, b^{3}\right)} \cos\left(6 \, d x + 6 \, c\right)^{2} - 4 \, {\left(256 \, a^{3} - 248 \, a^{2} b + 97 \, a b^{2} - 15 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(12 \, a^{2} b - 11 \, a b^{2} + 5 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(12 \, a^{2} b - 11 \, a b^{2} + 5 \, b^{3}\right)} \sin\left(6 \, d x + 6 \, c\right)^{2} - 4 \, {\left(256 \, a^{3} - 248 \, a^{2} b + 97 \, a b^{2} - 15 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, {\left(96 \, a^{3} - 252 \, a^{2} b + 149 \, a b^{2} - 35 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, {\left(12 \, a^{2} b - 11 \, a b^{2} + 5 \, b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - {\left({\left(12 \, a^{2} b - 11 \, a b^{2} + 5 \, b^{3}\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left(32 \, a^{2} b - 19 \, a b^{2} + 5 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right) + {\left(12 \, a^{2} b - 11 \, a b^{2} + 5 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) - {\left(12 \, a^{2} b - 11 \, a b^{2} + 5 \, b^{3} - 2 \, {\left(96 \, a^{3} - 252 \, a^{2} b + 149 \, a b^{2} - 35 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(12 \, a^{2} b - 11 \, a b^{2} + 5 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) + 2 \, {\left(32 \, a^{2} b - 19 \, a b^{2} + 5 \, b^{3} + {\left(96 \, a^{3} - 252 \, a^{2} b + 149 \, a b^{2} - 35 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - {\left(12 \, a^{2} b - 11 \, a b^{2} + 5 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right) - {\left({\left(12 \, a^{2} b - 11 \, a b^{2} + 5 \, b^{3}\right)} \sin\left(6 \, d x + 6 \, c\right) - 2 \, {\left(32 \, a^{2} b - 19 \, a b^{2} + 5 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) + {\left(12 \, a^{2} b - 11 \, a b^{2} + 5 \, b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 2 \, {\left({\left(96 \, a^{3} - 252 \, a^{2} b + 149 \, a b^{2} - 35 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) + 4 \, {\left(12 \, a^{2} b - 11 \, a b^{2} + 5 \, b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}{a^{4} b^{2} - 2 \, a^{3} b^{3} + a^{2} b^{4} + {\left(a^{4} b^{2} - 2 \, a^{3} b^{3} + a^{2} b^{4}\right)} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a^{4} b^{2} - 2 \, a^{3} b^{3} + a^{2} b^{4}\right)} \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{6} - 176 \, a^{5} b + 169 \, a^{4} b^{2} - 66 \, a^{3} b^{3} + 9 \, a^{2} b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(a^{4} b^{2} - 2 \, a^{3} b^{3} + a^{2} b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{4} b^{2} - 2 \, a^{3} b^{3} + a^{2} b^{4}\right)} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a^{4} b^{2} - 2 \, a^{3} b^{3} + a^{2} b^{4}\right)} \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{6} - 176 \, a^{5} b + 169 \, a^{4} b^{2} - 66 \, a^{3} b^{3} + 9 \, a^{2} b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(8 \, a^{5} b - 19 \, a^{4} b^{2} + 14 \, a^{3} b^{3} - 3 \, a^{2} b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, {\left(a^{4} b^{2} - 2 \, a^{3} b^{3} + a^{2} b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{4} b^{2} - 2 \, a^{3} b^{3} + a^{2} b^{4} - 4 \, {\left(a^{4} b^{2} - 2 \, a^{3} b^{3} + a^{2} b^{4}\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left(8 \, a^{5} b - 19 \, a^{4} b^{2} + 14 \, a^{3} b^{3} - 3 \, a^{2} b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a^{4} b^{2} - 2 \, a^{3} b^{3} + a^{2} b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) - 8 \, {\left(a^{4} b^{2} - 2 \, a^{3} b^{3} + a^{2} b^{4} - 2 \, {\left(8 \, a^{5} b - 19 \, a^{4} b^{2} + 14 \, a^{3} b^{3} - 3 \, a^{2} b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a^{4} b^{2} - 2 \, a^{3} b^{3} + a^{2} b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(8 \, a^{5} b - 19 \, a^{4} b^{2} + 14 \, a^{3} b^{3} - 3 \, a^{2} b^{4} - 4 \, {\left(8 \, a^{5} b - 19 \, a^{4} b^{2} + 14 \, a^{3} b^{3} - 3 \, a^{2} b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(a^{4} b^{2} - 2 \, a^{3} b^{3} + a^{2} b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right) - 4 \, {\left(2 \, {\left(a^{4} b^{2} - 2 \, a^{3} b^{3} + a^{2} b^{4}\right)} \sin\left(6 \, d x + 6 \, c\right) + {\left(8 \, a^{5} b - 19 \, a^{4} b^{2} + 14 \, a^{3} b^{3} - 3 \, a^{2} b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a^{4} b^{2} - 2 \, a^{3} b^{3} + a^{2} b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left({\left(8 \, a^{5} b - 19 \, a^{4} b^{2} + 14 \, a^{3} b^{3} - 3 \, a^{2} b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a^{4} b^{2} - 2 \, a^{3} b^{3} + a^{2} b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}\,{d x} - {\left(11 \, a b^{4} - 5 \, b^{5} + {\left(12 \, a^{2} b^{3} - 11 \, a b^{4} + 5 \, b^{5}\right)} \cos\left(14 \, d x + 14 \, c\right) - {\left(104 \, a^{2} b^{3} - 85 \, a b^{4} + 35 \, b^{5}\right)} \cos\left(12 \, d x + 12 \, c\right) - {\left(320 \, a^{3} b^{2} - 652 \, a^{2} b^{3} + 407 \, a b^{4} - 105 \, b^{5}\right)} \cos\left(10 \, d x + 10 \, c\right) + {\left(1408 \, a^{3} b^{2} - 1696 \, a^{2} b^{3} + 865 \, a b^{4} - 175 \, b^{5}\right)} \cos\left(8 \, d x + 8 \, c\right) + {\left(320 \, a^{3} b^{2} + 756 \, a^{2} b^{3} - 849 \, a b^{4} + 175 \, b^{5}\right)} \cos\left(6 \, d x + 6 \, c\right) - {\left(248 \, a^{2} b^{3} - 383 \, a b^{4} + 105 \, b^{5}\right)} \cos\left(4 \, d x + 4 \, c\right) - {\left(12 \, a^{2} b^{3} + 77 \, a b^{4} - 35 \, b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(16 \, d x + 16 \, c\right) + {\left(12 \, a^{2} b^{3} + 77 \, a b^{4} - 35 \, b^{5} - 4 \, {\left(96 \, a^{3} b^{2} + 36 \, a^{2} b^{3} - 53 \, a b^{4} + 35 \, b^{5}\right)} \cos\left(12 \, d x + 12 \, c\right) - 16 \, {\left(64 \, a^{3} b^{2} - 196 \, a^{2} b^{3} + 125 \, a b^{4} - 35 \, b^{5}\right)} \cos\left(10 \, d x + 10 \, c\right) + 6 \, {\left(512 \, a^{4} b + 1024 \, a^{3} b^{2} - 1556 \, a^{2} b^{3} + 865 \, a b^{4} - 175 \, b^{5}\right)} \cos\left(8 \, d x + 8 \, c\right) + 32 \, {\left(128 \, a^{3} b^{2} + 124 \, a^{2} b^{3} - 173 \, a b^{4} + 35 \, b^{5}\right)} \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(96 \, a^{3} b^{2} + 324 \, a^{2} b^{3} - 649 \, a b^{4} + 175 \, b^{5}\right)} \cos\left(4 \, d x + 4 \, c\right) - 48 \, {\left(4 \, a^{2} b^{3} + 11 \, a b^{4} - 5 \, b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(14 \, d x + 14 \, c\right) + {\left(248 \, a^{2} b^{3} - 383 \, a b^{4} + 105 \, b^{5} - 4 \, {\left(2560 \, a^{4} b - 4128 \, a^{3} b^{2} + 3644 \, a^{2} b^{3} - 1379 \, a b^{4} + 245 \, b^{5}\right)} \cos\left(10 \, d x + 10 \, c\right) + 2 \, {\left(9216 \, a^{4} b - 25984 \, a^{3} b^{2} + 21304 \, a^{2} b^{3} - 8575 \, a b^{4} + 1225 \, b^{5}\right)} \cos\left(8 \, d x + 8 \, c\right) + 4 \, {\left(2560 \, a^{4} b + 480 \, a^{3} b^{2} - 7908 \, a^{2} b^{3} + 5033 \, a b^{4} - 735 \, b^{5}\right)} \cos\left(6 \, d x + 6 \, c\right) - 8 \, {\left(576 \, a^{3} b^{2} - 1696 \, a^{2} b^{3} + 1323 \, a b^{4} - 245 \, b^{5}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(96 \, a^{3} b^{2} + 324 \, a^{2} b^{3} - 649 \, a b^{4} + 175 \, b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(12 \, d x + 12 \, c\right) - {\left(320 \, a^{3} b^{2} + 756 \, a^{2} b^{3} - 849 \, a b^{4} + 175 \, b^{5} + 2 \, {\left(40960 \, a^{5} - 24064 \, a^{4} b - 22080 \, a^{3} b^{2} + 27516 \, a^{2} b^{3} - 11095 \, a b^{4} + 1225 \, b^{5}\right)} \cos\left(8 \, d x + 8 \, c\right) + 16 \, {\left(5120 \, a^{4} b - 1408 \, a^{3} b^{2} - 3900 \, a^{2} b^{3} + 2107 \, a b^{4} - 245 \, b^{5}\right)} \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(2560 \, a^{4} b + 480 \, a^{3} b^{2} - 7908 \, a^{2} b^{3} + 5033 \, a b^{4} - 735 \, b^{5}\right)} \cos\left(4 \, d x + 4 \, c\right) - 32 \, {\left(128 \, a^{3} b^{2} + 124 \, a^{2} b^{3} - 173 \, a b^{4} + 35 \, b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) - {\left(1408 \, a^{3} b^{2} - 1696 \, a^{2} b^{3} + 865 \, a b^{4} - 175 \, b^{5} + 2 \, {\left(40960 \, a^{5} - 24064 \, a^{4} b - 22080 \, a^{3} b^{2} + 27516 \, a^{2} b^{3} - 11095 \, a b^{4} + 1225 \, b^{5}\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left(9216 \, a^{4} b - 25984 \, a^{3} b^{2} + 21304 \, a^{2} b^{3} - 8575 \, a b^{4} + 1225 \, b^{5}\right)} \cos\left(4 \, d x + 4 \, c\right) - 6 \, {\left(512 \, a^{4} b + 1024 \, a^{3} b^{2} - 1556 \, a^{2} b^{3} + 865 \, a b^{4} - 175 \, b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + {\left(320 \, a^{3} b^{2} - 652 \, a^{2} b^{3} + 407 \, a b^{4} - 105 \, b^{5} - 4 \, {\left(2560 \, a^{4} b - 4128 \, a^{3} b^{2} + 3644 \, a^{2} b^{3} - 1379 \, a b^{4} + 245 \, b^{5}\right)} \cos\left(4 \, d x + 4 \, c\right) - 16 \, {\left(64 \, a^{3} b^{2} - 196 \, a^{2} b^{3} + 125 \, a b^{4} - 35 \, b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + {\left(104 \, a^{2} b^{3} - 85 \, a b^{4} + 35 \, b^{5} - 4 \, {\left(96 \, a^{3} b^{2} + 36 \, a^{2} b^{3} - 53 \, a b^{4} + 35 \, b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) - {\left(12 \, a^{2} b^{3} - 11 \, a b^{4} + 5 \, b^{5}\right)} \sin\left(2 \, d x + 2 \, c\right)}{16 \, {\left({\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cos\left(16 \, d x + 16 \, c\right)^{2} + 64 \, {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cos\left(14 \, d x + 14 \, c\right)^{2} + 16 \, {\left(64 \, a^{6} b^{2} - 240 \, a^{5} b^{3} + 337 \, a^{4} b^{4} - 210 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \cos\left(12 \, d x + 12 \, c\right)^{2} + 64 \, {\left(256 \, a^{6} b^{2} - 736 \, a^{5} b^{3} + 753 \, a^{4} b^{4} - 322 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \cos\left(10 \, d x + 10 \, c\right)^{2} + 4 \, {\left(16384 \, a^{8} - 57344 \, a^{7} b + 83712 \, a^{6} b^{2} - 67648 \, a^{5} b^{3} + 32841 \, a^{4} b^{4} - 9170 \, a^{3} b^{5} + 1225 \, a^{2} b^{6}\right)} d \cos\left(8 \, d x + 8 \, c\right)^{2} + 64 \, {\left(256 \, a^{6} b^{2} - 736 \, a^{5} b^{3} + 753 \, a^{4} b^{4} - 322 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \cos\left(6 \, d x + 6 \, c\right)^{2} + 16 \, {\left(64 \, a^{6} b^{2} - 240 \, a^{5} b^{3} + 337 \, a^{4} b^{4} - 210 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \cos\left(4 \, d x + 4 \, c\right)^{2} + 64 \, {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \sin\left(16 \, d x + 16 \, c\right)^{2} + 64 \, {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \sin\left(14 \, d x + 14 \, c\right)^{2} + 16 \, {\left(64 \, a^{6} b^{2} - 240 \, a^{5} b^{3} + 337 \, a^{4} b^{4} - 210 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \sin\left(12 \, d x + 12 \, c\right)^{2} + 64 \, {\left(256 \, a^{6} b^{2} - 736 \, a^{5} b^{3} + 753 \, a^{4} b^{4} - 322 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \sin\left(10 \, d x + 10 \, c\right)^{2} + 4 \, {\left(16384 \, a^{8} - 57344 \, a^{7} b + 83712 \, a^{6} b^{2} - 67648 \, a^{5} b^{3} + 32841 \, a^{4} b^{4} - 9170 \, a^{3} b^{5} + 1225 \, a^{2} b^{6}\right)} d \sin\left(8 \, d x + 8 \, c\right)^{2} + 64 \, {\left(256 \, a^{6} b^{2} - 736 \, a^{5} b^{3} + 753 \, a^{4} b^{4} - 322 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \sin\left(6 \, d x + 6 \, c\right)^{2} + 16 \, {\left(64 \, a^{6} b^{2} - 240 \, a^{5} b^{3} + 337 \, a^{4} b^{4} - 210 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right)^{2} + 64 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 64 \, {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \sin\left(2 \, d x + 2 \, c\right)^{2} - 16 \, {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d - 2 \, {\left(8 \, {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cos\left(14 \, d x + 14 \, c\right) + 4 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(12 \, d x + 12 \, c\right) - 8 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(10 \, d x + 10 \, c\right) - 2 \, {\left(128 \, a^{6} b^{2} - 352 \, a^{5} b^{3} + 355 \, a^{4} b^{4} - 166 \, a^{3} b^{5} + 35 \, a^{2} b^{6}\right)} d \cos\left(8 \, d x + 8 \, c\right) - 8 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(6 \, d x + 6 \, c\right) + 4 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d\right)} \cos\left(16 \, d x + 16 \, c\right) + 16 \, {\left(4 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(12 \, d x + 12 \, c\right) - 8 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(10 \, d x + 10 \, c\right) - 2 \, {\left(128 \, a^{6} b^{2} - 352 \, a^{5} b^{3} + 355 \, a^{4} b^{4} - 166 \, a^{3} b^{5} + 35 \, a^{2} b^{6}\right)} d \cos\left(8 \, d x + 8 \, c\right) - 8 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(6 \, d x + 6 \, c\right) + 4 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d\right)} \cos\left(14 \, d x + 14 \, c\right) - 8 \, {\left(8 \, {\left(128 \, a^{6} b^{2} - 424 \, a^{5} b^{3} + 513 \, a^{4} b^{4} - 266 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \cos\left(10 \, d x + 10 \, c\right) + 2 \, {\left(1024 \, a^{7} b - 3712 \, a^{6} b^{2} + 5304 \, a^{5} b^{3} - 3813 \, a^{4} b^{4} + 1442 \, a^{3} b^{5} - 245 \, a^{2} b^{6}\right)} d \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(128 \, a^{6} b^{2} - 424 \, a^{5} b^{3} + 513 \, a^{4} b^{4} - 266 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(64 \, a^{6} b^{2} - 240 \, a^{5} b^{3} + 337 \, a^{4} b^{4} - 210 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d\right)} \cos\left(12 \, d x + 12 \, c\right) + 16 \, {\left(2 \, {\left(2048 \, a^{7} b - 6528 \, a^{6} b^{2} + 8144 \, a^{5} b^{3} - 5141 \, a^{4} b^{4} + 1722 \, a^{3} b^{5} - 245 \, a^{2} b^{6}\right)} d \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(256 \, a^{6} b^{2} - 736 \, a^{5} b^{3} + 753 \, a^{4} b^{4} - 322 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(128 \, a^{6} b^{2} - 424 \, a^{5} b^{3} + 513 \, a^{4} b^{4} - 266 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d\right)} \cos\left(10 \, d x + 10 \, c\right) + 4 \, {\left(8 \, {\left(2048 \, a^{7} b - 6528 \, a^{6} b^{2} + 8144 \, a^{5} b^{3} - 5141 \, a^{4} b^{4} + 1722 \, a^{3} b^{5} - 245 \, a^{2} b^{6}\right)} d \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(1024 \, a^{7} b - 3712 \, a^{6} b^{2} + 5304 \, a^{5} b^{3} - 3813 \, a^{4} b^{4} + 1442 \, a^{3} b^{5} - 245 \, a^{2} b^{6}\right)} d \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(128 \, a^{6} b^{2} - 352 \, a^{5} b^{3} + 355 \, a^{4} b^{4} - 166 \, a^{3} b^{5} + 35 \, a^{2} b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(128 \, a^{6} b^{2} - 352 \, a^{5} b^{3} + 355 \, a^{4} b^{4} - 166 \, a^{3} b^{5} + 35 \, a^{2} b^{6}\right)} d\right)} \cos\left(8 \, d x + 8 \, c\right) - 16 \, {\left(4 \, {\left(128 \, a^{6} b^{2} - 424 \, a^{5} b^{3} + 513 \, a^{4} b^{4} - 266 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d\right)} \cos\left(6 \, d x + 6 \, c\right) + 8 \, {\left(8 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(4 \, {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \sin\left(14 \, d x + 14 \, c\right) + 2 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(12 \, d x + 12 \, c\right) - 4 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(10 \, d x + 10 \, c\right) - {\left(128 \, a^{6} b^{2} - 352 \, a^{5} b^{3} + 355 \, a^{4} b^{4} - 166 \, a^{3} b^{5} + 35 \, a^{2} b^{6}\right)} d \sin\left(8 \, d x + 8 \, c\right) - 4 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(6 \, d x + 6 \, c\right) + 2 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(16 \, d x + 16 \, c\right) + 32 \, {\left(2 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(12 \, d x + 12 \, c\right) - 4 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(10 \, d x + 10 \, c\right) - {\left(128 \, a^{6} b^{2} - 352 \, a^{5} b^{3} + 355 \, a^{4} b^{4} - 166 \, a^{3} b^{5} + 35 \, a^{2} b^{6}\right)} d \sin\left(8 \, d x + 8 \, c\right) - 4 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(6 \, d x + 6 \, c\right) + 2 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(14 \, d x + 14 \, c\right) - 16 \, {\left(4 \, {\left(128 \, a^{6} b^{2} - 424 \, a^{5} b^{3} + 513 \, a^{4} b^{4} - 266 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \sin\left(10 \, d x + 10 \, c\right) + {\left(1024 \, a^{7} b - 3712 \, a^{6} b^{2} + 5304 \, a^{5} b^{3} - 3813 \, a^{4} b^{4} + 1442 \, a^{3} b^{5} - 245 \, a^{2} b^{6}\right)} d \sin\left(8 \, d x + 8 \, c\right) + 4 \, {\left(128 \, a^{6} b^{2} - 424 \, a^{5} b^{3} + 513 \, a^{4} b^{4} - 266 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \sin\left(6 \, d x + 6 \, c\right) - 2 \, {\left(64 \, a^{6} b^{2} - 240 \, a^{5} b^{3} + 337 \, a^{4} b^{4} - 210 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right) - 4 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(12 \, d x + 12 \, c\right) + 32 \, {\left({\left(2048 \, a^{7} b - 6528 \, a^{6} b^{2} + 8144 \, a^{5} b^{3} - 5141 \, a^{4} b^{4} + 1722 \, a^{3} b^{5} - 245 \, a^{2} b^{6}\right)} d \sin\left(8 \, d x + 8 \, c\right) + 4 \, {\left(256 \, a^{6} b^{2} - 736 \, a^{5} b^{3} + 753 \, a^{4} b^{4} - 322 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \sin\left(6 \, d x + 6 \, c\right) - 2 \, {\left(128 \, a^{6} b^{2} - 424 \, a^{5} b^{3} + 513 \, a^{4} b^{4} - 266 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right) - 4 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + 16 \, {\left(2 \, {\left(2048 \, a^{7} b - 6528 \, a^{6} b^{2} + 8144 \, a^{5} b^{3} - 5141 \, a^{4} b^{4} + 1722 \, a^{3} b^{5} - 245 \, a^{2} b^{6}\right)} d \sin\left(6 \, d x + 6 \, c\right) - {\left(1024 \, a^{7} b - 3712 \, a^{6} b^{2} + 5304 \, a^{5} b^{3} - 3813 \, a^{4} b^{4} + 1442 \, a^{3} b^{5} - 245 \, a^{2} b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(128 \, a^{6} b^{2} - 352 \, a^{5} b^{3} + 355 \, a^{4} b^{4} - 166 \, a^{3} b^{5} + 35 \, a^{2} b^{6}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) - 64 \, {\left({\left(128 \, a^{6} b^{2} - 424 \, a^{5} b^{3} + 513 \, a^{4} b^{4} - 266 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)}}"," ",0,"1/16*(4*(96*a^3*b^2 + 36*a^2*b^3 - 53*a*b^4 + 35*b^5)*cos(4*d*x + 4*c)*sin(2*d*x + 2*c) + ((12*a^2*b^3 - 11*a*b^4 + 5*b^5)*sin(14*d*x + 14*c) - (104*a^2*b^3 - 85*a*b^4 + 35*b^5)*sin(12*d*x + 12*c) - (320*a^3*b^2 - 652*a^2*b^3 + 407*a*b^4 - 105*b^5)*sin(10*d*x + 10*c) + (1408*a^3*b^2 - 1696*a^2*b^3 + 865*a*b^4 - 175*b^5)*sin(8*d*x + 8*c) + (320*a^3*b^2 + 756*a^2*b^3 - 849*a*b^4 + 175*b^5)*sin(6*d*x + 6*c) - (248*a^2*b^3 - 383*a*b^4 + 105*b^5)*sin(4*d*x + 4*c) - (12*a^2*b^3 + 77*a*b^4 - 35*b^5)*sin(2*d*x + 2*c))*cos(16*d*x + 16*c) + 2*(2*(96*a^3*b^2 + 36*a^2*b^3 - 53*a*b^4 + 35*b^5)*sin(12*d*x + 12*c) + 8*(64*a^3*b^2 - 196*a^2*b^3 + 125*a*b^4 - 35*b^5)*sin(10*d*x + 10*c) - 3*(512*a^4*b + 1024*a^3*b^2 - 1556*a^2*b^3 + 865*a*b^4 - 175*b^5)*sin(8*d*x + 8*c) - 16*(128*a^3*b^2 + 124*a^2*b^3 - 173*a*b^4 + 35*b^5)*sin(6*d*x + 6*c) + 2*(96*a^3*b^2 + 324*a^2*b^3 - 649*a*b^4 + 175*b^5)*sin(4*d*x + 4*c) + 24*(4*a^2*b^3 + 11*a*b^4 - 5*b^5)*sin(2*d*x + 2*c))*cos(14*d*x + 14*c) + 2*(2*(2560*a^4*b - 4128*a^3*b^2 + 3644*a^2*b^3 - 1379*a*b^4 + 245*b^5)*sin(10*d*x + 10*c) - (9216*a^4*b - 25984*a^3*b^2 + 21304*a^2*b^3 - 8575*a*b^4 + 1225*b^5)*sin(8*d*x + 8*c) - 2*(2560*a^4*b + 480*a^3*b^2 - 7908*a^2*b^3 + 5033*a*b^4 - 735*b^5)*sin(6*d*x + 6*c) + 4*(576*a^3*b^2 - 1696*a^2*b^3 + 1323*a*b^4 - 245*b^5)*sin(4*d*x + 4*c) + 2*(96*a^3*b^2 + 324*a^2*b^3 - 649*a*b^4 + 175*b^5)*sin(2*d*x + 2*c))*cos(12*d*x + 12*c) + 2*((40960*a^5 - 24064*a^4*b - 22080*a^3*b^2 + 27516*a^2*b^3 - 11095*a*b^4 + 1225*b^5)*sin(8*d*x + 8*c) + 8*(5120*a^4*b - 1408*a^3*b^2 - 3900*a^2*b^3 + 2107*a*b^4 - 245*b^5)*sin(6*d*x + 6*c) - 2*(2560*a^4*b + 480*a^3*b^2 - 7908*a^2*b^3 + 5033*a*b^4 - 735*b^5)*sin(4*d*x + 4*c) - 16*(128*a^3*b^2 + 124*a^2*b^3 - 173*a*b^4 + 35*b^5)*sin(2*d*x + 2*c))*cos(10*d*x + 10*c) + 2*((40960*a^5 - 24064*a^4*b - 22080*a^3*b^2 + 27516*a^2*b^3 - 11095*a*b^4 + 1225*b^5)*sin(6*d*x + 6*c) - (9216*a^4*b - 25984*a^3*b^2 + 21304*a^2*b^3 - 8575*a*b^4 + 1225*b^5)*sin(4*d*x + 4*c) - 3*(512*a^4*b + 1024*a^3*b^2 - 1556*a^2*b^3 + 865*a*b^4 - 175*b^5)*sin(2*d*x + 2*c))*cos(8*d*x + 8*c) + 4*((2560*a^4*b - 4128*a^3*b^2 + 3644*a^2*b^3 - 1379*a*b^4 + 245*b^5)*sin(4*d*x + 4*c) + 4*(64*a^3*b^2 - 196*a^2*b^3 + 125*a*b^4 - 35*b^5)*sin(2*d*x + 2*c))*cos(6*d*x + 6*c) + 16*((a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*cos(16*d*x + 16*c)^2 + 64*(a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*cos(14*d*x + 14*c)^2 + 16*(64*a^6*b^2 - 240*a^5*b^3 + 337*a^4*b^4 - 210*a^3*b^5 + 49*a^2*b^6)*d*cos(12*d*x + 12*c)^2 + 64*(256*a^6*b^2 - 736*a^5*b^3 + 753*a^4*b^4 - 322*a^3*b^5 + 49*a^2*b^6)*d*cos(10*d*x + 10*c)^2 + 4*(16384*a^8 - 57344*a^7*b + 83712*a^6*b^2 - 67648*a^5*b^3 + 32841*a^4*b^4 - 9170*a^3*b^5 + 1225*a^2*b^6)*d*cos(8*d*x + 8*c)^2 + 64*(256*a^6*b^2 - 736*a^5*b^3 + 753*a^4*b^4 - 322*a^3*b^5 + 49*a^2*b^6)*d*cos(6*d*x + 6*c)^2 + 16*(64*a^6*b^2 - 240*a^5*b^3 + 337*a^4*b^4 - 210*a^3*b^5 + 49*a^2*b^6)*d*cos(4*d*x + 4*c)^2 + 64*(a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*cos(2*d*x + 2*c)^2 + (a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*sin(16*d*x + 16*c)^2 + 64*(a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*sin(14*d*x + 14*c)^2 + 16*(64*a^6*b^2 - 240*a^5*b^3 + 337*a^4*b^4 - 210*a^3*b^5 + 49*a^2*b^6)*d*sin(12*d*x + 12*c)^2 + 64*(256*a^6*b^2 - 736*a^5*b^3 + 753*a^4*b^4 - 322*a^3*b^5 + 49*a^2*b^6)*d*sin(10*d*x + 10*c)^2 + 4*(16384*a^8 - 57344*a^7*b + 83712*a^6*b^2 - 67648*a^5*b^3 + 32841*a^4*b^4 - 9170*a^3*b^5 + 1225*a^2*b^6)*d*sin(8*d*x + 8*c)^2 + 64*(256*a^6*b^2 - 736*a^5*b^3 + 753*a^4*b^4 - 322*a^3*b^5 + 49*a^2*b^6)*d*sin(6*d*x + 6*c)^2 + 16*(64*a^6*b^2 - 240*a^5*b^3 + 337*a^4*b^4 - 210*a^3*b^5 + 49*a^2*b^6)*d*sin(4*d*x + 4*c)^2 + 64*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 64*(a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*sin(2*d*x + 2*c)^2 - 16*(a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*cos(2*d*x + 2*c) + (a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d - 2*(8*(a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*cos(14*d*x + 14*c) + 4*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*cos(12*d*x + 12*c) - 8*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*cos(10*d*x + 10*c) - 2*(128*a^6*b^2 - 352*a^5*b^3 + 355*a^4*b^4 - 166*a^3*b^5 + 35*a^2*b^6)*d*cos(8*d*x + 8*c) - 8*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*cos(6*d*x + 6*c) + 4*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*cos(4*d*x + 4*c) + 8*(a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*cos(2*d*x + 2*c) - (a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d)*cos(16*d*x + 16*c) + 16*(4*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*cos(12*d*x + 12*c) - 8*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*cos(10*d*x + 10*c) - 2*(128*a^6*b^2 - 352*a^5*b^3 + 355*a^4*b^4 - 166*a^3*b^5 + 35*a^2*b^6)*d*cos(8*d*x + 8*c) - 8*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*cos(6*d*x + 6*c) + 4*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*cos(4*d*x + 4*c) + 8*(a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*cos(2*d*x + 2*c) - (a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d)*cos(14*d*x + 14*c) - 8*(8*(128*a^6*b^2 - 424*a^5*b^3 + 513*a^4*b^4 - 266*a^3*b^5 + 49*a^2*b^6)*d*cos(10*d*x + 10*c) + 2*(1024*a^7*b - 3712*a^6*b^2 + 5304*a^5*b^3 - 3813*a^4*b^4 + 1442*a^3*b^5 - 245*a^2*b^6)*d*cos(8*d*x + 8*c) + 8*(128*a^6*b^2 - 424*a^5*b^3 + 513*a^4*b^4 - 266*a^3*b^5 + 49*a^2*b^6)*d*cos(6*d*x + 6*c) - 4*(64*a^6*b^2 - 240*a^5*b^3 + 337*a^4*b^4 - 210*a^3*b^5 + 49*a^2*b^6)*d*cos(4*d*x + 4*c) - 8*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*cos(2*d*x + 2*c) + (8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d)*cos(12*d*x + 12*c) + 16*(2*(2048*a^7*b - 6528*a^6*b^2 + 8144*a^5*b^3 - 5141*a^4*b^4 + 1722*a^3*b^5 - 245*a^2*b^6)*d*cos(8*d*x + 8*c) + 8*(256*a^6*b^2 - 736*a^5*b^3 + 753*a^4*b^4 - 322*a^3*b^5 + 49*a^2*b^6)*d*cos(6*d*x + 6*c) - 4*(128*a^6*b^2 - 424*a^5*b^3 + 513*a^4*b^4 - 266*a^3*b^5 + 49*a^2*b^6)*d*cos(4*d*x + 4*c) - 8*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*cos(2*d*x + 2*c) + (16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d)*cos(10*d*x + 10*c) + 4*(8*(2048*a^7*b - 6528*a^6*b^2 + 8144*a^5*b^3 - 5141*a^4*b^4 + 1722*a^3*b^5 - 245*a^2*b^6)*d*cos(6*d*x + 6*c) - 4*(1024*a^7*b - 3712*a^6*b^2 + 5304*a^5*b^3 - 3813*a^4*b^4 + 1442*a^3*b^5 - 245*a^2*b^6)*d*cos(4*d*x + 4*c) - 8*(128*a^6*b^2 - 352*a^5*b^3 + 355*a^4*b^4 - 166*a^3*b^5 + 35*a^2*b^6)*d*cos(2*d*x + 2*c) + (128*a^6*b^2 - 352*a^5*b^3 + 355*a^4*b^4 - 166*a^3*b^5 + 35*a^2*b^6)*d)*cos(8*d*x + 8*c) - 16*(4*(128*a^6*b^2 - 424*a^5*b^3 + 513*a^4*b^4 - 266*a^3*b^5 + 49*a^2*b^6)*d*cos(4*d*x + 4*c) + 8*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*cos(2*d*x + 2*c) - (16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d)*cos(6*d*x + 6*c) + 8*(8*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*cos(2*d*x + 2*c) - (8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d)*cos(4*d*x + 4*c) - 4*(4*(a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*sin(14*d*x + 14*c) + 2*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*sin(12*d*x + 12*c) - 4*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*sin(10*d*x + 10*c) - (128*a^6*b^2 - 352*a^5*b^3 + 355*a^4*b^4 - 166*a^3*b^5 + 35*a^2*b^6)*d*sin(8*d*x + 8*c) - 4*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*sin(6*d*x + 6*c) + 2*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*sin(4*d*x + 4*c) + 4*(a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*sin(2*d*x + 2*c))*sin(16*d*x + 16*c) + 32*(2*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*sin(12*d*x + 12*c) - 4*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*sin(10*d*x + 10*c) - (128*a^6*b^2 - 352*a^5*b^3 + 355*a^4*b^4 - 166*a^3*b^5 + 35*a^2*b^6)*d*sin(8*d*x + 8*c) - 4*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*sin(6*d*x + 6*c) + 2*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*sin(4*d*x + 4*c) + 4*(a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*sin(2*d*x + 2*c))*sin(14*d*x + 14*c) - 16*(4*(128*a^6*b^2 - 424*a^5*b^3 + 513*a^4*b^4 - 266*a^3*b^5 + 49*a^2*b^6)*d*sin(10*d*x + 10*c) + (1024*a^7*b - 3712*a^6*b^2 + 5304*a^5*b^3 - 3813*a^4*b^4 + 1442*a^3*b^5 - 245*a^2*b^6)*d*sin(8*d*x + 8*c) + 4*(128*a^6*b^2 - 424*a^5*b^3 + 513*a^4*b^4 - 266*a^3*b^5 + 49*a^2*b^6)*d*sin(6*d*x + 6*c) - 2*(64*a^6*b^2 - 240*a^5*b^3 + 337*a^4*b^4 - 210*a^3*b^5 + 49*a^2*b^6)*d*sin(4*d*x + 4*c) - 4*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*sin(2*d*x + 2*c))*sin(12*d*x + 12*c) + 32*((2048*a^7*b - 6528*a^6*b^2 + 8144*a^5*b^3 - 5141*a^4*b^4 + 1722*a^3*b^5 - 245*a^2*b^6)*d*sin(8*d*x + 8*c) + 4*(256*a^6*b^2 - 736*a^5*b^3 + 753*a^4*b^4 - 322*a^3*b^5 + 49*a^2*b^6)*d*sin(6*d*x + 6*c) - 2*(128*a^6*b^2 - 424*a^5*b^3 + 513*a^4*b^4 - 266*a^3*b^5 + 49*a^2*b^6)*d*sin(4*d*x + 4*c) - 4*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*sin(2*d*x + 2*c))*sin(10*d*x + 10*c) + 16*(2*(2048*a^7*b - 6528*a^6*b^2 + 8144*a^5*b^3 - 5141*a^4*b^4 + 1722*a^3*b^5 - 245*a^2*b^6)*d*sin(6*d*x + 6*c) - (1024*a^7*b - 3712*a^6*b^2 + 5304*a^5*b^3 - 3813*a^4*b^4 + 1442*a^3*b^5 - 245*a^2*b^6)*d*sin(4*d*x + 4*c) - 2*(128*a^6*b^2 - 352*a^5*b^3 + 355*a^4*b^4 - 166*a^3*b^5 + 35*a^2*b^6)*d*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) - 64*((128*a^6*b^2 - 424*a^5*b^3 + 513*a^4*b^4 - 266*a^3*b^5 + 49*a^2*b^6)*d*sin(4*d*x + 4*c) + 2*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*integrate(-1/8*(4*(12*a^2*b - 11*a*b^2 + 5*b^3)*cos(6*d*x + 6*c)^2 - 4*(256*a^3 - 248*a^2*b + 97*a*b^2 - 15*b^3)*cos(4*d*x + 4*c)^2 + 4*(12*a^2*b - 11*a*b^2 + 5*b^3)*cos(2*d*x + 2*c)^2 + 4*(12*a^2*b - 11*a*b^2 + 5*b^3)*sin(6*d*x + 6*c)^2 - 4*(256*a^3 - 248*a^2*b + 97*a*b^2 - 15*b^3)*sin(4*d*x + 4*c)^2 + 2*(96*a^3 - 252*a^2*b + 149*a*b^2 - 35*b^3)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*(12*a^2*b - 11*a*b^2 + 5*b^3)*sin(2*d*x + 2*c)^2 - ((12*a^2*b - 11*a*b^2 + 5*b^3)*cos(6*d*x + 6*c) - 2*(32*a^2*b - 19*a*b^2 + 5*b^3)*cos(4*d*x + 4*c) + (12*a^2*b - 11*a*b^2 + 5*b^3)*cos(2*d*x + 2*c))*cos(8*d*x + 8*c) - (12*a^2*b - 11*a*b^2 + 5*b^3 - 2*(96*a^3 - 252*a^2*b + 149*a*b^2 - 35*b^3)*cos(4*d*x + 4*c) - 8*(12*a^2*b - 11*a*b^2 + 5*b^3)*cos(2*d*x + 2*c))*cos(6*d*x + 6*c) + 2*(32*a^2*b - 19*a*b^2 + 5*b^3 + (96*a^3 - 252*a^2*b + 149*a*b^2 - 35*b^3)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - (12*a^2*b - 11*a*b^2 + 5*b^3)*cos(2*d*x + 2*c) - ((12*a^2*b - 11*a*b^2 + 5*b^3)*sin(6*d*x + 6*c) - 2*(32*a^2*b - 19*a*b^2 + 5*b^3)*sin(4*d*x + 4*c) + (12*a^2*b - 11*a*b^2 + 5*b^3)*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 2*((96*a^3 - 252*a^2*b + 149*a*b^2 - 35*b^3)*sin(4*d*x + 4*c) + 4*(12*a^2*b - 11*a*b^2 + 5*b^3)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))/(a^4*b^2 - 2*a^3*b^3 + a^2*b^4 + (a^4*b^2 - 2*a^3*b^3 + a^2*b^4)*cos(8*d*x + 8*c)^2 + 16*(a^4*b^2 - 2*a^3*b^3 + a^2*b^4)*cos(6*d*x + 6*c)^2 + 4*(64*a^6 - 176*a^5*b + 169*a^4*b^2 - 66*a^3*b^3 + 9*a^2*b^4)*cos(4*d*x + 4*c)^2 + 16*(a^4*b^2 - 2*a^3*b^3 + a^2*b^4)*cos(2*d*x + 2*c)^2 + (a^4*b^2 - 2*a^3*b^3 + a^2*b^4)*sin(8*d*x + 8*c)^2 + 16*(a^4*b^2 - 2*a^3*b^3 + a^2*b^4)*sin(6*d*x + 6*c)^2 + 4*(64*a^6 - 176*a^5*b + 169*a^4*b^2 - 66*a^3*b^3 + 9*a^2*b^4)*sin(4*d*x + 4*c)^2 + 16*(8*a^5*b - 19*a^4*b^2 + 14*a^3*b^3 - 3*a^2*b^4)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*(a^4*b^2 - 2*a^3*b^3 + a^2*b^4)*sin(2*d*x + 2*c)^2 + 2*(a^4*b^2 - 2*a^3*b^3 + a^2*b^4 - 4*(a^4*b^2 - 2*a^3*b^3 + a^2*b^4)*cos(6*d*x + 6*c) - 2*(8*a^5*b - 19*a^4*b^2 + 14*a^3*b^3 - 3*a^2*b^4)*cos(4*d*x + 4*c) - 4*(a^4*b^2 - 2*a^3*b^3 + a^2*b^4)*cos(2*d*x + 2*c))*cos(8*d*x + 8*c) - 8*(a^4*b^2 - 2*a^3*b^3 + a^2*b^4 - 2*(8*a^5*b - 19*a^4*b^2 + 14*a^3*b^3 - 3*a^2*b^4)*cos(4*d*x + 4*c) - 4*(a^4*b^2 - 2*a^3*b^3 + a^2*b^4)*cos(2*d*x + 2*c))*cos(6*d*x + 6*c) - 4*(8*a^5*b - 19*a^4*b^2 + 14*a^3*b^3 - 3*a^2*b^4 - 4*(8*a^5*b - 19*a^4*b^2 + 14*a^3*b^3 - 3*a^2*b^4)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 8*(a^4*b^2 - 2*a^3*b^3 + a^2*b^4)*cos(2*d*x + 2*c) - 4*(2*(a^4*b^2 - 2*a^3*b^3 + a^2*b^4)*sin(6*d*x + 6*c) + (8*a^5*b - 19*a^4*b^2 + 14*a^3*b^3 - 3*a^2*b^4)*sin(4*d*x + 4*c) + 2*(a^4*b^2 - 2*a^3*b^3 + a^2*b^4)*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*((8*a^5*b - 19*a^4*b^2 + 14*a^3*b^3 - 3*a^2*b^4)*sin(4*d*x + 4*c) + 2*(a^4*b^2 - 2*a^3*b^3 + a^2*b^4)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c)), x) - (11*a*b^4 - 5*b^5 + (12*a^2*b^3 - 11*a*b^4 + 5*b^5)*cos(14*d*x + 14*c) - (104*a^2*b^3 - 85*a*b^4 + 35*b^5)*cos(12*d*x + 12*c) - (320*a^3*b^2 - 652*a^2*b^3 + 407*a*b^4 - 105*b^5)*cos(10*d*x + 10*c) + (1408*a^3*b^2 - 1696*a^2*b^3 + 865*a*b^4 - 175*b^5)*cos(8*d*x + 8*c) + (320*a^3*b^2 + 756*a^2*b^3 - 849*a*b^4 + 175*b^5)*cos(6*d*x + 6*c) - (248*a^2*b^3 - 383*a*b^4 + 105*b^5)*cos(4*d*x + 4*c) - (12*a^2*b^3 + 77*a*b^4 - 35*b^5)*cos(2*d*x + 2*c))*sin(16*d*x + 16*c) + (12*a^2*b^3 + 77*a*b^4 - 35*b^5 - 4*(96*a^3*b^2 + 36*a^2*b^3 - 53*a*b^4 + 35*b^5)*cos(12*d*x + 12*c) - 16*(64*a^3*b^2 - 196*a^2*b^3 + 125*a*b^4 - 35*b^5)*cos(10*d*x + 10*c) + 6*(512*a^4*b + 1024*a^3*b^2 - 1556*a^2*b^3 + 865*a*b^4 - 175*b^5)*cos(8*d*x + 8*c) + 32*(128*a^3*b^2 + 124*a^2*b^3 - 173*a*b^4 + 35*b^5)*cos(6*d*x + 6*c) - 4*(96*a^3*b^2 + 324*a^2*b^3 - 649*a*b^4 + 175*b^5)*cos(4*d*x + 4*c) - 48*(4*a^2*b^3 + 11*a*b^4 - 5*b^5)*cos(2*d*x + 2*c))*sin(14*d*x + 14*c) + (248*a^2*b^3 - 383*a*b^4 + 105*b^5 - 4*(2560*a^4*b - 4128*a^3*b^2 + 3644*a^2*b^3 - 1379*a*b^4 + 245*b^5)*cos(10*d*x + 10*c) + 2*(9216*a^4*b - 25984*a^3*b^2 + 21304*a^2*b^3 - 8575*a*b^4 + 1225*b^5)*cos(8*d*x + 8*c) + 4*(2560*a^4*b + 480*a^3*b^2 - 7908*a^2*b^3 + 5033*a*b^4 - 735*b^5)*cos(6*d*x + 6*c) - 8*(576*a^3*b^2 - 1696*a^2*b^3 + 1323*a*b^4 - 245*b^5)*cos(4*d*x + 4*c) - 4*(96*a^3*b^2 + 324*a^2*b^3 - 649*a*b^4 + 175*b^5)*cos(2*d*x + 2*c))*sin(12*d*x + 12*c) - (320*a^3*b^2 + 756*a^2*b^3 - 849*a*b^4 + 175*b^5 + 2*(40960*a^5 - 24064*a^4*b - 22080*a^3*b^2 + 27516*a^2*b^3 - 11095*a*b^4 + 1225*b^5)*cos(8*d*x + 8*c) + 16*(5120*a^4*b - 1408*a^3*b^2 - 3900*a^2*b^3 + 2107*a*b^4 - 245*b^5)*cos(6*d*x + 6*c) - 4*(2560*a^4*b + 480*a^3*b^2 - 7908*a^2*b^3 + 5033*a*b^4 - 735*b^5)*cos(4*d*x + 4*c) - 32*(128*a^3*b^2 + 124*a^2*b^3 - 173*a*b^4 + 35*b^5)*cos(2*d*x + 2*c))*sin(10*d*x + 10*c) - (1408*a^3*b^2 - 1696*a^2*b^3 + 865*a*b^4 - 175*b^5 + 2*(40960*a^5 - 24064*a^4*b - 22080*a^3*b^2 + 27516*a^2*b^3 - 11095*a*b^4 + 1225*b^5)*cos(6*d*x + 6*c) - 2*(9216*a^4*b - 25984*a^3*b^2 + 21304*a^2*b^3 - 8575*a*b^4 + 1225*b^5)*cos(4*d*x + 4*c) - 6*(512*a^4*b + 1024*a^3*b^2 - 1556*a^2*b^3 + 865*a*b^4 - 175*b^5)*cos(2*d*x + 2*c))*sin(8*d*x + 8*c) + (320*a^3*b^2 - 652*a^2*b^3 + 407*a*b^4 - 105*b^5 - 4*(2560*a^4*b - 4128*a^3*b^2 + 3644*a^2*b^3 - 1379*a*b^4 + 245*b^5)*cos(4*d*x + 4*c) - 16*(64*a^3*b^2 - 196*a^2*b^3 + 125*a*b^4 - 35*b^5)*cos(2*d*x + 2*c))*sin(6*d*x + 6*c) + (104*a^2*b^3 - 85*a*b^4 + 35*b^5 - 4*(96*a^3*b^2 + 36*a^2*b^3 - 53*a*b^4 + 35*b^5)*cos(2*d*x + 2*c))*sin(4*d*x + 4*c) - (12*a^2*b^3 - 11*a*b^4 + 5*b^5)*sin(2*d*x + 2*c))/((a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*cos(16*d*x + 16*c)^2 + 64*(a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*cos(14*d*x + 14*c)^2 + 16*(64*a^6*b^2 - 240*a^5*b^3 + 337*a^4*b^4 - 210*a^3*b^5 + 49*a^2*b^6)*d*cos(12*d*x + 12*c)^2 + 64*(256*a^6*b^2 - 736*a^5*b^3 + 753*a^4*b^4 - 322*a^3*b^5 + 49*a^2*b^6)*d*cos(10*d*x + 10*c)^2 + 4*(16384*a^8 - 57344*a^7*b + 83712*a^6*b^2 - 67648*a^5*b^3 + 32841*a^4*b^4 - 9170*a^3*b^5 + 1225*a^2*b^6)*d*cos(8*d*x + 8*c)^2 + 64*(256*a^6*b^2 - 736*a^5*b^3 + 753*a^4*b^4 - 322*a^3*b^5 + 49*a^2*b^6)*d*cos(6*d*x + 6*c)^2 + 16*(64*a^6*b^2 - 240*a^5*b^3 + 337*a^4*b^4 - 210*a^3*b^5 + 49*a^2*b^6)*d*cos(4*d*x + 4*c)^2 + 64*(a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*cos(2*d*x + 2*c)^2 + (a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*sin(16*d*x + 16*c)^2 + 64*(a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*sin(14*d*x + 14*c)^2 + 16*(64*a^6*b^2 - 240*a^5*b^3 + 337*a^4*b^4 - 210*a^3*b^5 + 49*a^2*b^6)*d*sin(12*d*x + 12*c)^2 + 64*(256*a^6*b^2 - 736*a^5*b^3 + 753*a^4*b^4 - 322*a^3*b^5 + 49*a^2*b^6)*d*sin(10*d*x + 10*c)^2 + 4*(16384*a^8 - 57344*a^7*b + 83712*a^6*b^2 - 67648*a^5*b^3 + 32841*a^4*b^4 - 9170*a^3*b^5 + 1225*a^2*b^6)*d*sin(8*d*x + 8*c)^2 + 64*(256*a^6*b^2 - 736*a^5*b^3 + 753*a^4*b^4 - 322*a^3*b^5 + 49*a^2*b^6)*d*sin(6*d*x + 6*c)^2 + 16*(64*a^6*b^2 - 240*a^5*b^3 + 337*a^4*b^4 - 210*a^3*b^5 + 49*a^2*b^6)*d*sin(4*d*x + 4*c)^2 + 64*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 64*(a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*sin(2*d*x + 2*c)^2 - 16*(a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*cos(2*d*x + 2*c) + (a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d - 2*(8*(a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*cos(14*d*x + 14*c) + 4*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*cos(12*d*x + 12*c) - 8*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*cos(10*d*x + 10*c) - 2*(128*a^6*b^2 - 352*a^5*b^3 + 355*a^4*b^4 - 166*a^3*b^5 + 35*a^2*b^6)*d*cos(8*d*x + 8*c) - 8*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*cos(6*d*x + 6*c) + 4*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*cos(4*d*x + 4*c) + 8*(a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*cos(2*d*x + 2*c) - (a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d)*cos(16*d*x + 16*c) + 16*(4*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*cos(12*d*x + 12*c) - 8*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*cos(10*d*x + 10*c) - 2*(128*a^6*b^2 - 352*a^5*b^3 + 355*a^4*b^4 - 166*a^3*b^5 + 35*a^2*b^6)*d*cos(8*d*x + 8*c) - 8*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*cos(6*d*x + 6*c) + 4*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*cos(4*d*x + 4*c) + 8*(a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*cos(2*d*x + 2*c) - (a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d)*cos(14*d*x + 14*c) - 8*(8*(128*a^6*b^2 - 424*a^5*b^3 + 513*a^4*b^4 - 266*a^3*b^5 + 49*a^2*b^6)*d*cos(10*d*x + 10*c) + 2*(1024*a^7*b - 3712*a^6*b^2 + 5304*a^5*b^3 - 3813*a^4*b^4 + 1442*a^3*b^5 - 245*a^2*b^6)*d*cos(8*d*x + 8*c) + 8*(128*a^6*b^2 - 424*a^5*b^3 + 513*a^4*b^4 - 266*a^3*b^5 + 49*a^2*b^6)*d*cos(6*d*x + 6*c) - 4*(64*a^6*b^2 - 240*a^5*b^3 + 337*a^4*b^4 - 210*a^3*b^5 + 49*a^2*b^6)*d*cos(4*d*x + 4*c) - 8*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*cos(2*d*x + 2*c) + (8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d)*cos(12*d*x + 12*c) + 16*(2*(2048*a^7*b - 6528*a^6*b^2 + 8144*a^5*b^3 - 5141*a^4*b^4 + 1722*a^3*b^5 - 245*a^2*b^6)*d*cos(8*d*x + 8*c) + 8*(256*a^6*b^2 - 736*a^5*b^3 + 753*a^4*b^4 - 322*a^3*b^5 + 49*a^2*b^6)*d*cos(6*d*x + 6*c) - 4*(128*a^6*b^2 - 424*a^5*b^3 + 513*a^4*b^4 - 266*a^3*b^5 + 49*a^2*b^6)*d*cos(4*d*x + 4*c) - 8*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*cos(2*d*x + 2*c) + (16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d)*cos(10*d*x + 10*c) + 4*(8*(2048*a^7*b - 6528*a^6*b^2 + 8144*a^5*b^3 - 5141*a^4*b^4 + 1722*a^3*b^5 - 245*a^2*b^6)*d*cos(6*d*x + 6*c) - 4*(1024*a^7*b - 3712*a^6*b^2 + 5304*a^5*b^3 - 3813*a^4*b^4 + 1442*a^3*b^5 - 245*a^2*b^6)*d*cos(4*d*x + 4*c) - 8*(128*a^6*b^2 - 352*a^5*b^3 + 355*a^4*b^4 - 166*a^3*b^5 + 35*a^2*b^6)*d*cos(2*d*x + 2*c) + (128*a^6*b^2 - 352*a^5*b^3 + 355*a^4*b^4 - 166*a^3*b^5 + 35*a^2*b^6)*d)*cos(8*d*x + 8*c) - 16*(4*(128*a^6*b^2 - 424*a^5*b^3 + 513*a^4*b^4 - 266*a^3*b^5 + 49*a^2*b^6)*d*cos(4*d*x + 4*c) + 8*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*cos(2*d*x + 2*c) - (16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d)*cos(6*d*x + 6*c) + 8*(8*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*cos(2*d*x + 2*c) - (8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d)*cos(4*d*x + 4*c) - 4*(4*(a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*sin(14*d*x + 14*c) + 2*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*sin(12*d*x + 12*c) - 4*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*sin(10*d*x + 10*c) - (128*a^6*b^2 - 352*a^5*b^3 + 355*a^4*b^4 - 166*a^3*b^5 + 35*a^2*b^6)*d*sin(8*d*x + 8*c) - 4*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*sin(6*d*x + 6*c) + 2*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*sin(4*d*x + 4*c) + 4*(a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*sin(2*d*x + 2*c))*sin(16*d*x + 16*c) + 32*(2*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*sin(12*d*x + 12*c) - 4*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*sin(10*d*x + 10*c) - (128*a^6*b^2 - 352*a^5*b^3 + 355*a^4*b^4 - 166*a^3*b^5 + 35*a^2*b^6)*d*sin(8*d*x + 8*c) - 4*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*sin(6*d*x + 6*c) + 2*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*sin(4*d*x + 4*c) + 4*(a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*sin(2*d*x + 2*c))*sin(14*d*x + 14*c) - 16*(4*(128*a^6*b^2 - 424*a^5*b^3 + 513*a^4*b^4 - 266*a^3*b^5 + 49*a^2*b^6)*d*sin(10*d*x + 10*c) + (1024*a^7*b - 3712*a^6*b^2 + 5304*a^5*b^3 - 3813*a^4*b^4 + 1442*a^3*b^5 - 245*a^2*b^6)*d*sin(8*d*x + 8*c) + 4*(128*a^6*b^2 - 424*a^5*b^3 + 513*a^4*b^4 - 266*a^3*b^5 + 49*a^2*b^6)*d*sin(6*d*x + 6*c) - 2*(64*a^6*b^2 - 240*a^5*b^3 + 337*a^4*b^4 - 210*a^3*b^5 + 49*a^2*b^6)*d*sin(4*d*x + 4*c) - 4*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*sin(2*d*x + 2*c))*sin(12*d*x + 12*c) + 32*((2048*a^7*b - 6528*a^6*b^2 + 8144*a^5*b^3 - 5141*a^4*b^4 + 1722*a^3*b^5 - 245*a^2*b^6)*d*sin(8*d*x + 8*c) + 4*(256*a^6*b^2 - 736*a^5*b^3 + 753*a^4*b^4 - 322*a^3*b^5 + 49*a^2*b^6)*d*sin(6*d*x + 6*c) - 2*(128*a^6*b^2 - 424*a^5*b^3 + 513*a^4*b^4 - 266*a^3*b^5 + 49*a^2*b^6)*d*sin(4*d*x + 4*c) - 4*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*sin(2*d*x + 2*c))*sin(10*d*x + 10*c) + 16*(2*(2048*a^7*b - 6528*a^6*b^2 + 8144*a^5*b^3 - 5141*a^4*b^4 + 1722*a^3*b^5 - 245*a^2*b^6)*d*sin(6*d*x + 6*c) - (1024*a^7*b - 3712*a^6*b^2 + 5304*a^5*b^3 - 3813*a^4*b^4 + 1442*a^3*b^5 - 245*a^2*b^6)*d*sin(4*d*x + 4*c) - 2*(128*a^6*b^2 - 352*a^5*b^3 + 355*a^4*b^4 - 166*a^3*b^5 + 35*a^2*b^6)*d*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) - 64*((128*a^6*b^2 - 424*a^5*b^3 + 513*a^4*b^4 - 266*a^3*b^5 + 49*a^2*b^6)*d*sin(4*d*x + 4*c) + 2*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))","F",0
234,0,0,0,0.000000," ","integrate(1/(a-b*sin(d*x+c)^4)^3,x, algorithm=""maxima"")","\frac{4 \, {\left(120 \, a^{2} b^{3} - 77 \, a b^{4} + 14 \, b^{5}\right)} \cos\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + {\left({\left(7 \, a b^{4} - 4 \, b^{5}\right)} \sin\left(14 \, d x + 14 \, c\right) - {\left(32 \, a^{2} b^{3} + 2 \, a b^{4} - 7 \, b^{5}\right)} \sin\left(12 \, d x + 12 \, c\right) - {\left(16 \, a^{2} b^{3} - 3 \, a b^{4} - 28 \, b^{5}\right)} \sin\left(10 \, d x + 10 \, c\right) + 3 \, {\left(256 \, a^{3} b^{2} - 320 \, a^{2} b^{3} + 166 \, a b^{4} - 35 \, b^{5}\right)} \sin\left(8 \, d x + 8 \, c\right) + {\left(784 \, a^{2} b^{3} - 723 \, a b^{4} + 140 \, b^{5}\right)} \sin\left(6 \, d x + 6 \, c\right) - {\left(160 \, a^{2} b^{3} - 266 \, a b^{4} + 91 \, b^{5}\right)} \sin\left(4 \, d x + 4 \, c\right) - {\left(55 \, a b^{4} - 28 \, b^{5}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(16 \, d x + 16 \, c\right) + 2 \, {\left(2 \, {\left(120 \, a^{2} b^{3} - 77 \, a b^{4} + 14 \, b^{5}\right)} \sin\left(12 \, d x + 12 \, c\right) - 8 \, {\left(48 \, a^{2} b^{3} - 55 \, a b^{4} + 28 \, b^{5}\right)} \sin\left(10 \, d x + 10 \, c\right) - {\left(3968 \, a^{3} b^{2} - 5024 \, a^{2} b^{3} + 2621 \, a b^{4} - 560 \, b^{5}\right)} \sin\left(8 \, d x + 8 \, c\right) - 16 \, {\left(224 \, a^{2} b^{3} - 209 \, a b^{4} + 42 \, b^{5}\right)} \sin\left(6 \, d x + 6 \, c\right) + 2 \, {\left(376 \, a^{2} b^{3} - 613 \, a b^{4} + 210 \, b^{5}\right)} \sin\left(4 \, d x + 4 \, c\right) + 8 \, {\left(31 \, a b^{4} - 16 \, b^{5}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(14 \, d x + 14 \, c\right) + 2 \, {\left(2 \, {\left(1152 \, a^{3} b^{2} - 520 \, a^{2} b^{3} - 455 \, a b^{4} + 294 \, b^{5}\right)} \sin\left(10 \, d x + 10 \, c\right) - {\left(8192 \, a^{4} b - 23296 \, a^{3} b^{2} + 21376 \, a^{2} b^{3} - 9394 \, a b^{4} + 1715 \, b^{5}\right)} \sin\left(8 \, d x + 8 \, c\right) - 2 \, {\left(5248 \, a^{3} b^{2} - 10888 \, a^{2} b^{3} + 6433 \, a b^{4} - 1078 \, b^{5}\right)} \sin\left(6 \, d x + 6 \, c\right) + 4 \, {\left(512 \, a^{3} b^{2} - 1520 \, a^{2} b^{3} + 1330 \, a b^{4} - 343 \, b^{5}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(376 \, a^{2} b^{3} - 613 \, a b^{4} + 210 \, b^{5}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(12 \, d x + 12 \, c\right) + 2 \, {\left({\left(51200 \, a^{4} b - 84864 \, a^{3} b^{2} + 56016 \, a^{2} b^{3} - 18081 \, a b^{4} + 1960 \, b^{5}\right)} \sin\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6400 \, a^{3} b^{2} - 8608 \, a^{2} b^{3} + 3437 \, a b^{4} - 392 \, b^{5}\right)} \sin\left(6 \, d x + 6 \, c\right) - 2 \, {\left(5248 \, a^{3} b^{2} - 10888 \, a^{2} b^{3} + 6433 \, a b^{4} - 1078 \, b^{5}\right)} \sin\left(4 \, d x + 4 \, c\right) - 16 \, {\left(224 \, a^{2} b^{3} - 209 \, a b^{4} + 42 \, b^{5}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(10 \, d x + 10 \, c\right) + 2 \, {\left({\left(51200 \, a^{4} b - 84864 \, a^{3} b^{2} + 56016 \, a^{2} b^{3} - 18081 \, a b^{4} + 1960 \, b^{5}\right)} \sin\left(6 \, d x + 6 \, c\right) - {\left(8192 \, a^{4} b - 23296 \, a^{3} b^{2} + 21376 \, a^{2} b^{3} - 9394 \, a b^{4} + 1715 \, b^{5}\right)} \sin\left(4 \, d x + 4 \, c\right) - {\left(3968 \, a^{3} b^{2} - 5024 \, a^{2} b^{3} + 2621 \, a b^{4} - 560 \, b^{5}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) + 4 \, {\left({\left(1152 \, a^{3} b^{2} - 520 \, a^{2} b^{3} - 455 \, a b^{4} + 294 \, b^{5}\right)} \sin\left(4 \, d x + 4 \, c\right) - 4 \, {\left(48 \, a^{2} b^{3} - 55 \, a b^{4} + 28 \, b^{5}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left({\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cos\left(16 \, d x + 16 \, c\right)^{2} + 64 \, {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cos\left(14 \, d x + 14 \, c\right)^{2} + 16 \, {\left(64 \, a^{6} b^{2} - 240 \, a^{5} b^{3} + 337 \, a^{4} b^{4} - 210 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \cos\left(12 \, d x + 12 \, c\right)^{2} + 64 \, {\left(256 \, a^{6} b^{2} - 736 \, a^{5} b^{3} + 753 \, a^{4} b^{4} - 322 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \cos\left(10 \, d x + 10 \, c\right)^{2} + 4 \, {\left(16384 \, a^{8} - 57344 \, a^{7} b + 83712 \, a^{6} b^{2} - 67648 \, a^{5} b^{3} + 32841 \, a^{4} b^{4} - 9170 \, a^{3} b^{5} + 1225 \, a^{2} b^{6}\right)} d \cos\left(8 \, d x + 8 \, c\right)^{2} + 64 \, {\left(256 \, a^{6} b^{2} - 736 \, a^{5} b^{3} + 753 \, a^{4} b^{4} - 322 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \cos\left(6 \, d x + 6 \, c\right)^{2} + 16 \, {\left(64 \, a^{6} b^{2} - 240 \, a^{5} b^{3} + 337 \, a^{4} b^{4} - 210 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \cos\left(4 \, d x + 4 \, c\right)^{2} + 64 \, {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \sin\left(16 \, d x + 16 \, c\right)^{2} + 64 \, {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \sin\left(14 \, d x + 14 \, c\right)^{2} + 16 \, {\left(64 \, a^{6} b^{2} - 240 \, a^{5} b^{3} + 337 \, a^{4} b^{4} - 210 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \sin\left(12 \, d x + 12 \, c\right)^{2} + 64 \, {\left(256 \, a^{6} b^{2} - 736 \, a^{5} b^{3} + 753 \, a^{4} b^{4} - 322 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \sin\left(10 \, d x + 10 \, c\right)^{2} + 4 \, {\left(16384 \, a^{8} - 57344 \, a^{7} b + 83712 \, a^{6} b^{2} - 67648 \, a^{5} b^{3} + 32841 \, a^{4} b^{4} - 9170 \, a^{3} b^{5} + 1225 \, a^{2} b^{6}\right)} d \sin\left(8 \, d x + 8 \, c\right)^{2} + 64 \, {\left(256 \, a^{6} b^{2} - 736 \, a^{5} b^{3} + 753 \, a^{4} b^{4} - 322 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \sin\left(6 \, d x + 6 \, c\right)^{2} + 16 \, {\left(64 \, a^{6} b^{2} - 240 \, a^{5} b^{3} + 337 \, a^{4} b^{4} - 210 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right)^{2} + 64 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 64 \, {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \sin\left(2 \, d x + 2 \, c\right)^{2} - 16 \, {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d - 2 \, {\left(8 \, {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cos\left(14 \, d x + 14 \, c\right) + 4 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(12 \, d x + 12 \, c\right) - 8 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(10 \, d x + 10 \, c\right) - 2 \, {\left(128 \, a^{6} b^{2} - 352 \, a^{5} b^{3} + 355 \, a^{4} b^{4} - 166 \, a^{3} b^{5} + 35 \, a^{2} b^{6}\right)} d \cos\left(8 \, d x + 8 \, c\right) - 8 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(6 \, d x + 6 \, c\right) + 4 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d\right)} \cos\left(16 \, d x + 16 \, c\right) + 16 \, {\left(4 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(12 \, d x + 12 \, c\right) - 8 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(10 \, d x + 10 \, c\right) - 2 \, {\left(128 \, a^{6} b^{2} - 352 \, a^{5} b^{3} + 355 \, a^{4} b^{4} - 166 \, a^{3} b^{5} + 35 \, a^{2} b^{6}\right)} d \cos\left(8 \, d x + 8 \, c\right) - 8 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(6 \, d x + 6 \, c\right) + 4 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d\right)} \cos\left(14 \, d x + 14 \, c\right) - 8 \, {\left(8 \, {\left(128 \, a^{6} b^{2} - 424 \, a^{5} b^{3} + 513 \, a^{4} b^{4} - 266 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \cos\left(10 \, d x + 10 \, c\right) + 2 \, {\left(1024 \, a^{7} b - 3712 \, a^{6} b^{2} + 5304 \, a^{5} b^{3} - 3813 \, a^{4} b^{4} + 1442 \, a^{3} b^{5} - 245 \, a^{2} b^{6}\right)} d \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(128 \, a^{6} b^{2} - 424 \, a^{5} b^{3} + 513 \, a^{4} b^{4} - 266 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(64 \, a^{6} b^{2} - 240 \, a^{5} b^{3} + 337 \, a^{4} b^{4} - 210 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d\right)} \cos\left(12 \, d x + 12 \, c\right) + 16 \, {\left(2 \, {\left(2048 \, a^{7} b - 6528 \, a^{6} b^{2} + 8144 \, a^{5} b^{3} - 5141 \, a^{4} b^{4} + 1722 \, a^{3} b^{5} - 245 \, a^{2} b^{6}\right)} d \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(256 \, a^{6} b^{2} - 736 \, a^{5} b^{3} + 753 \, a^{4} b^{4} - 322 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(128 \, a^{6} b^{2} - 424 \, a^{5} b^{3} + 513 \, a^{4} b^{4} - 266 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d\right)} \cos\left(10 \, d x + 10 \, c\right) + 4 \, {\left(8 \, {\left(2048 \, a^{7} b - 6528 \, a^{6} b^{2} + 8144 \, a^{5} b^{3} - 5141 \, a^{4} b^{4} + 1722 \, a^{3} b^{5} - 245 \, a^{2} b^{6}\right)} d \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(1024 \, a^{7} b - 3712 \, a^{6} b^{2} + 5304 \, a^{5} b^{3} - 3813 \, a^{4} b^{4} + 1442 \, a^{3} b^{5} - 245 \, a^{2} b^{6}\right)} d \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(128 \, a^{6} b^{2} - 352 \, a^{5} b^{3} + 355 \, a^{4} b^{4} - 166 \, a^{3} b^{5} + 35 \, a^{2} b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(128 \, a^{6} b^{2} - 352 \, a^{5} b^{3} + 355 \, a^{4} b^{4} - 166 \, a^{3} b^{5} + 35 \, a^{2} b^{6}\right)} d\right)} \cos\left(8 \, d x + 8 \, c\right) - 16 \, {\left(4 \, {\left(128 \, a^{6} b^{2} - 424 \, a^{5} b^{3} + 513 \, a^{4} b^{4} - 266 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d\right)} \cos\left(6 \, d x + 6 \, c\right) + 8 \, {\left(8 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(4 \, {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \sin\left(14 \, d x + 14 \, c\right) + 2 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(12 \, d x + 12 \, c\right) - 4 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(10 \, d x + 10 \, c\right) - {\left(128 \, a^{6} b^{2} - 352 \, a^{5} b^{3} + 355 \, a^{4} b^{4} - 166 \, a^{3} b^{5} + 35 \, a^{2} b^{6}\right)} d \sin\left(8 \, d x + 8 \, c\right) - 4 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(6 \, d x + 6 \, c\right) + 2 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(16 \, d x + 16 \, c\right) + 32 \, {\left(2 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(12 \, d x + 12 \, c\right) - 4 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(10 \, d x + 10 \, c\right) - {\left(128 \, a^{6} b^{2} - 352 \, a^{5} b^{3} + 355 \, a^{4} b^{4} - 166 \, a^{3} b^{5} + 35 \, a^{2} b^{6}\right)} d \sin\left(8 \, d x + 8 \, c\right) - 4 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(6 \, d x + 6 \, c\right) + 2 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(14 \, d x + 14 \, c\right) - 16 \, {\left(4 \, {\left(128 \, a^{6} b^{2} - 424 \, a^{5} b^{3} + 513 \, a^{4} b^{4} - 266 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \sin\left(10 \, d x + 10 \, c\right) + {\left(1024 \, a^{7} b - 3712 \, a^{6} b^{2} + 5304 \, a^{5} b^{3} - 3813 \, a^{4} b^{4} + 1442 \, a^{3} b^{5} - 245 \, a^{2} b^{6}\right)} d \sin\left(8 \, d x + 8 \, c\right) + 4 \, {\left(128 \, a^{6} b^{2} - 424 \, a^{5} b^{3} + 513 \, a^{4} b^{4} - 266 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \sin\left(6 \, d x + 6 \, c\right) - 2 \, {\left(64 \, a^{6} b^{2} - 240 \, a^{5} b^{3} + 337 \, a^{4} b^{4} - 210 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right) - 4 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(12 \, d x + 12 \, c\right) + 32 \, {\left({\left(2048 \, a^{7} b - 6528 \, a^{6} b^{2} + 8144 \, a^{5} b^{3} - 5141 \, a^{4} b^{4} + 1722 \, a^{3} b^{5} - 245 \, a^{2} b^{6}\right)} d \sin\left(8 \, d x + 8 \, c\right) + 4 \, {\left(256 \, a^{6} b^{2} - 736 \, a^{5} b^{3} + 753 \, a^{4} b^{4} - 322 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \sin\left(6 \, d x + 6 \, c\right) - 2 \, {\left(128 \, a^{6} b^{2} - 424 \, a^{5} b^{3} + 513 \, a^{4} b^{4} - 266 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right) - 4 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + 16 \, {\left(2 \, {\left(2048 \, a^{7} b - 6528 \, a^{6} b^{2} + 8144 \, a^{5} b^{3} - 5141 \, a^{4} b^{4} + 1722 \, a^{3} b^{5} - 245 \, a^{2} b^{6}\right)} d \sin\left(6 \, d x + 6 \, c\right) - {\left(1024 \, a^{7} b - 3712 \, a^{6} b^{2} + 5304 \, a^{5} b^{3} - 3813 \, a^{4} b^{4} + 1442 \, a^{3} b^{5} - 245 \, a^{2} b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(128 \, a^{6} b^{2} - 352 \, a^{5} b^{3} + 355 \, a^{4} b^{4} - 166 \, a^{3} b^{5} + 35 \, a^{2} b^{6}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) - 64 \, {\left({\left(128 \, a^{6} b^{2} - 424 \, a^{5} b^{3} + 513 \, a^{4} b^{4} - 266 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \int \frac{4 \, {\left(7 \, a b^{2} - 4 \, b^{3}\right)} \cos\left(6 \, d x + 6 \, c\right)^{2} - 4 \, {\left(256 \, a^{3} - 416 \, a^{2} b + 256 \, a b^{2} - 51 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(7 \, a b^{2} - 4 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(7 \, a b^{2} - 4 \, b^{3}\right)} \sin\left(6 \, d x + 6 \, c\right)^{2} - 4 \, {\left(256 \, a^{3} - 416 \, a^{2} b + 256 \, a b^{2} - 51 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, {\left(72 \, a^{2} b - 107 \, a b^{2} + 56 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, {\left(7 \, a b^{2} - 4 \, b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - {\left({\left(7 \, a b^{2} - 4 \, b^{3}\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left(32 \, a^{2} b - 40 \, a b^{2} + 17 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right) + {\left(7 \, a b^{2} - 4 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) - {\left(7 \, a b^{2} - 4 \, b^{3} + 2 \, {\left(72 \, a^{2} b - 107 \, a b^{2} + 56 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(7 \, a b^{2} - 4 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) + 2 \, {\left(32 \, a^{2} b - 40 \, a b^{2} + 17 \, b^{3} - {\left(72 \, a^{2} b - 107 \, a b^{2} + 56 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - {\left(7 \, a b^{2} - 4 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right) - {\left({\left(7 \, a b^{2} - 4 \, b^{3}\right)} \sin\left(6 \, d x + 6 \, c\right) - 2 \, {\left(32 \, a^{2} b - 40 \, a b^{2} + 17 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) + {\left(7 \, a b^{2} - 4 \, b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) - 2 \, {\left({\left(72 \, a^{2} b - 107 \, a b^{2} + 56 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) - 4 \, {\left(7 \, a b^{2} - 4 \, b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}{a^{4} b^{2} - 2 \, a^{3} b^{3} + a^{2} b^{4} + {\left(a^{4} b^{2} - 2 \, a^{3} b^{3} + a^{2} b^{4}\right)} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a^{4} b^{2} - 2 \, a^{3} b^{3} + a^{2} b^{4}\right)} \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{6} - 176 \, a^{5} b + 169 \, a^{4} b^{2} - 66 \, a^{3} b^{3} + 9 \, a^{2} b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(a^{4} b^{2} - 2 \, a^{3} b^{3} + a^{2} b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{4} b^{2} - 2 \, a^{3} b^{3} + a^{2} b^{4}\right)} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a^{4} b^{2} - 2 \, a^{3} b^{3} + a^{2} b^{4}\right)} \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{6} - 176 \, a^{5} b + 169 \, a^{4} b^{2} - 66 \, a^{3} b^{3} + 9 \, a^{2} b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(8 \, a^{5} b - 19 \, a^{4} b^{2} + 14 \, a^{3} b^{3} - 3 \, a^{2} b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, {\left(a^{4} b^{2} - 2 \, a^{3} b^{3} + a^{2} b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{4} b^{2} - 2 \, a^{3} b^{3} + a^{2} b^{4} - 4 \, {\left(a^{4} b^{2} - 2 \, a^{3} b^{3} + a^{2} b^{4}\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left(8 \, a^{5} b - 19 \, a^{4} b^{2} + 14 \, a^{3} b^{3} - 3 \, a^{2} b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a^{4} b^{2} - 2 \, a^{3} b^{3} + a^{2} b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) - 8 \, {\left(a^{4} b^{2} - 2 \, a^{3} b^{3} + a^{2} b^{4} - 2 \, {\left(8 \, a^{5} b - 19 \, a^{4} b^{2} + 14 \, a^{3} b^{3} - 3 \, a^{2} b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a^{4} b^{2} - 2 \, a^{3} b^{3} + a^{2} b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(8 \, a^{5} b - 19 \, a^{4} b^{2} + 14 \, a^{3} b^{3} - 3 \, a^{2} b^{4} - 4 \, {\left(8 \, a^{5} b - 19 \, a^{4} b^{2} + 14 \, a^{3} b^{3} - 3 \, a^{2} b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(a^{4} b^{2} - 2 \, a^{3} b^{3} + a^{2} b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right) - 4 \, {\left(2 \, {\left(a^{4} b^{2} - 2 \, a^{3} b^{3} + a^{2} b^{4}\right)} \sin\left(6 \, d x + 6 \, c\right) + {\left(8 \, a^{5} b - 19 \, a^{4} b^{2} + 14 \, a^{3} b^{3} - 3 \, a^{2} b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a^{4} b^{2} - 2 \, a^{3} b^{3} + a^{2} b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left({\left(8 \, a^{5} b - 19 \, a^{4} b^{2} + 14 \, a^{3} b^{3} - 3 \, a^{2} b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a^{4} b^{2} - 2 \, a^{3} b^{3} + a^{2} b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}\,{d x} - {\left(6 \, a b^{4} - 3 \, b^{5} + {\left(7 \, a b^{4} - 4 \, b^{5}\right)} \cos\left(14 \, d x + 14 \, c\right) - {\left(32 \, a^{2} b^{3} + 2 \, a b^{4} - 7 \, b^{5}\right)} \cos\left(12 \, d x + 12 \, c\right) - {\left(16 \, a^{2} b^{3} - 3 \, a b^{4} - 28 \, b^{5}\right)} \cos\left(10 \, d x + 10 \, c\right) + 3 \, {\left(256 \, a^{3} b^{2} - 320 \, a^{2} b^{3} + 166 \, a b^{4} - 35 \, b^{5}\right)} \cos\left(8 \, d x + 8 \, c\right) + {\left(784 \, a^{2} b^{3} - 723 \, a b^{4} + 140 \, b^{5}\right)} \cos\left(6 \, d x + 6 \, c\right) - {\left(160 \, a^{2} b^{3} - 266 \, a b^{4} + 91 \, b^{5}\right)} \cos\left(4 \, d x + 4 \, c\right) - {\left(55 \, a b^{4} - 28 \, b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(16 \, d x + 16 \, c\right) + {\left(55 \, a b^{4} - 28 \, b^{5} - 4 \, {\left(120 \, a^{2} b^{3} - 77 \, a b^{4} + 14 \, b^{5}\right)} \cos\left(12 \, d x + 12 \, c\right) + 16 \, {\left(48 \, a^{2} b^{3} - 55 \, a b^{4} + 28 \, b^{5}\right)} \cos\left(10 \, d x + 10 \, c\right) + 2 \, {\left(3968 \, a^{3} b^{2} - 5024 \, a^{2} b^{3} + 2621 \, a b^{4} - 560 \, b^{5}\right)} \cos\left(8 \, d x + 8 \, c\right) + 32 \, {\left(224 \, a^{2} b^{3} - 209 \, a b^{4} + 42 \, b^{5}\right)} \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(376 \, a^{2} b^{3} - 613 \, a b^{4} + 210 \, b^{5}\right)} \cos\left(4 \, d x + 4 \, c\right) - 16 \, {\left(31 \, a b^{4} - 16 \, b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(14 \, d x + 14 \, c\right) + {\left(160 \, a^{2} b^{3} - 266 \, a b^{4} + 91 \, b^{5} - 4 \, {\left(1152 \, a^{3} b^{2} - 520 \, a^{2} b^{3} - 455 \, a b^{4} + 294 \, b^{5}\right)} \cos\left(10 \, d x + 10 \, c\right) + 2 \, {\left(8192 \, a^{4} b - 23296 \, a^{3} b^{2} + 21376 \, a^{2} b^{3} - 9394 \, a b^{4} + 1715 \, b^{5}\right)} \cos\left(8 \, d x + 8 \, c\right) + 4 \, {\left(5248 \, a^{3} b^{2} - 10888 \, a^{2} b^{3} + 6433 \, a b^{4} - 1078 \, b^{5}\right)} \cos\left(6 \, d x + 6 \, c\right) - 8 \, {\left(512 \, a^{3} b^{2} - 1520 \, a^{2} b^{3} + 1330 \, a b^{4} - 343 \, b^{5}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(376 \, a^{2} b^{3} - 613 \, a b^{4} + 210 \, b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(12 \, d x + 12 \, c\right) - {\left(784 \, a^{2} b^{3} - 723 \, a b^{4} + 140 \, b^{5} + 2 \, {\left(51200 \, a^{4} b - 84864 \, a^{3} b^{2} + 56016 \, a^{2} b^{3} - 18081 \, a b^{4} + 1960 \, b^{5}\right)} \cos\left(8 \, d x + 8 \, c\right) + 16 \, {\left(6400 \, a^{3} b^{2} - 8608 \, a^{2} b^{3} + 3437 \, a b^{4} - 392 \, b^{5}\right)} \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(5248 \, a^{3} b^{2} - 10888 \, a^{2} b^{3} + 6433 \, a b^{4} - 1078 \, b^{5}\right)} \cos\left(4 \, d x + 4 \, c\right) - 32 \, {\left(224 \, a^{2} b^{3} - 209 \, a b^{4} + 42 \, b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) - {\left(768 \, a^{3} b^{2} - 960 \, a^{2} b^{3} + 498 \, a b^{4} - 105 \, b^{5} + 2 \, {\left(51200 \, a^{4} b - 84864 \, a^{3} b^{2} + 56016 \, a^{2} b^{3} - 18081 \, a b^{4} + 1960 \, b^{5}\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left(8192 \, a^{4} b - 23296 \, a^{3} b^{2} + 21376 \, a^{2} b^{3} - 9394 \, a b^{4} + 1715 \, b^{5}\right)} \cos\left(4 \, d x + 4 \, c\right) - 2 \, {\left(3968 \, a^{3} b^{2} - 5024 \, a^{2} b^{3} + 2621 \, a b^{4} - 560 \, b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + {\left(16 \, a^{2} b^{3} - 3 \, a b^{4} - 28 \, b^{5} - 4 \, {\left(1152 \, a^{3} b^{2} - 520 \, a^{2} b^{3} - 455 \, a b^{4} + 294 \, b^{5}\right)} \cos\left(4 \, d x + 4 \, c\right) + 16 \, {\left(48 \, a^{2} b^{3} - 55 \, a b^{4} + 28 \, b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + {\left(32 \, a^{2} b^{3} + 2 \, a b^{4} - 7 \, b^{5} - 4 \, {\left(120 \, a^{2} b^{3} - 77 \, a b^{4} + 14 \, b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) - {\left(7 \, a b^{4} - 4 \, b^{5}\right)} \sin\left(2 \, d x + 2 \, c\right)}{8 \, {\left({\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cos\left(16 \, d x + 16 \, c\right)^{2} + 64 \, {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cos\left(14 \, d x + 14 \, c\right)^{2} + 16 \, {\left(64 \, a^{6} b^{2} - 240 \, a^{5} b^{3} + 337 \, a^{4} b^{4} - 210 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \cos\left(12 \, d x + 12 \, c\right)^{2} + 64 \, {\left(256 \, a^{6} b^{2} - 736 \, a^{5} b^{3} + 753 \, a^{4} b^{4} - 322 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \cos\left(10 \, d x + 10 \, c\right)^{2} + 4 \, {\left(16384 \, a^{8} - 57344 \, a^{7} b + 83712 \, a^{6} b^{2} - 67648 \, a^{5} b^{3} + 32841 \, a^{4} b^{4} - 9170 \, a^{3} b^{5} + 1225 \, a^{2} b^{6}\right)} d \cos\left(8 \, d x + 8 \, c\right)^{2} + 64 \, {\left(256 \, a^{6} b^{2} - 736 \, a^{5} b^{3} + 753 \, a^{4} b^{4} - 322 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \cos\left(6 \, d x + 6 \, c\right)^{2} + 16 \, {\left(64 \, a^{6} b^{2} - 240 \, a^{5} b^{3} + 337 \, a^{4} b^{4} - 210 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \cos\left(4 \, d x + 4 \, c\right)^{2} + 64 \, {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \sin\left(16 \, d x + 16 \, c\right)^{2} + 64 \, {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \sin\left(14 \, d x + 14 \, c\right)^{2} + 16 \, {\left(64 \, a^{6} b^{2} - 240 \, a^{5} b^{3} + 337 \, a^{4} b^{4} - 210 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \sin\left(12 \, d x + 12 \, c\right)^{2} + 64 \, {\left(256 \, a^{6} b^{2} - 736 \, a^{5} b^{3} + 753 \, a^{4} b^{4} - 322 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \sin\left(10 \, d x + 10 \, c\right)^{2} + 4 \, {\left(16384 \, a^{8} - 57344 \, a^{7} b + 83712 \, a^{6} b^{2} - 67648 \, a^{5} b^{3} + 32841 \, a^{4} b^{4} - 9170 \, a^{3} b^{5} + 1225 \, a^{2} b^{6}\right)} d \sin\left(8 \, d x + 8 \, c\right)^{2} + 64 \, {\left(256 \, a^{6} b^{2} - 736 \, a^{5} b^{3} + 753 \, a^{4} b^{4} - 322 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \sin\left(6 \, d x + 6 \, c\right)^{2} + 16 \, {\left(64 \, a^{6} b^{2} - 240 \, a^{5} b^{3} + 337 \, a^{4} b^{4} - 210 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right)^{2} + 64 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 64 \, {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \sin\left(2 \, d x + 2 \, c\right)^{2} - 16 \, {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d - 2 \, {\left(8 \, {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cos\left(14 \, d x + 14 \, c\right) + 4 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(12 \, d x + 12 \, c\right) - 8 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(10 \, d x + 10 \, c\right) - 2 \, {\left(128 \, a^{6} b^{2} - 352 \, a^{5} b^{3} + 355 \, a^{4} b^{4} - 166 \, a^{3} b^{5} + 35 \, a^{2} b^{6}\right)} d \cos\left(8 \, d x + 8 \, c\right) - 8 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(6 \, d x + 6 \, c\right) + 4 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d\right)} \cos\left(16 \, d x + 16 \, c\right) + 16 \, {\left(4 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(12 \, d x + 12 \, c\right) - 8 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(10 \, d x + 10 \, c\right) - 2 \, {\left(128 \, a^{6} b^{2} - 352 \, a^{5} b^{3} + 355 \, a^{4} b^{4} - 166 \, a^{3} b^{5} + 35 \, a^{2} b^{6}\right)} d \cos\left(8 \, d x + 8 \, c\right) - 8 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(6 \, d x + 6 \, c\right) + 4 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d\right)} \cos\left(14 \, d x + 14 \, c\right) - 8 \, {\left(8 \, {\left(128 \, a^{6} b^{2} - 424 \, a^{5} b^{3} + 513 \, a^{4} b^{4} - 266 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \cos\left(10 \, d x + 10 \, c\right) + 2 \, {\left(1024 \, a^{7} b - 3712 \, a^{6} b^{2} + 5304 \, a^{5} b^{3} - 3813 \, a^{4} b^{4} + 1442 \, a^{3} b^{5} - 245 \, a^{2} b^{6}\right)} d \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(128 \, a^{6} b^{2} - 424 \, a^{5} b^{3} + 513 \, a^{4} b^{4} - 266 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(64 \, a^{6} b^{2} - 240 \, a^{5} b^{3} + 337 \, a^{4} b^{4} - 210 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d\right)} \cos\left(12 \, d x + 12 \, c\right) + 16 \, {\left(2 \, {\left(2048 \, a^{7} b - 6528 \, a^{6} b^{2} + 8144 \, a^{5} b^{3} - 5141 \, a^{4} b^{4} + 1722 \, a^{3} b^{5} - 245 \, a^{2} b^{6}\right)} d \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(256 \, a^{6} b^{2} - 736 \, a^{5} b^{3} + 753 \, a^{4} b^{4} - 322 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(128 \, a^{6} b^{2} - 424 \, a^{5} b^{3} + 513 \, a^{4} b^{4} - 266 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d\right)} \cos\left(10 \, d x + 10 \, c\right) + 4 \, {\left(8 \, {\left(2048 \, a^{7} b - 6528 \, a^{6} b^{2} + 8144 \, a^{5} b^{3} - 5141 \, a^{4} b^{4} + 1722 \, a^{3} b^{5} - 245 \, a^{2} b^{6}\right)} d \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(1024 \, a^{7} b - 3712 \, a^{6} b^{2} + 5304 \, a^{5} b^{3} - 3813 \, a^{4} b^{4} + 1442 \, a^{3} b^{5} - 245 \, a^{2} b^{6}\right)} d \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(128 \, a^{6} b^{2} - 352 \, a^{5} b^{3} + 355 \, a^{4} b^{4} - 166 \, a^{3} b^{5} + 35 \, a^{2} b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(128 \, a^{6} b^{2} - 352 \, a^{5} b^{3} + 355 \, a^{4} b^{4} - 166 \, a^{3} b^{5} + 35 \, a^{2} b^{6}\right)} d\right)} \cos\left(8 \, d x + 8 \, c\right) - 16 \, {\left(4 \, {\left(128 \, a^{6} b^{2} - 424 \, a^{5} b^{3} + 513 \, a^{4} b^{4} - 266 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d\right)} \cos\left(6 \, d x + 6 \, c\right) + 8 \, {\left(8 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \cos\left(2 \, d x + 2 \, c\right) - {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(4 \, {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \sin\left(14 \, d x + 14 \, c\right) + 2 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(12 \, d x + 12 \, c\right) - 4 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(10 \, d x + 10 \, c\right) - {\left(128 \, a^{6} b^{2} - 352 \, a^{5} b^{3} + 355 \, a^{4} b^{4} - 166 \, a^{3} b^{5} + 35 \, a^{2} b^{6}\right)} d \sin\left(8 \, d x + 8 \, c\right) - 4 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(6 \, d x + 6 \, c\right) + 2 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(16 \, d x + 16 \, c\right) + 32 \, {\left(2 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(12 \, d x + 12 \, c\right) - 4 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(10 \, d x + 10 \, c\right) - {\left(128 \, a^{6} b^{2} - 352 \, a^{5} b^{3} + 355 \, a^{4} b^{4} - 166 \, a^{3} b^{5} + 35 \, a^{2} b^{6}\right)} d \sin\left(8 \, d x + 8 \, c\right) - 4 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(6 \, d x + 6 \, c\right) + 2 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a^{4} b^{4} - 2 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(14 \, d x + 14 \, c\right) - 16 \, {\left(4 \, {\left(128 \, a^{6} b^{2} - 424 \, a^{5} b^{3} + 513 \, a^{4} b^{4} - 266 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \sin\left(10 \, d x + 10 \, c\right) + {\left(1024 \, a^{7} b - 3712 \, a^{6} b^{2} + 5304 \, a^{5} b^{3} - 3813 \, a^{4} b^{4} + 1442 \, a^{3} b^{5} - 245 \, a^{2} b^{6}\right)} d \sin\left(8 \, d x + 8 \, c\right) + 4 \, {\left(128 \, a^{6} b^{2} - 424 \, a^{5} b^{3} + 513 \, a^{4} b^{4} - 266 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \sin\left(6 \, d x + 6 \, c\right) - 2 \, {\left(64 \, a^{6} b^{2} - 240 \, a^{5} b^{3} + 337 \, a^{4} b^{4} - 210 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right) - 4 \, {\left(8 \, a^{5} b^{3} - 23 \, a^{4} b^{4} + 22 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(12 \, d x + 12 \, c\right) + 32 \, {\left({\left(2048 \, a^{7} b - 6528 \, a^{6} b^{2} + 8144 \, a^{5} b^{3} - 5141 \, a^{4} b^{4} + 1722 \, a^{3} b^{5} - 245 \, a^{2} b^{6}\right)} d \sin\left(8 \, d x + 8 \, c\right) + 4 \, {\left(256 \, a^{6} b^{2} - 736 \, a^{5} b^{3} + 753 \, a^{4} b^{4} - 322 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \sin\left(6 \, d x + 6 \, c\right) - 2 \, {\left(128 \, a^{6} b^{2} - 424 \, a^{5} b^{3} + 513 \, a^{4} b^{4} - 266 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right) - 4 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + 16 \, {\left(2 \, {\left(2048 \, a^{7} b - 6528 \, a^{6} b^{2} + 8144 \, a^{5} b^{3} - 5141 \, a^{4} b^{4} + 1722 \, a^{3} b^{5} - 245 \, a^{2} b^{6}\right)} d \sin\left(6 \, d x + 6 \, c\right) - {\left(1024 \, a^{7} b - 3712 \, a^{6} b^{2} + 5304 \, a^{5} b^{3} - 3813 \, a^{4} b^{4} + 1442 \, a^{3} b^{5} - 245 \, a^{2} b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(128 \, a^{6} b^{2} - 352 \, a^{5} b^{3} + 355 \, a^{4} b^{4} - 166 \, a^{3} b^{5} + 35 \, a^{2} b^{6}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) - 64 \, {\left({\left(128 \, a^{6} b^{2} - 424 \, a^{5} b^{3} + 513 \, a^{4} b^{4} - 266 \, a^{3} b^{5} + 49 \, a^{2} b^{6}\right)} d \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(16 \, a^{5} b^{3} - 39 \, a^{4} b^{4} + 30 \, a^{3} b^{5} - 7 \, a^{2} b^{6}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)}}"," ",0,"1/8*(4*(120*a^2*b^3 - 77*a*b^4 + 14*b^5)*cos(4*d*x + 4*c)*sin(2*d*x + 2*c) + ((7*a*b^4 - 4*b^5)*sin(14*d*x + 14*c) - (32*a^2*b^3 + 2*a*b^4 - 7*b^5)*sin(12*d*x + 12*c) - (16*a^2*b^3 - 3*a*b^4 - 28*b^5)*sin(10*d*x + 10*c) + 3*(256*a^3*b^2 - 320*a^2*b^3 + 166*a*b^4 - 35*b^5)*sin(8*d*x + 8*c) + (784*a^2*b^3 - 723*a*b^4 + 140*b^5)*sin(6*d*x + 6*c) - (160*a^2*b^3 - 266*a*b^4 + 91*b^5)*sin(4*d*x + 4*c) - (55*a*b^4 - 28*b^5)*sin(2*d*x + 2*c))*cos(16*d*x + 16*c) + 2*(2*(120*a^2*b^3 - 77*a*b^4 + 14*b^5)*sin(12*d*x + 12*c) - 8*(48*a^2*b^3 - 55*a*b^4 + 28*b^5)*sin(10*d*x + 10*c) - (3968*a^3*b^2 - 5024*a^2*b^3 + 2621*a*b^4 - 560*b^5)*sin(8*d*x + 8*c) - 16*(224*a^2*b^3 - 209*a*b^4 + 42*b^5)*sin(6*d*x + 6*c) + 2*(376*a^2*b^3 - 613*a*b^4 + 210*b^5)*sin(4*d*x + 4*c) + 8*(31*a*b^4 - 16*b^5)*sin(2*d*x + 2*c))*cos(14*d*x + 14*c) + 2*(2*(1152*a^3*b^2 - 520*a^2*b^3 - 455*a*b^4 + 294*b^5)*sin(10*d*x + 10*c) - (8192*a^4*b - 23296*a^3*b^2 + 21376*a^2*b^3 - 9394*a*b^4 + 1715*b^5)*sin(8*d*x + 8*c) - 2*(5248*a^3*b^2 - 10888*a^2*b^3 + 6433*a*b^4 - 1078*b^5)*sin(6*d*x + 6*c) + 4*(512*a^3*b^2 - 1520*a^2*b^3 + 1330*a*b^4 - 343*b^5)*sin(4*d*x + 4*c) + 2*(376*a^2*b^3 - 613*a*b^4 + 210*b^5)*sin(2*d*x + 2*c))*cos(12*d*x + 12*c) + 2*((51200*a^4*b - 84864*a^3*b^2 + 56016*a^2*b^3 - 18081*a*b^4 + 1960*b^5)*sin(8*d*x + 8*c) + 8*(6400*a^3*b^2 - 8608*a^2*b^3 + 3437*a*b^4 - 392*b^5)*sin(6*d*x + 6*c) - 2*(5248*a^3*b^2 - 10888*a^2*b^3 + 6433*a*b^4 - 1078*b^5)*sin(4*d*x + 4*c) - 16*(224*a^2*b^3 - 209*a*b^4 + 42*b^5)*sin(2*d*x + 2*c))*cos(10*d*x + 10*c) + 2*((51200*a^4*b - 84864*a^3*b^2 + 56016*a^2*b^3 - 18081*a*b^4 + 1960*b^5)*sin(6*d*x + 6*c) - (8192*a^4*b - 23296*a^3*b^2 + 21376*a^2*b^3 - 9394*a*b^4 + 1715*b^5)*sin(4*d*x + 4*c) - (3968*a^3*b^2 - 5024*a^2*b^3 + 2621*a*b^4 - 560*b^5)*sin(2*d*x + 2*c))*cos(8*d*x + 8*c) + 4*((1152*a^3*b^2 - 520*a^2*b^3 - 455*a*b^4 + 294*b^5)*sin(4*d*x + 4*c) - 4*(48*a^2*b^3 - 55*a*b^4 + 28*b^5)*sin(2*d*x + 2*c))*cos(6*d*x + 6*c) - 8*((a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*cos(16*d*x + 16*c)^2 + 64*(a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*cos(14*d*x + 14*c)^2 + 16*(64*a^6*b^2 - 240*a^5*b^3 + 337*a^4*b^4 - 210*a^3*b^5 + 49*a^2*b^6)*d*cos(12*d*x + 12*c)^2 + 64*(256*a^6*b^2 - 736*a^5*b^3 + 753*a^4*b^4 - 322*a^3*b^5 + 49*a^2*b^6)*d*cos(10*d*x + 10*c)^2 + 4*(16384*a^8 - 57344*a^7*b + 83712*a^6*b^2 - 67648*a^5*b^3 + 32841*a^4*b^4 - 9170*a^3*b^5 + 1225*a^2*b^6)*d*cos(8*d*x + 8*c)^2 + 64*(256*a^6*b^2 - 736*a^5*b^3 + 753*a^4*b^4 - 322*a^3*b^5 + 49*a^2*b^6)*d*cos(6*d*x + 6*c)^2 + 16*(64*a^6*b^2 - 240*a^5*b^3 + 337*a^4*b^4 - 210*a^3*b^5 + 49*a^2*b^6)*d*cos(4*d*x + 4*c)^2 + 64*(a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*cos(2*d*x + 2*c)^2 + (a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*sin(16*d*x + 16*c)^2 + 64*(a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*sin(14*d*x + 14*c)^2 + 16*(64*a^6*b^2 - 240*a^5*b^3 + 337*a^4*b^4 - 210*a^3*b^5 + 49*a^2*b^6)*d*sin(12*d*x + 12*c)^2 + 64*(256*a^6*b^2 - 736*a^5*b^3 + 753*a^4*b^4 - 322*a^3*b^5 + 49*a^2*b^6)*d*sin(10*d*x + 10*c)^2 + 4*(16384*a^8 - 57344*a^7*b + 83712*a^6*b^2 - 67648*a^5*b^3 + 32841*a^4*b^4 - 9170*a^3*b^5 + 1225*a^2*b^6)*d*sin(8*d*x + 8*c)^2 + 64*(256*a^6*b^2 - 736*a^5*b^3 + 753*a^4*b^4 - 322*a^3*b^5 + 49*a^2*b^6)*d*sin(6*d*x + 6*c)^2 + 16*(64*a^6*b^2 - 240*a^5*b^3 + 337*a^4*b^4 - 210*a^3*b^5 + 49*a^2*b^6)*d*sin(4*d*x + 4*c)^2 + 64*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 64*(a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*sin(2*d*x + 2*c)^2 - 16*(a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*cos(2*d*x + 2*c) + (a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d - 2*(8*(a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*cos(14*d*x + 14*c) + 4*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*cos(12*d*x + 12*c) - 8*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*cos(10*d*x + 10*c) - 2*(128*a^6*b^2 - 352*a^5*b^3 + 355*a^4*b^4 - 166*a^3*b^5 + 35*a^2*b^6)*d*cos(8*d*x + 8*c) - 8*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*cos(6*d*x + 6*c) + 4*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*cos(4*d*x + 4*c) + 8*(a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*cos(2*d*x + 2*c) - (a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d)*cos(16*d*x + 16*c) + 16*(4*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*cos(12*d*x + 12*c) - 8*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*cos(10*d*x + 10*c) - 2*(128*a^6*b^2 - 352*a^5*b^3 + 355*a^4*b^4 - 166*a^3*b^5 + 35*a^2*b^6)*d*cos(8*d*x + 8*c) - 8*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*cos(6*d*x + 6*c) + 4*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*cos(4*d*x + 4*c) + 8*(a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*cos(2*d*x + 2*c) - (a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d)*cos(14*d*x + 14*c) - 8*(8*(128*a^6*b^2 - 424*a^5*b^3 + 513*a^4*b^4 - 266*a^3*b^5 + 49*a^2*b^6)*d*cos(10*d*x + 10*c) + 2*(1024*a^7*b - 3712*a^6*b^2 + 5304*a^5*b^3 - 3813*a^4*b^4 + 1442*a^3*b^5 - 245*a^2*b^6)*d*cos(8*d*x + 8*c) + 8*(128*a^6*b^2 - 424*a^5*b^3 + 513*a^4*b^4 - 266*a^3*b^5 + 49*a^2*b^6)*d*cos(6*d*x + 6*c) - 4*(64*a^6*b^2 - 240*a^5*b^3 + 337*a^4*b^4 - 210*a^3*b^5 + 49*a^2*b^6)*d*cos(4*d*x + 4*c) - 8*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*cos(2*d*x + 2*c) + (8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d)*cos(12*d*x + 12*c) + 16*(2*(2048*a^7*b - 6528*a^6*b^2 + 8144*a^5*b^3 - 5141*a^4*b^4 + 1722*a^3*b^5 - 245*a^2*b^6)*d*cos(8*d*x + 8*c) + 8*(256*a^6*b^2 - 736*a^5*b^3 + 753*a^4*b^4 - 322*a^3*b^5 + 49*a^2*b^6)*d*cos(6*d*x + 6*c) - 4*(128*a^6*b^2 - 424*a^5*b^3 + 513*a^4*b^4 - 266*a^3*b^5 + 49*a^2*b^6)*d*cos(4*d*x + 4*c) - 8*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*cos(2*d*x + 2*c) + (16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d)*cos(10*d*x + 10*c) + 4*(8*(2048*a^7*b - 6528*a^6*b^2 + 8144*a^5*b^3 - 5141*a^4*b^4 + 1722*a^3*b^5 - 245*a^2*b^6)*d*cos(6*d*x + 6*c) - 4*(1024*a^7*b - 3712*a^6*b^2 + 5304*a^5*b^3 - 3813*a^4*b^4 + 1442*a^3*b^5 - 245*a^2*b^6)*d*cos(4*d*x + 4*c) - 8*(128*a^6*b^2 - 352*a^5*b^3 + 355*a^4*b^4 - 166*a^3*b^5 + 35*a^2*b^6)*d*cos(2*d*x + 2*c) + (128*a^6*b^2 - 352*a^5*b^3 + 355*a^4*b^4 - 166*a^3*b^5 + 35*a^2*b^6)*d)*cos(8*d*x + 8*c) - 16*(4*(128*a^6*b^2 - 424*a^5*b^3 + 513*a^4*b^4 - 266*a^3*b^5 + 49*a^2*b^6)*d*cos(4*d*x + 4*c) + 8*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*cos(2*d*x + 2*c) - (16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d)*cos(6*d*x + 6*c) + 8*(8*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*cos(2*d*x + 2*c) - (8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d)*cos(4*d*x + 4*c) - 4*(4*(a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*sin(14*d*x + 14*c) + 2*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*sin(12*d*x + 12*c) - 4*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*sin(10*d*x + 10*c) - (128*a^6*b^2 - 352*a^5*b^3 + 355*a^4*b^4 - 166*a^3*b^5 + 35*a^2*b^6)*d*sin(8*d*x + 8*c) - 4*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*sin(6*d*x + 6*c) + 2*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*sin(4*d*x + 4*c) + 4*(a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*sin(2*d*x + 2*c))*sin(16*d*x + 16*c) + 32*(2*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*sin(12*d*x + 12*c) - 4*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*sin(10*d*x + 10*c) - (128*a^6*b^2 - 352*a^5*b^3 + 355*a^4*b^4 - 166*a^3*b^5 + 35*a^2*b^6)*d*sin(8*d*x + 8*c) - 4*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*sin(6*d*x + 6*c) + 2*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*sin(4*d*x + 4*c) + 4*(a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*sin(2*d*x + 2*c))*sin(14*d*x + 14*c) - 16*(4*(128*a^6*b^2 - 424*a^5*b^3 + 513*a^4*b^4 - 266*a^3*b^5 + 49*a^2*b^6)*d*sin(10*d*x + 10*c) + (1024*a^7*b - 3712*a^6*b^2 + 5304*a^5*b^3 - 3813*a^4*b^4 + 1442*a^3*b^5 - 245*a^2*b^6)*d*sin(8*d*x + 8*c) + 4*(128*a^6*b^2 - 424*a^5*b^3 + 513*a^4*b^4 - 266*a^3*b^5 + 49*a^2*b^6)*d*sin(6*d*x + 6*c) - 2*(64*a^6*b^2 - 240*a^5*b^3 + 337*a^4*b^4 - 210*a^3*b^5 + 49*a^2*b^6)*d*sin(4*d*x + 4*c) - 4*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*sin(2*d*x + 2*c))*sin(12*d*x + 12*c) + 32*((2048*a^7*b - 6528*a^6*b^2 + 8144*a^5*b^3 - 5141*a^4*b^4 + 1722*a^3*b^5 - 245*a^2*b^6)*d*sin(8*d*x + 8*c) + 4*(256*a^6*b^2 - 736*a^5*b^3 + 753*a^4*b^4 - 322*a^3*b^5 + 49*a^2*b^6)*d*sin(6*d*x + 6*c) - 2*(128*a^6*b^2 - 424*a^5*b^3 + 513*a^4*b^4 - 266*a^3*b^5 + 49*a^2*b^6)*d*sin(4*d*x + 4*c) - 4*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*sin(2*d*x + 2*c))*sin(10*d*x + 10*c) + 16*(2*(2048*a^7*b - 6528*a^6*b^2 + 8144*a^5*b^3 - 5141*a^4*b^4 + 1722*a^3*b^5 - 245*a^2*b^6)*d*sin(6*d*x + 6*c) - (1024*a^7*b - 3712*a^6*b^2 + 5304*a^5*b^3 - 3813*a^4*b^4 + 1442*a^3*b^5 - 245*a^2*b^6)*d*sin(4*d*x + 4*c) - 2*(128*a^6*b^2 - 352*a^5*b^3 + 355*a^4*b^4 - 166*a^3*b^5 + 35*a^2*b^6)*d*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) - 64*((128*a^6*b^2 - 424*a^5*b^3 + 513*a^4*b^4 - 266*a^3*b^5 + 49*a^2*b^6)*d*sin(4*d*x + 4*c) + 2*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*integrate(1/4*(4*(7*a*b^2 - 4*b^3)*cos(6*d*x + 6*c)^2 - 4*(256*a^3 - 416*a^2*b + 256*a*b^2 - 51*b^3)*cos(4*d*x + 4*c)^2 + 4*(7*a*b^2 - 4*b^3)*cos(2*d*x + 2*c)^2 + 4*(7*a*b^2 - 4*b^3)*sin(6*d*x + 6*c)^2 - 4*(256*a^3 - 416*a^2*b + 256*a*b^2 - 51*b^3)*sin(4*d*x + 4*c)^2 - 2*(72*a^2*b - 107*a*b^2 + 56*b^3)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*(7*a*b^2 - 4*b^3)*sin(2*d*x + 2*c)^2 - ((7*a*b^2 - 4*b^3)*cos(6*d*x + 6*c) - 2*(32*a^2*b - 40*a*b^2 + 17*b^3)*cos(4*d*x + 4*c) + (7*a*b^2 - 4*b^3)*cos(2*d*x + 2*c))*cos(8*d*x + 8*c) - (7*a*b^2 - 4*b^3 + 2*(72*a^2*b - 107*a*b^2 + 56*b^3)*cos(4*d*x + 4*c) - 8*(7*a*b^2 - 4*b^3)*cos(2*d*x + 2*c))*cos(6*d*x + 6*c) + 2*(32*a^2*b - 40*a*b^2 + 17*b^3 - (72*a^2*b - 107*a*b^2 + 56*b^3)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - (7*a*b^2 - 4*b^3)*cos(2*d*x + 2*c) - ((7*a*b^2 - 4*b^3)*sin(6*d*x + 6*c) - 2*(32*a^2*b - 40*a*b^2 + 17*b^3)*sin(4*d*x + 4*c) + (7*a*b^2 - 4*b^3)*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) - 2*((72*a^2*b - 107*a*b^2 + 56*b^3)*sin(4*d*x + 4*c) - 4*(7*a*b^2 - 4*b^3)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))/(a^4*b^2 - 2*a^3*b^3 + a^2*b^4 + (a^4*b^2 - 2*a^3*b^3 + a^2*b^4)*cos(8*d*x + 8*c)^2 + 16*(a^4*b^2 - 2*a^3*b^3 + a^2*b^4)*cos(6*d*x + 6*c)^2 + 4*(64*a^6 - 176*a^5*b + 169*a^4*b^2 - 66*a^3*b^3 + 9*a^2*b^4)*cos(4*d*x + 4*c)^2 + 16*(a^4*b^2 - 2*a^3*b^3 + a^2*b^4)*cos(2*d*x + 2*c)^2 + (a^4*b^2 - 2*a^3*b^3 + a^2*b^4)*sin(8*d*x + 8*c)^2 + 16*(a^4*b^2 - 2*a^3*b^3 + a^2*b^4)*sin(6*d*x + 6*c)^2 + 4*(64*a^6 - 176*a^5*b + 169*a^4*b^2 - 66*a^3*b^3 + 9*a^2*b^4)*sin(4*d*x + 4*c)^2 + 16*(8*a^5*b - 19*a^4*b^2 + 14*a^3*b^3 - 3*a^2*b^4)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*(a^4*b^2 - 2*a^3*b^3 + a^2*b^4)*sin(2*d*x + 2*c)^2 + 2*(a^4*b^2 - 2*a^3*b^3 + a^2*b^4 - 4*(a^4*b^2 - 2*a^3*b^3 + a^2*b^4)*cos(6*d*x + 6*c) - 2*(8*a^5*b - 19*a^4*b^2 + 14*a^3*b^3 - 3*a^2*b^4)*cos(4*d*x + 4*c) - 4*(a^4*b^2 - 2*a^3*b^3 + a^2*b^4)*cos(2*d*x + 2*c))*cos(8*d*x + 8*c) - 8*(a^4*b^2 - 2*a^3*b^3 + a^2*b^4 - 2*(8*a^5*b - 19*a^4*b^2 + 14*a^3*b^3 - 3*a^2*b^4)*cos(4*d*x + 4*c) - 4*(a^4*b^2 - 2*a^3*b^3 + a^2*b^4)*cos(2*d*x + 2*c))*cos(6*d*x + 6*c) - 4*(8*a^5*b - 19*a^4*b^2 + 14*a^3*b^3 - 3*a^2*b^4 - 4*(8*a^5*b - 19*a^4*b^2 + 14*a^3*b^3 - 3*a^2*b^4)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 8*(a^4*b^2 - 2*a^3*b^3 + a^2*b^4)*cos(2*d*x + 2*c) - 4*(2*(a^4*b^2 - 2*a^3*b^3 + a^2*b^4)*sin(6*d*x + 6*c) + (8*a^5*b - 19*a^4*b^2 + 14*a^3*b^3 - 3*a^2*b^4)*sin(4*d*x + 4*c) + 2*(a^4*b^2 - 2*a^3*b^3 + a^2*b^4)*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*((8*a^5*b - 19*a^4*b^2 + 14*a^3*b^3 - 3*a^2*b^4)*sin(4*d*x + 4*c) + 2*(a^4*b^2 - 2*a^3*b^3 + a^2*b^4)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c)), x) - (6*a*b^4 - 3*b^5 + (7*a*b^4 - 4*b^5)*cos(14*d*x + 14*c) - (32*a^2*b^3 + 2*a*b^4 - 7*b^5)*cos(12*d*x + 12*c) - (16*a^2*b^3 - 3*a*b^4 - 28*b^5)*cos(10*d*x + 10*c) + 3*(256*a^3*b^2 - 320*a^2*b^3 + 166*a*b^4 - 35*b^5)*cos(8*d*x + 8*c) + (784*a^2*b^3 - 723*a*b^4 + 140*b^5)*cos(6*d*x + 6*c) - (160*a^2*b^3 - 266*a*b^4 + 91*b^5)*cos(4*d*x + 4*c) - (55*a*b^4 - 28*b^5)*cos(2*d*x + 2*c))*sin(16*d*x + 16*c) + (55*a*b^4 - 28*b^5 - 4*(120*a^2*b^3 - 77*a*b^4 + 14*b^5)*cos(12*d*x + 12*c) + 16*(48*a^2*b^3 - 55*a*b^4 + 28*b^5)*cos(10*d*x + 10*c) + 2*(3968*a^3*b^2 - 5024*a^2*b^3 + 2621*a*b^4 - 560*b^5)*cos(8*d*x + 8*c) + 32*(224*a^2*b^3 - 209*a*b^4 + 42*b^5)*cos(6*d*x + 6*c) - 4*(376*a^2*b^3 - 613*a*b^4 + 210*b^5)*cos(4*d*x + 4*c) - 16*(31*a*b^4 - 16*b^5)*cos(2*d*x + 2*c))*sin(14*d*x + 14*c) + (160*a^2*b^3 - 266*a*b^4 + 91*b^5 - 4*(1152*a^3*b^2 - 520*a^2*b^3 - 455*a*b^4 + 294*b^5)*cos(10*d*x + 10*c) + 2*(8192*a^4*b - 23296*a^3*b^2 + 21376*a^2*b^3 - 9394*a*b^4 + 1715*b^5)*cos(8*d*x + 8*c) + 4*(5248*a^3*b^2 - 10888*a^2*b^3 + 6433*a*b^4 - 1078*b^5)*cos(6*d*x + 6*c) - 8*(512*a^3*b^2 - 1520*a^2*b^3 + 1330*a*b^4 - 343*b^5)*cos(4*d*x + 4*c) - 4*(376*a^2*b^3 - 613*a*b^4 + 210*b^5)*cos(2*d*x + 2*c))*sin(12*d*x + 12*c) - (784*a^2*b^3 - 723*a*b^4 + 140*b^5 + 2*(51200*a^4*b - 84864*a^3*b^2 + 56016*a^2*b^3 - 18081*a*b^4 + 1960*b^5)*cos(8*d*x + 8*c) + 16*(6400*a^3*b^2 - 8608*a^2*b^3 + 3437*a*b^4 - 392*b^5)*cos(6*d*x + 6*c) - 4*(5248*a^3*b^2 - 10888*a^2*b^3 + 6433*a*b^4 - 1078*b^5)*cos(4*d*x + 4*c) - 32*(224*a^2*b^3 - 209*a*b^4 + 42*b^5)*cos(2*d*x + 2*c))*sin(10*d*x + 10*c) - (768*a^3*b^2 - 960*a^2*b^3 + 498*a*b^4 - 105*b^5 + 2*(51200*a^4*b - 84864*a^3*b^2 + 56016*a^2*b^3 - 18081*a*b^4 + 1960*b^5)*cos(6*d*x + 6*c) - 2*(8192*a^4*b - 23296*a^3*b^2 + 21376*a^2*b^3 - 9394*a*b^4 + 1715*b^5)*cos(4*d*x + 4*c) - 2*(3968*a^3*b^2 - 5024*a^2*b^3 + 2621*a*b^4 - 560*b^5)*cos(2*d*x + 2*c))*sin(8*d*x + 8*c) + (16*a^2*b^3 - 3*a*b^4 - 28*b^5 - 4*(1152*a^3*b^2 - 520*a^2*b^3 - 455*a*b^4 + 294*b^5)*cos(4*d*x + 4*c) + 16*(48*a^2*b^3 - 55*a*b^4 + 28*b^5)*cos(2*d*x + 2*c))*sin(6*d*x + 6*c) + (32*a^2*b^3 + 2*a*b^4 - 7*b^5 - 4*(120*a^2*b^3 - 77*a*b^4 + 14*b^5)*cos(2*d*x + 2*c))*sin(4*d*x + 4*c) - (7*a*b^4 - 4*b^5)*sin(2*d*x + 2*c))/((a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*cos(16*d*x + 16*c)^2 + 64*(a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*cos(14*d*x + 14*c)^2 + 16*(64*a^6*b^2 - 240*a^5*b^3 + 337*a^4*b^4 - 210*a^3*b^5 + 49*a^2*b^6)*d*cos(12*d*x + 12*c)^2 + 64*(256*a^6*b^2 - 736*a^5*b^3 + 753*a^4*b^4 - 322*a^3*b^5 + 49*a^2*b^6)*d*cos(10*d*x + 10*c)^2 + 4*(16384*a^8 - 57344*a^7*b + 83712*a^6*b^2 - 67648*a^5*b^3 + 32841*a^4*b^4 - 9170*a^3*b^5 + 1225*a^2*b^6)*d*cos(8*d*x + 8*c)^2 + 64*(256*a^6*b^2 - 736*a^5*b^3 + 753*a^4*b^4 - 322*a^3*b^5 + 49*a^2*b^6)*d*cos(6*d*x + 6*c)^2 + 16*(64*a^6*b^2 - 240*a^5*b^3 + 337*a^4*b^4 - 210*a^3*b^5 + 49*a^2*b^6)*d*cos(4*d*x + 4*c)^2 + 64*(a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*cos(2*d*x + 2*c)^2 + (a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*sin(16*d*x + 16*c)^2 + 64*(a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*sin(14*d*x + 14*c)^2 + 16*(64*a^6*b^2 - 240*a^5*b^3 + 337*a^4*b^4 - 210*a^3*b^5 + 49*a^2*b^6)*d*sin(12*d*x + 12*c)^2 + 64*(256*a^6*b^2 - 736*a^5*b^3 + 753*a^4*b^4 - 322*a^3*b^5 + 49*a^2*b^6)*d*sin(10*d*x + 10*c)^2 + 4*(16384*a^8 - 57344*a^7*b + 83712*a^6*b^2 - 67648*a^5*b^3 + 32841*a^4*b^4 - 9170*a^3*b^5 + 1225*a^2*b^6)*d*sin(8*d*x + 8*c)^2 + 64*(256*a^6*b^2 - 736*a^5*b^3 + 753*a^4*b^4 - 322*a^3*b^5 + 49*a^2*b^6)*d*sin(6*d*x + 6*c)^2 + 16*(64*a^6*b^2 - 240*a^5*b^3 + 337*a^4*b^4 - 210*a^3*b^5 + 49*a^2*b^6)*d*sin(4*d*x + 4*c)^2 + 64*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 64*(a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*sin(2*d*x + 2*c)^2 - 16*(a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*cos(2*d*x + 2*c) + (a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d - 2*(8*(a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*cos(14*d*x + 14*c) + 4*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*cos(12*d*x + 12*c) - 8*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*cos(10*d*x + 10*c) - 2*(128*a^6*b^2 - 352*a^5*b^3 + 355*a^4*b^4 - 166*a^3*b^5 + 35*a^2*b^6)*d*cos(8*d*x + 8*c) - 8*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*cos(6*d*x + 6*c) + 4*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*cos(4*d*x + 4*c) + 8*(a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*cos(2*d*x + 2*c) - (a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d)*cos(16*d*x + 16*c) + 16*(4*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*cos(12*d*x + 12*c) - 8*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*cos(10*d*x + 10*c) - 2*(128*a^6*b^2 - 352*a^5*b^3 + 355*a^4*b^4 - 166*a^3*b^5 + 35*a^2*b^6)*d*cos(8*d*x + 8*c) - 8*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*cos(6*d*x + 6*c) + 4*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*cos(4*d*x + 4*c) + 8*(a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*cos(2*d*x + 2*c) - (a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d)*cos(14*d*x + 14*c) - 8*(8*(128*a^6*b^2 - 424*a^5*b^3 + 513*a^4*b^4 - 266*a^3*b^5 + 49*a^2*b^6)*d*cos(10*d*x + 10*c) + 2*(1024*a^7*b - 3712*a^6*b^2 + 5304*a^5*b^3 - 3813*a^4*b^4 + 1442*a^3*b^5 - 245*a^2*b^6)*d*cos(8*d*x + 8*c) + 8*(128*a^6*b^2 - 424*a^5*b^3 + 513*a^4*b^4 - 266*a^3*b^5 + 49*a^2*b^6)*d*cos(6*d*x + 6*c) - 4*(64*a^6*b^2 - 240*a^5*b^3 + 337*a^4*b^4 - 210*a^3*b^5 + 49*a^2*b^6)*d*cos(4*d*x + 4*c) - 8*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*cos(2*d*x + 2*c) + (8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d)*cos(12*d*x + 12*c) + 16*(2*(2048*a^7*b - 6528*a^6*b^2 + 8144*a^5*b^3 - 5141*a^4*b^4 + 1722*a^3*b^5 - 245*a^2*b^6)*d*cos(8*d*x + 8*c) + 8*(256*a^6*b^2 - 736*a^5*b^3 + 753*a^4*b^4 - 322*a^3*b^5 + 49*a^2*b^6)*d*cos(6*d*x + 6*c) - 4*(128*a^6*b^2 - 424*a^5*b^3 + 513*a^4*b^4 - 266*a^3*b^5 + 49*a^2*b^6)*d*cos(4*d*x + 4*c) - 8*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*cos(2*d*x + 2*c) + (16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d)*cos(10*d*x + 10*c) + 4*(8*(2048*a^7*b - 6528*a^6*b^2 + 8144*a^5*b^3 - 5141*a^4*b^4 + 1722*a^3*b^5 - 245*a^2*b^6)*d*cos(6*d*x + 6*c) - 4*(1024*a^7*b - 3712*a^6*b^2 + 5304*a^5*b^3 - 3813*a^4*b^4 + 1442*a^3*b^5 - 245*a^2*b^6)*d*cos(4*d*x + 4*c) - 8*(128*a^6*b^2 - 352*a^5*b^3 + 355*a^4*b^4 - 166*a^3*b^5 + 35*a^2*b^6)*d*cos(2*d*x + 2*c) + (128*a^6*b^2 - 352*a^5*b^3 + 355*a^4*b^4 - 166*a^3*b^5 + 35*a^2*b^6)*d)*cos(8*d*x + 8*c) - 16*(4*(128*a^6*b^2 - 424*a^5*b^3 + 513*a^4*b^4 - 266*a^3*b^5 + 49*a^2*b^6)*d*cos(4*d*x + 4*c) + 8*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*cos(2*d*x + 2*c) - (16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d)*cos(6*d*x + 6*c) + 8*(8*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*cos(2*d*x + 2*c) - (8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d)*cos(4*d*x + 4*c) - 4*(4*(a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*sin(14*d*x + 14*c) + 2*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*sin(12*d*x + 12*c) - 4*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*sin(10*d*x + 10*c) - (128*a^6*b^2 - 352*a^5*b^3 + 355*a^4*b^4 - 166*a^3*b^5 + 35*a^2*b^6)*d*sin(8*d*x + 8*c) - 4*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*sin(6*d*x + 6*c) + 2*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*sin(4*d*x + 4*c) + 4*(a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*sin(2*d*x + 2*c))*sin(16*d*x + 16*c) + 32*(2*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*sin(12*d*x + 12*c) - 4*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*sin(10*d*x + 10*c) - (128*a^6*b^2 - 352*a^5*b^3 + 355*a^4*b^4 - 166*a^3*b^5 + 35*a^2*b^6)*d*sin(8*d*x + 8*c) - 4*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*sin(6*d*x + 6*c) + 2*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*sin(4*d*x + 4*c) + 4*(a^4*b^4 - 2*a^3*b^5 + a^2*b^6)*d*sin(2*d*x + 2*c))*sin(14*d*x + 14*c) - 16*(4*(128*a^6*b^2 - 424*a^5*b^3 + 513*a^4*b^4 - 266*a^3*b^5 + 49*a^2*b^6)*d*sin(10*d*x + 10*c) + (1024*a^7*b - 3712*a^6*b^2 + 5304*a^5*b^3 - 3813*a^4*b^4 + 1442*a^3*b^5 - 245*a^2*b^6)*d*sin(8*d*x + 8*c) + 4*(128*a^6*b^2 - 424*a^5*b^3 + 513*a^4*b^4 - 266*a^3*b^5 + 49*a^2*b^6)*d*sin(6*d*x + 6*c) - 2*(64*a^6*b^2 - 240*a^5*b^3 + 337*a^4*b^4 - 210*a^3*b^5 + 49*a^2*b^6)*d*sin(4*d*x + 4*c) - 4*(8*a^5*b^3 - 23*a^4*b^4 + 22*a^3*b^5 - 7*a^2*b^6)*d*sin(2*d*x + 2*c))*sin(12*d*x + 12*c) + 32*((2048*a^7*b - 6528*a^6*b^2 + 8144*a^5*b^3 - 5141*a^4*b^4 + 1722*a^3*b^5 - 245*a^2*b^6)*d*sin(8*d*x + 8*c) + 4*(256*a^6*b^2 - 736*a^5*b^3 + 753*a^4*b^4 - 322*a^3*b^5 + 49*a^2*b^6)*d*sin(6*d*x + 6*c) - 2*(128*a^6*b^2 - 424*a^5*b^3 + 513*a^4*b^4 - 266*a^3*b^5 + 49*a^2*b^6)*d*sin(4*d*x + 4*c) - 4*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*sin(2*d*x + 2*c))*sin(10*d*x + 10*c) + 16*(2*(2048*a^7*b - 6528*a^6*b^2 + 8144*a^5*b^3 - 5141*a^4*b^4 + 1722*a^3*b^5 - 245*a^2*b^6)*d*sin(6*d*x + 6*c) - (1024*a^7*b - 3712*a^6*b^2 + 5304*a^5*b^3 - 3813*a^4*b^4 + 1442*a^3*b^5 - 245*a^2*b^6)*d*sin(4*d*x + 4*c) - 2*(128*a^6*b^2 - 352*a^5*b^3 + 355*a^4*b^4 - 166*a^3*b^5 + 35*a^2*b^6)*d*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) - 64*((128*a^6*b^2 - 424*a^5*b^3 + 513*a^4*b^4 - 266*a^3*b^5 + 49*a^2*b^6)*d*sin(4*d*x + 4*c) + 2*(16*a^5*b^3 - 39*a^4*b^4 + 30*a^3*b^5 - 7*a^2*b^6)*d*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))","F",0
235,-1,0,0,0.000000," ","integrate(csc(d*x+c)^2/(a-b*sin(d*x+c)^4)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
236,1,17,0,0.442880," ","integrate(1/(1-sin(x)^4),x, algorithm=""maxima"")","\frac{1}{4} \, \sqrt{2} \arctan\left(\sqrt{2} \tan\left(x\right)\right) + \frac{1}{2} \, \tan\left(x\right)"," ",0,"1/4*sqrt(2)*arctan(sqrt(2)*tan(x)) + 1/2*tan(x)","A",0
237,0,0,0,0.000000," ","integrate(1/(a+b*sin(x)^4),x, algorithm=""maxima"")","\int \frac{1}{b \sin\left(x\right)^{4} + a}\,{d x}"," ",0,"integrate(1/(b*sin(x)^4 + a), x)","F",0
238,0,0,0,0.000000," ","integrate(1/(1+sin(x)^4),x, algorithm=""maxima"")","\int \frac{1}{\sin\left(x\right)^{4} + 1}\,{d x}"," ",0,"integrate(1/(sin(x)^4 + 1), x)","F",0
239,0,0,0,0.000000," ","integrate(sin(d*x+c)*(a+b*sin(d*x+c)^4)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sin\left(d x + c\right)^{4} + a} \sin\left(d x + c\right)\,{d x}"," ",0,"integrate(sqrt(b*sin(d*x + c)^4 + a)*sin(d*x + c), x)","F",0
240,0,0,0,0.000000," ","integrate(csc(d*x+c)*(a+b*sin(d*x+c)^4)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sin\left(d x + c\right)^{4} + a} \csc\left(d x + c\right)\,{d x}"," ",0,"integrate(sqrt(b*sin(d*x + c)^4 + a)*csc(d*x + c), x)","F",0
241,0,0,0,0.000000," ","integrate(sin(d*x+c)^5/(a+b*sin(d*x+c)^4)^(1/2),x, algorithm=""maxima"")","\int \frac{\sin\left(d x + c\right)^{5}}{\sqrt{b \sin\left(d x + c\right)^{4} + a}}\,{d x}"," ",0,"integrate(sin(d*x + c)^5/sqrt(b*sin(d*x + c)^4 + a), x)","F",0
242,0,0,0,0.000000," ","integrate(sin(d*x+c)^3/(a+b*sin(d*x+c)^4)^(1/2),x, algorithm=""maxima"")","\int \frac{\sin\left(d x + c\right)^{3}}{\sqrt{b \sin\left(d x + c\right)^{4} + a}}\,{d x}"," ",0,"integrate(sin(d*x + c)^3/sqrt(b*sin(d*x + c)^4 + a), x)","F",0
243,0,0,0,0.000000," ","integrate(sin(d*x+c)/(a+b*sin(d*x+c)^4)^(1/2),x, algorithm=""maxima"")","\int \frac{\sin\left(d x + c\right)}{\sqrt{b \sin\left(d x + c\right)^{4} + a}}\,{d x}"," ",0,"integrate(sin(d*x + c)/sqrt(b*sin(d*x + c)^4 + a), x)","F",0
244,0,0,0,0.000000," ","integrate(csc(d*x+c)/(a+b*sin(d*x+c)^4)^(1/2),x, algorithm=""maxima"")","\int \frac{\csc\left(d x + c\right)}{\sqrt{b \sin\left(d x + c\right)^{4} + a}}\,{d x}"," ",0,"integrate(csc(d*x + c)/sqrt(b*sin(d*x + c)^4 + a), x)","F",0
245,0,0,0,0.000000," ","integrate(csc(d*x+c)^3/(a+b*sin(d*x+c)^4)^(1/2),x, algorithm=""maxima"")","\int \frac{\csc\left(d x + c\right)^{3}}{\sqrt{b \sin\left(d x + c\right)^{4} + a}}\,{d x}"," ",0,"integrate(csc(d*x + c)^3/sqrt(b*sin(d*x + c)^4 + a), x)","F",0
246,0,0,0,0.000000," ","integrate(sin(d*x+c)^2/(a+b*sin(d*x+c)^4)^(1/2),x, algorithm=""maxima"")","\int \frac{\sin\left(d x + c\right)^{2}}{\sqrt{b \sin\left(d x + c\right)^{4} + a}}\,{d x}"," ",0,"integrate(sin(d*x + c)^2/sqrt(b*sin(d*x + c)^4 + a), x)","F",0
247,0,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c)^4)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \sin\left(d x + c\right)^{4} + a}}\,{d x}"," ",0,"integrate(1/sqrt(b*sin(d*x + c)^4 + a), x)","F",0
248,0,0,0,0.000000," ","integrate(csc(d*x+c)^2/(a+b*sin(d*x+c)^4)^(1/2),x, algorithm=""maxima"")","\int \frac{\csc\left(d x + c\right)^{2}}{\sqrt{b \sin\left(d x + c\right)^{4} + a}}\,{d x}"," ",0,"integrate(csc(d*x + c)^2/sqrt(b*sin(d*x + c)^4 + a), x)","F",0
249,0,0,0,0.000000," ","integrate(1/(a+b*sin(x)^5),x, algorithm=""maxima"")","\int \frac{1}{b \sin\left(x\right)^{5} + a}\,{d x}"," ",0,"integrate(1/(b*sin(x)^5 + a), x)","F",0
250,0,0,0,0.000000," ","integrate(1/(a+b*sin(x)^6),x, algorithm=""maxima"")","\int \frac{1}{b \sin\left(x\right)^{6} + a}\,{d x}"," ",0,"integrate(1/(b*sin(x)^6 + a), x)","F",0
251,0,0,0,0.000000," ","integrate(1/(a+b*sin(x)^8),x, algorithm=""maxima"")","\int \frac{1}{b \sin\left(x\right)^{8} + a}\,{d x}"," ",0,"integrate(1/(b*sin(x)^8 + a), x)","F",0
252,0,0,0,0.000000," ","integrate(1/(a-b*sin(x)^5),x, algorithm=""maxima"")","-\int \frac{1}{b \sin\left(x\right)^{5} - a}\,{d x}"," ",0,"-integrate(1/(b*sin(x)^5 - a), x)","F",0
253,0,0,0,0.000000," ","integrate(1/(a-b*sin(x)^6),x, algorithm=""maxima"")","-\int \frac{1}{b \sin\left(x\right)^{6} - a}\,{d x}"," ",0,"-integrate(1/(b*sin(x)^6 - a), x)","F",0
254,0,0,0,0.000000," ","integrate(1/(a-b*sin(x)^8),x, algorithm=""maxima"")","-\int \frac{1}{b \sin\left(x\right)^{8} - a}\,{d x}"," ",0,"-integrate(1/(b*sin(x)^8 - a), x)","F",0
255,0,0,0,0.000000," ","integrate(1/(1+sin(x)^5),x, algorithm=""maxima"")","-\frac{-2 \, {\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sin\left(x\right) + 1\right)} \int \frac{{\left(4 \, \cos\left(6 \, x\right) - 40 \, \cos\left(4 \, x\right) + 4 \, \cos\left(2 \, x\right) - \sin\left(7 \, x\right) + 15 \, \sin\left(5 \, x\right) - 15 \, \sin\left(3 \, x\right) + \sin\left(x\right)\right)} \cos\left(8 \, x\right) + 2 \, {\left(22 \, \cos\left(5 \, x\right) - 22 \, \cos\left(3 \, x\right) + 2 \, \cos\left(x\right) - 8 \, \sin\left(6 \, x\right) + 55 \, \sin\left(4 \, x\right) - 8 \, \sin\left(2 \, x\right)\right)} \cos\left(7 \, x\right) - 2 \, \cos\left(7 \, x\right)^{2} + 4 \, {\left(110 \, \cos\left(4 \, x\right) - 16 \, \cos\left(2 \, x\right) - 44 \, \sin\left(5 \, x\right) + 44 \, \sin\left(3 \, x\right) - 4 \, \sin\left(x\right) + 1\right)} \cos\left(6 \, x\right) - 32 \, \cos\left(6 \, x\right)^{2} + 2 \, {\left(210 \, \cos\left(3 \, x\right) - 22 \, \cos\left(x\right) - 505 \, \sin\left(4 \, x\right) + 88 \, \sin\left(2 \, x\right)\right)} \cos\left(5 \, x\right) - 210 \, \cos\left(5 \, x\right)^{2} + 10 \, {\left(44 \, \cos\left(2 \, x\right) - 101 \, \sin\left(3 \, x\right) + 11 \, \sin\left(x\right) - 4\right)} \cos\left(4 \, x\right) - 1200 \, \cos\left(4 \, x\right)^{2} + 44 \, {\left(\cos\left(x\right) - 4 \, \sin\left(2 \, x\right)\right)} \cos\left(3 \, x\right) - 210 \, \cos\left(3 \, x\right)^{2} - 4 \, {\left(4 \, \sin\left(x\right) - 1\right)} \cos\left(2 \, x\right) - 32 \, \cos\left(2 \, x\right)^{2} - 2 \, \cos\left(x\right)^{2} + {\left(\cos\left(7 \, x\right) - 15 \, \cos\left(5 \, x\right) + 15 \, \cos\left(3 \, x\right) - \cos\left(x\right) + 4 \, \sin\left(6 \, x\right) - 40 \, \sin\left(4 \, x\right) + 4 \, \sin\left(2 \, x\right)\right)} \sin\left(8 \, x\right) + {\left(16 \, \cos\left(6 \, x\right) - 110 \, \cos\left(4 \, x\right) + 16 \, \cos\left(2 \, x\right) + 44 \, \sin\left(5 \, x\right) - 44 \, \sin\left(3 \, x\right) + 4 \, \sin\left(x\right) - 1\right)} \sin\left(7 \, x\right) - 2 \, \sin\left(7 \, x\right)^{2} + 8 \, {\left(22 \, \cos\left(5 \, x\right) - 22 \, \cos\left(3 \, x\right) + 2 \, \cos\left(x\right) + 55 \, \sin\left(4 \, x\right) - 8 \, \sin\left(2 \, x\right)\right)} \sin\left(6 \, x\right) - 32 \, \sin\left(6 \, x\right)^{2} + {\left(1010 \, \cos\left(4 \, x\right) - 176 \, \cos\left(2 \, x\right) + 420 \, \sin\left(3 \, x\right) - 44 \, \sin\left(x\right) + 15\right)} \sin\left(5 \, x\right) - 210 \, \sin\left(5 \, x\right)^{2} + 10 \, {\left(101 \, \cos\left(3 \, x\right) - 11 \, \cos\left(x\right) + 44 \, \sin\left(2 \, x\right)\right)} \sin\left(4 \, x\right) - 1200 \, \sin\left(4 \, x\right)^{2} + {\left(176 \, \cos\left(2 \, x\right) + 44 \, \sin\left(x\right) - 15\right)} \sin\left(3 \, x\right) - 210 \, \sin\left(3 \, x\right)^{2} + 16 \, \cos\left(x\right) \sin\left(2 \, x\right) - 32 \, \sin\left(2 \, x\right)^{2} - 2 \, \sin\left(x\right)^{2} + \sin\left(x\right)}{2 \, {\left(8 \, \cos\left(6 \, x\right) - 30 \, \cos\left(4 \, x\right) + 8 \, \cos\left(2 \, x\right) - 2 \, \sin\left(7 \, x\right) + 14 \, \sin\left(5 \, x\right) - 14 \, \sin\left(3 \, x\right) + 2 \, \sin\left(x\right) - 1\right)} \cos\left(8 \, x\right) - \cos\left(8 \, x\right)^{2} + 8 \, {\left(7 \, \cos\left(5 \, x\right) - 7 \, \cos\left(3 \, x\right) + \cos\left(x\right) - 4 \, \sin\left(6 \, x\right) + 15 \, \sin\left(4 \, x\right) - 4 \, \sin\left(2 \, x\right)\right)} \cos\left(7 \, x\right) - 4 \, \cos\left(7 \, x\right)^{2} + 16 \, {\left(30 \, \cos\left(4 \, x\right) - 8 \, \cos\left(2 \, x\right) - 14 \, \sin\left(5 \, x\right) + 14 \, \sin\left(3 \, x\right) - 2 \, \sin\left(x\right) + 1\right)} \cos\left(6 \, x\right) - 64 \, \cos\left(6 \, x\right)^{2} + 56 \, {\left(7 \, \cos\left(3 \, x\right) - \cos\left(x\right) - 15 \, \sin\left(4 \, x\right) + 4 \, \sin\left(2 \, x\right)\right)} \cos\left(5 \, x\right) - 196 \, \cos\left(5 \, x\right)^{2} + 60 \, {\left(8 \, \cos\left(2 \, x\right) - 14 \, \sin\left(3 \, x\right) + 2 \, \sin\left(x\right) - 1\right)} \cos\left(4 \, x\right) - 900 \, \cos\left(4 \, x\right)^{2} + 56 \, {\left(\cos\left(x\right) - 4 \, \sin\left(2 \, x\right)\right)} \cos\left(3 \, x\right) - 196 \, \cos\left(3 \, x\right)^{2} - 16 \, {\left(2 \, \sin\left(x\right) - 1\right)} \cos\left(2 \, x\right) - 64 \, \cos\left(2 \, x\right)^{2} - 4 \, \cos\left(x\right)^{2} + 4 \, {\left(\cos\left(7 \, x\right) - 7 \, \cos\left(5 \, x\right) + 7 \, \cos\left(3 \, x\right) - \cos\left(x\right) + 4 \, \sin\left(6 \, x\right) - 15 \, \sin\left(4 \, x\right) + 4 \, \sin\left(2 \, x\right)\right)} \sin\left(8 \, x\right) - \sin\left(8 \, x\right)^{2} + 4 \, {\left(8 \, \cos\left(6 \, x\right) - 30 \, \cos\left(4 \, x\right) + 8 \, \cos\left(2 \, x\right) + 14 \, \sin\left(5 \, x\right) - 14 \, \sin\left(3 \, x\right) + 2 \, \sin\left(x\right) - 1\right)} \sin\left(7 \, x\right) - 4 \, \sin\left(7 \, x\right)^{2} + 32 \, {\left(7 \, \cos\left(5 \, x\right) - 7 \, \cos\left(3 \, x\right) + \cos\left(x\right) + 15 \, \sin\left(4 \, x\right) - 4 \, \sin\left(2 \, x\right)\right)} \sin\left(6 \, x\right) - 64 \, \sin\left(6 \, x\right)^{2} + 28 \, {\left(30 \, \cos\left(4 \, x\right) - 8 \, \cos\left(2 \, x\right) + 14 \, \sin\left(3 \, x\right) - 2 \, \sin\left(x\right) + 1\right)} \sin\left(5 \, x\right) - 196 \, \sin\left(5 \, x\right)^{2} + 120 \, {\left(7 \, \cos\left(3 \, x\right) - \cos\left(x\right) + 4 \, \sin\left(2 \, x\right)\right)} \sin\left(4 \, x\right) - 900 \, \sin\left(4 \, x\right)^{2} + 28 \, {\left(8 \, \cos\left(2 \, x\right) + 2 \, \sin\left(x\right) - 1\right)} \sin\left(3 \, x\right) - 196 \, \sin\left(3 \, x\right)^{2} + 32 \, \cos\left(x\right) \sin\left(2 \, x\right) - 64 \, \sin\left(2 \, x\right)^{2} - 4 \, \sin\left(x\right)^{2} + 4 \, \sin\left(x\right) - 1}\,{d x} + 2 \, \cos\left(x\right)}{5 \, {\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sin\left(x\right) + 1\right)}}"," ",0,"-1/5*(5*(cos(x)^2 + sin(x)^2 + 2*sin(x) + 1)*integrate(-2/5*((4*cos(6*x) - 40*cos(4*x) + 4*cos(2*x) - sin(7*x) + 15*sin(5*x) - 15*sin(3*x) + sin(x))*cos(8*x) + 2*(22*cos(5*x) - 22*cos(3*x) + 2*cos(x) - 8*sin(6*x) + 55*sin(4*x) - 8*sin(2*x))*cos(7*x) - 2*cos(7*x)^2 + 4*(110*cos(4*x) - 16*cos(2*x) - 44*sin(5*x) + 44*sin(3*x) - 4*sin(x) + 1)*cos(6*x) - 32*cos(6*x)^2 + 2*(210*cos(3*x) - 22*cos(x) - 505*sin(4*x) + 88*sin(2*x))*cos(5*x) - 210*cos(5*x)^2 + 10*(44*cos(2*x) - 101*sin(3*x) + 11*sin(x) - 4)*cos(4*x) - 1200*cos(4*x)^2 + 44*(cos(x) - 4*sin(2*x))*cos(3*x) - 210*cos(3*x)^2 - 4*(4*sin(x) - 1)*cos(2*x) - 32*cos(2*x)^2 - 2*cos(x)^2 + (cos(7*x) - 15*cos(5*x) + 15*cos(3*x) - cos(x) + 4*sin(6*x) - 40*sin(4*x) + 4*sin(2*x))*sin(8*x) + (16*cos(6*x) - 110*cos(4*x) + 16*cos(2*x) + 44*sin(5*x) - 44*sin(3*x) + 4*sin(x) - 1)*sin(7*x) - 2*sin(7*x)^2 + 8*(22*cos(5*x) - 22*cos(3*x) + 2*cos(x) + 55*sin(4*x) - 8*sin(2*x))*sin(6*x) - 32*sin(6*x)^2 + (1010*cos(4*x) - 176*cos(2*x) + 420*sin(3*x) - 44*sin(x) + 15)*sin(5*x) - 210*sin(5*x)^2 + 10*(101*cos(3*x) - 11*cos(x) + 44*sin(2*x))*sin(4*x) - 1200*sin(4*x)^2 + (176*cos(2*x) + 44*sin(x) - 15)*sin(3*x) - 210*sin(3*x)^2 + 16*cos(x)*sin(2*x) - 32*sin(2*x)^2 - 2*sin(x)^2 + sin(x))/(2*(8*cos(6*x) - 30*cos(4*x) + 8*cos(2*x) - 2*sin(7*x) + 14*sin(5*x) - 14*sin(3*x) + 2*sin(x) - 1)*cos(8*x) - cos(8*x)^2 + 8*(7*cos(5*x) - 7*cos(3*x) + cos(x) - 4*sin(6*x) + 15*sin(4*x) - 4*sin(2*x))*cos(7*x) - 4*cos(7*x)^2 + 16*(30*cos(4*x) - 8*cos(2*x) - 14*sin(5*x) + 14*sin(3*x) - 2*sin(x) + 1)*cos(6*x) - 64*cos(6*x)^2 + 56*(7*cos(3*x) - cos(x) - 15*sin(4*x) + 4*sin(2*x))*cos(5*x) - 196*cos(5*x)^2 + 60*(8*cos(2*x) - 14*sin(3*x) + 2*sin(x) - 1)*cos(4*x) - 900*cos(4*x)^2 + 56*(cos(x) - 4*sin(2*x))*cos(3*x) - 196*cos(3*x)^2 - 16*(2*sin(x) - 1)*cos(2*x) - 64*cos(2*x)^2 - 4*cos(x)^2 + 4*(cos(7*x) - 7*cos(5*x) + 7*cos(3*x) - cos(x) + 4*sin(6*x) - 15*sin(4*x) + 4*sin(2*x))*sin(8*x) - sin(8*x)^2 + 4*(8*cos(6*x) - 30*cos(4*x) + 8*cos(2*x) + 14*sin(5*x) - 14*sin(3*x) + 2*sin(x) - 1)*sin(7*x) - 4*sin(7*x)^2 + 32*(7*cos(5*x) - 7*cos(3*x) + cos(x) + 15*sin(4*x) - 4*sin(2*x))*sin(6*x) - 64*sin(6*x)^2 + 28*(30*cos(4*x) - 8*cos(2*x) + 14*sin(3*x) - 2*sin(x) + 1)*sin(5*x) - 196*sin(5*x)^2 + 120*(7*cos(3*x) - cos(x) + 4*sin(2*x))*sin(4*x) - 900*sin(4*x)^2 + 28*(8*cos(2*x) + 2*sin(x) - 1)*sin(3*x) - 196*sin(3*x)^2 + 32*cos(x)*sin(2*x) - 64*sin(2*x)^2 - 4*sin(x)^2 + 4*sin(x) - 1), x) + 2*cos(x))/(cos(x)^2 + sin(x)^2 + 2*sin(x) + 1)","F",0
256,1,71,0,0.441634," ","integrate(1/(1+sin(x)^6),x, algorithm=""maxima"")","\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, \tan\left(x\right) + 1\right)}\right) + \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, \tan\left(x\right) - 1\right)}\right) + \frac{1}{6} \, \sqrt{2} \arctan\left(\sqrt{2} \tan\left(x\right)\right) + \frac{1}{12} \, \log\left(\tan\left(x\right)^{2} + \tan\left(x\right) + 1\right) - \frac{1}{12} \, \log\left(\tan\left(x\right)^{2} - \tan\left(x\right) + 1\right)"," ",0,"1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*tan(x) + 1)) + 1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*tan(x) - 1)) + 1/6*sqrt(2)*arctan(sqrt(2)*tan(x)) + 1/12*log(tan(x)^2 + tan(x) + 1) - 1/12*log(tan(x)^2 - tan(x) + 1)","A",0
257,0,0,0,0.000000," ","integrate(1/(1+sin(x)^8),x, algorithm=""maxima"")","\int \frac{1}{\sin\left(x\right)^{8} + 1}\,{d x}"," ",0,"integrate(1/(sin(x)^8 + 1), x)","F",0
258,0,0,0,0.000000," ","integrate(1/(1-sin(x)^5),x, algorithm=""maxima"")","\frac{2 \, {\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sin\left(x\right) + 1\right)} \int \frac{{\left(4 \, \cos\left(6 \, x\right) - 40 \, \cos\left(4 \, x\right) + 4 \, \cos\left(2 \, x\right) + \sin\left(7 \, x\right) - 15 \, \sin\left(5 \, x\right) + 15 \, \sin\left(3 \, x\right) - \sin\left(x\right)\right)} \cos\left(8 \, x\right) + 2 \, {\left(22 \, \cos\left(5 \, x\right) - 22 \, \cos\left(3 \, x\right) + 2 \, \cos\left(x\right) + 8 \, \sin\left(6 \, x\right) - 55 \, \sin\left(4 \, x\right) + 8 \, \sin\left(2 \, x\right)\right)} \cos\left(7 \, x\right) - 2 \, \cos\left(7 \, x\right)^{2} + 4 \, {\left(110 \, \cos\left(4 \, x\right) - 16 \, \cos\left(2 \, x\right) + 44 \, \sin\left(5 \, x\right) - 44 \, \sin\left(3 \, x\right) + 4 \, \sin\left(x\right) + 1\right)} \cos\left(6 \, x\right) - 32 \, \cos\left(6 \, x\right)^{2} + 2 \, {\left(210 \, \cos\left(3 \, x\right) - 22 \, \cos\left(x\right) + 505 \, \sin\left(4 \, x\right) - 88 \, \sin\left(2 \, x\right)\right)} \cos\left(5 \, x\right) - 210 \, \cos\left(5 \, x\right)^{2} + 10 \, {\left(44 \, \cos\left(2 \, x\right) + 101 \, \sin\left(3 \, x\right) - 11 \, \sin\left(x\right) - 4\right)} \cos\left(4 \, x\right) - 1200 \, \cos\left(4 \, x\right)^{2} + 44 \, {\left(\cos\left(x\right) + 4 \, \sin\left(2 \, x\right)\right)} \cos\left(3 \, x\right) - 210 \, \cos\left(3 \, x\right)^{2} + 4 \, {\left(4 \, \sin\left(x\right) + 1\right)} \cos\left(2 \, x\right) - 32 \, \cos\left(2 \, x\right)^{2} - 2 \, \cos\left(x\right)^{2} - {\left(\cos\left(7 \, x\right) - 15 \, \cos\left(5 \, x\right) + 15 \, \cos\left(3 \, x\right) - \cos\left(x\right) - 4 \, \sin\left(6 \, x\right) + 40 \, \sin\left(4 \, x\right) - 4 \, \sin\left(2 \, x\right)\right)} \sin\left(8 \, x\right) - {\left(16 \, \cos\left(6 \, x\right) - 110 \, \cos\left(4 \, x\right) + 16 \, \cos\left(2 \, x\right) - 44 \, \sin\left(5 \, x\right) + 44 \, \sin\left(3 \, x\right) - 4 \, \sin\left(x\right) - 1\right)} \sin\left(7 \, x\right) - 2 \, \sin\left(7 \, x\right)^{2} - 8 \, {\left(22 \, \cos\left(5 \, x\right) - 22 \, \cos\left(3 \, x\right) + 2 \, \cos\left(x\right) - 55 \, \sin\left(4 \, x\right) + 8 \, \sin\left(2 \, x\right)\right)} \sin\left(6 \, x\right) - 32 \, \sin\left(6 \, x\right)^{2} - {\left(1010 \, \cos\left(4 \, x\right) - 176 \, \cos\left(2 \, x\right) - 420 \, \sin\left(3 \, x\right) + 44 \, \sin\left(x\right) + 15\right)} \sin\left(5 \, x\right) - 210 \, \sin\left(5 \, x\right)^{2} - 10 \, {\left(101 \, \cos\left(3 \, x\right) - 11 \, \cos\left(x\right) - 44 \, \sin\left(2 \, x\right)\right)} \sin\left(4 \, x\right) - 1200 \, \sin\left(4 \, x\right)^{2} - {\left(176 \, \cos\left(2 \, x\right) - 44 \, \sin\left(x\right) - 15\right)} \sin\left(3 \, x\right) - 210 \, \sin\left(3 \, x\right)^{2} - 16 \, \cos\left(x\right) \sin\left(2 \, x\right) - 32 \, \sin\left(2 \, x\right)^{2} - 2 \, \sin\left(x\right)^{2} - \sin\left(x\right)}{2 \, {\left(8 \, \cos\left(6 \, x\right) - 30 \, \cos\left(4 \, x\right) + 8 \, \cos\left(2 \, x\right) + 2 \, \sin\left(7 \, x\right) - 14 \, \sin\left(5 \, x\right) + 14 \, \sin\left(3 \, x\right) - 2 \, \sin\left(x\right) - 1\right)} \cos\left(8 \, x\right) - \cos\left(8 \, x\right)^{2} + 8 \, {\left(7 \, \cos\left(5 \, x\right) - 7 \, \cos\left(3 \, x\right) + \cos\left(x\right) + 4 \, \sin\left(6 \, x\right) - 15 \, \sin\left(4 \, x\right) + 4 \, \sin\left(2 \, x\right)\right)} \cos\left(7 \, x\right) - 4 \, \cos\left(7 \, x\right)^{2} + 16 \, {\left(30 \, \cos\left(4 \, x\right) - 8 \, \cos\left(2 \, x\right) + 14 \, \sin\left(5 \, x\right) - 14 \, \sin\left(3 \, x\right) + 2 \, \sin\left(x\right) + 1\right)} \cos\left(6 \, x\right) - 64 \, \cos\left(6 \, x\right)^{2} + 56 \, {\left(7 \, \cos\left(3 \, x\right) - \cos\left(x\right) + 15 \, \sin\left(4 \, x\right) - 4 \, \sin\left(2 \, x\right)\right)} \cos\left(5 \, x\right) - 196 \, \cos\left(5 \, x\right)^{2} + 60 \, {\left(8 \, \cos\left(2 \, x\right) + 14 \, \sin\left(3 \, x\right) - 2 \, \sin\left(x\right) - 1\right)} \cos\left(4 \, x\right) - 900 \, \cos\left(4 \, x\right)^{2} + 56 \, {\left(\cos\left(x\right) + 4 \, \sin\left(2 \, x\right)\right)} \cos\left(3 \, x\right) - 196 \, \cos\left(3 \, x\right)^{2} + 16 \, {\left(2 \, \sin\left(x\right) + 1\right)} \cos\left(2 \, x\right) - 64 \, \cos\left(2 \, x\right)^{2} - 4 \, \cos\left(x\right)^{2} - 4 \, {\left(\cos\left(7 \, x\right) - 7 \, \cos\left(5 \, x\right) + 7 \, \cos\left(3 \, x\right) - \cos\left(x\right) - 4 \, \sin\left(6 \, x\right) + 15 \, \sin\left(4 \, x\right) - 4 \, \sin\left(2 \, x\right)\right)} \sin\left(8 \, x\right) - \sin\left(8 \, x\right)^{2} - 4 \, {\left(8 \, \cos\left(6 \, x\right) - 30 \, \cos\left(4 \, x\right) + 8 \, \cos\left(2 \, x\right) - 14 \, \sin\left(5 \, x\right) + 14 \, \sin\left(3 \, x\right) - 2 \, \sin\left(x\right) - 1\right)} \sin\left(7 \, x\right) - 4 \, \sin\left(7 \, x\right)^{2} - 32 \, {\left(7 \, \cos\left(5 \, x\right) - 7 \, \cos\left(3 \, x\right) + \cos\left(x\right) - 15 \, \sin\left(4 \, x\right) + 4 \, \sin\left(2 \, x\right)\right)} \sin\left(6 \, x\right) - 64 \, \sin\left(6 \, x\right)^{2} - 28 \, {\left(30 \, \cos\left(4 \, x\right) - 8 \, \cos\left(2 \, x\right) - 14 \, \sin\left(3 \, x\right) + 2 \, \sin\left(x\right) + 1\right)} \sin\left(5 \, x\right) - 196 \, \sin\left(5 \, x\right)^{2} - 120 \, {\left(7 \, \cos\left(3 \, x\right) - \cos\left(x\right) - 4 \, \sin\left(2 \, x\right)\right)} \sin\left(4 \, x\right) - 900 \, \sin\left(4 \, x\right)^{2} - 28 \, {\left(8 \, \cos\left(2 \, x\right) - 2 \, \sin\left(x\right) - 1\right)} \sin\left(3 \, x\right) - 196 \, \sin\left(3 \, x\right)^{2} - 32 \, \cos\left(x\right) \sin\left(2 \, x\right) - 64 \, \sin\left(2 \, x\right)^{2} - 4 \, \sin\left(x\right)^{2} - 4 \, \sin\left(x\right) - 1}\,{d x} + 2 \, \cos\left(x\right)}{5 \, {\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sin\left(x\right) + 1\right)}}"," ",0,"1/5*(5*(cos(x)^2 + sin(x)^2 - 2*sin(x) + 1)*integrate(2/5*((4*cos(6*x) - 40*cos(4*x) + 4*cos(2*x) + sin(7*x) - 15*sin(5*x) + 15*sin(3*x) - sin(x))*cos(8*x) + 2*(22*cos(5*x) - 22*cos(3*x) + 2*cos(x) + 8*sin(6*x) - 55*sin(4*x) + 8*sin(2*x))*cos(7*x) - 2*cos(7*x)^2 + 4*(110*cos(4*x) - 16*cos(2*x) + 44*sin(5*x) - 44*sin(3*x) + 4*sin(x) + 1)*cos(6*x) - 32*cos(6*x)^2 + 2*(210*cos(3*x) - 22*cos(x) + 505*sin(4*x) - 88*sin(2*x))*cos(5*x) - 210*cos(5*x)^2 + 10*(44*cos(2*x) + 101*sin(3*x) - 11*sin(x) - 4)*cos(4*x) - 1200*cos(4*x)^2 + 44*(cos(x) + 4*sin(2*x))*cos(3*x) - 210*cos(3*x)^2 + 4*(4*sin(x) + 1)*cos(2*x) - 32*cos(2*x)^2 - 2*cos(x)^2 - (cos(7*x) - 15*cos(5*x) + 15*cos(3*x) - cos(x) - 4*sin(6*x) + 40*sin(4*x) - 4*sin(2*x))*sin(8*x) - (16*cos(6*x) - 110*cos(4*x) + 16*cos(2*x) - 44*sin(5*x) + 44*sin(3*x) - 4*sin(x) - 1)*sin(7*x) - 2*sin(7*x)^2 - 8*(22*cos(5*x) - 22*cos(3*x) + 2*cos(x) - 55*sin(4*x) + 8*sin(2*x))*sin(6*x) - 32*sin(6*x)^2 - (1010*cos(4*x) - 176*cos(2*x) - 420*sin(3*x) + 44*sin(x) + 15)*sin(5*x) - 210*sin(5*x)^2 - 10*(101*cos(3*x) - 11*cos(x) - 44*sin(2*x))*sin(4*x) - 1200*sin(4*x)^2 - (176*cos(2*x) - 44*sin(x) - 15)*sin(3*x) - 210*sin(3*x)^2 - 16*cos(x)*sin(2*x) - 32*sin(2*x)^2 - 2*sin(x)^2 - sin(x))/(2*(8*cos(6*x) - 30*cos(4*x) + 8*cos(2*x) + 2*sin(7*x) - 14*sin(5*x) + 14*sin(3*x) - 2*sin(x) - 1)*cos(8*x) - cos(8*x)^2 + 8*(7*cos(5*x) - 7*cos(3*x) + cos(x) + 4*sin(6*x) - 15*sin(4*x) + 4*sin(2*x))*cos(7*x) - 4*cos(7*x)^2 + 16*(30*cos(4*x) - 8*cos(2*x) + 14*sin(5*x) - 14*sin(3*x) + 2*sin(x) + 1)*cos(6*x) - 64*cos(6*x)^2 + 56*(7*cos(3*x) - cos(x) + 15*sin(4*x) - 4*sin(2*x))*cos(5*x) - 196*cos(5*x)^2 + 60*(8*cos(2*x) + 14*sin(3*x) - 2*sin(x) - 1)*cos(4*x) - 900*cos(4*x)^2 + 56*(cos(x) + 4*sin(2*x))*cos(3*x) - 196*cos(3*x)^2 + 16*(2*sin(x) + 1)*cos(2*x) - 64*cos(2*x)^2 - 4*cos(x)^2 - 4*(cos(7*x) - 7*cos(5*x) + 7*cos(3*x) - cos(x) - 4*sin(6*x) + 15*sin(4*x) - 4*sin(2*x))*sin(8*x) - sin(8*x)^2 - 4*(8*cos(6*x) - 30*cos(4*x) + 8*cos(2*x) - 14*sin(5*x) + 14*sin(3*x) - 2*sin(x) - 1)*sin(7*x) - 4*sin(7*x)^2 - 32*(7*cos(5*x) - 7*cos(3*x) + cos(x) - 15*sin(4*x) + 4*sin(2*x))*sin(6*x) - 64*sin(6*x)^2 - 28*(30*cos(4*x) - 8*cos(2*x) - 14*sin(3*x) + 2*sin(x) + 1)*sin(5*x) - 196*sin(5*x)^2 - 120*(7*cos(3*x) - cos(x) - 4*sin(2*x))*sin(4*x) - 900*sin(4*x)^2 - 28*(8*cos(2*x) - 2*sin(x) - 1)*sin(3*x) - 196*sin(3*x)^2 - 32*cos(x)*sin(2*x) - 64*sin(2*x)^2 - 4*sin(x)^2 - 4*sin(x) - 1), x) + 2*cos(x))/(cos(x)^2 + sin(x)^2 - 2*sin(x) + 1)","F",0
259,0,0,0,0.000000," ","integrate(1/(1-sin(x)^6),x, algorithm=""maxima"")","-\frac{-4 \, {\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1\right)} \int \frac{{\left(\cos\left(6 \, x\right) - 10 \, \cos\left(4 \, x\right) + \cos\left(2 \, x\right)\right)} \cos\left(8 \, x\right) + {\left(110 \, \cos\left(4 \, x\right) - 16 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(6 \, x\right) - 8 \, \cos\left(6 \, x\right)^{2} + 10 \, {\left(11 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) - 300 \, \cos\left(4 \, x\right)^{2} - 8 \, \cos\left(2 \, x\right)^{2} + {\left(\sin\left(6 \, x\right) - 10 \, \sin\left(4 \, x\right) + \sin\left(2 \, x\right)\right)} \sin\left(8 \, x\right) + 2 \, {\left(55 \, \sin\left(4 \, x\right) - 8 \, \sin\left(2 \, x\right)\right)} \sin\left(6 \, x\right) - 8 \, \sin\left(6 \, x\right)^{2} - 300 \, \sin\left(4 \, x\right)^{2} + 110 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) - 8 \, \sin\left(2 \, x\right)^{2} + \cos\left(2 \, x\right)}{2 \, {\left(8 \, \cos\left(6 \, x\right) - 30 \, \cos\left(4 \, x\right) + 8 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(8 \, x\right) - \cos\left(8 \, x\right)^{2} + 16 \, {\left(30 \, \cos\left(4 \, x\right) - 8 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(6 \, x\right) - 64 \, \cos\left(6 \, x\right)^{2} + 60 \, {\left(8 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) - 900 \, \cos\left(4 \, x\right)^{2} - 64 \, \cos\left(2 \, x\right)^{2} + 4 \, {\left(4 \, \sin\left(6 \, x\right) - 15 \, \sin\left(4 \, x\right) + 4 \, \sin\left(2 \, x\right)\right)} \sin\left(8 \, x\right) - \sin\left(8 \, x\right)^{2} + 32 \, {\left(15 \, \sin\left(4 \, x\right) - 4 \, \sin\left(2 \, x\right)\right)} \sin\left(6 \, x\right) - 64 \, \sin\left(6 \, x\right)^{2} - 900 \, \sin\left(4 \, x\right)^{2} + 480 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) - 64 \, \sin\left(2 \, x\right)^{2} + 16 \, \cos\left(2 \, x\right) - 1}\,{d x} - 2 \, \sin\left(2 \, x\right)}{3 \, {\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1\right)}}"," ",0,"-1/3*(3*(cos(2*x)^2 + sin(2*x)^2 + 2*cos(2*x) + 1)*integrate(-4/3*((cos(6*x) - 10*cos(4*x) + cos(2*x))*cos(8*x) + (110*cos(4*x) - 16*cos(2*x) + 1)*cos(6*x) - 8*cos(6*x)^2 + 10*(11*cos(2*x) - 1)*cos(4*x) - 300*cos(4*x)^2 - 8*cos(2*x)^2 + (sin(6*x) - 10*sin(4*x) + sin(2*x))*sin(8*x) + 2*(55*sin(4*x) - 8*sin(2*x))*sin(6*x) - 8*sin(6*x)^2 - 300*sin(4*x)^2 + 110*sin(4*x)*sin(2*x) - 8*sin(2*x)^2 + cos(2*x))/(2*(8*cos(6*x) - 30*cos(4*x) + 8*cos(2*x) - 1)*cos(8*x) - cos(8*x)^2 + 16*(30*cos(4*x) - 8*cos(2*x) + 1)*cos(6*x) - 64*cos(6*x)^2 + 60*(8*cos(2*x) - 1)*cos(4*x) - 900*cos(4*x)^2 - 64*cos(2*x)^2 + 4*(4*sin(6*x) - 15*sin(4*x) + 4*sin(2*x))*sin(8*x) - sin(8*x)^2 + 32*(15*sin(4*x) - 4*sin(2*x))*sin(6*x) - 64*sin(6*x)^2 - 900*sin(4*x)^2 + 480*sin(4*x)*sin(2*x) - 64*sin(2*x)^2 + 16*cos(2*x) - 1), x) - 2*sin(2*x))/(cos(2*x)^2 + sin(2*x)^2 + 2*cos(2*x) + 1)","F",0
260,0,0,0,0.000000," ","integrate(1/(1-sin(x)^8),x, algorithm=""maxima"")","\frac{{\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1\right)} {\left(2 \, {\left(\pi \left \lfloor \frac{x}{\pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(\left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{-\sqrt{2} + 2} + 2 \, \tan\left(x\right)\right)}}{\sqrt{\sqrt{2} + 2}}\right)\right)} \sqrt{\sqrt{2} + 1} + 2 \, {\left(\pi \left \lfloor \frac{x}{\pi} + \frac{1}{2} \right \rfloor + \arctan\left(-\frac{2 \, \left(\frac{1}{2}\right)^{\frac{3}{4}} {\left(\left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{-\sqrt{2} + 2} - 2 \, \tan\left(x\right)\right)}}{\sqrt{\sqrt{2} + 2}}\right)\right)} \sqrt{\sqrt{2} + 1} + \sqrt{\sqrt{2} - 1} \log\left(\tan\left(x\right)^{2} + \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{-\sqrt{2} + 2} \tan\left(x\right) + \sqrt{\frac{1}{2}}\right) - \sqrt{\sqrt{2} - 1} \log\left(\tan\left(x\right)^{2} - \left(\frac{1}{2}\right)^{\frac{1}{4}} \sqrt{-\sqrt{2} + 2} \tan\left(x\right) + \sqrt{\frac{1}{2}}\right)\right)} + {\left(\sqrt{2} \cos\left(2 \, x\right)^{2} + \sqrt{2} \sin\left(2 \, x\right)^{2} + 2 \, \sqrt{2} \cos\left(2 \, x\right) + \sqrt{2}\right)} \arctan\left(\frac{2 \, \sqrt{2} \sin\left(x\right)}{2 \, {\left(\sqrt{2} + 1\right)} \cos\left(x\right) + \cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sqrt{2} + 3}, \frac{\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) - 1}{2 \, {\left(\sqrt{2} + 1\right)} \cos\left(x\right) + \cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sqrt{2} + 3}\right) - {\left(\sqrt{2} \cos\left(2 \, x\right)^{2} + \sqrt{2} \sin\left(2 \, x\right)^{2} + 2 \, \sqrt{2} \cos\left(2 \, x\right) + \sqrt{2}\right)} \arctan\left(\frac{2 \, \sqrt{2} \sin\left(x\right)}{2 \, {\left(\sqrt{2} - 1\right)} \cos\left(x\right) + \cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sqrt{2} + 3}, \frac{\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) - 1}{2 \, {\left(\sqrt{2} - 1\right)} \cos\left(x\right) + \cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sqrt{2} + 3}\right) + 8 \, \sin\left(2 \, x\right)}{16 \, {\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1\right)}}"," ",0,"1/16*((sqrt(2)*cos(2*x)^2 + sqrt(2)*sin(2*x)^2 + 2*sqrt(2)*cos(2*x) + sqrt(2))*arctan2(2*sqrt(2)*sin(x)/(2*(sqrt(2) + 1)*cos(x) + cos(x)^2 + sin(x)^2 + 2*sqrt(2) + 3), (cos(x)^2 + sin(x)^2 + 2*cos(x) - 1)/(2*(sqrt(2) + 1)*cos(x) + cos(x)^2 + sin(x)^2 + 2*sqrt(2) + 3)) - (sqrt(2)*cos(2*x)^2 + sqrt(2)*sin(2*x)^2 + 2*sqrt(2)*cos(2*x) + sqrt(2))*arctan2(2*sqrt(2)*sin(x)/(2*(sqrt(2) - 1)*cos(x) + cos(x)^2 + sin(x)^2 - 2*sqrt(2) + 3), (cos(x)^2 + sin(x)^2 - 2*cos(x) - 1)/(2*(sqrt(2) - 1)*cos(x) + cos(x)^2 + sin(x)^2 - 2*sqrt(2) + 3)) + 128*(cos(2*x)^2 + sin(2*x)^2 + 2*cos(2*x) + 1)*integrate(((4*cos(2*x) - 1)*cos(4*x) - cos(8*x)*cos(4*x) + 4*cos(6*x)*cos(4*x) - 22*cos(4*x)^2 - sin(8*x)*sin(4*x) + 4*sin(6*x)*sin(4*x) - 22*sin(4*x)^2 + 4*sin(4*x)*sin(2*x))/(2*(4*cos(6*x) - 22*cos(4*x) + 4*cos(2*x) - 1)*cos(8*x) - cos(8*x)^2 + 8*(22*cos(4*x) - 4*cos(2*x) + 1)*cos(6*x) - 16*cos(6*x)^2 + 44*(4*cos(2*x) - 1)*cos(4*x) - 484*cos(4*x)^2 - 16*cos(2*x)^2 + 4*(2*sin(6*x) - 11*sin(4*x) + 2*sin(2*x))*sin(8*x) - sin(8*x)^2 + 16*(11*sin(4*x) - 2*sin(2*x))*sin(6*x) - 16*sin(6*x)^2 - 484*sin(4*x)^2 + 176*sin(4*x)*sin(2*x) - 16*sin(2*x)^2 + 8*cos(2*x) - 1), x) + 8*sin(2*x))/(cos(2*x)^2 + sin(2*x)^2 + 2*cos(2*x) + 1)","F",0
261,1,28,0,0.355314," ","integrate(cos(x)^9/(a-a*sin(x)^2),x, algorithm=""maxima"")","-\frac{5 \, \sin\left(x\right)^{7} - 21 \, \sin\left(x\right)^{5} + 35 \, \sin\left(x\right)^{3} - 35 \, \sin\left(x\right)}{35 \, a}"," ",0,"-1/35*(5*sin(x)^7 - 21*sin(x)^5 + 35*sin(x)^3 - 35*sin(x))/a","A",0
262,1,22,0,0.351163," ","integrate(cos(x)^7/(a-a*sin(x)^2),x, algorithm=""maxima"")","\frac{3 \, \sin\left(x\right)^{5} - 10 \, \sin\left(x\right)^{3} + 15 \, \sin\left(x\right)}{15 \, a}"," ",0,"1/15*(3*sin(x)^5 - 10*sin(x)^3 + 15*sin(x))/a","A",0
263,1,14,0,0.324444," ","integrate(cos(x)^5/(a-a*sin(x)^2),x, algorithm=""maxima"")","-\frac{\sin\left(x\right)^{3} - 3 \, \sin\left(x\right)}{3 \, a}"," ",0,"-1/3*(sin(x)^3 - 3*sin(x))/a","A",0
264,1,6,0,0.334999," ","integrate(cos(x)^3/(a-a*sin(x)^2),x, algorithm=""maxima"")","\frac{\sin\left(x\right)}{a}"," ",0,"sin(x)/a","A",0
265,1,21,0,0.350072," ","integrate(cos(x)/(a-a*sin(x)^2),x, algorithm=""maxima"")","\frac{\log\left(\sin\left(x\right) + 1\right)}{2 \, a} - \frac{\log\left(\sin\left(x\right) - 1\right)}{2 \, a}"," ",0,"1/2*log(sin(x) + 1)/a - 1/2*log(sin(x) - 1)/a","B",0
266,1,51,0,0.341239," ","integrate(sec(x)^3/(a-a*sin(x)^2),x, algorithm=""maxima"")","-\frac{3 \, \sin\left(x\right)^{3} - 5 \, \sin\left(x\right)}{8 \, {\left(a \sin\left(x\right)^{4} - 2 \, a \sin\left(x\right)^{2} + a\right)}} + \frac{3 \, \log\left(\sin\left(x\right) + 1\right)}{16 \, a} - \frac{3 \, \log\left(\sin\left(x\right) - 1\right)}{16 \, a}"," ",0,"-1/8*(3*sin(x)^3 - 5*sin(x))/(a*sin(x)^4 - 2*a*sin(x)^2 + a) + 3/16*log(sin(x) + 1)/a - 3/16*log(sin(x) - 1)/a","A",0
267,1,37,0,0.449051," ","integrate(cos(x)^6/(a-a*sin(x)^2),x, algorithm=""maxima"")","\frac{3 \, \tan\left(x\right)^{3} + 5 \, \tan\left(x\right)}{8 \, {\left(a \tan\left(x\right)^{4} + 2 \, a \tan\left(x\right)^{2} + a\right)}} + \frac{3 \, x}{8 \, a}"," ",0,"1/8*(3*tan(x)^3 + 5*tan(x))/(a*tan(x)^4 + 2*a*tan(x)^2 + a) + 3/8*x/a","A",0
268,1,21,0,1.404250," ","integrate(cos(x)^4/(a-a*sin(x)^2),x, algorithm=""maxima"")","\frac{x}{2 \, a} + \frac{\tan\left(x\right)}{2 \, {\left(a \tan\left(x\right)^{2} + a\right)}}"," ",0,"1/2*x/a + 1/2*tan(x)/(a*tan(x)^2 + a)","A",0
269,1,5,0,0.478418," ","integrate(cos(x)^2/(a-a*sin(x)^2),x, algorithm=""maxima"")","\frac{x}{a}"," ",0,"x/a","A",0
270,1,37,0,0.348873," ","integrate(sec(x)/(a-a*sin(x)^2),x, algorithm=""maxima"")","\frac{\log\left(\sin\left(x\right) + 1\right)}{4 \, a} - \frac{\log\left(\sin\left(x\right) - 1\right)}{4 \, a} - \frac{\sin\left(x\right)}{2 \, {\left(a \sin\left(x\right)^{2} - a\right)}}"," ",0,"1/4*log(sin(x) + 1)/a - 1/4*log(sin(x) - 1)/a - 1/2*sin(x)/(a*sin(x)^2 - a)","B",0
271,1,14,0,0.375743," ","integrate(sec(x)^2/(a-a*sin(x)^2),x, algorithm=""maxima"")","\frac{\tan\left(x\right)^{3} + 3 \, \tan\left(x\right)}{3 \, a}"," ",0,"1/3*(tan(x)^3 + 3*tan(x))/a","A",0
272,1,22,0,0.393119," ","integrate(sec(x)^4/(a-a*sin(x)^2),x, algorithm=""maxima"")","\frac{3 \, \tan\left(x\right)^{5} + 10 \, \tan\left(x\right)^{3} + 15 \, \tan\left(x\right)}{15 \, a}"," ",0,"1/15*(3*tan(x)^5 + 10*tan(x)^3 + 15*tan(x))/a","A",0
273,1,22,0,0.350471," ","integrate(cos(x)^9/(a-a*sin(x)^2)^2,x, algorithm=""maxima"")","\frac{3 \, \sin\left(x\right)^{5} - 10 \, \sin\left(x\right)^{3} + 15 \, \sin\left(x\right)}{15 \, a^{2}}"," ",0,"1/15*(3*sin(x)^5 - 10*sin(x)^3 + 15*sin(x))/a^2","A",0
274,1,14,0,0.349492," ","integrate(cos(x)^7/(a-a*sin(x)^2)^2,x, algorithm=""maxima"")","-\frac{\sin\left(x\right)^{3} - 3 \, \sin\left(x\right)}{3 \, a^{2}}"," ",0,"-1/3*(sin(x)^3 - 3*sin(x))/a^2","A",0
275,1,6,0,0.331675," ","integrate(cos(x)^5/(a-a*sin(x)^2)^2,x, algorithm=""maxima"")","\frac{\sin\left(x\right)}{a^{2}}"," ",0,"sin(x)/a^2","A",0
276,1,21,0,0.329690," ","integrate(cos(x)^3/(a-a*sin(x)^2)^2,x, algorithm=""maxima"")","\frac{\log\left(\sin\left(x\right) + 1\right)}{2 \, a^{2}} - \frac{\log\left(\sin\left(x\right) - 1\right)}{2 \, a^{2}}"," ",0,"1/2*log(sin(x) + 1)/a^2 - 1/2*log(sin(x) - 1)/a^2","B",0
277,1,41,0,0.365278," ","integrate(cos(x)/(a-a*sin(x)^2)^2,x, algorithm=""maxima"")","-\frac{\sin\left(x\right)}{2 \, {\left(a^{2} \sin\left(x\right)^{2} - a^{2}\right)}} + \frac{\log\left(\sin\left(x\right) + 1\right)}{4 \, a^{2}} - \frac{\log\left(\sin\left(x\right) - 1\right)}{4 \, a^{2}}"," ",0,"-1/2*sin(x)/(a^2*sin(x)^2 - a^2) + 1/4*log(sin(x) + 1)/a^2 - 1/4*log(sin(x) - 1)/a^2","B",0
278,1,57,0,0.371544," ","integrate(sec(x)/(a-a*sin(x)^2)^2,x, algorithm=""maxima"")","-\frac{3 \, \sin\left(x\right)^{3} - 5 \, \sin\left(x\right)}{8 \, {\left(a^{2} \sin\left(x\right)^{4} - 2 \, a^{2} \sin\left(x\right)^{2} + a^{2}\right)}} + \frac{3 \, \log\left(\sin\left(x\right) + 1\right)}{16 \, a^{2}} - \frac{3 \, \log\left(\sin\left(x\right) - 1\right)}{16 \, a^{2}}"," ",0,"-1/8*(3*sin(x)^3 - 5*sin(x))/(a^2*sin(x)^4 - 2*a^2*sin(x)^2 + a^2) + 3/16*log(sin(x) + 1)/a^2 - 3/16*log(sin(x) - 1)/a^2","A",0
279,1,43,0,0.511778," ","integrate(cos(x)^8/(a-a*sin(x)^2)^2,x, algorithm=""maxima"")","\frac{3 \, \tan\left(x\right)^{3} + 5 \, \tan\left(x\right)}{8 \, {\left(a^{2} \tan\left(x\right)^{4} + 2 \, a^{2} \tan\left(x\right)^{2} + a^{2}\right)}} + \frac{3 \, x}{8 \, a^{2}}"," ",0,"1/8*(3*tan(x)^3 + 5*tan(x))/(a^2*tan(x)^4 + 2*a^2*tan(x)^2 + a^2) + 3/8*x/a^2","A",0
280,1,25,0,0.445527," ","integrate(cos(x)^6/(a-a*sin(x)^2)^2,x, algorithm=""maxima"")","\frac{\tan\left(x\right)}{2 \, {\left(a^{2} \tan\left(x\right)^{2} + a^{2}\right)}} + \frac{x}{2 \, a^{2}}"," ",0,"1/2*tan(x)/(a^2*tan(x)^2 + a^2) + 1/2*x/a^2","A",0
281,1,5,0,0.444749," ","integrate(cos(x)^4/(a-a*sin(x)^2)^2,x, algorithm=""maxima"")","\frac{x}{a^{2}}"," ",0,"x/a^2","A",0
282,1,6,0,0.366208," ","integrate(cos(x)^2/(a-a*sin(x)^2)^2,x, algorithm=""maxima"")","\frac{\tan\left(x\right)}{a^{2}}"," ",0,"tan(x)/a^2","A",0
283,1,22,0,0.346051," ","integrate(sec(x)^2/(a-a*sin(x)^2)^2,x, algorithm=""maxima"")","\frac{3 \, \tan\left(x\right)^{5} + 10 \, \tan\left(x\right)^{3} + 15 \, \tan\left(x\right)}{15 \, a^{2}}"," ",0,"1/15*(3*tan(x)^5 + 10*tan(x)^3 + 15*tan(x))/a^2","A",0
284,1,28,0,0.357574," ","integrate(sec(x)^4/(a-a*sin(x)^2)^2,x, algorithm=""maxima"")","\frac{5 \, \tan\left(x\right)^{7} + 21 \, \tan\left(x\right)^{5} + 35 \, \tan\left(x\right)^{3} + 35 \, \tan\left(x\right)}{35 \, a^{2}}"," ",0,"1/35*(5*tan(x)^7 + 21*tan(x)^5 + 35*tan(x)^3 + 35*tan(x))/a^2","A",0
285,1,122,0,0.474169," ","integrate(cos(f*x+e)^6*(a+b*sin(f*x+e)^2),x, algorithm=""maxima"")","\frac{15 \, {\left(f x + e\right)} {\left(8 \, a + b\right)} + \frac{15 \, {\left(8 \, a + b\right)} \tan\left(f x + e\right)^{7} + 55 \, {\left(8 \, a + b\right)} \tan\left(f x + e\right)^{5} + 73 \, {\left(8 \, a + b\right)} \tan\left(f x + e\right)^{3} + 3 \, {\left(88 \, a - 5 \, b\right)} \tan\left(f x + e\right)}{\tan\left(f x + e\right)^{8} + 4 \, \tan\left(f x + e\right)^{6} + 6 \, \tan\left(f x + e\right)^{4} + 4 \, \tan\left(f x + e\right)^{2} + 1}}{384 \, f}"," ",0,"1/384*(15*(f*x + e)*(8*a + b) + (15*(8*a + b)*tan(f*x + e)^7 + 55*(8*a + b)*tan(f*x + e)^5 + 73*(8*a + b)*tan(f*x + e)^3 + 3*(88*a - 5*b)*tan(f*x + e))/(tan(f*x + e)^8 + 4*tan(f*x + e)^6 + 6*tan(f*x + e)^4 + 4*tan(f*x + e)^2 + 1))/f","A",0
286,1,97,0,0.455677," ","integrate(cos(f*x+e)^4*(a+b*sin(f*x+e)^2),x, algorithm=""maxima"")","\frac{3 \, {\left(f x + e\right)} {\left(6 \, a + b\right)} + \frac{3 \, {\left(6 \, a + b\right)} \tan\left(f x + e\right)^{5} + 8 \, {\left(6 \, a + b\right)} \tan\left(f x + e\right)^{3} + 3 \, {\left(10 \, a - b\right)} \tan\left(f x + e\right)}{\tan\left(f x + e\right)^{6} + 3 \, \tan\left(f x + e\right)^{4} + 3 \, \tan\left(f x + e\right)^{2} + 1}}{48 \, f}"," ",0,"1/48*(3*(f*x + e)*(6*a + b) + (3*(6*a + b)*tan(f*x + e)^5 + 8*(6*a + b)*tan(f*x + e)^3 + 3*(10*a - b)*tan(f*x + e))/(tan(f*x + e)^6 + 3*tan(f*x + e)^4 + 3*tan(f*x + e)^2 + 1))/f","A",0
287,1,69,0,0.463227," ","integrate(cos(f*x+e)^2*(a+b*sin(f*x+e)^2),x, algorithm=""maxima"")","\frac{{\left(f x + e\right)} {\left(4 \, a + b\right)} + \frac{{\left(4 \, a + b\right)} \tan\left(f x + e\right)^{3} + {\left(4 \, a - b\right)} \tan\left(f x + e\right)}{\tan\left(f x + e\right)^{4} + 2 \, \tan\left(f x + e\right)^{2} + 1}}{8 \, f}"," ",0,"1/8*((f*x + e)*(4*a + b) + ((4*a + b)*tan(f*x + e)^3 + (4*a - b)*tan(f*x + e))/(tan(f*x + e)^4 + 2*tan(f*x + e)^2 + 1))/f","A",0
288,1,29,0,0.360113," ","integrate(a+b*sin(f*x+e)^2,x, algorithm=""maxima"")","a x + \frac{{\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} b}{4 \, f}"," ",0,"a*x + 1/4*(2*f*x + 2*e - sin(2*f*x + 2*e))*b/f","A",0
289,1,30,0,0.457101," ","integrate(sec(f*x+e)^2*(a+b*sin(f*x+e)^2),x, algorithm=""maxima"")","-\frac{{\left(f x + e - \tan\left(f x + e\right)\right)} b - a \tan\left(f x + e\right)}{f}"," ",0,"-((f*x + e - tan(f*x + e))*b - a*tan(f*x + e))/f","A",0
290,1,27,0,0.361584," ","integrate(sec(f*x+e)^4*(a+b*sin(f*x+e)^2),x, algorithm=""maxima"")","\frac{{\left(a + b\right)} \tan\left(f x + e\right)^{3} + 3 \, a \tan\left(f x + e\right)}{3 \, f}"," ",0,"1/3*((a + b)*tan(f*x + e)^3 + 3*a*tan(f*x + e))/f","A",0
291,1,43,0,0.346923," ","integrate(sec(f*x+e)^6*(a+b*sin(f*x+e)^2),x, algorithm=""maxima"")","\frac{3 \, {\left(a + b\right)} \tan\left(f x + e\right)^{5} + 5 \, {\left(2 \, a + b\right)} \tan\left(f x + e\right)^{3} + 15 \, a \tan\left(f x + e\right)}{15 \, f}"," ",0,"1/15*(3*(a + b)*tan(f*x + e)^5 + 5*(2*a + b)*tan(f*x + e)^3 + 15*a*tan(f*x + e))/f","A",0
292,1,60,0,0.381999," ","integrate(sec(f*x+e)^8*(a+b*sin(f*x+e)^2),x, algorithm=""maxima"")","\frac{15 \, {\left(a + b\right)} \tan\left(f x + e\right)^{7} + 21 \, {\left(3 \, a + 2 \, b\right)} \tan\left(f x + e\right)^{5} + 35 \, {\left(3 \, a + b\right)} \tan\left(f x + e\right)^{3} + 105 \, a \tan\left(f x + e\right)}{105 \, f}"," ",0,"1/105*(15*(a + b)*tan(f*x + e)^7 + 21*(3*a + 2*b)*tan(f*x + e)^5 + 35*(3*a + b)*tan(f*x + e)^3 + 105*a*tan(f*x + e))/f","A",0
293,1,169,0,0.500454," ","integrate(cos(f*x+e)^4*(a+b*sin(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{3 \, {\left(48 \, a^{2} + 16 \, a b + 3 \, b^{2}\right)} {\left(f x + e\right)} + \frac{3 \, {\left(48 \, a^{2} + 16 \, a b + 3 \, b^{2}\right)} \tan\left(f x + e\right)^{7} + 11 \, {\left(48 \, a^{2} + 16 \, a b + 3 \, b^{2}\right)} \tan\left(f x + e\right)^{5} + {\left(624 \, a^{2} + 80 \, a b - 33 \, b^{2}\right)} \tan\left(f x + e\right)^{3} + 3 \, {\left(80 \, a^{2} - 16 \, a b - 3 \, b^{2}\right)} \tan\left(f x + e\right)}{\tan\left(f x + e\right)^{8} + 4 \, \tan\left(f x + e\right)^{6} + 6 \, \tan\left(f x + e\right)^{4} + 4 \, \tan\left(f x + e\right)^{2} + 1}}{384 \, f}"," ",0,"1/384*(3*(48*a^2 + 16*a*b + 3*b^2)*(f*x + e) + (3*(48*a^2 + 16*a*b + 3*b^2)*tan(f*x + e)^7 + 11*(48*a^2 + 16*a*b + 3*b^2)*tan(f*x + e)^5 + (624*a^2 + 80*a*b - 33*b^2)*tan(f*x + e)^3 + 3*(80*a^2 - 16*a*b - 3*b^2)*tan(f*x + e))/(tan(f*x + e)^8 + 4*tan(f*x + e)^6 + 6*tan(f*x + e)^4 + 4*tan(f*x + e)^2 + 1))/f","A",0
294,1,127,0,0.493913," ","integrate(cos(f*x+e)^2*(a+b*sin(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{3 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} {\left(f x + e\right)} + \frac{3 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \tan\left(f x + e\right)^{5} + 8 \, {\left(6 \, a^{2} - b^{2}\right)} \tan\left(f x + e\right)^{3} + 3 \, {\left(8 \, a^{2} - 4 \, a b - b^{2}\right)} \tan\left(f x + e\right)}{\tan\left(f x + e\right)^{6} + 3 \, \tan\left(f x + e\right)^{4} + 3 \, \tan\left(f x + e\right)^{2} + 1}}{48 \, f}"," ",0,"1/48*(3*(8*a^2 + 4*a*b + b^2)*(f*x + e) + (3*(8*a^2 + 4*a*b + b^2)*tan(f*x + e)^5 + 8*(6*a^2 - b^2)*tan(f*x + e)^3 + 3*(8*a^2 - 4*a*b - b^2)*tan(f*x + e))/(tan(f*x + e)^6 + 3*tan(f*x + e)^4 + 3*tan(f*x + e)^2 + 1))/f","A",0
295,1,68,0,0.319175," ","integrate((a+b*sin(f*x+e)^2)^2,x, algorithm=""maxima"")","a^{2} x + \frac{{\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a b}{2 \, 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^{2}}{32 \, f}"," ",0,"a^2*x + 1/2*(2*f*x + 2*e - sin(2*f*x + 2*e))*a*b/f + 1/32*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*b^2/f","A",0
296,1,74,0,0.456552," ","integrate(sec(f*x+e)^2*(a+b*sin(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{4 \, {\left(f x + e - \tan\left(f x + e\right)\right)} a b + {\left(3 \, f x + 3 \, e - \frac{\tan\left(f x + e\right)}{\tan\left(f x + e\right)^{2} + 1} - 2 \, \tan\left(f x + e\right)\right)} b^{2} - 2 \, a^{2} \tan\left(f x + e\right)}{2 \, f}"," ",0,"-1/2*(4*(f*x + e - tan(f*x + e))*a*b + (3*f*x + 3*e - tan(f*x + e)/(tan(f*x + e)^2 + 1) - 2*tan(f*x + e))*b^2 - 2*a^2*tan(f*x + e))/f","A",0
297,1,53,0,0.468246," ","integrate(sec(f*x+e)^4*(a+b*sin(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} \tan\left(f x + e\right)^{3} + 3 \, {\left(f x + e\right)} b^{2} + 3 \, {\left(a^{2} - b^{2}\right)} \tan\left(f x + e\right)}{3 \, f}"," ",0,"1/3*((a^2 + 2*a*b + b^2)*tan(f*x + e)^3 + 3*(f*x + e)*b^2 + 3*(a^2 - b^2)*tan(f*x + e))/f","A",0
298,1,55,0,0.320623," ","integrate(sec(f*x+e)^6*(a+b*sin(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \tan\left(f x + e\right)^{5} + 10 \, {\left(a^{2} + a b\right)} \tan\left(f x + e\right)^{3} + 15 \, a^{2} \tan\left(f x + e\right)}{15 \, f}"," ",0,"1/15*(3*(a^2 + 2*a*b + b^2)*tan(f*x + e)^5 + 10*(a^2 + a*b)*tan(f*x + e)^3 + 15*a^2*tan(f*x + e))/f","A",0
299,1,81,0,0.348561," ","integrate(sec(f*x+e)^8*(a+b*sin(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \tan\left(f x + e\right)^{7} + 21 \, {\left(3 \, a^{2} + 4 \, a b + b^{2}\right)} \tan\left(f x + e\right)^{5} + 35 \, {\left(3 \, a^{2} + 2 \, a b\right)} \tan\left(f x + e\right)^{3} + 105 \, a^{2} \tan\left(f x + e\right)}{105 \, f}"," ",0,"1/105*(15*(a^2 + 2*a*b + b^2)*tan(f*x + e)^7 + 21*(3*a^2 + 4*a*b + b^2)*tan(f*x + e)^5 + 35*(3*a^2 + 2*a*b)*tan(f*x + e)^3 + 105*a^2*tan(f*x + e))/f","A",0
300,1,103,0,0.350000," ","integrate(sec(f*x+e)^10*(a+b*sin(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \tan\left(f x + e\right)^{9} + 90 \, {\left(2 \, a^{2} + 3 \, a b + b^{2}\right)} \tan\left(f x + e\right)^{7} + 63 \, {\left(6 \, a^{2} + 6 \, a b + b^{2}\right)} \tan\left(f x + e\right)^{5} + 210 \, {\left(2 \, a^{2} + a b\right)} \tan\left(f x + e\right)^{3} + 315 \, a^{2} \tan\left(f x + e\right)}{315 \, f}"," ",0,"1/315*(35*(a^2 + 2*a*b + b^2)*tan(f*x + e)^9 + 90*(2*a^2 + 3*a*b + b^2)*tan(f*x + e)^7 + 63*(6*a^2 + 6*a*b + b^2)*tan(f*x + e)^5 + 210*(2*a^2 + a*b)*tan(f*x + e)^3 + 315*a^2*tan(f*x + e))/f","A",0
301,1,86,0,0.449446," ","integrate(cos(x)^7/(a+b*sin(x)^2),x, algorithm=""maxima"")","\frac{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \arctan\left(\frac{b \sin\left(x\right)}{\sqrt{a b}}\right)}{\sqrt{a b} b^{3}} - \frac{3 \, b^{2} \sin\left(x\right)^{5} - 5 \, {\left(a b + 3 \, b^{2}\right)} \sin\left(x\right)^{3} + 15 \, {\left(a^{2} + 3 \, a b + 3 \, b^{2}\right)} \sin\left(x\right)}{15 \, b^{3}}"," ",0,"(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*arctan(b*sin(x)/sqrt(a*b))/(sqrt(a*b)*b^3) - 1/15*(3*b^2*sin(x)^5 - 5*(a*b + 3*b^2)*sin(x)^3 + 15*(a^2 + 3*a*b + 3*b^2)*sin(x))/b^3","A",0
302,1,114,0,0.466978," ","integrate(cos(x)^6/(a+b*sin(x)^2),x, algorithm=""maxima"")","-\frac{{\left(4 \, a + 7 \, b\right)} \tan\left(x\right)^{3} + {\left(4 \, a + 9 \, b\right)} \tan\left(x\right)}{8 \, {\left(b^{2} \tan\left(x\right)^{4} + 2 \, b^{2} \tan\left(x\right)^{2} + b^{2}\right)}} - \frac{{\left(8 \, a^{2} + 20 \, a b + 15 \, b^{2}\right)} x}{8 \, b^{3}} + \frac{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \arctan\left(\frac{{\left(a + b\right)} \tan\left(x\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{\sqrt{{\left(a + b\right)} a} b^{3}}"," ",0,"-1/8*((4*a + 7*b)*tan(x)^3 + (4*a + 9*b)*tan(x))/(b^2*tan(x)^4 + 2*b^2*tan(x)^2 + b^2) - 1/8*(8*a^2 + 20*a*b + 15*b^2)*x/b^3 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*arctan((a + b)*tan(x)/sqrt((a + b)*a))/(sqrt((a + b)*a)*b^3)","A",0
303,1,52,0,0.483878," ","integrate(cos(x)^5/(a+b*sin(x)^2),x, algorithm=""maxima"")","\frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} \arctan\left(\frac{b \sin\left(x\right)}{\sqrt{a b}}\right)}{\sqrt{a b} b^{2}} + \frac{b \sin\left(x\right)^{3} - 3 \, {\left(a + 2 \, b\right)} \sin\left(x\right)}{3 \, b^{2}}"," ",0,"(a^2 + 2*a*b + b^2)*arctan(b*sin(x)/sqrt(a*b))/(sqrt(a*b)*b^2) + 1/3*(b*sin(x)^3 - 3*(a + 2*b)*sin(x))/b^2","A",0
304,1,64,0,0.464386," ","integrate(cos(x)^4/(a+b*sin(x)^2),x, algorithm=""maxima"")","-\frac{{\left(2 \, a + 3 \, b\right)} x}{2 \, b^{2}} - \frac{\tan\left(x\right)}{2 \, {\left(b \tan\left(x\right)^{2} + b\right)}} + \frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} \arctan\left(\frac{{\left(a + b\right)} \tan\left(x\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{\sqrt{{\left(a + b\right)} a} b^{2}}"," ",0,"-1/2*(2*a + 3*b)*x/b^2 - 1/2*tan(x)/(b*tan(x)^2 + b) + (a^2 + 2*a*b + b^2)*arctan((a + b)*tan(x)/sqrt((a + b)*a))/(sqrt((a + b)*a)*b^2)","A",0
305,1,30,0,0.468262," ","integrate(cos(x)^3/(a+b*sin(x)^2),x, algorithm=""maxima"")","\frac{{\left(a + b\right)} \arctan\left(\frac{b \sin\left(x\right)}{\sqrt{a b}}\right)}{\sqrt{a b} b} - \frac{\sin\left(x\right)}{b}"," ",0,"(a + b)*arctan(b*sin(x)/sqrt(a*b))/(sqrt(a*b)*b) - sin(x)/b","A",0
306,1,35,0,1.439376," ","integrate(cos(x)^2/(a+b*sin(x)^2),x, algorithm=""maxima"")","\frac{{\left(a + b\right)} \arctan\left(\frac{{\left(a + b\right)} \tan\left(x\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{\sqrt{{\left(a + b\right)} a} b} - \frac{x}{b}"," ",0,"(a + b)*arctan((a + b)*tan(x)/sqrt((a + b)*a))/(sqrt((a + b)*a)*b) - x/b","A",0
307,1,16,0,0.464079," ","integrate(cos(x)/(a+b*sin(x)^2),x, algorithm=""maxima"")","\frac{\arctan\left(\frac{b \sin\left(x\right)}{\sqrt{a b}}\right)}{\sqrt{a b}}"," ",0,"arctan(b*sin(x)/sqrt(a*b))/sqrt(a*b)","A",0
308,1,47,0,0.455274," ","integrate(sec(x)/(a+b*sin(x)^2),x, algorithm=""maxima"")","\frac{b \arctan\left(\frac{b \sin\left(x\right)}{\sqrt{a b}}\right)}{\sqrt{a b} {\left(a + b\right)}} + \frac{\log\left(\sin\left(x\right) + 1\right)}{2 \, {\left(a + b\right)}} - \frac{\log\left(\sin\left(x\right) - 1\right)}{2 \, {\left(a + b\right)}}"," ",0,"b*arctan(b*sin(x)/sqrt(a*b))/(sqrt(a*b)*(a + b)) + 1/2*log(sin(x) + 1)/(a + b) - 1/2*log(sin(x) - 1)/(a + b)","A",0
309,1,37,0,0.455227," ","integrate(sec(x)^2/(a+b*sin(x)^2),x, algorithm=""maxima"")","\frac{b \arctan\left(\frac{{\left(a + b\right)} \tan\left(x\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{\sqrt{{\left(a + b\right)} a} {\left(a + b\right)}} + \frac{\tan\left(x\right)}{a + b}"," ",0,"b*arctan((a + b)*tan(x)/sqrt((a + b)*a))/(sqrt((a + b)*a)*(a + b)) + tan(x)/(a + b)","A",0
310,1,104,0,0.591219," ","integrate(sec(x)^3/(a+b*sin(x)^2),x, algorithm=""maxima"")","\frac{b^{2} \arctan\left(\frac{b \sin\left(x\right)}{\sqrt{a b}}\right)}{{\left(a^{2} + 2 \, a b + b^{2}\right)} \sqrt{a b}} + \frac{{\left(a + 3 \, b\right)} \log\left(\sin\left(x\right) + 1\right)}{4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)}} - \frac{{\left(a + 3 \, b\right)} \log\left(\sin\left(x\right) - 1\right)}{4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)}} - \frac{\sin\left(x\right)}{2 \, {\left({\left(a + b\right)} \sin\left(x\right)^{2} - a - b\right)}}"," ",0,"b^2*arctan(b*sin(x)/sqrt(a*b))/((a^2 + 2*a*b + b^2)*sqrt(a*b)) + 1/4*(a + 3*b)*log(sin(x) + 1)/(a^2 + 2*a*b + b^2) - 1/4*(a + 3*b)*log(sin(x) - 1)/(a^2 + 2*a*b + b^2) - 1/2*sin(x)/((a + b)*sin(x)^2 - a - b)","B",0
311,1,72,0,0.474857," ","integrate(sec(x)^4/(a+b*sin(x)^2),x, algorithm=""maxima"")","\frac{b^{2} \arctan\left(\frac{{\left(a + b\right)} \tan\left(x\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{\sqrt{{\left(a + b\right)} a} {\left(a^{2} + 2 \, a b + b^{2}\right)}} + \frac{{\left(a + b\right)} \tan\left(x\right)^{3} + 3 \, {\left(a + 2 \, b\right)} \tan\left(x\right)}{3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)}}"," ",0,"b^2*arctan((a + b)*tan(x)/sqrt((a + b)*a))/(sqrt((a + b)*a)*(a^2 + 2*a*b + b^2)) + 1/3*((a + b)*tan(x)^3 + 3*(a + 2*b)*tan(x))/(a^2 + 2*a*b + b^2)","A",0
312,1,199,0,0.482470," ","integrate(sec(x)^5/(a+b*sin(x)^2),x, algorithm=""maxima"")","\frac{b^{3} \arctan\left(\frac{b \sin\left(x\right)}{\sqrt{a b}}\right)}{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sqrt{a b}} + \frac{{\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \log\left(\sin\left(x\right) + 1\right)}{16 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)}} - \frac{{\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} \log\left(\sin\left(x\right) - 1\right)}{16 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)}} - \frac{{\left(3 \, a + 7 \, b\right)} \sin\left(x\right)^{3} - {\left(5 \, a + 9 \, b\right)} \sin\left(x\right)}{8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \sin\left(x\right)^{4} - 2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \sin\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2}\right)}}"," ",0,"b^3*arctan(b*sin(x)/sqrt(a*b))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sqrt(a*b)) + 1/16*(3*a^2 + 10*a*b + 15*b^2)*log(sin(x) + 1)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) - 1/16*(3*a^2 + 10*a*b + 15*b^2)*log(sin(x) - 1)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) - 1/8*((3*a + 7*b)*sin(x)^3 - (5*a + 9*b)*sin(x))/((a^2 + 2*a*b + b^2)*sin(x)^4 - 2*(a^2 + 2*a*b + b^2)*sin(x)^2 + a^2 + 2*a*b + b^2)","B",0
313,1,126,0,0.458209," ","integrate(sec(x)^6/(a+b*sin(x)^2),x, algorithm=""maxima"")","\frac{b^{3} \arctan\left(\frac{{\left(a + b\right)} \tan\left(x\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sqrt{{\left(a + b\right)} a}} + \frac{3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \tan\left(x\right)^{5} + 5 \, {\left(2 \, a^{2} + 5 \, a b + 3 \, b^{2}\right)} \tan\left(x\right)^{3} + 15 \, {\left(a^{2} + 3 \, a b + 3 \, b^{2}\right)} \tan\left(x\right)}{15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)}}"," ",0,"b^3*arctan((a + b)*tan(x)/sqrt((a + b)*a))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sqrt((a + b)*a)) + 1/15*(3*(a^2 + 2*a*b + b^2)*tan(x)^5 + 5*(2*a^2 + 5*a*b + 3*b^2)*tan(x)^3 + 15*(a^2 + 3*a*b + 3*b^2)*tan(x))/(a^3 + 3*a^2*b + 3*a*b^2 + b^3)","A",0
314,1,150,0,0.480691," ","integrate(cos(x)^6/(a+b*sin(x)^2)^2,x, algorithm=""maxima"")","\frac{{\left(2 \, a^{2} + 3 \, a b + b^{2}\right)} \tan\left(x\right)^{3} + {\left(2 \, a^{2} + 2 \, a b + b^{2}\right)} \tan\left(x\right)}{2 \, {\left({\left(a^{2} b^{2} + a b^{3}\right)} \tan\left(x\right)^{4} + a^{2} b^{2} + {\left(2 \, a^{2} b^{2} + a b^{3}\right)} \tan\left(x\right)^{2}\right)}} + \frac{{\left(4 \, a + 5 \, b\right)} x}{2 \, b^{3}} - \frac{{\left(4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - b^{3}\right)} \arctan\left(\frac{{\left(a + b\right)} \tan\left(x\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{2 \, \sqrt{{\left(a + b\right)} a} a b^{3}}"," ",0,"1/2*((2*a^2 + 3*a*b + b^2)*tan(x)^3 + (2*a^2 + 2*a*b + b^2)*tan(x))/((a^2*b^2 + a*b^3)*tan(x)^4 + a^2*b^2 + (2*a^2*b^2 + a*b^3)*tan(x)^2) + 1/2*(4*a + 5*b)*x/b^3 - 1/2*(4*a^3 + 7*a^2*b + 2*a*b^2 - b^3)*arctan((a + b)*tan(x)/sqrt((a + b)*a))/(sqrt((a + b)*a)*a*b^3)","A",0
315,1,79,0,0.511668," ","integrate(cos(x)^5/(a+b*sin(x)^2)^2,x, algorithm=""maxima"")","\frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} \sin\left(x\right)}{2 \, {\left(a b^{3} \sin\left(x\right)^{2} + a^{2} b^{2}\right)}} + \frac{\sin\left(x\right)}{b^{2}} - \frac{{\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \arctan\left(\frac{b \sin\left(x\right)}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a b^{2}}"," ",0,"1/2*(a^2 + 2*a*b + b^2)*sin(x)/(a*b^3*sin(x)^2 + a^2*b^2) + sin(x)/b^2 - 1/2*(3*a^2 + 2*a*b - b^2)*arctan(b*sin(x)/sqrt(a*b))/(sqrt(a*b)*a*b^2)","A",0
316,1,80,0,0.947260," ","integrate(cos(x)^4/(a+b*sin(x)^2)^2,x, algorithm=""maxima"")","\frac{{\left(a + b\right)} \tan\left(x\right)}{2 \, {\left(a^{2} b + {\left(a^{2} b + a b^{2}\right)} \tan\left(x\right)^{2}\right)}} + \frac{x}{b^{2}} - \frac{{\left(2 \, a^{2} + a b - b^{2}\right)} \arctan\left(\frac{{\left(a + b\right)} \tan\left(x\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{2 \, \sqrt{{\left(a + b\right)} a} a b^{2}}"," ",0,"1/2*(a + b)*tan(x)/(a^2*b + (a^2*b + a*b^2)*tan(x)^2) + x/b^2 - 1/2*(2*a^2 + a*b - b^2)*arctan((a + b)*tan(x)/sqrt((a + b)*a))/(sqrt((a + b)*a)*a*b^2)","A",0
317,1,53,0,1.829173," ","integrate(cos(x)^3/(a+b*sin(x)^2)^2,x, algorithm=""maxima"")","\frac{{\left(a + b\right)} \sin\left(x\right)}{2 \, {\left(a b^{2} \sin\left(x\right)^{2} + a^{2} b\right)}} - \frac{{\left(a - b\right)} \arctan\left(\frac{b \sin\left(x\right)}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a b}"," ",0,"1/2*(a + b)*sin(x)/(a*b^2*sin(x)^2 + a^2*b) - 1/2*(a - b)*arctan(b*sin(x)/sqrt(a*b))/(sqrt(a*b)*a*b)","A",0
318,1,49,0,0.723904," ","integrate(cos(x)^2/(a+b*sin(x)^2)^2,x, algorithm=""maxima"")","\frac{\tan\left(x\right)}{2 \, {\left({\left(a^{2} + a b\right)} \tan\left(x\right)^{2} + a^{2}\right)}} + \frac{\arctan\left(\frac{{\left(a + b\right)} \tan\left(x\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{2 \, \sqrt{{\left(a + b\right)} a} a}"," ",0,"1/2*tan(x)/((a^2 + a*b)*tan(x)^2 + a^2) + 1/2*arctan((a + b)*tan(x)/sqrt((a + b)*a))/(sqrt((a + b)*a)*a)","A",0
319,1,38,0,0.698328," ","integrate(cos(x)/(a+b*sin(x)^2)^2,x, algorithm=""maxima"")","\frac{\sin\left(x\right)}{2 \, {\left(a b \sin\left(x\right)^{2} + a^{2}\right)}} + \frac{\arctan\left(\frac{b \sin\left(x\right)}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a}"," ",0,"1/2*sin(x)/(a*b*sin(x)^2 + a^2) + 1/2*arctan(b*sin(x)/sqrt(a*b))/(sqrt(a*b)*a)","A",0
320,1,115,0,0.777993," ","integrate(sec(x)/(a+b*sin(x)^2)^2,x, algorithm=""maxima"")","\frac{b \sin\left(x\right)}{2 \, {\left(a^{3} + a^{2} b + {\left(a^{2} b + a b^{2}\right)} \sin\left(x\right)^{2}\right)}} + \frac{{\left(3 \, a b + b^{2}\right)} \arctan\left(\frac{b \sin\left(x\right)}{\sqrt{a b}}\right)}{2 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sqrt{a b}} + \frac{\log\left(\sin\left(x\right) + 1\right)}{2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)}} - \frac{\log\left(\sin\left(x\right) - 1\right)}{2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)}}"," ",0,"1/2*b*sin(x)/(a^3 + a^2*b + (a^2*b + a*b^2)*sin(x)^2) + 1/2*(3*a*b + b^2)*arctan(b*sin(x)/sqrt(a*b))/((a^3 + 2*a^2*b + a*b^2)*sqrt(a*b)) + 1/2*log(sin(x) + 1)/(a^2 + 2*a*b + b^2) - 1/2*log(sin(x) - 1)/(a^2 + 2*a*b + b^2)","A",0
321,1,119,0,0.548651," ","integrate(sec(x)^2/(a+b*sin(x)^2)^2,x, algorithm=""maxima"")","\frac{b^{2} \tan\left(x\right)}{2 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2} + {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \tan\left(x\right)^{2}\right)}} + \frac{{\left(4 \, a b + b^{2}\right)} \arctan\left(\frac{{\left(a + b\right)} \tan\left(x\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{2 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sqrt{{\left(a + b\right)} a}} + \frac{\tan\left(x\right)}{a^{2} + 2 \, a b + b^{2}}"," ",0,"1/2*b^2*tan(x)/(a^4 + 2*a^3*b + a^2*b^2 + (a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*tan(x)^2) + 1/2*(4*a*b + b^2)*arctan((a + b)*tan(x)/sqrt((a + b)*a))/((a^3 + 2*a^2*b + a*b^2)*sqrt((a + b)*a)) + tan(x)/(a^2 + 2*a*b + b^2)","A",0
322,1,220,0,0.650648," ","integrate(sec(x)^3/(a+b*sin(x)^2)^2,x, algorithm=""maxima"")","\frac{{\left(a + 5 \, b\right)} \log\left(\sin\left(x\right) + 1\right)}{4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)}} - \frac{{\left(a + 5 \, b\right)} \log\left(\sin\left(x\right) - 1\right)}{4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)}} + \frac{{\left(5 \, a b^{2} + b^{3}\right)} \arctan\left(\frac{b \sin\left(x\right)}{\sqrt{a b}}\right)}{2 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \sqrt{a b}} - \frac{{\left(a b - b^{2}\right)} \sin\left(x\right)^{3} + {\left(a^{2} + b^{2}\right)} \sin\left(x\right)}{2 \, {\left({\left(a^{3} b + 2 \, a^{2} b^{2} + a b^{3}\right)} \sin\left(x\right)^{4} - a^{4} - 2 \, a^{3} b - a^{2} b^{2} + {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} \sin\left(x\right)^{2}\right)}}"," ",0,"1/4*(a + 5*b)*log(sin(x) + 1)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) - 1/4*(a + 5*b)*log(sin(x) - 1)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) + 1/2*(5*a*b^2 + b^3)*arctan(b*sin(x)/sqrt(a*b))/((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*sqrt(a*b)) - 1/2*((a*b - b^2)*sin(x)^3 + (a^2 + b^2)*sin(x))/((a^3*b + 2*a^2*b^2 + a*b^3)*sin(x)^4 - a^4 - 2*a^3*b - a^2*b^2 + (a^4 + a^3*b - a^2*b^2 - a*b^3)*sin(x)^2)","B",0
323,1,170,0,0.700282," ","integrate(sec(x)^4/(a+b*sin(x)^2)^2,x, algorithm=""maxima"")","\frac{b^{3} \tan\left(x\right)}{2 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3} + {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \tan\left(x\right)^{2}\right)}} + \frac{{\left(6 \, a b^{2} + b^{3}\right)} \arctan\left(\frac{{\left(a + b\right)} \tan\left(x\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{2 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \sqrt{{\left(a + b\right)} a}} + \frac{{\left(a + b\right)} \tan\left(x\right)^{3} + 3 \, {\left(a + 3 \, b\right)} \tan\left(x\right)}{3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)}}"," ",0,"1/2*b^3*tan(x)/(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3 + (a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*tan(x)^2) + 1/2*(6*a*b^2 + b^3)*arctan((a + b)*tan(x)/sqrt((a + b)*a))/((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*sqrt((a + b)*a)) + 1/3*((a + b)*tan(x)^3 + 3*(a + 3*b)*tan(x))/(a^3 + 3*a^2*b + 3*a*b^2 + b^3)","B",0
324,1,119,0,0.642106," ","integrate(cos(f*x+e)^3*(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\frac{\frac{a^{2} \operatorname{arsinh}\left(\frac{b \sin\left(f x + e\right)}{\sqrt{a b}}\right)}{b^{\frac{3}{2}}} + \frac{4 \, a \operatorname{arsinh}\left(\frac{b \sin\left(f x + e\right)}{\sqrt{a b}}\right)}{\sqrt{b}} + 4 \, \sqrt{b \sin\left(f x + e\right)^{2} + a} \sin\left(f x + e\right) - \frac{2 \, {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \sin\left(f x + e\right)}{b} + \frac{\sqrt{b \sin\left(f x + e\right)^{2} + a} a \sin\left(f x + e\right)}{b}}{8 \, f}"," ",0,"1/8*(a^2*arcsinh(b*sin(f*x + e)/sqrt(a*b))/b^(3/2) + 4*a*arcsinh(b*sin(f*x + e)/sqrt(a*b))/sqrt(b) + 4*sqrt(b*sin(f*x + e)^2 + a)*sin(f*x + e) - 2*(b*sin(f*x + e)^2 + a)^(3/2)*sin(f*x + e)/b + sqrt(b*sin(f*x + e)^2 + a)*a*sin(f*x + e)/b)/f","A",0
325,1,46,0,0.337708," ","integrate(cos(f*x+e)*(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\frac{\frac{a \operatorname{arsinh}\left(\frac{b \sin\left(f x + e\right)}{\sqrt{a b}}\right)}{\sqrt{b}} + \sqrt{b \sin\left(f x + e\right)^{2} + a} \sin\left(f x + e\right)}{2 \, f}"," ",0,"1/2*(a*arcsinh(b*sin(f*x + e)/sqrt(a*b))/sqrt(b) + sqrt(b*sin(f*x + e)^2 + a)*sin(f*x + e))/f","A",0
326,1,126,0,0.491839," ","integrate(sec(f*x+e)*(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{b} \operatorname{arsinh}\left(\frac{b \sin\left(f x + e\right)}{\sqrt{a b}}\right) - \sqrt{a + b} \operatorname{arsinh}\left(\frac{b \sin\left(f x + e\right)}{\sqrt{a b} {\left(\sin\left(f x + e\right) + 1\right)}} - \frac{a}{\sqrt{a b} {\left(\sin\left(f x + e\right) + 1\right)}}\right) - \sqrt{a + b} \operatorname{arsinh}\left(-\frac{b \sin\left(f x + e\right)}{\sqrt{a b} {\left(\sin\left(f x + e\right) - 1\right)}} - \frac{a}{\sqrt{a b} {\left(\sin\left(f x + e\right) - 1\right)}}\right)}{2 \, f}"," ",0,"-1/2*(2*sqrt(b)*arcsinh(b*sin(f*x + e)/sqrt(a*b)) - sqrt(a + b)*arcsinh(b*sin(f*x + e)/(sqrt(a*b)*(sin(f*x + e) + 1)) - a/(sqrt(a*b)*(sin(f*x + e) + 1))) - sqrt(a + b)*arcsinh(-b*sin(f*x + e)/(sqrt(a*b)*(sin(f*x + e) - 1)) - a/(sqrt(a*b)*(sin(f*x + e) - 1))))/f","A",0
327,0,0,0,0.000000," ","integrate(sec(f*x+e)^3*(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sin\left(f x + e\right)^{2} + a} \sec\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e)^2 + a)*sec(f*x + e)^3, x)","F",0
328,0,0,0,0.000000," ","integrate(sec(f*x+e)^5*(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sin\left(f x + e\right)^{2} + a} \sec\left(f x + e\right)^{5}\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e)^2 + a)*sec(f*x + e)^5, x)","F",0
329,0,0,0,0.000000," ","integrate(cos(f*x+e)^4*(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sin\left(f x + e\right)^{2} + a} \cos\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e)^2 + a)*cos(f*x + e)^4, x)","F",0
330,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sin\left(f x + e\right)^{2} + a} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e)^2 + a)*cos(f*x + e)^2, x)","F",0
331,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sin\left(f x + e\right)^{2} + a}\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e)^2 + a), x)","F",0
332,0,0,0,0.000000," ","integrate(sec(f*x+e)^2*(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sin\left(f x + e\right)^{2} + a} \sec\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e)^2 + a)*sec(f*x + e)^2, x)","F",0
333,0,0,0,0.000000," ","integrate(sec(f*x+e)^4*(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sin\left(f x + e\right)^{2} + a} \sec\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e)^2 + a)*sec(f*x + e)^4, x)","F",0
334,1,174,0,0.368279," ","integrate(cos(f*x+e)^3*(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\frac{\frac{3 \, a^{3} \operatorname{arsinh}\left(\frac{b \sin\left(f x + e\right)}{\sqrt{a b}}\right)}{b^{\frac{3}{2}}} + \frac{18 \, a^{2} \operatorname{arsinh}\left(\frac{b \sin\left(f x + e\right)}{\sqrt{a b}}\right)}{\sqrt{b}} + 12 \, {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \sin\left(f x + e\right) + 18 \, \sqrt{b \sin\left(f x + e\right)^{2} + a} a \sin\left(f x + e\right) - \frac{8 \, {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{5}{2}} \sin\left(f x + e\right)}{b} + \frac{2 \, {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} a \sin\left(f x + e\right)}{b} + \frac{3 \, \sqrt{b \sin\left(f x + e\right)^{2} + a} a^{2} \sin\left(f x + e\right)}{b}}{48 \, f}"," ",0,"1/48*(3*a^3*arcsinh(b*sin(f*x + e)/sqrt(a*b))/b^(3/2) + 18*a^2*arcsinh(b*sin(f*x + e)/sqrt(a*b))/sqrt(b) + 12*(b*sin(f*x + e)^2 + a)^(3/2)*sin(f*x + e) + 18*sqrt(b*sin(f*x + e)^2 + a)*a*sin(f*x + e) - 8*(b*sin(f*x + e)^2 + a)^(5/2)*sin(f*x + e)/b + 2*(b*sin(f*x + e)^2 + a)^(3/2)*a*sin(f*x + e)/b + 3*sqrt(b*sin(f*x + e)^2 + a)*a^2*sin(f*x + e)/b)/f","A",0
335,1,73,0,0.360630," ","integrate(cos(f*x+e)*(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\frac{\frac{3 \, a^{2} \operatorname{arsinh}\left(\frac{b \sin\left(f x + e\right)}{\sqrt{a b}}\right)}{\sqrt{b}} + 2 \, {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \sin\left(f x + e\right) + 3 \, \sqrt{b \sin\left(f x + e\right)^{2} + a} a \sin\left(f x + e\right)}{8 \, f}"," ",0,"1/8*(3*a^2*arcsinh(b*sin(f*x + e)/sqrt(a*b))/sqrt(b) + 2*(b*sin(f*x + e)^2 + a)^(3/2)*sin(f*x + e) + 3*sqrt(b*sin(f*x + e)^2 + a)*a*sin(f*x + e))/f","A",0
336,1,168,0,0.472616," ","integrate(sec(f*x+e)*(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","-\frac{3 \, a \sqrt{b} \operatorname{arsinh}\left(\frac{b \sin\left(f x + e\right)}{\sqrt{a b}}\right) + 2 \, b^{\frac{3}{2}} \operatorname{arsinh}\left(\frac{b \sin\left(f x + e\right)}{\sqrt{a b}}\right) - {\left(a + b\right)}^{\frac{3}{2}} \operatorname{arsinh}\left(\frac{b \sin\left(f x + e\right)}{\sqrt{a b} {\left(\sin\left(f x + e\right) + 1\right)}} - \frac{a}{\sqrt{a b} {\left(\sin\left(f x + e\right) + 1\right)}}\right) - {\left(a + b\right)}^{\frac{3}{2}} \operatorname{arsinh}\left(-\frac{b \sin\left(f x + e\right)}{\sqrt{a b} {\left(\sin\left(f x + e\right) - 1\right)}} - \frac{a}{\sqrt{a b} {\left(\sin\left(f x + e\right) - 1\right)}}\right) + \sqrt{b \sin\left(f x + e\right)^{2} + a} b \sin\left(f x + e\right)}{2 \, f}"," ",0,"-1/2*(3*a*sqrt(b)*arcsinh(b*sin(f*x + e)/sqrt(a*b)) + 2*b^(3/2)*arcsinh(b*sin(f*x + e)/sqrt(a*b)) - (a + b)^(3/2)*arcsinh(b*sin(f*x + e)/(sqrt(a*b)*(sin(f*x + e) + 1)) - a/(sqrt(a*b)*(sin(f*x + e) + 1))) - (a + b)^(3/2)*arcsinh(-b*sin(f*x + e)/(sqrt(a*b)*(sin(f*x + e) - 1)) - a/(sqrt(a*b)*(sin(f*x + e) - 1))) + sqrt(b*sin(f*x + e)^2 + a)*b*sin(f*x + e))/f","A",0
337,0,0,0,0.000000," ","integrate(sec(f*x+e)^3*(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \sec\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^(3/2)*sec(f*x + e)^3, x)","F",0
338,0,0,0,0.000000," ","integrate(sec(f*x+e)^5*(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \sec\left(f x + e\right)^{5}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^(3/2)*sec(f*x + e)^5, x)","F",0
339,0,0,0,0.000000," ","integrate(sec(f*x+e)^7*(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \sec\left(f x + e\right)^{7}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^(3/2)*sec(f*x + e)^7, x)","F",0
340,0,0,0,0.000000," ","integrate(cos(f*x+e)^4*(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \cos\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^(3/2)*cos(f*x + e)^4, x)","F",0
341,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^(3/2)*cos(f*x + e)^2, x)","F",0
342,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^(3/2), x)","F",0
343,0,0,0,0.000000," ","integrate(sec(f*x+e)^2*(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \sec\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^(3/2)*sec(f*x + e)^2, x)","F",0
344,0,0,0,0.000000," ","integrate(sec(f*x+e)^4*(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \sec\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^(3/2)*sec(f*x + e)^4, x)","F",0
345,1,69,0,0.343677," ","integrate(cos(f*x+e)^3/(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\frac{\frac{a \operatorname{arsinh}\left(\frac{b \sin\left(f x + e\right)}{\sqrt{a b}}\right)}{b^{\frac{3}{2}}} + \frac{2 \, \operatorname{arsinh}\left(\frac{b \sin\left(f x + e\right)}{\sqrt{a b}}\right)}{\sqrt{b}} - \frac{\sqrt{b \sin\left(f x + e\right)^{2} + a} \sin\left(f x + e\right)}{b}}{2 \, f}"," ",0,"1/2*(a*arcsinh(b*sin(f*x + e)/sqrt(a*b))/b^(3/2) + 2*arcsinh(b*sin(f*x + e)/sqrt(a*b))/sqrt(b) - sqrt(b*sin(f*x + e)^2 + a)*sin(f*x + e)/b)/f","A",0
346,1,21,0,0.348947," ","integrate(cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\frac{\operatorname{arsinh}\left(\frac{b \sin\left(f x + e\right)}{\sqrt{a b}}\right)}{\sqrt{b} f}"," ",0,"arcsinh(b*sin(f*x + e)/sqrt(a*b))/(sqrt(b)*f)","A",0
347,1,105,0,0.457430," ","integrate(sec(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\frac{\frac{\operatorname{arsinh}\left(\frac{b \sin\left(f x + e\right)}{\sqrt{a b} {\left(\sin\left(f x + e\right) + 1\right)}} - \frac{a}{\sqrt{a b} {\left(\sin\left(f x + e\right) + 1\right)}}\right)}{\sqrt{a + b}} + \frac{\operatorname{arsinh}\left(-\frac{b \sin\left(f x + e\right)}{\sqrt{a b} {\left(\sin\left(f x + e\right) - 1\right)}} - \frac{a}{\sqrt{a b} {\left(\sin\left(f x + e\right) - 1\right)}}\right)}{\sqrt{a + b}}}{2 \, f}"," ",0,"1/2*(arcsinh(b*sin(f*x + e)/(sqrt(a*b)*(sin(f*x + e) + 1)) - a/(sqrt(a*b)*(sin(f*x + e) + 1)))/sqrt(a + b) + arcsinh(-b*sin(f*x + e)/(sqrt(a*b)*(sin(f*x + e) - 1)) - a/(sqrt(a*b)*(sin(f*x + e) - 1)))/sqrt(a + b))/f","B",0
348,0,0,0,0.000000," ","integrate(sec(f*x+e)^3/(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(f x + e\right)^{3}}{\sqrt{b \sin\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(sec(f*x + e)^3/sqrt(b*sin(f*x + e)^2 + a), x)","F",0
349,0,0,0,0.000000," ","integrate(cos(f*x+e)^4/(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(f x + e\right)^{4}}{\sqrt{b \sin\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(cos(f*x + e)^4/sqrt(b*sin(f*x + e)^2 + a), x)","F",0
350,0,0,0,0.000000," ","integrate(cos(f*x+e)^2/(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(f x + e\right)^{2}}{\sqrt{b \sin\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(cos(f*x + e)^2/sqrt(b*sin(f*x + e)^2 + a), x)","F",0
351,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \sin\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(1/sqrt(b*sin(f*x + e)^2 + a), x)","F",0
352,0,0,0,0.000000," ","integrate(sec(f*x+e)^2/(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(f x + e\right)^{2}}{\sqrt{b \sin\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(sec(f*x + e)^2/sqrt(b*sin(f*x + e)^2 + a), x)","F",0
353,0,0,0,0.000000," ","integrate(sec(f*x+e)^4/(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(f x + e\right)^{4}}{\sqrt{b \sin\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(sec(f*x + e)^4/sqrt(b*sin(f*x + e)^2 + a), x)","F",0
354,1,74,0,0.339026," ","integrate(cos(f*x+e)^3/(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","-\frac{\frac{\operatorname{arsinh}\left(\frac{b \sin\left(f x + e\right)}{\sqrt{a b}}\right)}{b^{\frac{3}{2}}} - \frac{\sin\left(f x + e\right)}{\sqrt{b \sin\left(f x + e\right)^{2} + a} a} - \frac{\sin\left(f x + e\right)}{\sqrt{b \sin\left(f x + e\right)^{2} + a} b}}{f}"," ",0,"-(arcsinh(b*sin(f*x + e)/sqrt(a*b))/b^(3/2) - sin(f*x + e)/(sqrt(b*sin(f*x + e)^2 + a)*a) - sin(f*x + e)/(sqrt(b*sin(f*x + e)^2 + a)*b))/f","A",0
355,1,27,0,0.331093," ","integrate(cos(f*x+e)/(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\frac{\sin\left(f x + e\right)}{\sqrt{b \sin\left(f x + e\right)^{2} + a} a f}"," ",0,"sin(f*x + e)/(sqrt(b*sin(f*x + e)^2 + a)*a*f)","A",0
356,1,152,0,0.446968," ","integrate(sec(f*x+e)/(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\frac{\frac{2 \, b \sin\left(f x + e\right)}{\sqrt{b \sin\left(f x + e\right)^{2} + a} a^{2} + \sqrt{b \sin\left(f x + e\right)^{2} + a} a b} + \frac{\operatorname{arsinh}\left(\frac{b \sin\left(f x + e\right)}{\sqrt{a b} {\left(\sin\left(f x + e\right) + 1\right)}} - \frac{a}{\sqrt{a b} {\left(\sin\left(f x + e\right) + 1\right)}}\right)}{{\left(a + b\right)}^{\frac{3}{2}}} + \frac{\operatorname{arsinh}\left(-\frac{b \sin\left(f x + e\right)}{\sqrt{a b} {\left(\sin\left(f x + e\right) - 1\right)}} - \frac{a}{\sqrt{a b} {\left(\sin\left(f x + e\right) - 1\right)}}\right)}{{\left(a + b\right)}^{\frac{3}{2}}}}{2 \, f}"," ",0,"1/2*(2*b*sin(f*x + e)/(sqrt(b*sin(f*x + e)^2 + a)*a^2 + sqrt(b*sin(f*x + e)^2 + a)*a*b) + arcsinh(b*sin(f*x + e)/(sqrt(a*b)*(sin(f*x + e) + 1)) - a/(sqrt(a*b)*(sin(f*x + e) + 1)))/(a + b)^(3/2) + arcsinh(-b*sin(f*x + e)/(sqrt(a*b)*(sin(f*x + e) - 1)) - a/(sqrt(a*b)*(sin(f*x + e) - 1)))/(a + b)^(3/2))/f","B",0
357,0,0,0,0.000000," ","integrate(sec(f*x+e)^3/(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(f x + e\right)^{3}}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(f*x + e)^3/(b*sin(f*x + e)^2 + a)^(3/2), x)","F",0
358,0,0,0,0.000000," ","integrate(cos(f*x+e)^6/(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(f x + e\right)^{6}}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(f*x + e)^6/(b*sin(f*x + e)^2 + a)^(3/2), x)","F",0
359,0,0,0,0.000000," ","integrate(cos(f*x+e)^4/(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(f x + e\right)^{4}}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(f*x + e)^4/(b*sin(f*x + e)^2 + a)^(3/2), x)","F",0
360,0,0,0,0.000000," ","integrate(cos(f*x+e)^2/(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(f x + e\right)^{2}}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(f*x + e)^2/(b*sin(f*x + e)^2 + a)^(3/2), x)","F",0
361,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^(-3/2), x)","F",0
362,0,0,0,0.000000," ","integrate(sec(f*x+e)^2/(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(f x + e\right)^{2}}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(f*x + e)^2/(b*sin(f*x + e)^2 + a)^(3/2), x)","F",0
363,1,207,0,1.360460," ","integrate(cos(f*x+e)^5/(a+b*sin(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","-\frac{{\left(\frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} b} + \frac{2 \, a}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} b^{2}}\right)} \sin\left(f x + e\right) - \frac{3 \, \operatorname{arsinh}\left(\frac{b \sin\left(f x + e\right)}{\sqrt{a b}}\right)}{b^{\frac{5}{2}}} - \frac{2 \, \sin\left(f x + e\right)}{\sqrt{b \sin\left(f x + e\right)^{2} + a} a^{2}} - \frac{\sin\left(f x + e\right)}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} a} + \frac{\sin\left(f x + e\right)}{\sqrt{b \sin\left(f x + e\right)^{2} + a} b^{2}} - \frac{2 \, \sin\left(f x + e\right)}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} b} + \frac{2 \, \sin\left(f x + e\right)}{\sqrt{b \sin\left(f x + e\right)^{2} + a} a b}}{3 \, f}"," ",0,"-1/3*((3*sin(f*x + e)^2/((b*sin(f*x + e)^2 + a)^(3/2)*b) + 2*a/((b*sin(f*x + e)^2 + a)^(3/2)*b^2))*sin(f*x + e) - 3*arcsinh(b*sin(f*x + e)/sqrt(a*b))/b^(5/2) - 2*sin(f*x + e)/(sqrt(b*sin(f*x + e)^2 + a)*a^2) - sin(f*x + e)/((b*sin(f*x + e)^2 + a)^(3/2)*a) + sin(f*x + e)/(sqrt(b*sin(f*x + e)^2 + a)*b^2) - 2*sin(f*x + e)/((b*sin(f*x + e)^2 + a)^(3/2)*b) + 2*sin(f*x + e)/(sqrt(b*sin(f*x + e)^2 + a)*a*b))/f","A",0
364,1,107,0,0.778481," ","integrate(cos(f*x+e)^3/(a+b*sin(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\frac{\frac{2 \, \sin\left(f x + e\right)}{\sqrt{b \sin\left(f x + e\right)^{2} + a} a^{2}} + \frac{\sin\left(f x + e\right)}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} a} + \frac{\sin\left(f x + e\right)}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} b} - \frac{\sin\left(f x + e\right)}{\sqrt{b \sin\left(f x + e\right)^{2} + a} a b}}{3 \, f}"," ",0,"1/3*(2*sin(f*x + e)/(sqrt(b*sin(f*x + e)^2 + a)*a^2) + sin(f*x + e)/((b*sin(f*x + e)^2 + a)^(3/2)*a) + sin(f*x + e)/((b*sin(f*x + e)^2 + a)^(3/2)*b) - sin(f*x + e)/(sqrt(b*sin(f*x + e)^2 + a)*a*b))/f","A",0
365,1,55,0,0.338849," ","integrate(cos(f*x+e)/(a+b*sin(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\frac{\frac{2 \, \sin\left(f x + e\right)}{\sqrt{b \sin\left(f x + e\right)^{2} + a} a^{2}} + \frac{\sin\left(f x + e\right)}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} a}}{3 \, f}"," ",0,"1/3*(2*sin(f*x + e)/(sqrt(b*sin(f*x + e)^2 + a)*a^2) + sin(f*x + e)/((b*sin(f*x + e)^2 + a)^(3/2)*a))/f","A",0
366,1,272,0,0.576745," ","integrate(sec(f*x+e)/(a+b*sin(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\frac{\frac{2 \, b \sin\left(f x + e\right)}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} a^{2} + {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} a b} + \frac{6 \, b \sin\left(f x + e\right)}{\sqrt{b \sin\left(f x + e\right)^{2} + a} a^{3} + 2 \, \sqrt{b \sin\left(f x + e\right)^{2} + a} a^{2} b + \sqrt{b \sin\left(f x + e\right)^{2} + a} a b^{2}} + \frac{4 \, b \sin\left(f x + e\right)}{\sqrt{b \sin\left(f x + e\right)^{2} + a} a^{3} + \sqrt{b \sin\left(f x + e\right)^{2} + a} a^{2} b} + \frac{3 \, \operatorname{arsinh}\left(\frac{b \sin\left(f x + e\right)}{\sqrt{a b} {\left(\sin\left(f x + e\right) + 1\right)}} - \frac{a}{\sqrt{a b} {\left(\sin\left(f x + e\right) + 1\right)}}\right)}{{\left(a + b\right)}^{\frac{5}{2}}} + \frac{3 \, \operatorname{arsinh}\left(-\frac{b \sin\left(f x + e\right)}{\sqrt{a b} {\left(\sin\left(f x + e\right) - 1\right)}} - \frac{a}{\sqrt{a b} {\left(\sin\left(f x + e\right) - 1\right)}}\right)}{{\left(a + b\right)}^{\frac{5}{2}}}}{6 \, f}"," ",0,"1/6*(2*b*sin(f*x + e)/((b*sin(f*x + e)^2 + a)^(3/2)*a^2 + (b*sin(f*x + e)^2 + a)^(3/2)*a*b) + 6*b*sin(f*x + e)/(sqrt(b*sin(f*x + e)^2 + a)*a^3 + 2*sqrt(b*sin(f*x + e)^2 + a)*a^2*b + sqrt(b*sin(f*x + e)^2 + a)*a*b^2) + 4*b*sin(f*x + e)/(sqrt(b*sin(f*x + e)^2 + a)*a^3 + sqrt(b*sin(f*x + e)^2 + a)*a^2*b) + 3*arcsinh(b*sin(f*x + e)/(sqrt(a*b)*(sin(f*x + e) + 1)) - a/(sqrt(a*b)*(sin(f*x + e) + 1)))/(a + b)^(5/2) + 3*arcsinh(-b*sin(f*x + e)/(sqrt(a*b)*(sin(f*x + e) - 1)) - a/(sqrt(a*b)*(sin(f*x + e) - 1)))/(a + b)^(5/2))/f","B",0
367,0,0,0,0.000000," ","integrate(cos(f*x+e)^6/(a+b*sin(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(f x + e\right)^{6}}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(f*x + e)^6/(b*sin(f*x + e)^2 + a)^(5/2), x)","F",0
368,0,0,0,0.000000," ","integrate(cos(f*x+e)^4/(a+b*sin(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(f x + e\right)^{4}}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(f*x + e)^4/(b*sin(f*x + e)^2 + a)^(5/2), x)","F",0
369,0,0,0,0.000000," ","integrate(cos(f*x+e)^2/(a+b*sin(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(f x + e\right)^{2}}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(f*x + e)^2/(b*sin(f*x + e)^2 + a)^(5/2), x)","F",0
370,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^(-5/2), x)","F",0
371,0,0,0,0.000000," ","integrate(sec(f*x+e)^2/(a+b*sin(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\sec\left(f x + e\right)^{2}}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(f*x + e)^2/(b*sin(f*x + e)^2 + a)^(5/2), x)","F",0
372,0,0,0,0.000000," ","integrate((d*cos(f*x+e))^m*(a+b*sin(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{p} \left(d \cos\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^p*(d*cos(f*x + e))^m, x)","F",0
373,0,0,0,0.000000," ","integrate(cos(f*x+e)^5*(a+b*sin(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{p} \cos\left(f x + e\right)^{5}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^p*cos(f*x + e)^5, x)","F",0
374,0,0,0,0.000000," ","integrate(cos(f*x+e)^3*(a+b*sin(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{p} \cos\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^p*cos(f*x + e)^3, x)","F",0
375,0,0,0,0.000000," ","integrate(cos(f*x+e)*(a+b*sin(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{p} \cos\left(f x + e\right)\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^p*cos(f*x + e), x)","F",0
376,0,0,0,0.000000," ","integrate(sec(f*x+e)*(a+b*sin(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{p} \sec\left(f x + e\right)\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^p*sec(f*x + e), x)","F",0
377,0,0,0,0.000000," ","integrate(sec(f*x+e)^3*(a+b*sin(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{p} \sec\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^p*sec(f*x + e)^3, x)","F",0
378,0,0,0,0.000000," ","integrate(cos(f*x+e)^4*(a+b*sin(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{p} \cos\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^p*cos(f*x + e)^4, x)","F",0
379,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+b*sin(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{p} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^p*cos(f*x + e)^2, x)","F",0
380,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{p}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^p, x)","F",0
381,0,0,0,0.000000," ","integrate(sec(f*x+e)^2*(a+b*sin(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{p} \sec\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^p*sec(f*x + e)^2, x)","F",0
382,0,0,0,0.000000," ","integrate(sec(f*x+e)^4*(a+b*sin(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{p} \sec\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^p*sec(f*x + e)^4, x)","F",0
383,1,210,0,0.893298," ","integrate(cos(d*x+c)^5/(a+b*sin(d*x+c)^3),x, algorithm=""maxima"")","\frac{\frac{9 \, \sin\left(d x + c\right)^{2}}{b} - \frac{2 \, \sqrt{3} {\left(a {\left(3 \, \left(\frac{a}{b}\right)^{\frac{2}{3}} - 4\right)} - b {\left(3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}} - \frac{4 \, a}{b}\right)}\right)} \arctan\left(-\frac{\sqrt{3} {\left(\left(\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, \sin\left(d x + c\right)\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{a b} - \frac{3 \, {\left(b {\left(4 \, \left(\frac{a}{b}\right)^{\frac{2}{3}} + 1\right)} + a \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)} \log\left(\sin\left(d x + c\right)^{2} - \left(\frac{a}{b}\right)^{\frac{1}{3}} \sin\left(d x + c\right) + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{6 \, {\left(b {\left(2 \, \left(\frac{a}{b}\right)^{\frac{2}{3}} - 1\right)} - a \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)} \log\left(\left(\frac{a}{b}\right)^{\frac{1}{3}} + \sin\left(d x + c\right)\right)}{b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}}}{18 \, d}"," ",0,"1/18*(9*sin(d*x + c)^2/b - 2*sqrt(3)*(a*(3*(a/b)^(2/3) - 4) - b*(3*(a/b)^(1/3) - 4*a/b))*arctan(-1/3*sqrt(3)*((a/b)^(1/3) - 2*sin(d*x + c))/(a/b)^(1/3))/(a*b) - 3*(b*(4*(a/b)^(2/3) + 1) + a*(a/b)^(1/3))*log(sin(d*x + c)^2 - (a/b)^(1/3)*sin(d*x + c) + (a/b)^(2/3))/(b^2*(a/b)^(2/3)) - 6*(b*(2*(a/b)^(2/3) - 1) - a*(a/b)^(1/3))*log((a/b)^(1/3) + sin(d*x + c))/(b^2*(a/b)^(2/3)))/d","A",0
384,1,159,0,0.449651," ","integrate(cos(d*x+c)^3/(a+b*sin(d*x+c)^3),x, algorithm=""maxima"")","\frac{\frac{2 \, \sqrt{3} {\left(b {\left(3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}} - \frac{2 \, a}{b}\right)} + 2 \, a\right)} \arctan\left(-\frac{\sqrt{3} {\left(\left(\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, \sin\left(d x + c\right)\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{a b} - \frac{3 \, {\left(2 \, \left(\frac{a}{b}\right)^{\frac{2}{3}} + 1\right)} \log\left(\sin\left(d x + c\right)^{2} - \left(\frac{a}{b}\right)^{\frac{1}{3}} \sin\left(d x + c\right) + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{b \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{6 \, {\left(\left(\frac{a}{b}\right)^{\frac{2}{3}} - 1\right)} \log\left(\left(\frac{a}{b}\right)^{\frac{1}{3}} + \sin\left(d x + c\right)\right)}{b \left(\frac{a}{b}\right)^{\frac{2}{3}}}}{18 \, d}"," ",0,"1/18*(2*sqrt(3)*(b*(3*(a/b)^(1/3) - 2*a/b) + 2*a)*arctan(-1/3*sqrt(3)*((a/b)^(1/3) - 2*sin(d*x + c))/(a/b)^(1/3))/(a*b) - 3*(2*(a/b)^(2/3) + 1)*log(sin(d*x + c)^2 - (a/b)^(1/3)*sin(d*x + c) + (a/b)^(2/3))/(b*(a/b)^(2/3)) - 6*((a/b)^(2/3) - 1)*log((a/b)^(1/3) + sin(d*x + c))/(b*(a/b)^(2/3)))/d","A",0
385,1,121,0,0.436663," ","integrate(cos(d*x+c)/(a+b*sin(d*x+c)^3),x, algorithm=""maxima"")","\frac{\frac{2 \, \sqrt{3} \arctan\left(-\frac{\sqrt{3} {\left(\left(\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, \sin\left(d x + c\right)\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{b \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{\log\left(\sin\left(d x + c\right)^{2} - \left(\frac{a}{b}\right)^{\frac{1}{3}} \sin\left(d x + c\right) + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{b \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{2 \, \log\left(\left(\frac{a}{b}\right)^{\frac{1}{3}} + \sin\left(d x + c\right)\right)}{b \left(\frac{a}{b}\right)^{\frac{2}{3}}}}{6 \, d}"," ",0,"1/6*(2*sqrt(3)*arctan(-1/3*sqrt(3)*((a/b)^(1/3) - 2*sin(d*x + c))/(a/b)^(1/3))/(b*(a/b)^(2/3)) - log(sin(d*x + c)^2 - (a/b)^(1/3)*sin(d*x + c) + (a/b)^(2/3))/(b*(a/b)^(2/3)) + 2*log((a/b)^(1/3) + sin(d*x + c))/(b*(a/b)^(2/3)))/d","A",0
386,1,288,0,0.510919," ","integrate(sec(d*x+c)/(a+b*sin(d*x+c)^3),x, algorithm=""maxima"")","\frac{\frac{2 \, \sqrt{3} {\left(a {\left(3 \, \left(\frac{a}{b}\right)^{\frac{2}{3}} + 2\right)} - b {\left(3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}} + \frac{2 \, a}{b}\right)}\right)} \arctan\left(-\frac{\sqrt{3} {\left(\left(\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, \sin\left(d x + c\right)\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{{\left(a^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}} - b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)} \left(\frac{a}{b}\right)^{\frac{1}{3}}} - \frac{3 \, {\left(b {\left(2 \, \left(\frac{a}{b}\right)^{\frac{2}{3}} - 1\right)} - a \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)} \log\left(\sin\left(d x + c\right)^{2} - \left(\frac{a}{b}\right)^{\frac{1}{3}} \sin\left(d x + c\right) + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{a^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}} - b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{6 \, {\left(b {\left(\left(\frac{a}{b}\right)^{\frac{2}{3}} + 1\right)} + a \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)} \log\left(\left(\frac{a}{b}\right)^{\frac{1}{3}} + \sin\left(d x + c\right)\right)}{a^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}} - b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{9 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a - b} - \frac{9 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a + b}}{18 \, d}"," ",0,"1/18*(2*sqrt(3)*(a*(3*(a/b)^(2/3) + 2) - b*(3*(a/b)^(1/3) + 2*a/b))*arctan(-1/3*sqrt(3)*((a/b)^(1/3) - 2*sin(d*x + c))/(a/b)^(1/3))/((a^2*(a/b)^(2/3) - b^2*(a/b)^(2/3))*(a/b)^(1/3)) - 3*(b*(2*(a/b)^(2/3) - 1) - a*(a/b)^(1/3))*log(sin(d*x + c)^2 - (a/b)^(1/3)*sin(d*x + c) + (a/b)^(2/3))/(a^2*(a/b)^(2/3) - b^2*(a/b)^(2/3)) - 6*(b*((a/b)^(2/3) + 1) + a*(a/b)^(1/3))*log((a/b)^(1/3) + sin(d*x + c))/(a^2*(a/b)^(2/3) - b^2*(a/b)^(2/3)) + 9*log(sin(d*x + c) + 1)/(a - b) - 9*log(sin(d*x + c) - 1)/(a + b))/d","A",0
387,1,470,0,0.441053," ","integrate(sec(d*x+c)^3/(a+b*sin(d*x+c)^3),x, algorithm=""maxima"")","-\frac{\frac{4 \, \sqrt{3} {\left(a b^{2} {\left(9 \, \left(\frac{a}{b}\right)^{\frac{2}{3}} + 4\right)} - b^{3} {\left(3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}} + \frac{4 \, a}{b}\right)} - 2 \, a^{2} b {\left(3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}} + \frac{a}{b}\right)} + 2 \, a^{3}\right)} \arctan\left(-\frac{\sqrt{3} {\left(\left(\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, \sin\left(d x + c\right)\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{{\left(a^{4} \left(\frac{a}{b}\right)^{\frac{2}{3}} - 2 \, a^{2} b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}} + b^{4} \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)} \left(\frac{a}{b}\right)^{\frac{1}{3}}} - \frac{6 \, {\left(b^{3} {\left(4 \, \left(\frac{a}{b}\right)^{\frac{2}{3}} - 1\right)} + 2 \, a^{2} b {\left(\left(\frac{a}{b}\right)^{\frac{2}{3}} - 1\right)} - 3 \, a b^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)} \log\left(\sin\left(d x + c\right)^{2} - \left(\frac{a}{b}\right)^{\frac{1}{3}} \sin\left(d x + c\right) + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{a^{4} \left(\frac{a}{b}\right)^{\frac{2}{3}} - 2 \, a^{2} b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}} + b^{4} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{12 \, {\left(b^{3} {\left(2 \, \left(\frac{a}{b}\right)^{\frac{2}{3}} + 1\right)} + a^{2} b {\left(\left(\frac{a}{b}\right)^{\frac{2}{3}} + 2\right)} + 3 \, a b^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)} \log\left(\left(\frac{a}{b}\right)^{\frac{1}{3}} + \sin\left(d x + c\right)\right)}{a^{4} \left(\frac{a}{b}\right)^{\frac{2}{3}} - 2 \, a^{2} b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}} + b^{4} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{9 \, {\left(a - 4 \, b\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a^{2} - 2 \, a b + b^{2}} + \frac{9 \, {\left(a + 4 \, b\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a^{2} + 2 \, a b + b^{2}} + \frac{18 \, {\left(a \sin\left(d x + c\right) - b\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)^{2} - a^{2} + b^{2}}}{36 \, d}"," ",0,"-1/36*(4*sqrt(3)*(a*b^2*(9*(a/b)^(2/3) + 4) - b^3*(3*(a/b)^(1/3) + 4*a/b) - 2*a^2*b*(3*(a/b)^(1/3) + a/b) + 2*a^3)*arctan(-1/3*sqrt(3)*((a/b)^(1/3) - 2*sin(d*x + c))/(a/b)^(1/3))/((a^4*(a/b)^(2/3) - 2*a^2*b^2*(a/b)^(2/3) + b^4*(a/b)^(2/3))*(a/b)^(1/3)) - 6*(b^3*(4*(a/b)^(2/3) - 1) + 2*a^2*b*((a/b)^(2/3) - 1) - 3*a*b^2*(a/b)^(1/3))*log(sin(d*x + c)^2 - (a/b)^(1/3)*sin(d*x + c) + (a/b)^(2/3))/(a^4*(a/b)^(2/3) - 2*a^2*b^2*(a/b)^(2/3) + b^4*(a/b)^(2/3)) - 12*(b^3*(2*(a/b)^(2/3) + 1) + a^2*b*((a/b)^(2/3) + 2) + 3*a*b^2*(a/b)^(1/3))*log((a/b)^(1/3) + sin(d*x + c))/(a^4*(a/b)^(2/3) - 2*a^2*b^2*(a/b)^(2/3) + b^4*(a/b)^(2/3)) - 9*(a - 4*b)*log(sin(d*x + c) + 1)/(a^2 - 2*a*b + b^2) + 9*(a + 4*b)*log(sin(d*x + c) - 1)/(a^2 + 2*a*b + b^2) + 18*(a*sin(d*x + c) - b)/((a^2 - b^2)*sin(d*x + c)^2 - a^2 + b^2))/d","A",0
388,-1,0,0,0.000000," ","integrate(cos(d*x+c)^4/(a+b*sin(d*x+c)^3),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
389,0,0,0,0.000000," ","integrate(cos(d*x+c)^2/(a+b*sin(d*x+c)^3),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{2}}{b \sin\left(d x + c\right)^{3} + a}\,{d x}"," ",0,"integrate(cos(d*x + c)^2/(b*sin(d*x + c)^3 + a), x)","F",0
390,0,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c)^3),x, algorithm=""maxima"")","\int \frac{1}{b \sin\left(d x + c\right)^{3} + a}\,{d x}"," ",0,"integrate(1/(b*sin(d*x + c)^3 + a), x)","F",0
391,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+b*sin(d*x+c)^3),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
392,-1,0,0,0.000000," ","integrate(sec(d*x+c)^4/(a+b*sin(d*x+c)^3),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
393,1,263,0,0.448968," ","integrate(cos(d*x+c)^7/(a+b*sin(d*x+c)^3)^2,x, algorithm=""maxima"")","-\frac{\frac{3 \, {\left(3 \, a b \sin\left(d x + c\right)^{2} - 3 \, a b + {\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)\right)}}{a b^{3} \sin\left(d x + c\right)^{3} + a^{2} b^{2}} + \frac{9 \, \sin\left(d x + c\right)}{b^{2}} - \frac{2 \, \sqrt{3} {\left(3 \, a b \left(\frac{a}{b}\right)^{\frac{1}{3}} + 2 \, a^{2} + b^{2}\right)} \arctan\left(-\frac{\sqrt{3} {\left(\left(\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, \sin\left(d x + c\right)\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{a b^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(3 \, a b \left(\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, a^{2} - b^{2}\right)} \log\left(\sin\left(d x + c\right)^{2} - \left(\frac{a}{b}\right)^{\frac{1}{3}} \sin\left(d x + c\right) + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{a b^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{2 \, {\left(3 \, a b \left(\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, a^{2} - b^{2}\right)} \log\left(\left(\frac{a}{b}\right)^{\frac{1}{3}} + \sin\left(d x + c\right)\right)}{a b^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}}}{9 \, d}"," ",0,"-1/9*(3*(3*a*b*sin(d*x + c)^2 - 3*a*b + (a^2 - b^2)*sin(d*x + c))/(a*b^3*sin(d*x + c)^3 + a^2*b^2) + 9*sin(d*x + c)/b^2 - 2*sqrt(3)*(3*a*b*(a/b)^(1/3) + 2*a^2 + b^2)*arctan(-1/3*sqrt(3)*((a/b)^(1/3) - 2*sin(d*x + c))/(a/b)^(1/3))/(a*b^3*(a/b)^(2/3)) - (3*a*b*(a/b)^(1/3) - 2*a^2 - b^2)*log(sin(d*x + c)^2 - (a/b)^(1/3)*sin(d*x + c) + (a/b)^(2/3))/(a*b^3*(a/b)^(2/3)) + 2*(3*a*b*(a/b)^(1/3) - 2*a^2 - b^2)*log((a/b)^(1/3) + sin(d*x + c))/(a*b^3*(a/b)^(2/3)))/d","A",0
394,1,213,0,0.449873," ","integrate(cos(d*x+c)^5/(a+b*sin(d*x+c)^3)^2,x, algorithm=""maxima"")","-\frac{\frac{3 \, {\left(a \sin\left(d x + c\right)^{2} - b \sin\left(d x + c\right) - 2 \, a\right)}}{a b^{2} \sin\left(d x + c\right)^{3} + a^{2} b} - \frac{2 \, \sqrt{3} {\left(a \left(\frac{a}{b}\right)^{\frac{1}{3}} + b\right)} \arctan\left(-\frac{\sqrt{3} {\left(\left(\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, \sin\left(d x + c\right)\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{a b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(a \left(\frac{a}{b}\right)^{\frac{1}{3}} - b\right)} \log\left(\sin\left(d x + c\right)^{2} - \left(\frac{a}{b}\right)^{\frac{1}{3}} \sin\left(d x + c\right) + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{a b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{2 \, {\left(a \left(\frac{a}{b}\right)^{\frac{1}{3}} - b\right)} \log\left(\left(\frac{a}{b}\right)^{\frac{1}{3}} + \sin\left(d x + c\right)\right)}{a b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}}}{9 \, d}"," ",0,"-1/9*(3*(a*sin(d*x + c)^2 - b*sin(d*x + c) - 2*a)/(a*b^2*sin(d*x + c)^3 + a^2*b) - 2*sqrt(3)*(a*(a/b)^(1/3) + b)*arctan(-1/3*sqrt(3)*((a/b)^(1/3) - 2*sin(d*x + c))/(a/b)^(1/3))/(a*b^2*(a/b)^(2/3)) - (a*(a/b)^(1/3) - b)*log(sin(d*x + c)^2 - (a/b)^(1/3)*sin(d*x + c) + (a/b)^(2/3))/(a*b^2*(a/b)^(2/3)) + 2*(a*(a/b)^(1/3) - b)*log((a/b)^(1/3) + sin(d*x + c))/(a*b^2*(a/b)^(2/3)))/d","A",0
395,1,163,0,0.468628," ","integrate(cos(d*x+c)^3/(a+b*sin(d*x+c)^3)^2,x, algorithm=""maxima"")","\frac{\frac{3 \, {\left(b \sin\left(d x + c\right) + a\right)}}{a b^{2} \sin\left(d x + c\right)^{3} + a^{2} b} + \frac{2 \, \sqrt{3} \arctan\left(-\frac{\sqrt{3} {\left(\left(\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, \sin\left(d x + c\right)\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{a b \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{\log\left(\sin\left(d x + c\right)^{2} - \left(\frac{a}{b}\right)^{\frac{1}{3}} \sin\left(d x + c\right) + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{a b \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{2 \, \log\left(\left(\frac{a}{b}\right)^{\frac{1}{3}} + \sin\left(d x + c\right)\right)}{a b \left(\frac{a}{b}\right)^{\frac{2}{3}}}}{9 \, d}"," ",0,"1/9*(3*(b*sin(d*x + c) + a)/(a*b^2*sin(d*x + c)^3 + a^2*b) + 2*sqrt(3)*arctan(-1/3*sqrt(3)*((a/b)^(1/3) - 2*sin(d*x + c))/(a/b)^(1/3))/(a*b*(a/b)^(2/3)) - log(sin(d*x + c)^2 - (a/b)^(1/3)*sin(d*x + c) + (a/b)^(2/3))/(a*b*(a/b)^(2/3)) + 2*log((a/b)^(1/3) + sin(d*x + c))/(a*b*(a/b)^(2/3)))/d","A",0
396,1,155,0,0.433698," ","integrate(cos(d*x+c)/(a+b*sin(d*x+c)^3)^2,x, algorithm=""maxima"")","\frac{\frac{3 \, \sin\left(d x + c\right)}{a b \sin\left(d x + c\right)^{3} + a^{2}} + \frac{2 \, \sqrt{3} \arctan\left(-\frac{\sqrt{3} {\left(\left(\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, \sin\left(d x + c\right)\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{a b \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{\log\left(\sin\left(d x + c\right)^{2} - \left(\frac{a}{b}\right)^{\frac{1}{3}} \sin\left(d x + c\right) + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{a b \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{2 \, \log\left(\left(\frac{a}{b}\right)^{\frac{1}{3}} + \sin\left(d x + c\right)\right)}{a b \left(\frac{a}{b}\right)^{\frac{2}{3}}}}{9 \, d}"," ",0,"1/9*(3*sin(d*x + c)/(a*b*sin(d*x + c)^3 + a^2) + 2*sqrt(3)*arctan(-1/3*sqrt(3)*((a/b)^(1/3) - 2*sin(d*x + c))/(a/b)^(1/3))/(a*b*(a/b)^(2/3)) - log(sin(d*x + c)^2 - (a/b)^(1/3)*sin(d*x + c) + (a/b)^(2/3))/(a*b*(a/b)^(2/3)) + 2*log((a/b)^(1/3) + sin(d*x + c))/(a*b*(a/b)^(2/3)))/d","A",0
397,1,483,0,0.452373," ","integrate(sec(d*x+c)/(a+b*sin(d*x+c)^3)^2,x, algorithm=""maxima"")","\frac{\frac{4 \, \sqrt{3} {\left(2 \, a^{3} {\left(\left(\frac{a}{b}\right)^{\frac{2}{3}} + 1\right)} - 2 \, a^{2} b {\left(2 \, \left(\frac{a}{b}\right)^{\frac{1}{3}} + \frac{a}{b}\right)} + a b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}} + b^{3} \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)} \arctan\left(-\frac{\sqrt{3} {\left(\left(\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, \sin\left(d x + c\right)\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{{\left(a^{5} \left(\frac{a}{b}\right)^{\frac{2}{3}} - 2 \, a^{3} b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}} + a b^{4} \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)} \left(\frac{a}{b}\right)^{\frac{1}{3}}} - \frac{2 \, {\left(2 \, a^{2} b {\left(3 \, \left(\frac{a}{b}\right)^{\frac{2}{3}} - 2\right)} - 2 \, a^{3} \left(\frac{a}{b}\right)^{\frac{1}{3}} - a b^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}} + b^{3}\right)} \log\left(\sin\left(d x + c\right)^{2} - \left(\frac{a}{b}\right)^{\frac{1}{3}} \sin\left(d x + c\right) + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{a^{5} \left(\frac{a}{b}\right)^{\frac{2}{3}} - 2 \, a^{3} b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}} + a b^{4} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{4 \, {\left(a^{2} b {\left(3 \, \left(\frac{a}{b}\right)^{\frac{2}{3}} + 4\right)} + 2 \, a^{3} \left(\frac{a}{b}\right)^{\frac{1}{3}} + a b^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}} - b^{3}\right)} \log\left(\left(\frac{a}{b}\right)^{\frac{1}{3}} + \sin\left(d x + c\right)\right)}{a^{5} \left(\frac{a}{b}\right)^{\frac{2}{3}} - 2 \, a^{3} b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}} + a b^{4} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{6 \, {\left(a b \sin\left(d x + c\right)^{2} - b^{2} \sin\left(d x + c\right) + a b\right)}}{a^{4} - a^{2} b^{2} + {\left(a^{3} b - a b^{3}\right)} \sin\left(d x + c\right)^{3}} + \frac{9 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{2} - 2 \, a b + b^{2}} - \frac{9 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a^{2} + 2 \, a b + b^{2}}}{18 \, d}"," ",0,"1/18*(4*sqrt(3)*(2*a^3*((a/b)^(2/3) + 1) - 2*a^2*b*(2*(a/b)^(1/3) + a/b) + a*b^2*(a/b)^(2/3) + b^3*(a/b)^(1/3))*arctan(-1/3*sqrt(3)*((a/b)^(1/3) - 2*sin(d*x + c))/(a/b)^(1/3))/((a^5*(a/b)^(2/3) - 2*a^3*b^2*(a/b)^(2/3) + a*b^4*(a/b)^(2/3))*(a/b)^(1/3)) - 2*(2*a^2*b*(3*(a/b)^(2/3) - 2) - 2*a^3*(a/b)^(1/3) - a*b^2*(a/b)^(1/3) + b^3)*log(sin(d*x + c)^2 - (a/b)^(1/3)*sin(d*x + c) + (a/b)^(2/3))/(a^5*(a/b)^(2/3) - 2*a^3*b^2*(a/b)^(2/3) + a*b^4*(a/b)^(2/3)) - 4*(a^2*b*(3*(a/b)^(2/3) + 4) + 2*a^3*(a/b)^(1/3) + a*b^2*(a/b)^(1/3) - b^3)*log((a/b)^(1/3) + sin(d*x + c))/(a^5*(a/b)^(2/3) - 2*a^3*b^2*(a/b)^(2/3) + a*b^4*(a/b)^(2/3)) + 6*(a*b*sin(d*x + c)^2 - b^2*sin(d*x + c) + a*b)/(a^4 - a^2*b^2 + (a^3*b - a*b^3)*sin(d*x + c)^3) + 9*log(sin(d*x + c) + 1)/(a^2 - 2*a*b + b^2) - 9*log(sin(d*x + c) - 1)/(a^2 + 2*a*b + b^2))/d","A",0
398,1,788,0,0.449837," ","integrate(sec(d*x+c)^3/(a+b*sin(d*x+c)^3)^2,x, algorithm=""maxima"")","-\frac{\frac{8 \, \sqrt{3} {\left(5 \, a^{3} b^{2} {\left(3 \, \left(\frac{a}{b}\right)^{\frac{2}{3}} + 2\right)} - a^{2} b^{3} {\left(11 \, \left(\frac{a}{b}\right)^{\frac{1}{3}} + \frac{10 \, a}{b}\right)} - 2 \, a^{4} b {\left(4 \, \left(\frac{a}{b}\right)^{\frac{1}{3}} + \frac{a}{b}\right)} + 3 \, a b^{4} \left(\frac{a}{b}\right)^{\frac{2}{3}} + b^{5} \left(\frac{a}{b}\right)^{\frac{1}{3}} + 2 \, a^{5}\right)} \arctan\left(-\frac{\sqrt{3} {\left(\left(\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, \sin\left(d x + c\right)\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{{\left(a^{7} \left(\frac{a}{b}\right)^{\frac{2}{3}} - 3 \, a^{5} b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}} + 3 \, a^{3} b^{4} \left(\frac{a}{b}\right)^{\frac{2}{3}} - a b^{6} \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)} \left(\frac{a}{b}\right)^{\frac{1}{3}}} - \frac{4 \, {\left(a^{2} b^{3} {\left(30 \, \left(\frac{a}{b}\right)^{\frac{2}{3}} - 11\right)} + 2 \, a^{4} b {\left(3 \, \left(\frac{a}{b}\right)^{\frac{2}{3}} - 4\right)} - 15 \, a^{3} b^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}} - 3 \, a b^{4} \left(\frac{a}{b}\right)^{\frac{1}{3}} + b^{5}\right)} \log\left(\sin\left(d x + c\right)^{2} - \left(\frac{a}{b}\right)^{\frac{1}{3}} \sin\left(d x + c\right) + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{a^{7} \left(\frac{a}{b}\right)^{\frac{2}{3}} - 3 \, a^{5} b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}} + 3 \, a^{3} b^{4} \left(\frac{a}{b}\right)^{\frac{2}{3}} - a b^{6} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{8 \, {\left(a^{2} b^{3} {\left(15 \, \left(\frac{a}{b}\right)^{\frac{2}{3}} + 11\right)} + a^{4} b {\left(3 \, \left(\frac{a}{b}\right)^{\frac{2}{3}} + 8\right)} + 15 \, a^{3} b^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}} + 3 \, a b^{4} \left(\frac{a}{b}\right)^{\frac{1}{3}} - b^{5}\right)} \log\left(\left(\frac{a}{b}\right)^{\frac{1}{3}} + \sin\left(d x + c\right)\right)}{a^{7} \left(\frac{a}{b}\right)^{\frac{2}{3}} - 3 \, a^{5} b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}} + 3 \, a^{3} b^{4} \left(\frac{a}{b}\right)^{\frac{2}{3}} - a b^{6} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{9 \, {\left(a - 7 \, b\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} + \frac{9 \, {\left(a + 7 \, b\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} - \frac{6 \, {\left(3 \, {\left(a^{3} b + 3 \, a b^{3}\right)} \sin\left(d x + c\right)^{4} - 8 \, a^{3} b - 4 \, a b^{3} - 2 \, {\left(5 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)^{3} + 2 \, {\left(a^{3} b - a b^{3}\right)} \sin\left(d x + c\right)^{2} + {\left(3 \, a^{4} + 7 \, a^{2} b^{2} + 2 \, b^{4}\right)} \sin\left(d x + c\right)\right)}}{a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4} - {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} \sin\left(d x + c\right)^{5} + {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} \sin\left(d x + c\right)^{3} - {\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} \sin\left(d x + c\right)^{2}}}{36 \, d}"," ",0,"-1/36*(8*sqrt(3)*(5*a^3*b^2*(3*(a/b)^(2/3) + 2) - a^2*b^3*(11*(a/b)^(1/3) + 10*a/b) - 2*a^4*b*(4*(a/b)^(1/3) + a/b) + 3*a*b^4*(a/b)^(2/3) + b^5*(a/b)^(1/3) + 2*a^5)*arctan(-1/3*sqrt(3)*((a/b)^(1/3) - 2*sin(d*x + c))/(a/b)^(1/3))/((a^7*(a/b)^(2/3) - 3*a^5*b^2*(a/b)^(2/3) + 3*a^3*b^4*(a/b)^(2/3) - a*b^6*(a/b)^(2/3))*(a/b)^(1/3)) - 4*(a^2*b^3*(30*(a/b)^(2/3) - 11) + 2*a^4*b*(3*(a/b)^(2/3) - 4) - 15*a^3*b^2*(a/b)^(1/3) - 3*a*b^4*(a/b)^(1/3) + b^5)*log(sin(d*x + c)^2 - (a/b)^(1/3)*sin(d*x + c) + (a/b)^(2/3))/(a^7*(a/b)^(2/3) - 3*a^5*b^2*(a/b)^(2/3) + 3*a^3*b^4*(a/b)^(2/3) - a*b^6*(a/b)^(2/3)) - 8*(a^2*b^3*(15*(a/b)^(2/3) + 11) + a^4*b*(3*(a/b)^(2/3) + 8) + 15*a^3*b^2*(a/b)^(1/3) + 3*a*b^4*(a/b)^(1/3) - b^5)*log((a/b)^(1/3) + sin(d*x + c))/(a^7*(a/b)^(2/3) - 3*a^5*b^2*(a/b)^(2/3) + 3*a^3*b^4*(a/b)^(2/3) - a*b^6*(a/b)^(2/3)) - 9*(a - 7*b)*log(sin(d*x + c) + 1)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) + 9*(a + 7*b)*log(sin(d*x + c) - 1)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) - 6*(3*(a^3*b + 3*a*b^3)*sin(d*x + c)^4 - 8*a^3*b - 4*a*b^3 - 2*(5*a^2*b^2 + b^4)*sin(d*x + c)^3 + 2*(a^3*b - a*b^3)*sin(d*x + c)^2 + (3*a^4 + 7*a^2*b^2 + 2*b^4)*sin(d*x + c))/(a^6 - 2*a^4*b^2 + a^2*b^4 - (a^5*b - 2*a^3*b^3 + a*b^5)*sin(d*x + c)^5 + (a^5*b - 2*a^3*b^3 + a*b^5)*sin(d*x + c)^3 - (a^6 - 2*a^4*b^2 + a^2*b^4)*sin(d*x + c)^2))/d","A",0
399,-1,0,0,0.000000," ","integrate(cos(d*x+c)^4/(a+b*sin(d*x+c)^3)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
400,-1,0,0,0.000000," ","integrate(cos(d*x+c)^2/(a+b*sin(d*x+c)^3)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
401,-1,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c)^3)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
402,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+b*sin(d*x+c)^3)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
403,-1,0,0,0.000000," ","integrate(sec(d*x+c)^4/(a+b*sin(d*x+c)^3)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
404,1,177,0,0.643942," ","integrate(cos(d*x+c)^7/(a-b*sin(d*x+c)^4),x, algorithm=""maxima"")","\frac{\frac{4 \, {\left(\sin\left(d x + c\right)^{3} - 9 \, \sin\left(d x + c\right)\right)}}{b} + \frac{3 \, {\left(\frac{2 \, {\left(b {\left(3 \, \sqrt{a} + \sqrt{b}\right)} + a^{\frac{3}{2}} + 3 \, a \sqrt{b}\right)} \arctan\left(\frac{\sqrt{b} \sin\left(d x + c\right)}{\sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{{\left(b {\left(3 \, \sqrt{a} - \sqrt{b}\right)} + a^{\frac{3}{2}} - 3 \, a \sqrt{b}\right)} \log\left(\frac{\sqrt{b} \sin\left(d x + c\right) - \sqrt{\sqrt{a} \sqrt{b}}}{\sqrt{b} \sin\left(d x + c\right) + \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}}\right)}}{b}}{12 \, d}"," ",0,"1/12*(4*(sin(d*x + c)^3 - 9*sin(d*x + c))/b + 3*(2*(b*(3*sqrt(a) + sqrt(b)) + a^(3/2) + 3*a*sqrt(b))*arctan(sqrt(b)*sin(d*x + c)/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + (b*(3*sqrt(a) - sqrt(b)) + a^(3/2) - 3*a*sqrt(b))*log((sqrt(b)*sin(d*x + c) - sqrt(sqrt(a)*sqrt(b)))/(sqrt(b)*sin(d*x + c) + sqrt(sqrt(a)*sqrt(b))))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)))/b)/d","A",0
405,1,158,0,0.537811," ","integrate(cos(d*x+c)^5/(a-b*sin(d*x+c)^4),x, algorithm=""maxima"")","\frac{\frac{\frac{2 \, {\left(b {\left(2 \, \sqrt{a} + \sqrt{b}\right)} + a \sqrt{b}\right)} \arctan\left(\frac{\sqrt{b} \sin\left(d x + c\right)}{\sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{{\left(b {\left(2 \, \sqrt{a} - \sqrt{b}\right)} - a \sqrt{b}\right)} \log\left(\frac{\sqrt{b} \sin\left(d x + c\right) - \sqrt{\sqrt{a} \sqrt{b}}}{\sqrt{b} \sin\left(d x + c\right) + \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}}}{b} - \frac{4 \, \sin\left(d x + c\right)}{b}}{4 \, d}"," ",0,"1/4*((2*(b*(2*sqrt(a) + sqrt(b)) + a*sqrt(b))*arctan(sqrt(b)*sin(d*x + c)/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + (b*(2*sqrt(a) - sqrt(b)) - a*sqrt(b))*log((sqrt(b)*sin(d*x + c) - sqrt(sqrt(a)*sqrt(b)))/(sqrt(b)*sin(d*x + c) + sqrt(sqrt(a)*sqrt(b))))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)))/b - 4*sin(d*x + c)/b)/d","A",0
406,1,121,0,0.543821," ","integrate(cos(d*x+c)^3/(a-b*sin(d*x+c)^4),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(\sqrt{a} + \sqrt{b}\right)} \arctan\left(\frac{\sqrt{b} \sin\left(d x + c\right)}{\sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{{\left(\sqrt{a} - \sqrt{b}\right)} \log\left(\frac{\sqrt{b} \sin\left(d x + c\right) - \sqrt{\sqrt{a} \sqrt{b}}}{\sqrt{b} \sin\left(d x + c\right) + \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}}}{4 \, d}"," ",0,"1/4*(2*(sqrt(a) + sqrt(b))*arctan(sqrt(b)*sin(d*x + c)/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + (sqrt(a) - sqrt(b))*log((sqrt(b)*sin(d*x + c) - sqrt(sqrt(a)*sqrt(b)))/(sqrt(b)*sin(d*x + c) + sqrt(sqrt(a)*sqrt(b))))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)))/d","A",0
407,1,100,0,0.653895," ","integrate(cos(d*x+c)/(a-b*sin(d*x+c)^4),x, algorithm=""maxima"")","\frac{\frac{2 \, \arctan\left(\frac{\sqrt{b} \sin\left(d x + c\right)}{\sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} - \frac{\log\left(\frac{\sqrt{b} \sin\left(d x + c\right) - \sqrt{\sqrt{a} \sqrt{b}}}{\sqrt{b} \sin\left(d x + c\right) + \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}}}{4 \, d}"," ",0,"1/4*(2*arctan(sqrt(b)*sin(d*x + c)/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) - log((sqrt(b)*sin(d*x + c) - sqrt(sqrt(a)*sqrt(b)))/(sqrt(b)*sin(d*x + c) + sqrt(sqrt(a)*sqrt(b))))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))))/d","A",0
408,1,167,0,0.614262," ","integrate(sec(d*x+c)/(a-b*sin(d*x+c)^4),x, algorithm=""maxima"")","\frac{\frac{b {\left(\frac{2 \, {\left(\sqrt{a} - \sqrt{b}\right)} \arctan\left(\frac{\sqrt{b} \sin\left(d x + c\right)}{\sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{{\left(\sqrt{a} + \sqrt{b}\right)} \log\left(\frac{\sqrt{b} \sin\left(d x + c\right) - \sqrt{\sqrt{a} \sqrt{b}}}{\sqrt{b} \sin\left(d x + c\right) + \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}}\right)}}{a - b} + \frac{2 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a - b} - \frac{2 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a - b}}{4 \, d}"," ",0,"1/4*(b*(2*(sqrt(a) - sqrt(b))*arctan(sqrt(b)*sin(d*x + c)/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + (sqrt(a) + sqrt(b))*log((sqrt(b)*sin(d*x + c) - sqrt(sqrt(a)*sqrt(b)))/(sqrt(b)*sin(d*x + c) + sqrt(sqrt(a)*sqrt(b))))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)))/(a - b) + 2*log(sin(d*x + c) + 1)/(a - b) - 2*log(sin(d*x + c) - 1)/(a - b))/d","A",0
409,1,244,0,0.711988," ","integrate(sec(d*x+c)^3/(a-b*sin(d*x+c)^4),x, algorithm=""maxima"")","-\frac{\frac{b {\left(\frac{2 \, {\left(b {\left(2 \, \sqrt{a} - \sqrt{b}\right)} - a \sqrt{b}\right)} \arctan\left(\frac{\sqrt{b} \sin\left(d x + c\right)}{\sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{{\left(b {\left(2 \, \sqrt{a} + \sqrt{b}\right)} + a \sqrt{b}\right)} \log\left(\frac{\sqrt{b} \sin\left(d x + c\right) - \sqrt{\sqrt{a} \sqrt{b}}}{\sqrt{b} \sin\left(d x + c\right) + \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}}\right)}}{a^{2} - 2 \, a b + b^{2}} - \frac{{\left(a - 5 \, b\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a^{2} - 2 \, a b + b^{2}} + \frac{{\left(a - 5 \, b\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a^{2} - 2 \, a b + b^{2}} + \frac{2 \, \sin\left(d x + c\right)}{{\left(a - b\right)} \sin\left(d x + c\right)^{2} - a + b}}{4 \, d}"," ",0,"-1/4*(b*(2*(b*(2*sqrt(a) - sqrt(b)) - a*sqrt(b))*arctan(sqrt(b)*sin(d*x + c)/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + (b*(2*sqrt(a) + sqrt(b)) + a*sqrt(b))*log((sqrt(b)*sin(d*x + c) - sqrt(sqrt(a)*sqrt(b)))/(sqrt(b)*sin(d*x + c) + sqrt(sqrt(a)*sqrt(b))))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)))/(a^2 - 2*a*b + b^2) - (a - 5*b)*log(sin(d*x + c) + 1)/(a^2 - 2*a*b + b^2) + (a - 5*b)*log(sin(d*x + c) - 1)/(a^2 - 2*a*b + b^2) + 2*sin(d*x + c)/((a - b)*sin(d*x + c)^2 - a + b))/d","A",0
410,1,363,0,1.499815," ","integrate(sec(d*x+c)^5/(a-b*sin(d*x+c)^4),x, algorithm=""maxima"")","\frac{\frac{4 \, b^{2} {\left(\frac{2 \, {\left(b {\left(3 \, \sqrt{a} - \sqrt{b}\right)} + a^{\frac{3}{2}} - 3 \, a \sqrt{b}\right)} \arctan\left(\frac{\sqrt{b} \sin\left(d x + c\right)}{\sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{{\left(b {\left(3 \, \sqrt{a} + \sqrt{b}\right)} + a^{\frac{3}{2}} + 3 \, a \sqrt{b}\right)} \log\left(\frac{\sqrt{b} \sin\left(d x + c\right) - \sqrt{\sqrt{a} \sqrt{b}}}{\sqrt{b} \sin\left(d x + c\right) + \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}}\right)}}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} + \frac{{\left(3 \, a^{2} - 6 \, a b + 35 \, b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} - \frac{{\left(3 \, a^{2} - 6 \, a b + 35 \, b^{2}\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} - \frac{2 \, {\left({\left(3 \, a - 11 \, b\right)} \sin\left(d x + c\right)^{3} - {\left(5 \, a - 13 \, b\right)} \sin\left(d x + c\right)\right)}}{{\left(a^{2} - 2 \, a b + b^{2}\right)} \sin\left(d x + c\right)^{4} - 2 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \sin\left(d x + c\right)^{2} + a^{2} - 2 \, a b + b^{2}}}{16 \, d}"," ",0,"1/16*(4*b^2*(2*(b*(3*sqrt(a) - sqrt(b)) + a^(3/2) - 3*a*sqrt(b))*arctan(sqrt(b)*sin(d*x + c)/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + (b*(3*sqrt(a) + sqrt(b)) + a^(3/2) + 3*a*sqrt(b))*log((sqrt(b)*sin(d*x + c) - sqrt(sqrt(a)*sqrt(b)))/(sqrt(b)*sin(d*x + c) + sqrt(sqrt(a)*sqrt(b))))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)))/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) + (3*a^2 - 6*a*b + 35*b^2)*log(sin(d*x + c) + 1)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) - (3*a^2 - 6*a*b + 35*b^2)*log(sin(d*x + c) - 1)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) - 2*((3*a - 11*b)*sin(d*x + c)^3 - (5*a - 13*b)*sin(d*x + c))/((a^2 - 2*a*b + b^2)*sin(d*x + c)^4 - 2*(a^2 - 2*a*b + b^2)*sin(d*x + c)^2 + a^2 - 2*a*b + b^2))/d","A",0
411,0,0,0,0.000000," ","integrate(cos(d*x+c)^10/(a-b*sin(d*x+c)^4),x, algorithm=""maxima"")","-\frac{-768 \, b^{2} d \int \frac{4 \, {\left(a^{2} b + 10 \, a b^{2} + 5 \, b^{3}\right)} \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(72 \, a^{3} + 53 \, a^{2} b - 54 \, a b^{2} + 9 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a^{2} b + 10 \, a b^{2} + 5 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(a^{2} b + 10 \, a b^{2} + 5 \, b^{3}\right)} \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(72 \, a^{3} + 53 \, a^{2} b - 54 \, a b^{2} + 9 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, {\left(8 \, a^{3} + 113 \, a^{2} b + 50 \, a b^{2} - 27 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, {\left(a^{2} b + 10 \, a b^{2} + 5 \, b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - {\left({\left(a^{2} b + 10 \, a b^{2} + 5 \, b^{3}\right)} \cos\left(6 \, d x + 6 \, c\right) + 2 \, {\left(9 \, a^{2} b + 10 \, a b^{2} - 3 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right) + {\left(a^{2} b + 10 \, a b^{2} + 5 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) - {\left(a^{2} b + 10 \, a b^{2} + 5 \, b^{3} - 2 \, {\left(8 \, a^{3} + 113 \, a^{2} b + 50 \, a b^{2} - 27 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(a^{2} b + 10 \, a b^{2} + 5 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left(9 \, a^{2} b + 10 \, a b^{2} - 3 \, b^{3} - {\left(8 \, a^{3} + 113 \, a^{2} b + 50 \, a b^{2} - 27 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - {\left(a^{2} b + 10 \, a b^{2} + 5 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right) - {\left({\left(a^{2} b + 10 \, a b^{2} + 5 \, b^{3}\right)} \sin\left(6 \, d x + 6 \, c\right) + 2 \, {\left(9 \, a^{2} b + 10 \, a b^{2} - 3 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) + {\left(a^{2} b + 10 \, a b^{2} + 5 \, b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 2 \, {\left({\left(8 \, a^{3} + 113 \, a^{2} b + 50 \, a b^{2} - 27 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a^{2} b + 10 \, a b^{2} + 5 \, b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}{b^{4} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, b^{4} \cos\left(6 \, d x + 6 \, c\right)^{2} + 16 \, b^{4} \cos\left(2 \, d x + 2 \, c\right)^{2} + b^{4} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, b^{4} \sin\left(6 \, d x + 6 \, c\right)^{2} + 16 \, b^{4} \sin\left(2 \, d x + 2 \, c\right)^{2} - 8 \, b^{4} \cos\left(2 \, d x + 2 \, c\right) + b^{4} + 4 \, {\left(64 \, a^{2} b^{2} - 48 \, a b^{3} + 9 \, b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(64 \, a^{2} b^{2} - 48 \, a b^{3} + 9 \, b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(8 \, a b^{3} - 3 \, b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 2 \, {\left(4 \, b^{4} \cos\left(6 \, d x + 6 \, c\right) + 4 \, b^{4} \cos\left(2 \, d x + 2 \, c\right) - b^{4} + 2 \, {\left(8 \, a b^{3} - 3 \, b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(4 \, b^{4} \cos\left(2 \, d x + 2 \, c\right) - b^{4} + 2 \, {\left(8 \, a b^{3} - 3 \, b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(8 \, a b^{3} - 3 \, b^{4} - 4 \, {\left(8 \, a b^{3} - 3 \, b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(2 \, b^{4} \sin\left(6 \, d x + 6 \, c\right) + 2 \, b^{4} \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a b^{3} - 3 \, b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(2 \, b^{4} \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a b^{3} - 3 \, b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}\,{d x} + 36 \, {\left(24 \, a + 35 \, b\right)} d x + b \sin\left(6 \, d x + 6 \, c\right) + 21 \, b \sin\left(4 \, d x + 4 \, c\right) + 3 \, {\left(16 \, a + 95 \, b\right)} \sin\left(2 \, d x + 2 \, c\right)}{192 \, b^{2} d}"," ",0,"-1/192*(192*b^2*d*integrate(-4*(4*(a^2*b + 10*a*b^2 + 5*b^3)*cos(6*d*x + 6*c)^2 + 4*(72*a^3 + 53*a^2*b - 54*a*b^2 + 9*b^3)*cos(4*d*x + 4*c)^2 + 4*(a^2*b + 10*a*b^2 + 5*b^3)*cos(2*d*x + 2*c)^2 + 4*(a^2*b + 10*a*b^2 + 5*b^3)*sin(6*d*x + 6*c)^2 + 4*(72*a^3 + 53*a^2*b - 54*a*b^2 + 9*b^3)*sin(4*d*x + 4*c)^2 + 2*(8*a^3 + 113*a^2*b + 50*a*b^2 - 27*b^3)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*(a^2*b + 10*a*b^2 + 5*b^3)*sin(2*d*x + 2*c)^2 - ((a^2*b + 10*a*b^2 + 5*b^3)*cos(6*d*x + 6*c) + 2*(9*a^2*b + 10*a*b^2 - 3*b^3)*cos(4*d*x + 4*c) + (a^2*b + 10*a*b^2 + 5*b^3)*cos(2*d*x + 2*c))*cos(8*d*x + 8*c) - (a^2*b + 10*a*b^2 + 5*b^3 - 2*(8*a^3 + 113*a^2*b + 50*a*b^2 - 27*b^3)*cos(4*d*x + 4*c) - 8*(a^2*b + 10*a*b^2 + 5*b^3)*cos(2*d*x + 2*c))*cos(6*d*x + 6*c) - 2*(9*a^2*b + 10*a*b^2 - 3*b^3 - (8*a^3 + 113*a^2*b + 50*a*b^2 - 27*b^3)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - (a^2*b + 10*a*b^2 + 5*b^3)*cos(2*d*x + 2*c) - ((a^2*b + 10*a*b^2 + 5*b^3)*sin(6*d*x + 6*c) + 2*(9*a^2*b + 10*a*b^2 - 3*b^3)*sin(4*d*x + 4*c) + (a^2*b + 10*a*b^2 + 5*b^3)*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 2*((8*a^3 + 113*a^2*b + 50*a*b^2 - 27*b^3)*sin(4*d*x + 4*c) + 4*(a^2*b + 10*a*b^2 + 5*b^3)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))/(b^4*cos(8*d*x + 8*c)^2 + 16*b^4*cos(6*d*x + 6*c)^2 + 16*b^4*cos(2*d*x + 2*c)^2 + b^4*sin(8*d*x + 8*c)^2 + 16*b^4*sin(6*d*x + 6*c)^2 + 16*b^4*sin(2*d*x + 2*c)^2 - 8*b^4*cos(2*d*x + 2*c) + b^4 + 4*(64*a^2*b^2 - 48*a*b^3 + 9*b^4)*cos(4*d*x + 4*c)^2 + 4*(64*a^2*b^2 - 48*a*b^3 + 9*b^4)*sin(4*d*x + 4*c)^2 + 16*(8*a*b^3 - 3*b^4)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) - 2*(4*b^4*cos(6*d*x + 6*c) + 4*b^4*cos(2*d*x + 2*c) - b^4 + 2*(8*a*b^3 - 3*b^4)*cos(4*d*x + 4*c))*cos(8*d*x + 8*c) + 8*(4*b^4*cos(2*d*x + 2*c) - b^4 + 2*(8*a*b^3 - 3*b^4)*cos(4*d*x + 4*c))*cos(6*d*x + 6*c) - 4*(8*a*b^3 - 3*b^4 - 4*(8*a*b^3 - 3*b^4)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 4*(2*b^4*sin(6*d*x + 6*c) + 2*b^4*sin(2*d*x + 2*c) + (8*a*b^3 - 3*b^4)*sin(4*d*x + 4*c))*sin(8*d*x + 8*c) + 16*(2*b^4*sin(2*d*x + 2*c) + (8*a*b^3 - 3*b^4)*sin(4*d*x + 4*c))*sin(6*d*x + 6*c)), x) + 36*(24*a + 35*b)*d*x + b*sin(6*d*x + 6*c) + 21*b*sin(4*d*x + 4*c) + 3*(16*a + 95*b)*sin(2*d*x + 2*c))/(b^2*d)","F",0
412,0,0,0,0.000000," ","integrate(cos(d*x+c)^8/(a-b*sin(d*x+c)^4),x, algorithm=""maxima"")","-\frac{-512 \, b^{2} d \int \frac{4 \, {\left(a b^{2} + b^{3}\right)} \cos\left(6 \, d x + 6 \, c\right)^{2} + 2 \, {\left(8 \, a^{3} + 29 \, a^{2} b - 20 \, a b^{2} + 3 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a b^{2} + b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(a b^{2} + b^{3}\right)} \sin\left(6 \, d x + 6 \, c\right)^{2} + 2 \, {\left(8 \, a^{3} + 29 \, a^{2} b - 20 \, a b^{2} + 3 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, {\left(10 \, a^{2} b + 13 \, a b^{2} - 5 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, {\left(a b^{2} + b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - {\left({\left(a b^{2} + b^{3}\right)} \cos\left(6 \, d x + 6 \, c\right) + {\left(a^{2} b + 4 \, a b^{2} - b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right) + {\left(a b^{2} + b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) - {\left(a b^{2} + b^{3} - 2 \, {\left(10 \, a^{2} b + 13 \, a b^{2} - 5 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(a b^{2} + b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - {\left(a^{2} b + 4 \, a b^{2} - b^{3} - 2 \, {\left(10 \, a^{2} b + 13 \, a b^{2} - 5 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - {\left(a b^{2} + b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right) - {\left({\left(a b^{2} + b^{3}\right)} \sin\left(6 \, d x + 6 \, c\right) + {\left(a^{2} b + 4 \, a b^{2} - b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) + {\left(a b^{2} + b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 2 \, {\left({\left(10 \, a^{2} b + 13 \, a b^{2} - 5 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a b^{2} + b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}{b^{4} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, b^{4} \cos\left(6 \, d x + 6 \, c\right)^{2} + 16 \, b^{4} \cos\left(2 \, d x + 2 \, c\right)^{2} + b^{4} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, b^{4} \sin\left(6 \, d x + 6 \, c\right)^{2} + 16 \, b^{4} \sin\left(2 \, d x + 2 \, c\right)^{2} - 8 \, b^{4} \cos\left(2 \, d x + 2 \, c\right) + b^{4} + 4 \, {\left(64 \, a^{2} b^{2} - 48 \, a b^{3} + 9 \, b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(64 \, a^{2} b^{2} - 48 \, a b^{3} + 9 \, b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(8 \, a b^{3} - 3 \, b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 2 \, {\left(4 \, b^{4} \cos\left(6 \, d x + 6 \, c\right) + 4 \, b^{4} \cos\left(2 \, d x + 2 \, c\right) - b^{4} + 2 \, {\left(8 \, a b^{3} - 3 \, b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(4 \, b^{4} \cos\left(2 \, d x + 2 \, c\right) - b^{4} + 2 \, {\left(8 \, a b^{3} - 3 \, b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(8 \, a b^{3} - 3 \, b^{4} - 4 \, {\left(8 \, a b^{3} - 3 \, b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(2 \, b^{4} \sin\left(6 \, d x + 6 \, c\right) + 2 \, b^{4} \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a b^{3} - 3 \, b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(2 \, b^{4} \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a b^{3} - 3 \, b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}\,{d x} + 4 \, {\left(8 \, a + 35 \, b\right)} d x + b \sin\left(4 \, d x + 4 \, c\right) + 24 \, b \sin\left(2 \, d x + 2 \, c\right)}{32 \, b^{2} d}"," ",0,"-1/32*(32*b^2*d*integrate(-16*(4*(a*b^2 + b^3)*cos(6*d*x + 6*c)^2 + 2*(8*a^3 + 29*a^2*b - 20*a*b^2 + 3*b^3)*cos(4*d*x + 4*c)^2 + 4*(a*b^2 + b^3)*cos(2*d*x + 2*c)^2 + 4*(a*b^2 + b^3)*sin(6*d*x + 6*c)^2 + 2*(8*a^3 + 29*a^2*b - 20*a*b^2 + 3*b^3)*sin(4*d*x + 4*c)^2 + 2*(10*a^2*b + 13*a*b^2 - 5*b^3)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*(a*b^2 + b^3)*sin(2*d*x + 2*c)^2 - ((a*b^2 + b^3)*cos(6*d*x + 6*c) + (a^2*b + 4*a*b^2 - b^3)*cos(4*d*x + 4*c) + (a*b^2 + b^3)*cos(2*d*x + 2*c))*cos(8*d*x + 8*c) - (a*b^2 + b^3 - 2*(10*a^2*b + 13*a*b^2 - 5*b^3)*cos(4*d*x + 4*c) - 8*(a*b^2 + b^3)*cos(2*d*x + 2*c))*cos(6*d*x + 6*c) - (a^2*b + 4*a*b^2 - b^3 - 2*(10*a^2*b + 13*a*b^2 - 5*b^3)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - (a*b^2 + b^3)*cos(2*d*x + 2*c) - ((a*b^2 + b^3)*sin(6*d*x + 6*c) + (a^2*b + 4*a*b^2 - b^3)*sin(4*d*x + 4*c) + (a*b^2 + b^3)*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 2*((10*a^2*b + 13*a*b^2 - 5*b^3)*sin(4*d*x + 4*c) + 4*(a*b^2 + b^3)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))/(b^4*cos(8*d*x + 8*c)^2 + 16*b^4*cos(6*d*x + 6*c)^2 + 16*b^4*cos(2*d*x + 2*c)^2 + b^4*sin(8*d*x + 8*c)^2 + 16*b^4*sin(6*d*x + 6*c)^2 + 16*b^4*sin(2*d*x + 2*c)^2 - 8*b^4*cos(2*d*x + 2*c) + b^4 + 4*(64*a^2*b^2 - 48*a*b^3 + 9*b^4)*cos(4*d*x + 4*c)^2 + 4*(64*a^2*b^2 - 48*a*b^3 + 9*b^4)*sin(4*d*x + 4*c)^2 + 16*(8*a*b^3 - 3*b^4)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) - 2*(4*b^4*cos(6*d*x + 6*c) + 4*b^4*cos(2*d*x + 2*c) - b^4 + 2*(8*a*b^3 - 3*b^4)*cos(4*d*x + 4*c))*cos(8*d*x + 8*c) + 8*(4*b^4*cos(2*d*x + 2*c) - b^4 + 2*(8*a*b^3 - 3*b^4)*cos(4*d*x + 4*c))*cos(6*d*x + 6*c) - 4*(8*a*b^3 - 3*b^4 - 4*(8*a*b^3 - 3*b^4)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 4*(2*b^4*sin(6*d*x + 6*c) + 2*b^4*sin(2*d*x + 2*c) + (8*a*b^3 - 3*b^4)*sin(4*d*x + 4*c))*sin(8*d*x + 8*c) + 16*(2*b^4*sin(2*d*x + 2*c) + (8*a*b^3 - 3*b^4)*sin(4*d*x + 4*c))*sin(6*d*x + 6*c)), x) + 4*(8*a + 35*b)*d*x + b*sin(4*d*x + 4*c) + 24*b*sin(2*d*x + 2*c))/(b^2*d)","F",0
413,0,0,0,0.000000," ","integrate(cos(d*x+c)^6/(a-b*sin(d*x+c)^4),x, algorithm=""maxima"")","-\frac{-16 \, b d \int \frac{4 \, {\left(a b + 3 \, b^{2}\right)} \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(40 \, a^{2} - 23 \, a b + 3 \, b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a b + 3 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(a b + 3 \, b^{2}\right)} \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(40 \, a^{2} - 23 \, a b + 3 \, b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, {\left(8 \, a^{2} + 41 \, a b - 13 \, b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, {\left(a b + 3 \, b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - {\left({\left(a b + 3 \, b^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 2 \, {\left(5 \, a b - b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + {\left(a b + 3 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) - {\left(a b + 3 \, b^{2} - 2 \, {\left(8 \, a^{2} + 41 \, a b - 13 \, b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(a b + 3 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left(5 \, a b - b^{2} - {\left(8 \, a^{2} + 41 \, a b - 13 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - {\left(a b + 3 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) - {\left({\left(a b + 3 \, b^{2}\right)} \sin\left(6 \, d x + 6 \, c\right) + 2 \, {\left(5 \, a b - b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) + {\left(a b + 3 \, b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 2 \, {\left({\left(8 \, a^{2} + 41 \, a b - 13 \, b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a b + 3 \, b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}{b^{3} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, b^{3} \cos\left(6 \, d x + 6 \, c\right)^{2} + 16 \, b^{3} \cos\left(2 \, d x + 2 \, c\right)^{2} + b^{3} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, b^{3} \sin\left(6 \, d x + 6 \, c\right)^{2} + 16 \, b^{3} \sin\left(2 \, d x + 2 \, c\right)^{2} - 8 \, b^{3} \cos\left(2 \, d x + 2 \, c\right) + b^{3} + 4 \, {\left(64 \, a^{2} b - 48 \, a b^{2} + 9 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(64 \, a^{2} b - 48 \, a b^{2} + 9 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(8 \, a b^{2} - 3 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 2 \, {\left(4 \, b^{3} \cos\left(6 \, d x + 6 \, c\right) + 4 \, b^{3} \cos\left(2 \, d x + 2 \, c\right) - b^{3} + 2 \, {\left(8 \, a b^{2} - 3 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(4 \, b^{3} \cos\left(2 \, d x + 2 \, c\right) - b^{3} + 2 \, {\left(8 \, a b^{2} - 3 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(8 \, a b^{2} - 3 \, b^{3} - 4 \, {\left(8 \, a b^{2} - 3 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(2 \, b^{3} \sin\left(6 \, d x + 6 \, c\right) + 2 \, b^{3} \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a b^{2} - 3 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(2 \, b^{3} \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a b^{2} - 3 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}\,{d x} + 10 \, d x + \sin\left(2 \, d x + 2 \, c\right)}{4 \, b d}"," ",0,"-1/4*(4*b*d*integrate(-4*(4*(a*b + 3*b^2)*cos(6*d*x + 6*c)^2 + 4*(40*a^2 - 23*a*b + 3*b^2)*cos(4*d*x + 4*c)^2 + 4*(a*b + 3*b^2)*cos(2*d*x + 2*c)^2 + 4*(a*b + 3*b^2)*sin(6*d*x + 6*c)^2 + 4*(40*a^2 - 23*a*b + 3*b^2)*sin(4*d*x + 4*c)^2 + 2*(8*a^2 + 41*a*b - 13*b^2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*(a*b + 3*b^2)*sin(2*d*x + 2*c)^2 - ((a*b + 3*b^2)*cos(6*d*x + 6*c) + 2*(5*a*b - b^2)*cos(4*d*x + 4*c) + (a*b + 3*b^2)*cos(2*d*x + 2*c))*cos(8*d*x + 8*c) - (a*b + 3*b^2 - 2*(8*a^2 + 41*a*b - 13*b^2)*cos(4*d*x + 4*c) - 8*(a*b + 3*b^2)*cos(2*d*x + 2*c))*cos(6*d*x + 6*c) - 2*(5*a*b - b^2 - (8*a^2 + 41*a*b - 13*b^2)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - (a*b + 3*b^2)*cos(2*d*x + 2*c) - ((a*b + 3*b^2)*sin(6*d*x + 6*c) + 2*(5*a*b - b^2)*sin(4*d*x + 4*c) + (a*b + 3*b^2)*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 2*((8*a^2 + 41*a*b - 13*b^2)*sin(4*d*x + 4*c) + 4*(a*b + 3*b^2)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))/(b^3*cos(8*d*x + 8*c)^2 + 16*b^3*cos(6*d*x + 6*c)^2 + 16*b^3*cos(2*d*x + 2*c)^2 + b^3*sin(8*d*x + 8*c)^2 + 16*b^3*sin(6*d*x + 6*c)^2 + 16*b^3*sin(2*d*x + 2*c)^2 - 8*b^3*cos(2*d*x + 2*c) + b^3 + 4*(64*a^2*b - 48*a*b^2 + 9*b^3)*cos(4*d*x + 4*c)^2 + 4*(64*a^2*b - 48*a*b^2 + 9*b^3)*sin(4*d*x + 4*c)^2 + 16*(8*a*b^2 - 3*b^3)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) - 2*(4*b^3*cos(6*d*x + 6*c) + 4*b^3*cos(2*d*x + 2*c) - b^3 + 2*(8*a*b^2 - 3*b^3)*cos(4*d*x + 4*c))*cos(8*d*x + 8*c) + 8*(4*b^3*cos(2*d*x + 2*c) - b^3 + 2*(8*a*b^2 - 3*b^3)*cos(4*d*x + 4*c))*cos(6*d*x + 6*c) - 4*(8*a*b^2 - 3*b^3 - 4*(8*a*b^2 - 3*b^3)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 4*(2*b^3*sin(6*d*x + 6*c) + 2*b^3*sin(2*d*x + 2*c) + (8*a*b^2 - 3*b^3)*sin(4*d*x + 4*c))*sin(8*d*x + 8*c) + 16*(2*b^3*sin(2*d*x + 2*c) + (8*a*b^2 - 3*b^3)*sin(4*d*x + 4*c))*sin(6*d*x + 6*c)), x) + 10*d*x + sin(2*d*x + 2*c))/(b*d)","F",0
414,0,0,0,0.000000," ","integrate(cos(d*x+c)^4/(a-b*sin(d*x+c)^4),x, algorithm=""maxima"")","-\frac{-8 \, b \int \frac{4 \, b^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, b^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, b^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(8 \, a^{2} - 3 \, a b\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} - b^{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(8 \, a^{2} - 3 \, a b\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 6 \, {\left(4 \, a b - b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - {\left(b^{2} \cos\left(6 \, d x + 6 \, c\right) + 2 \, a b \cos\left(4 \, d x + 4 \, c\right) + b^{2} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) + {\left(8 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) - b^{2} + 6 \, {\left(4 \, a b - b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left(a b - 3 \, {\left(4 \, a b - b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - {\left(b^{2} \sin\left(6 \, d x + 6 \, c\right) + 2 \, a b \sin\left(4 \, d x + 4 \, c\right) + b^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 2 \, {\left(4 \, b^{2} \sin\left(2 \, d x + 2 \, c\right) + 3 \, {\left(4 \, a b - b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}{b^{3} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, b^{3} \cos\left(6 \, d x + 6 \, c\right)^{2} + 16 \, b^{3} \cos\left(2 \, d x + 2 \, c\right)^{2} + b^{3} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, b^{3} \sin\left(6 \, d x + 6 \, c\right)^{2} + 16 \, b^{3} \sin\left(2 \, d x + 2 \, c\right)^{2} - 8 \, b^{3} \cos\left(2 \, d x + 2 \, c\right) + b^{3} + 4 \, {\left(64 \, a^{2} b - 48 \, a b^{2} + 9 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(64 \, a^{2} b - 48 \, a b^{2} + 9 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(8 \, a b^{2} - 3 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 2 \, {\left(4 \, b^{3} \cos\left(6 \, d x + 6 \, c\right) + 4 \, b^{3} \cos\left(2 \, d x + 2 \, c\right) - b^{3} + 2 \, {\left(8 \, a b^{2} - 3 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(4 \, b^{3} \cos\left(2 \, d x + 2 \, c\right) - b^{3} + 2 \, {\left(8 \, a b^{2} - 3 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(8 \, a b^{2} - 3 \, b^{3} - 4 \, {\left(8 \, a b^{2} - 3 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(2 \, b^{3} \sin\left(6 \, d x + 6 \, c\right) + 2 \, b^{3} \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a b^{2} - 3 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(2 \, b^{3} \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a b^{2} - 3 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}\,{d x} + x}{b}"," ",0,"-(b*integrate(-8*(4*b^2*cos(6*d*x + 6*c)^2 + 4*b^2*cos(2*d*x + 2*c)^2 + 4*b^2*sin(6*d*x + 6*c)^2 + 4*b^2*sin(2*d*x + 2*c)^2 + 4*(8*a^2 - 3*a*b)*cos(4*d*x + 4*c)^2 - b^2*cos(2*d*x + 2*c) + 4*(8*a^2 - 3*a*b)*sin(4*d*x + 4*c)^2 + 6*(4*a*b - b^2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) - (b^2*cos(6*d*x + 6*c) + 2*a*b*cos(4*d*x + 4*c) + b^2*cos(2*d*x + 2*c))*cos(8*d*x + 8*c) + (8*b^2*cos(2*d*x + 2*c) - b^2 + 6*(4*a*b - b^2)*cos(4*d*x + 4*c))*cos(6*d*x + 6*c) - 2*(a*b - 3*(4*a*b - b^2)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - (b^2*sin(6*d*x + 6*c) + 2*a*b*sin(4*d*x + 4*c) + b^2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 2*(4*b^2*sin(2*d*x + 2*c) + 3*(4*a*b - b^2)*sin(4*d*x + 4*c))*sin(6*d*x + 6*c))/(b^3*cos(8*d*x + 8*c)^2 + 16*b^3*cos(6*d*x + 6*c)^2 + 16*b^3*cos(2*d*x + 2*c)^2 + b^3*sin(8*d*x + 8*c)^2 + 16*b^3*sin(6*d*x + 6*c)^2 + 16*b^3*sin(2*d*x + 2*c)^2 - 8*b^3*cos(2*d*x + 2*c) + b^3 + 4*(64*a^2*b - 48*a*b^2 + 9*b^3)*cos(4*d*x + 4*c)^2 + 4*(64*a^2*b - 48*a*b^2 + 9*b^3)*sin(4*d*x + 4*c)^2 + 16*(8*a*b^2 - 3*b^3)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) - 2*(4*b^3*cos(6*d*x + 6*c) + 4*b^3*cos(2*d*x + 2*c) - b^3 + 2*(8*a*b^2 - 3*b^3)*cos(4*d*x + 4*c))*cos(8*d*x + 8*c) + 8*(4*b^3*cos(2*d*x + 2*c) - b^3 + 2*(8*a*b^2 - 3*b^3)*cos(4*d*x + 4*c))*cos(6*d*x + 6*c) - 4*(8*a*b^2 - 3*b^3 - 4*(8*a*b^2 - 3*b^3)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 4*(2*b^3*sin(6*d*x + 6*c) + 2*b^3*sin(2*d*x + 2*c) + (8*a*b^2 - 3*b^3)*sin(4*d*x + 4*c))*sin(8*d*x + 8*c) + 16*(2*b^3*sin(2*d*x + 2*c) + (8*a*b^2 - 3*b^3)*sin(4*d*x + 4*c))*sin(6*d*x + 6*c)), x) + x)/b","F",0
415,0,0,0,0.000000," ","integrate(cos(d*x+c)^2/(a-b*sin(d*x+c)^4),x, algorithm=""maxima"")","-\int \frac{\cos\left(d x + c\right)^{2}}{b \sin\left(d x + c\right)^{4} - a}\,{d x}"," ",0,"-integrate(cos(d*x + c)^2/(b*sin(d*x + c)^4 - a), x)","F",0
416,0,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a-b*sin(d*x+c)^4),x, algorithm=""maxima"")","\frac{4 \, {\left({\left(a - b\right)} d \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a - b\right)} d \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a - b\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a - b\right)} d\right)} \int \frac{4 \, b^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, b^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, b^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} - 12 \, {\left(8 \, a b - 3 \, b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} - b^{2} \cos\left(2 \, d x + 2 \, c\right) - 12 \, {\left(8 \, a b - 3 \, b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, {\left(8 \, a b - 15 \, b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - {\left(b^{2} \cos\left(6 \, d x + 6 \, c\right) - 6 \, b^{2} \cos\left(4 \, d x + 4 \, c\right) + b^{2} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) + {\left(8 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) - b^{2} + 2 \, {\left(8 \, a b - 15 \, b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) + 2 \, {\left(3 \, b^{2} + {\left(8 \, a b - 15 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - {\left(b^{2} \sin\left(6 \, d x + 6 \, c\right) - 6 \, b^{2} \sin\left(4 \, d x + 4 \, c\right) + b^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 2 \, {\left(4 \, b^{2} \sin\left(2 \, d x + 2 \, c\right) + {\left(8 \, a b - 15 \, b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}{a b^{2} - b^{3} + {\left(a b^{2} - b^{3}\right)} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a b^{2} - b^{3}\right)} \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{3} - 112 \, a^{2} b + 57 \, a b^{2} - 9 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(a b^{2} - b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a b^{2} - b^{3}\right)} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a b^{2} - b^{3}\right)} \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{3} - 112 \, a^{2} b + 57 \, a b^{2} - 9 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, {\left(a b^{2} - b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a b^{2} - b^{3} - 4 \, {\left(a b^{2} - b^{3}\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a b^{2} - b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) - 8 \, {\left(a b^{2} - b^{3} - 2 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a b^{2} - b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3} - 4 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(a b^{2} - b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right) - 4 \, {\left(2 \, {\left(a b^{2} - b^{3}\right)} \sin\left(6 \, d x + 6 \, c\right) + {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a b^{2} - b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left({\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a b^{2} - b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}\,{d x} + 2 \, \sin\left(2 \, d x + 2 \, c\right)}{{\left(a - b\right)} d \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a - b\right)} d \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a - b\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a - b\right)} d}"," ",0,"(((a - b)*d*cos(2*d*x + 2*c)^2 + (a - b)*d*sin(2*d*x + 2*c)^2 + 2*(a - b)*d*cos(2*d*x + 2*c) + (a - b)*d)*integrate(4*(4*b^2*cos(6*d*x + 6*c)^2 + 4*b^2*cos(2*d*x + 2*c)^2 + 4*b^2*sin(6*d*x + 6*c)^2 + 4*b^2*sin(2*d*x + 2*c)^2 - 12*(8*a*b - 3*b^2)*cos(4*d*x + 4*c)^2 - b^2*cos(2*d*x + 2*c) - 12*(8*a*b - 3*b^2)*sin(4*d*x + 4*c)^2 + 2*(8*a*b - 15*b^2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) - (b^2*cos(6*d*x + 6*c) - 6*b^2*cos(4*d*x + 4*c) + b^2*cos(2*d*x + 2*c))*cos(8*d*x + 8*c) + (8*b^2*cos(2*d*x + 2*c) - b^2 + 2*(8*a*b - 15*b^2)*cos(4*d*x + 4*c))*cos(6*d*x + 6*c) + 2*(3*b^2 + (8*a*b - 15*b^2)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - (b^2*sin(6*d*x + 6*c) - 6*b^2*sin(4*d*x + 4*c) + b^2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 2*(4*b^2*sin(2*d*x + 2*c) + (8*a*b - 15*b^2)*sin(4*d*x + 4*c))*sin(6*d*x + 6*c))/(a*b^2 - b^3 + (a*b^2 - b^3)*cos(8*d*x + 8*c)^2 + 16*(a*b^2 - b^3)*cos(6*d*x + 6*c)^2 + 4*(64*a^3 - 112*a^2*b + 57*a*b^2 - 9*b^3)*cos(4*d*x + 4*c)^2 + 16*(a*b^2 - b^3)*cos(2*d*x + 2*c)^2 + (a*b^2 - b^3)*sin(8*d*x + 8*c)^2 + 16*(a*b^2 - b^3)*sin(6*d*x + 6*c)^2 + 4*(64*a^3 - 112*a^2*b + 57*a*b^2 - 9*b^3)*sin(4*d*x + 4*c)^2 + 16*(8*a^2*b - 11*a*b^2 + 3*b^3)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*(a*b^2 - b^3)*sin(2*d*x + 2*c)^2 + 2*(a*b^2 - b^3 - 4*(a*b^2 - b^3)*cos(6*d*x + 6*c) - 2*(8*a^2*b - 11*a*b^2 + 3*b^3)*cos(4*d*x + 4*c) - 4*(a*b^2 - b^3)*cos(2*d*x + 2*c))*cos(8*d*x + 8*c) - 8*(a*b^2 - b^3 - 2*(8*a^2*b - 11*a*b^2 + 3*b^3)*cos(4*d*x + 4*c) - 4*(a*b^2 - b^3)*cos(2*d*x + 2*c))*cos(6*d*x + 6*c) - 4*(8*a^2*b - 11*a*b^2 + 3*b^3 - 4*(8*a^2*b - 11*a*b^2 + 3*b^3)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 8*(a*b^2 - b^3)*cos(2*d*x + 2*c) - 4*(2*(a*b^2 - b^3)*sin(6*d*x + 6*c) + (8*a^2*b - 11*a*b^2 + 3*b^3)*sin(4*d*x + 4*c) + 2*(a*b^2 - b^3)*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*((8*a^2*b - 11*a*b^2 + 3*b^3)*sin(4*d*x + 4*c) + 2*(a*b^2 - b^3)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c)), x) + 2*sin(2*d*x + 2*c))/((a - b)*d*cos(2*d*x + 2*c)^2 + (a - b)*d*sin(2*d*x + 2*c)^2 + 2*(a - b)*d*cos(2*d*x + 2*c) + (a - b)*d)","F",0
417,0,0,0,0.000000," ","integrate(sec(d*x+c)^4/(a-b*sin(d*x+c)^4),x, algorithm=""maxima"")","-\frac{36 \, {\left(a - 2 \, b\right)} \cos\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 12 \, {\left(b \sin\left(4 \, d x + 4 \, c\right) - {\left(a - 3 \, b\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) + 24 \, {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} d \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{2} - 2 \, a b + b^{2}\right)} d \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{2} - 2 \, a b + b^{2}\right)} d + 2 \, {\left(3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{2} - 2 \, a b + b^{2}\right)} d\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{2} - 2 \, a b + b^{2}\right)} d\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} d \sin\left(4 \, d x + 4 \, c\right) + {\left(a^{2} - 2 \, a b + b^{2}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \int \frac{4 \, b^{3} \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, b^{3} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, b^{3} \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, b^{3} \sin\left(2 \, d x + 2 \, c\right)^{2} - b^{3} \cos\left(2 \, d x + 2 \, c\right) - 4 \, {\left(8 \, a^{2} b + 13 \, a b^{2} - 6 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} - 4 \, {\left(8 \, a^{2} b + 13 \, a b^{2} - 6 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, {\left(4 \, a b^{2} - 11 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - {\left(b^{3} \cos\left(6 \, d x + 6 \, c\right) + b^{3} \cos\left(2 \, d x + 2 \, c\right) - 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) + {\left(8 \, b^{3} \cos\left(2 \, d x + 2 \, c\right) - b^{3} + 2 \, {\left(4 \, a b^{2} - 11 \, b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) + 2 \, {\left(a b^{2} + 2 \, b^{3} + {\left(4 \, a b^{2} - 11 \, b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - {\left(b^{3} \sin\left(6 \, d x + 6 \, c\right) + b^{3} \sin\left(2 \, d x + 2 \, c\right) - 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 2 \, {\left(4 \, b^{3} \sin\left(2 \, d x + 2 \, c\right) + {\left(4 \, a b^{2} - 11 \, b^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}{a^{2} b^{2} - 2 \, a b^{3} + b^{4} + {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{4} - 176 \, a^{3} b + 169 \, a^{2} b^{2} - 66 \, a b^{3} + 9 \, b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{4} - 176 \, a^{3} b + 169 \, a^{2} b^{2} - 66 \, a b^{3} + 9 \, b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(8 \, a^{3} b - 19 \, a^{2} b^{2} + 14 \, a b^{3} - 3 \, b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4} - 4 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left(8 \, a^{3} b - 19 \, a^{2} b^{2} + 14 \, a b^{3} - 3 \, b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) - 8 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4} - 2 \, {\left(8 \, a^{3} b - 19 \, a^{2} b^{2} + 14 \, a b^{3} - 3 \, b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(8 \, a^{3} b - 19 \, a^{2} b^{2} + 14 \, a b^{3} - 3 \, b^{4} - 4 \, {\left(8 \, a^{3} b - 19 \, a^{2} b^{2} + 14 \, a b^{3} - 3 \, b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right) - 4 \, {\left(2 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \sin\left(6 \, d x + 6 \, c\right) + {\left(8 \, a^{3} b - 19 \, a^{2} b^{2} + 14 \, a b^{3} - 3 \, b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left({\left(8 \, a^{3} b - 19 \, a^{2} b^{2} + 14 \, a b^{3} - 3 \, b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}\,{d x} + 4 \, {\left(3 \, b \cos\left(4 \, d x + 4 \, c\right) - 3 \, {\left(a - 3 \, b\right)} \cos\left(2 \, d x + 2 \, c\right) - a + 4 \, b\right)} \sin\left(6 \, d x + 6 \, c\right) - 12 \, {\left(3 \, {\left(a - 2 \, b\right)} \cos\left(2 \, d x + 2 \, c\right) + a - 3 \, b\right)} \sin\left(4 \, d x + 4 \, c\right) + 12 \, b \sin\left(2 \, d x + 2 \, c\right)}{3 \, {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} d \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{2} - 2 \, a b + b^{2}\right)} d \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{2} - 2 \, a b + b^{2}\right)} d + 2 \, {\left(3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{2} - 2 \, a b + b^{2}\right)} d\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{2} - 2 \, a b + b^{2}\right)} d\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} d \sin\left(4 \, d x + 4 \, c\right) + {\left(a^{2} - 2 \, a b + b^{2}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)}}"," ",0,"-1/3*(36*(a - 2*b)*cos(4*d*x + 4*c)*sin(2*d*x + 2*c) - 12*(b*sin(4*d*x + 4*c) - (a - 3*b)*sin(2*d*x + 2*c))*cos(6*d*x + 6*c) - 3*((a^2 - 2*a*b + b^2)*d*cos(6*d*x + 6*c)^2 + 9*(a^2 - 2*a*b + b^2)*d*cos(4*d*x + 4*c)^2 + 9*(a^2 - 2*a*b + b^2)*d*cos(2*d*x + 2*c)^2 + (a^2 - 2*a*b + b^2)*d*sin(6*d*x + 6*c)^2 + 9*(a^2 - 2*a*b + b^2)*d*sin(4*d*x + 4*c)^2 + 18*(a^2 - 2*a*b + b^2)*d*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*(a^2 - 2*a*b + b^2)*d*sin(2*d*x + 2*c)^2 + 6*(a^2 - 2*a*b + b^2)*d*cos(2*d*x + 2*c) + (a^2 - 2*a*b + b^2)*d + 2*(3*(a^2 - 2*a*b + b^2)*d*cos(4*d*x + 4*c) + 3*(a^2 - 2*a*b + b^2)*d*cos(2*d*x + 2*c) + (a^2 - 2*a*b + b^2)*d)*cos(6*d*x + 6*c) + 6*(3*(a^2 - 2*a*b + b^2)*d*cos(2*d*x + 2*c) + (a^2 - 2*a*b + b^2)*d)*cos(4*d*x + 4*c) + 6*((a^2 - 2*a*b + b^2)*d*sin(4*d*x + 4*c) + (a^2 - 2*a*b + b^2)*d*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*integrate(-8*(4*b^3*cos(6*d*x + 6*c)^2 + 4*b^3*cos(2*d*x + 2*c)^2 + 4*b^3*sin(6*d*x + 6*c)^2 + 4*b^3*sin(2*d*x + 2*c)^2 - b^3*cos(2*d*x + 2*c) - 4*(8*a^2*b + 13*a*b^2 - 6*b^3)*cos(4*d*x + 4*c)^2 - 4*(8*a^2*b + 13*a*b^2 - 6*b^3)*sin(4*d*x + 4*c)^2 + 2*(4*a*b^2 - 11*b^3)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) - (b^3*cos(6*d*x + 6*c) + b^3*cos(2*d*x + 2*c) - 2*(a*b^2 + 2*b^3)*cos(4*d*x + 4*c))*cos(8*d*x + 8*c) + (8*b^3*cos(2*d*x + 2*c) - b^3 + 2*(4*a*b^2 - 11*b^3)*cos(4*d*x + 4*c))*cos(6*d*x + 6*c) + 2*(a*b^2 + 2*b^3 + (4*a*b^2 - 11*b^3)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - (b^3*sin(6*d*x + 6*c) + b^3*sin(2*d*x + 2*c) - 2*(a*b^2 + 2*b^3)*sin(4*d*x + 4*c))*sin(8*d*x + 8*c) + 2*(4*b^3*sin(2*d*x + 2*c) + (4*a*b^2 - 11*b^3)*sin(4*d*x + 4*c))*sin(6*d*x + 6*c))/(a^2*b^2 - 2*a*b^3 + b^4 + (a^2*b^2 - 2*a*b^3 + b^4)*cos(8*d*x + 8*c)^2 + 16*(a^2*b^2 - 2*a*b^3 + b^4)*cos(6*d*x + 6*c)^2 + 4*(64*a^4 - 176*a^3*b + 169*a^2*b^2 - 66*a*b^3 + 9*b^4)*cos(4*d*x + 4*c)^2 + 16*(a^2*b^2 - 2*a*b^3 + b^4)*cos(2*d*x + 2*c)^2 + (a^2*b^2 - 2*a*b^3 + b^4)*sin(8*d*x + 8*c)^2 + 16*(a^2*b^2 - 2*a*b^3 + b^4)*sin(6*d*x + 6*c)^2 + 4*(64*a^4 - 176*a^3*b + 169*a^2*b^2 - 66*a*b^3 + 9*b^4)*sin(4*d*x + 4*c)^2 + 16*(8*a^3*b - 19*a^2*b^2 + 14*a*b^3 - 3*b^4)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*(a^2*b^2 - 2*a*b^3 + b^4)*sin(2*d*x + 2*c)^2 + 2*(a^2*b^2 - 2*a*b^3 + b^4 - 4*(a^2*b^2 - 2*a*b^3 + b^4)*cos(6*d*x + 6*c) - 2*(8*a^3*b - 19*a^2*b^2 + 14*a*b^3 - 3*b^4)*cos(4*d*x + 4*c) - 4*(a^2*b^2 - 2*a*b^3 + b^4)*cos(2*d*x + 2*c))*cos(8*d*x + 8*c) - 8*(a^2*b^2 - 2*a*b^3 + b^4 - 2*(8*a^3*b - 19*a^2*b^2 + 14*a*b^3 - 3*b^4)*cos(4*d*x + 4*c) - 4*(a^2*b^2 - 2*a*b^3 + b^4)*cos(2*d*x + 2*c))*cos(6*d*x + 6*c) - 4*(8*a^3*b - 19*a^2*b^2 + 14*a*b^3 - 3*b^4 - 4*(8*a^3*b - 19*a^2*b^2 + 14*a*b^3 - 3*b^4)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 8*(a^2*b^2 - 2*a*b^3 + b^4)*cos(2*d*x + 2*c) - 4*(2*(a^2*b^2 - 2*a*b^3 + b^4)*sin(6*d*x + 6*c) + (8*a^3*b - 19*a^2*b^2 + 14*a*b^3 - 3*b^4)*sin(4*d*x + 4*c) + 2*(a^2*b^2 - 2*a*b^3 + b^4)*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*((8*a^3*b - 19*a^2*b^2 + 14*a*b^3 - 3*b^4)*sin(4*d*x + 4*c) + 2*(a^2*b^2 - 2*a*b^3 + b^4)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c)), x) + 4*(3*b*cos(4*d*x + 4*c) - 3*(a - 3*b)*cos(2*d*x + 2*c) - a + 4*b)*sin(6*d*x + 6*c) - 12*(3*(a - 2*b)*cos(2*d*x + 2*c) + a - 3*b)*sin(4*d*x + 4*c) + 12*b*sin(2*d*x + 2*c))/((a^2 - 2*a*b + b^2)*d*cos(6*d*x + 6*c)^2 + 9*(a^2 - 2*a*b + b^2)*d*cos(4*d*x + 4*c)^2 + 9*(a^2 - 2*a*b + b^2)*d*cos(2*d*x + 2*c)^2 + (a^2 - 2*a*b + b^2)*d*sin(6*d*x + 6*c)^2 + 9*(a^2 - 2*a*b + b^2)*d*sin(4*d*x + 4*c)^2 + 18*(a^2 - 2*a*b + b^2)*d*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*(a^2 - 2*a*b + b^2)*d*sin(2*d*x + 2*c)^2 + 6*(a^2 - 2*a*b + b^2)*d*cos(2*d*x + 2*c) + (a^2 - 2*a*b + b^2)*d + 2*(3*(a^2 - 2*a*b + b^2)*d*cos(4*d*x + 4*c) + 3*(a^2 - 2*a*b + b^2)*d*cos(2*d*x + 2*c) + (a^2 - 2*a*b + b^2)*d)*cos(6*d*x + 6*c) + 6*(3*(a^2 - 2*a*b + b^2)*d*cos(2*d*x + 2*c) + (a^2 - 2*a*b + b^2)*d)*cos(4*d*x + 4*c) + 6*((a^2 - 2*a*b + b^2)*d*sin(4*d*x + 4*c) + (a^2 - 2*a*b + b^2)*d*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))","F",0
418,0,0,0,0.000000," ","integrate(sec(d*x+c)^6/(a-b*sin(d*x+c)^4),x, algorithm=""maxima"")","\frac{300 \, {\left(a b - 5 \, b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 10 \, {\left(48 \, b^{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, {\left(a b + 3 \, b^{2}\right)} \sin\left(8 \, d x + 8 \, c\right) + 2 \, {\left(8 \, a^{2} - 21 \, a b + 49 \, b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) + 8 \, {\left(a^{2} - 3 \, a b + 8 \, b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(10 \, d x + 10 \, c\right) + 50 \, {\left(6 \, {\left(a b - 5 \, b^{2}\right)} \sin\left(6 \, d x + 6 \, c\right) - 16 \, {\left(a^{2} - 3 \, a b + 5 \, b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) - {\left(8 \, a^{2} - 27 \, a b + 55 \, b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) - 200 \, {\left({\left(8 \, a^{2} - 21 \, a b + 25 \, b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a^{2} - 3 \, a b + 5 \, b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) + 60 \, {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cos\left(10 \, d x + 10 \, c\right)^{2} + 25 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cos\left(8 \, d x + 8 \, c\right)^{2} + 100 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cos\left(6 \, d x + 6 \, c\right)^{2} + 100 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cos\left(4 \, d x + 4 \, c\right)^{2} + 25 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \sin\left(10 \, d x + 10 \, c\right)^{2} + 25 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \sin\left(8 \, d x + 8 \, c\right)^{2} + 100 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \sin\left(6 \, d x + 6 \, c\right)^{2} + 100 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \sin\left(4 \, d x + 4 \, c\right)^{2} + 100 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 25 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \sin\left(2 \, d x + 2 \, c\right)^{2} + 10 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d + 2 \, {\left(5 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cos\left(8 \, d x + 8 \, c\right) + 10 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cos\left(6 \, d x + 6 \, c\right) + 10 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 5 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d\right)} \cos\left(10 \, d x + 10 \, c\right) + 10 \, {\left(10 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cos\left(6 \, d x + 6 \, c\right) + 10 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 5 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d\right)} \cos\left(8 \, d x + 8 \, c\right) + 20 \, {\left(10 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 5 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d\right)} \cos\left(6 \, d x + 6 \, c\right) + 20 \, {\left(5 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d\right)} \cos\left(4 \, d x + 4 \, c\right) + 10 \, {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \sin\left(8 \, d x + 8 \, c\right) + 2 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \sin\left(6 \, d x + 6 \, c\right) + 2 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \sin\left(4 \, d x + 4 \, c\right) + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + 50 \, {\left(2 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \sin\left(6 \, d x + 6 \, c\right) + 2 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \sin\left(4 \, d x + 4 \, c\right) + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 100 \, {\left(2 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \sin\left(4 \, d x + 4 \, c\right) + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \int \frac{4 \, {\left(a b^{3} + 3 \, b^{4}\right)} \cos\left(6 \, d x + 6 \, c\right)^{2} - 4 \, {\left(56 \, a^{2} b^{2} + 19 \, a b^{3} - 15 \, b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a b^{3} + 3 \, b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(a b^{3} + 3 \, b^{4}\right)} \sin\left(6 \, d x + 6 \, c\right)^{2} - 4 \, {\left(56 \, a^{2} b^{2} + 19 \, a b^{3} - 15 \, b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, {\left(8 \, a^{2} b^{2} - 7 \, a b^{3} - 29 \, b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, {\left(a b^{3} + 3 \, b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - {\left({\left(a b^{3} + 3 \, b^{4}\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left(7 \, a b^{3} + 5 \, b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right) + {\left(a b^{3} + 3 \, b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) - {\left(a b^{3} + 3 \, b^{4} - 2 \, {\left(8 \, a^{2} b^{2} - 7 \, a b^{3} - 29 \, b^{4}\right)} \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(a b^{3} + 3 \, b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) + 2 \, {\left(7 \, a b^{3} + 5 \, b^{4} + {\left(8 \, a^{2} b^{2} - 7 \, a b^{3} - 29 \, b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - {\left(a b^{3} + 3 \, b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right) - {\left({\left(a b^{3} + 3 \, b^{4}\right)} \sin\left(6 \, d x + 6 \, c\right) - 2 \, {\left(7 \, a b^{3} + 5 \, b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right) + {\left(a b^{3} + 3 \, b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 2 \, {\left({\left(8 \, a^{2} b^{2} - 7 \, a b^{3} - 29 \, b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a b^{3} + 3 \, b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}{a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5} + {\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5}\right)} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5}\right)} \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{5} - 240 \, a^{4} b + 345 \, a^{3} b^{2} - 235 \, a^{2} b^{3} + 75 \, a b^{4} - 9 \, b^{5}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5}\right)} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5}\right)} \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, {\left(64 \, a^{5} - 240 \, a^{4} b + 345 \, a^{3} b^{2} - 235 \, a^{2} b^{3} + 75 \, a b^{4} - 9 \, b^{5}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(8 \, a^{4} b - 27 \, a^{3} b^{2} + 33 \, a^{2} b^{3} - 17 \, a b^{4} + 3 \, b^{5}\right)} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, {\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5} - 4 \, {\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5}\right)} \cos\left(6 \, d x + 6 \, c\right) - 2 \, {\left(8 \, a^{4} b - 27 \, a^{3} b^{2} + 33 \, a^{2} b^{3} - 17 \, a b^{4} + 3 \, b^{5}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) - 8 \, {\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5} - 2 \, {\left(8 \, a^{4} b - 27 \, a^{3} b^{2} + 33 \, a^{2} b^{3} - 17 \, a b^{4} + 3 \, b^{5}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 4 \, {\left(8 \, a^{4} b - 27 \, a^{3} b^{2} + 33 \, a^{2} b^{3} - 17 \, a b^{4} + 3 \, b^{5} - 4 \, {\left(8 \, a^{4} b - 27 \, a^{3} b^{2} + 33 \, a^{2} b^{3} - 17 \, a b^{4} + 3 \, b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right) - 4 \, {\left(2 \, {\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5}\right)} \sin\left(6 \, d x + 6 \, c\right) + {\left(8 \, a^{4} b - 27 \, a^{3} b^{2} + 33 \, a^{2} b^{3} - 17 \, a b^{4} + 3 \, b^{5}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left({\left(8 \, a^{4} b - 27 \, a^{3} b^{2} + 33 \, a^{2} b^{3} - 17 \, a b^{4} + 3 \, b^{5}\right)} \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)}\,{d x} + 2 \, {\left(240 \, b^{2} \cos\left(6 \, d x + 6 \, c\right) + 8 \, a^{2} - 21 \, a b + 73 \, b^{2} + 15 \, {\left(a b + 3 \, b^{2}\right)} \cos\left(8 \, d x + 8 \, c\right) + 10 \, {\left(8 \, a^{2} - 21 \, a b + 49 \, b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 40 \, {\left(a^{2} - 3 \, a b + 8 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + 10 \, {\left(8 \, a^{2} - 24 \, a b + 64 \, b^{2} - 30 \, {\left(a b - 5 \, b^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 80 \, {\left(a^{2} - 3 \, a b + 5 \, b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 5 \, {\left(8 \, a^{2} - 27 \, a b + 55 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 20 \, {\left(8 \, a^{2} - 21 \, a b + 49 \, b^{2} + 10 \, {\left(8 \, a^{2} - 21 \, a b + 25 \, b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 40 \, {\left(a^{2} - 3 \, a b + 5 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 60 \, {\left(8 \, b^{2} - 5 \, {\left(a b - 5 \, b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) + 30 \, {\left(a b + 3 \, b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)}{15 \, {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cos\left(10 \, d x + 10 \, c\right)^{2} + 25 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cos\left(8 \, d x + 8 \, c\right)^{2} + 100 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cos\left(6 \, d x + 6 \, c\right)^{2} + 100 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cos\left(4 \, d x + 4 \, c\right)^{2} + 25 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \sin\left(10 \, d x + 10 \, c\right)^{2} + 25 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \sin\left(8 \, d x + 8 \, c\right)^{2} + 100 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \sin\left(6 \, d x + 6 \, c\right)^{2} + 100 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \sin\left(4 \, d x + 4 \, c\right)^{2} + 100 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 25 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \sin\left(2 \, d x + 2 \, c\right)^{2} + 10 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d + 2 \, {\left(5 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cos\left(8 \, d x + 8 \, c\right) + 10 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cos\left(6 \, d x + 6 \, c\right) + 10 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 5 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d\right)} \cos\left(10 \, d x + 10 \, c\right) + 10 \, {\left(10 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cos\left(6 \, d x + 6 \, c\right) + 10 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 5 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d\right)} \cos\left(8 \, d x + 8 \, c\right) + 20 \, {\left(10 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cos\left(4 \, d x + 4 \, c\right) + 5 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d\right)} \cos\left(6 \, d x + 6 \, c\right) + 20 \, {\left(5 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d\right)} \cos\left(4 \, d x + 4 \, c\right) + 10 \, {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \sin\left(8 \, d x + 8 \, c\right) + 2 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \sin\left(6 \, d x + 6 \, c\right) + 2 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \sin\left(4 \, d x + 4 \, c\right) + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + 50 \, {\left(2 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \sin\left(6 \, d x + 6 \, c\right) + 2 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \sin\left(4 \, d x + 4 \, c\right) + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 100 \, {\left(2 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \sin\left(4 \, d x + 4 \, c\right) + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)}}"," ",0,"1/15*(300*(a*b - 5*b^2)*cos(4*d*x + 4*c)*sin(2*d*x + 2*c) - 10*(48*b^2*sin(6*d*x + 6*c) + 3*(a*b + 3*b^2)*sin(8*d*x + 8*c) + 2*(8*a^2 - 21*a*b + 49*b^2)*sin(4*d*x + 4*c) + 8*(a^2 - 3*a*b + 8*b^2)*sin(2*d*x + 2*c))*cos(10*d*x + 10*c) + 50*(6*(a*b - 5*b^2)*sin(6*d*x + 6*c) - 16*(a^2 - 3*a*b + 5*b^2)*sin(4*d*x + 4*c) - (8*a^2 - 27*a*b + 55*b^2)*sin(2*d*x + 2*c))*cos(8*d*x + 8*c) - 200*((8*a^2 - 21*a*b + 25*b^2)*sin(4*d*x + 4*c) + 4*(a^2 - 3*a*b + 5*b^2)*sin(2*d*x + 2*c))*cos(6*d*x + 6*c) + 15*((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cos(10*d*x + 10*c)^2 + 25*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cos(8*d*x + 8*c)^2 + 100*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cos(6*d*x + 6*c)^2 + 100*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cos(4*d*x + 4*c)^2 + 25*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cos(2*d*x + 2*c)^2 + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*sin(10*d*x + 10*c)^2 + 25*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*sin(8*d*x + 8*c)^2 + 100*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*sin(6*d*x + 6*c)^2 + 100*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*sin(4*d*x + 4*c)^2 + 100*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 25*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*sin(2*d*x + 2*c)^2 + 10*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cos(2*d*x + 2*c) + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d + 2*(5*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cos(8*d*x + 8*c) + 10*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cos(6*d*x + 6*c) + 10*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cos(4*d*x + 4*c) + 5*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cos(2*d*x + 2*c) + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d)*cos(10*d*x + 10*c) + 10*(10*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cos(6*d*x + 6*c) + 10*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cos(4*d*x + 4*c) + 5*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cos(2*d*x + 2*c) + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d)*cos(8*d*x + 8*c) + 20*(10*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cos(4*d*x + 4*c) + 5*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cos(2*d*x + 2*c) + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d)*cos(6*d*x + 6*c) + 20*(5*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cos(2*d*x + 2*c) + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d)*cos(4*d*x + 4*c) + 10*((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*sin(8*d*x + 8*c) + 2*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*sin(6*d*x + 6*c) + 2*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*sin(4*d*x + 4*c) + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*sin(2*d*x + 2*c))*sin(10*d*x + 10*c) + 50*(2*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*sin(6*d*x + 6*c) + 2*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*sin(4*d*x + 4*c) + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 100*(2*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*sin(4*d*x + 4*c) + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*integrate(4*(4*(a*b^3 + 3*b^4)*cos(6*d*x + 6*c)^2 - 4*(56*a^2*b^2 + 19*a*b^3 - 15*b^4)*cos(4*d*x + 4*c)^2 + 4*(a*b^3 + 3*b^4)*cos(2*d*x + 2*c)^2 + 4*(a*b^3 + 3*b^4)*sin(6*d*x + 6*c)^2 - 4*(56*a^2*b^2 + 19*a*b^3 - 15*b^4)*sin(4*d*x + 4*c)^2 + 2*(8*a^2*b^2 - 7*a*b^3 - 29*b^4)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*(a*b^3 + 3*b^4)*sin(2*d*x + 2*c)^2 - ((a*b^3 + 3*b^4)*cos(6*d*x + 6*c) - 2*(7*a*b^3 + 5*b^4)*cos(4*d*x + 4*c) + (a*b^3 + 3*b^4)*cos(2*d*x + 2*c))*cos(8*d*x + 8*c) - (a*b^3 + 3*b^4 - 2*(8*a^2*b^2 - 7*a*b^3 - 29*b^4)*cos(4*d*x + 4*c) - 8*(a*b^3 + 3*b^4)*cos(2*d*x + 2*c))*cos(6*d*x + 6*c) + 2*(7*a*b^3 + 5*b^4 + (8*a^2*b^2 - 7*a*b^3 - 29*b^4)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - (a*b^3 + 3*b^4)*cos(2*d*x + 2*c) - ((a*b^3 + 3*b^4)*sin(6*d*x + 6*c) - 2*(7*a*b^3 + 5*b^4)*sin(4*d*x + 4*c) + (a*b^3 + 3*b^4)*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 2*((8*a^2*b^2 - 7*a*b^3 - 29*b^4)*sin(4*d*x + 4*c) + 4*(a*b^3 + 3*b^4)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))/(a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5 + (a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5)*cos(8*d*x + 8*c)^2 + 16*(a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5)*cos(6*d*x + 6*c)^2 + 4*(64*a^5 - 240*a^4*b + 345*a^3*b^2 - 235*a^2*b^3 + 75*a*b^4 - 9*b^5)*cos(4*d*x + 4*c)^2 + 16*(a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5)*cos(2*d*x + 2*c)^2 + (a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5)*sin(8*d*x + 8*c)^2 + 16*(a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5)*sin(6*d*x + 6*c)^2 + 4*(64*a^5 - 240*a^4*b + 345*a^3*b^2 - 235*a^2*b^3 + 75*a*b^4 - 9*b^5)*sin(4*d*x + 4*c)^2 + 16*(8*a^4*b - 27*a^3*b^2 + 33*a^2*b^3 - 17*a*b^4 + 3*b^5)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*(a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5)*sin(2*d*x + 2*c)^2 + 2*(a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5 - 4*(a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5)*cos(6*d*x + 6*c) - 2*(8*a^4*b - 27*a^3*b^2 + 33*a^2*b^3 - 17*a*b^4 + 3*b^5)*cos(4*d*x + 4*c) - 4*(a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5)*cos(2*d*x + 2*c))*cos(8*d*x + 8*c) - 8*(a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5 - 2*(8*a^4*b - 27*a^3*b^2 + 33*a^2*b^3 - 17*a*b^4 + 3*b^5)*cos(4*d*x + 4*c) - 4*(a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5)*cos(2*d*x + 2*c))*cos(6*d*x + 6*c) - 4*(8*a^4*b - 27*a^3*b^2 + 33*a^2*b^3 - 17*a*b^4 + 3*b^5 - 4*(8*a^4*b - 27*a^3*b^2 + 33*a^2*b^3 - 17*a*b^4 + 3*b^5)*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 8*(a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5)*cos(2*d*x + 2*c) - 4*(2*(a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5)*sin(6*d*x + 6*c) + (8*a^4*b - 27*a^3*b^2 + 33*a^2*b^3 - 17*a*b^4 + 3*b^5)*sin(4*d*x + 4*c) + 2*(a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5)*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*((8*a^4*b - 27*a^3*b^2 + 33*a^2*b^3 - 17*a*b^4 + 3*b^5)*sin(4*d*x + 4*c) + 2*(a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c)), x) + 2*(240*b^2*cos(6*d*x + 6*c) + 8*a^2 - 21*a*b + 73*b^2 + 15*(a*b + 3*b^2)*cos(8*d*x + 8*c) + 10*(8*a^2 - 21*a*b + 49*b^2)*cos(4*d*x + 4*c) + 40*(a^2 - 3*a*b + 8*b^2)*cos(2*d*x + 2*c))*sin(10*d*x + 10*c) + 10*(8*a^2 - 24*a*b + 64*b^2 - 30*(a*b - 5*b^2)*cos(6*d*x + 6*c) + 80*(a^2 - 3*a*b + 5*b^2)*cos(4*d*x + 4*c) + 5*(8*a^2 - 27*a*b + 55*b^2)*cos(2*d*x + 2*c))*sin(8*d*x + 8*c) + 20*(8*a^2 - 21*a*b + 49*b^2 + 10*(8*a^2 - 21*a*b + 25*b^2)*cos(4*d*x + 4*c) + 40*(a^2 - 3*a*b + 5*b^2)*cos(2*d*x + 2*c))*sin(6*d*x + 6*c) + 60*(8*b^2 - 5*(a*b - 5*b^2)*cos(2*d*x + 2*c))*sin(4*d*x + 4*c) + 30*(a*b + 3*b^2)*sin(2*d*x + 2*c))/((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cos(10*d*x + 10*c)^2 + 25*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cos(8*d*x + 8*c)^2 + 100*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cos(6*d*x + 6*c)^2 + 100*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cos(4*d*x + 4*c)^2 + 25*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cos(2*d*x + 2*c)^2 + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*sin(10*d*x + 10*c)^2 + 25*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*sin(8*d*x + 8*c)^2 + 100*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*sin(6*d*x + 6*c)^2 + 100*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*sin(4*d*x + 4*c)^2 + 100*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 25*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*sin(2*d*x + 2*c)^2 + 10*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cos(2*d*x + 2*c) + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d + 2*(5*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cos(8*d*x + 8*c) + 10*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cos(6*d*x + 6*c) + 10*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cos(4*d*x + 4*c) + 5*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cos(2*d*x + 2*c) + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d)*cos(10*d*x + 10*c) + 10*(10*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cos(6*d*x + 6*c) + 10*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cos(4*d*x + 4*c) + 5*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cos(2*d*x + 2*c) + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d)*cos(8*d*x + 8*c) + 20*(10*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cos(4*d*x + 4*c) + 5*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cos(2*d*x + 2*c) + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d)*cos(6*d*x + 6*c) + 20*(5*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cos(2*d*x + 2*c) + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d)*cos(4*d*x + 4*c) + 10*((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*sin(8*d*x + 8*c) + 2*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*sin(6*d*x + 6*c) + 2*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*sin(4*d*x + 4*c) + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*sin(2*d*x + 2*c))*sin(10*d*x + 10*c) + 50*(2*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*sin(6*d*x + 6*c) + 2*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*sin(4*d*x + 4*c) + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 100*(2*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*sin(4*d*x + 4*c) + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))","F",0
419,0,0,0,0.000000," ","integrate(cos(f*x+e)^m*(a+b*sin(f*x+e)^4)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{4} + a\right)}^{p} \cos\left(f x + e\right)^{m}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^4 + a)^p*cos(f*x + e)^m, x)","F",0
420,0,0,0,0.000000," ","integrate(cos(f*x+e)^5*(a+b*sin(f*x+e)^4)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{4} + a\right)}^{p} \cos\left(f x + e\right)^{5}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^4 + a)^p*cos(f*x + e)^5, x)","F",0
421,0,0,0,0.000000," ","integrate(cos(f*x+e)^3*(a+b*sin(f*x+e)^4)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{4} + a\right)}^{p} \cos\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^4 + a)^p*cos(f*x + e)^3, x)","F",0
422,0,0,0,0.000000," ","integrate(cos(f*x+e)*(a+b*sin(f*x+e)^4)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{4} + a\right)}^{p} \cos\left(f x + e\right)\,{d x}"," ",0,"integrate((b*sin(f*x + e)^4 + a)^p*cos(f*x + e), x)","F",0
423,0,0,0,0.000000," ","integrate(sec(f*x+e)*(a+b*sin(f*x+e)^4)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{4} + a\right)}^{p} \sec\left(f x + e\right)\,{d x}"," ",0,"integrate((b*sin(f*x + e)^4 + a)^p*sec(f*x + e), x)","F",0
424,0,0,0,0.000000," ","integrate(sec(f*x+e)^3*(a+b*sin(f*x+e)^4)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{4} + a\right)}^{p} \sec\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^4 + a)^p*sec(f*x + e)^3, x)","F",0
425,0,0,0,0.000000," ","integrate(cos(f*x+e)^4*(a+b*sin(f*x+e)^4)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{4} + a\right)}^{p} \cos\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^4 + a)^p*cos(f*x + e)^4, x)","F",0
426,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+b*sin(f*x+e)^4)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{4} + a\right)}^{p} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^4 + a)^p*cos(f*x + e)^2, x)","F",0
427,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e)^4)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{4} + a\right)}^{p}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^4 + a)^p, x)","F",0
428,0,0,0,0.000000," ","integrate(sec(f*x+e)^2*(a+b*sin(f*x+e)^4)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{4} + a\right)}^{p} \sec\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^4 + a)^p*sec(f*x + e)^2, x)","F",0
429,0,0,0,0.000000," ","integrate(sec(f*x+e)^4*(a+b*sin(f*x+e)^4)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{4} + a\right)}^{p} \sec\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^4 + a)^p*sec(f*x + e)^4, x)","F",0
430,0,0,0,0.000000," ","integrate(cos(f*x+e)^m*(a+b*sin(f*x+e)^n)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{n} + a\right)}^{p} \cos\left(f x + e\right)^{m}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^n + a)^p*cos(f*x + e)^m, x)","F",0
431,0,0,0,0.000000," ","integrate(cos(f*x+e)^5*(a+b*sin(f*x+e)^n)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{n} + a\right)}^{p} \cos\left(f x + e\right)^{5}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^n + a)^p*cos(f*x + e)^5, x)","F",0
432,0,0,0,0.000000," ","integrate(cos(f*x+e)^3*(a+b*sin(f*x+e)^n)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{n} + a\right)}^{p} \cos\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^n + a)^p*cos(f*x + e)^3, x)","F",0
433,0,0,0,0.000000," ","integrate(cos(f*x+e)*(a+b*sin(f*x+e)^n)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{n} + a\right)}^{p} \cos\left(f x + e\right)\,{d x}"," ",0,"integrate((b*sin(f*x + e)^n + a)^p*cos(f*x + e), x)","F",0
434,0,0,0,0.000000," ","integrate(sec(f*x+e)*(a+b*sin(f*x+e)^n)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{n} + a\right)}^{p} \sec\left(f x + e\right)\,{d x}"," ",0,"integrate((b*sin(f*x + e)^n + a)^p*sec(f*x + e), x)","F",0
435,0,0,0,0.000000," ","integrate(sec(f*x+e)^3*(a+b*sin(f*x+e)^n)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{n} + a\right)}^{p} \sec\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^n + a)^p*sec(f*x + e)^3, x)","F",0
436,0,0,0,0.000000," ","integrate(cos(f*x+e)^4*(a+b*sin(f*x+e)^n)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{n} + a\right)}^{p} \cos\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^n + a)^p*cos(f*x + e)^4, x)","F",0
437,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+b*sin(f*x+e)^n)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{n} + a\right)}^{p} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^n + a)^p*cos(f*x + e)^2, x)","F",0
438,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e)^n)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{n} + a\right)}^{p}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^n + a)^p, x)","F",0
439,0,0,0,0.000000," ","integrate(sec(f*x+e)^2*(a+b*sin(f*x+e)^n)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{n} + a\right)}^{p} \sec\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^n + a)^p*sec(f*x + e)^2, x)","F",0
440,0,0,0,0.000000," ","integrate(sec(f*x+e)^4*(a+b*sin(f*x+e)^n)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{n} + a\right)}^{p} \sec\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^n + a)^p*sec(f*x + e)^4, x)","F",0
441,1,273,0,0.335498," ","integrate(tan(d*x+c)^7/(a+b*sin(d*x+c)^2),x, algorithm=""maxima"")","-\frac{\frac{6 \, a^{3} \log\left(b \sin\left(d x + c\right)^{2} + a\right)}{a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}} - \frac{6 \, a^{3} \log\left(\sin\left(d x + c\right)^{2} - 1\right)}{a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}} + \frac{6 \, {\left(3 \, a^{2} + 3 \, a b + b^{2}\right)} \sin\left(d x + c\right)^{4} - 3 \, {\left(9 \, a^{2} + 7 \, a b + 2 \, b^{2}\right)} \sin\left(d x + c\right)^{2} + 11 \, a^{2} + 7 \, a b + 2 \, b^{2}}{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sin\left(d x + c\right)^{6} - 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sin\left(d x + c\right)^{4} - a^{3} - 3 \, a^{2} b - 3 \, a b^{2} - b^{3} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sin\left(d x + c\right)^{2}}}{12 \, d}"," ",0,"-1/12*(6*a^3*log(b*sin(d*x + c)^2 + a)/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4) - 6*a^3*log(sin(d*x + c)^2 - 1)/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4) + (6*(3*a^2 + 3*a*b + b^2)*sin(d*x + c)^4 - 3*(9*a^2 + 7*a*b + 2*b^2)*sin(d*x + c)^2 + 11*a^2 + 7*a*b + 2*b^2)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sin(d*x + c)^6 - 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sin(d*x + c)^4 - a^3 - 3*a^2*b - 3*a*b^2 - b^3 + 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sin(d*x + c)^2))/d","B",0
442,1,159,0,0.340075," ","integrate(tan(d*x+c)^5/(a+b*sin(d*x+c)^2),x, algorithm=""maxima"")","\frac{\frac{2 \, a^{2} \log\left(b \sin\left(d x + c\right)^{2} + a\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} - \frac{2 \, a^{2} \log\left(\sin\left(d x + c\right)^{2} - 1\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} + \frac{2 \, {\left(2 \, a + b\right)} \sin\left(d x + c\right)^{2} - 3 \, a - b}{{\left(a^{2} + 2 \, a b + b^{2}\right)} \sin\left(d x + c\right)^{4} - 2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \sin\left(d x + c\right)^{2} + a^{2} + 2 \, a b + b^{2}}}{4 \, d}"," ",0,"1/4*(2*a^2*log(b*sin(d*x + c)^2 + a)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) - 2*a^2*log(sin(d*x + c)^2 - 1)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) + (2*(2*a + b)*sin(d*x + c)^2 - 3*a - b)/((a^2 + 2*a*b + b^2)*sin(d*x + c)^4 - 2*(a^2 + 2*a*b + b^2)*sin(d*x + c)^2 + a^2 + 2*a*b + b^2))/d","A",0
443,1,82,0,0.320083," ","integrate(tan(d*x+c)^3/(a+b*sin(d*x+c)^2),x, algorithm=""maxima"")","-\frac{\frac{a \log\left(b \sin\left(d x + c\right)^{2} + a\right)}{a^{2} + 2 \, a b + b^{2}} - \frac{a \log\left(\sin\left(d x + c\right)^{2} - 1\right)}{a^{2} + 2 \, a b + b^{2}} + \frac{1}{{\left(a + b\right)} \sin\left(d x + c\right)^{2} - a - b}}{2 \, d}"," ",0,"-1/2*(a*log(b*sin(d*x + c)^2 + a)/(a^2 + 2*a*b + b^2) - a*log(sin(d*x + c)^2 - 1)/(a^2 + 2*a*b + b^2) + 1/((a + b)*sin(d*x + c)^2 - a - b))/d","A",0
444,1,43,0,0.323545," ","integrate(tan(d*x+c)/(a+b*sin(d*x+c)^2),x, algorithm=""maxima"")","\frac{\frac{\log\left(b \sin\left(d x + c\right)^{2} + a\right)}{a + b} - \frac{\log\left(\sin\left(d x + c\right)^{2} - 1\right)}{a + b}}{2 \, d}"," ",0,"1/2*(log(b*sin(d*x + c)^2 + a)/(a + b) - log(sin(d*x + c)^2 - 1)/(a + b))/d","A",0
445,1,37,0,0.333145," ","integrate(cot(d*x+c)/(a+b*sin(d*x+c)^2),x, algorithm=""maxima"")","-\frac{\frac{\log\left(b \sin\left(d x + c\right)^{2} + a\right)}{a} - \frac{\log\left(\sin\left(d x + c\right)^{2}\right)}{a}}{2 \, d}"," ",0,"-1/2*(log(b*sin(d*x + c)^2 + a)/a - log(sin(d*x + c)^2)/a)/d","A",0
446,1,56,0,0.322989," ","integrate(cot(d*x+c)^3/(a+b*sin(d*x+c)^2),x, algorithm=""maxima"")","\frac{\frac{{\left(a + b\right)} \log\left(b \sin\left(d x + c\right)^{2} + a\right)}{a^{2}} - \frac{{\left(a + b\right)} \log\left(\sin\left(d x + c\right)^{2}\right)}{a^{2}} - \frac{1}{a \sin\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"1/2*((a + b)*log(b*sin(d*x + c)^2 + a)/a^2 - (a + b)*log(sin(d*x + c)^2)/a^2 - 1/(a*sin(d*x + c)^2))/d","A",0
447,1,92,0,0.328182," ","integrate(cot(d*x+c)^5/(a+b*sin(d*x+c)^2),x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \log\left(b \sin\left(d x + c\right)^{2} + a\right)}{a^{3}} - \frac{2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \log\left(\sin\left(d x + c\right)^{2}\right)}{a^{3}} - \frac{2 \, {\left(2 \, a + b\right)} \sin\left(d x + c\right)^{2} - a}{a^{2} \sin\left(d x + c\right)^{4}}}{4 \, d}"," ",0,"-1/4*(2*(a^2 + 2*a*b + b^2)*log(b*sin(d*x + c)^2 + a)/a^3 - 2*(a^2 + 2*a*b + b^2)*log(sin(d*x + c)^2)/a^3 - (2*(2*a + b)*sin(d*x + c)^2 - a)/(a^2*sin(d*x + c)^4))/d","A",0
448,1,137,0,0.324743," ","integrate(cot(d*x+c)^7/(a+b*sin(d*x+c)^2),x, algorithm=""maxima"")","\frac{\frac{6 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \log\left(b \sin\left(d x + c\right)^{2} + a\right)}{a^{4}} - \frac{6 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \log\left(\sin\left(d x + c\right)^{2}\right)}{a^{4}} - \frac{6 \, {\left(3 \, a^{2} + 3 \, a b + b^{2}\right)} \sin\left(d x + c\right)^{4} - 3 \, {\left(3 \, a^{2} + a b\right)} \sin\left(d x + c\right)^{2} + 2 \, a^{2}}{a^{3} \sin\left(d x + c\right)^{6}}}{12 \, d}"," ",0,"1/12*(6*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*log(b*sin(d*x + c)^2 + a)/a^4 - 6*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*log(sin(d*x + c)^2)/a^4 - (6*(3*a^2 + 3*a*b + b^2)*sin(d*x + c)^4 - 3*(3*a^2 + a*b)*sin(d*x + c)^2 + 2*a^2)/(a^3*sin(d*x + c)^6))/d","A",0
449,1,180,0,0.424154," ","integrate(tan(d*x+c)^8/(a+b*sin(d*x+c)^2),x, algorithm=""maxima"")","\frac{\frac{105 \, a^{4} \arctan\left(\frac{{\left(a + b\right)} \tan\left(d x + c\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{{\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \sqrt{{\left(a + b\right)} a}} + \frac{15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \tan\left(d x + c\right)^{7} - 21 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \tan\left(d x + c\right)^{5} - 105 \, a^{3} \tan\left(d x + c\right) + 35 \, {\left(a^{3} + a^{2} b\right)} \tan\left(d x + c\right)^{3}}{a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}}}{105 \, d}"," ",0,"1/105*(105*a^4*arctan((a + b)*tan(d*x + c)/sqrt((a + b)*a))/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*sqrt((a + b)*a)) + (15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*tan(d*x + c)^7 - 21*(a^3 + 2*a^2*b + a*b^2)*tan(d*x + c)^5 - 105*a^3*tan(d*x + c) + 35*(a^3 + a^2*b)*tan(d*x + c)^3)/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4))/d","A",0
450,1,130,0,0.424365," ","integrate(tan(d*x+c)^6/(a+b*sin(d*x+c)^2),x, algorithm=""maxima"")","-\frac{\frac{15 \, a^{3} \arctan\left(\frac{{\left(a + b\right)} \tan\left(d x + c\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sqrt{{\left(a + b\right)} a}} - \frac{3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \tan\left(d x + c\right)^{5} - 5 \, {\left(a^{2} + a b\right)} \tan\left(d x + c\right)^{3} + 15 \, a^{2} \tan\left(d x + c\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}}}{15 \, d}"," ",0,"-1/15*(15*a^3*arctan((a + b)*tan(d*x + c)/sqrt((a + b)*a))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sqrt((a + b)*a)) - (3*(a^2 + 2*a*b + b^2)*tan(d*x + c)^5 - 5*(a^2 + a*b)*tan(d*x + c)^3 + 15*a^2*tan(d*x + c))/(a^3 + 3*a^2*b + 3*a*b^2 + b^3))/d","A",0
451,1,85,0,0.417002," ","integrate(tan(d*x+c)^4/(a+b*sin(d*x+c)^2),x, algorithm=""maxima"")","\frac{\frac{3 \, a^{2} \arctan\left(\frac{{\left(a + b\right)} \tan\left(d x + c\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{\sqrt{{\left(a + b\right)} a} {\left(a^{2} + 2 \, a b + b^{2}\right)}} + \frac{{\left(a + b\right)} \tan\left(d x + c\right)^{3} - 3 \, a \tan\left(d x + c\right)}{a^{2} + 2 \, a b + b^{2}}}{3 \, d}"," ",0,"1/3*(3*a^2*arctan((a + b)*tan(d*x + c)/sqrt((a + b)*a))/(sqrt((a + b)*a)*(a^2 + 2*a*b + b^2)) + ((a + b)*tan(d*x + c)^3 - 3*a*tan(d*x + c))/(a^2 + 2*a*b + b^2))/d","A",0
452,1,51,0,0.422964," ","integrate(tan(d*x+c)^2/(a+b*sin(d*x+c)^2),x, algorithm=""maxima"")","-\frac{\frac{a \arctan\left(\frac{{\left(a + b\right)} \tan\left(d x + c\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{\sqrt{{\left(a + b\right)} a} {\left(a + b\right)}} - \frac{\tan\left(d x + c\right)}{a + b}}{d}"," ",0,"-(a*arctan((a + b)*tan(d*x + c)/sqrt((a + b)*a))/(sqrt((a + b)*a)*(a + b)) - tan(d*x + c)/(a + b))/d","A",0
453,1,50,0,0.431289," ","integrate(cot(d*x+c)^2/(a+b*sin(d*x+c)^2),x, algorithm=""maxima"")","-\frac{\frac{{\left(a + b\right)} \arctan\left(\frac{{\left(a + b\right)} \tan\left(d x + c\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{\sqrt{{\left(a + b\right)} a} a} + \frac{1}{a \tan\left(d x + c\right)}}{d}"," ",0,"-((a + b)*arctan((a + b)*tan(d*x + c)/sqrt((a + b)*a))/(sqrt((a + b)*a)*a) + 1/(a*tan(d*x + c)))/d","A",0
454,1,76,0,0.436706," ","integrate(cot(d*x+c)^4/(a+b*sin(d*x+c)^2),x, algorithm=""maxima"")","\frac{\frac{3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \arctan\left(\frac{{\left(a + b\right)} \tan\left(d x + c\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{\sqrt{{\left(a + b\right)} a} a^{2}} + \frac{3 \, {\left(a + b\right)} \tan\left(d x + c\right)^{2} - a}{a^{2} \tan\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"1/3*(3*(a^2 + 2*a*b + b^2)*arctan((a + b)*tan(d*x + c)/sqrt((a + b)*a))/(sqrt((a + b)*a)*a^2) + (3*(a + b)*tan(d*x + c)^2 - a)/(a^2*tan(d*x + c)^3))/d","A",0
455,1,111,0,0.415731," ","integrate(cot(d*x+c)^6/(a+b*sin(d*x+c)^2),x, algorithm=""maxima"")","-\frac{\frac{15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \arctan\left(\frac{{\left(a + b\right)} \tan\left(d x + c\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{\sqrt{{\left(a + b\right)} a} a^{3}} + \frac{15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \tan\left(d x + c\right)^{4} - 5 \, {\left(a^{2} + a b\right)} \tan\left(d x + c\right)^{2} + 3 \, a^{2}}{a^{3} \tan\left(d x + c\right)^{5}}}{15 \, d}"," ",0,"-1/15*(15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*arctan((a + b)*tan(d*x + c)/sqrt((a + b)*a))/(sqrt((a + b)*a)*a^3) + (15*(a^2 + 2*a*b + b^2)*tan(d*x + c)^4 - 5*(a^2 + a*b)*tan(d*x + c)^2 + 3*a^2)/(a^3*tan(d*x + c)^5))/d","A",0
456,1,154,0,0.483861," ","integrate(cot(d*x+c)^8/(a+b*sin(d*x+c)^2),x, algorithm=""maxima"")","\frac{\frac{105 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \arctan\left(\frac{{\left(a + b\right)} \tan\left(d x + c\right)}{\sqrt{{\left(a + b\right)} a}}\right)}{\sqrt{{\left(a + b\right)} a} a^{4}} + \frac{105 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \tan\left(d x + c\right)^{6} - 35 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \tan\left(d x + c\right)^{4} - 15 \, a^{3} + 21 \, {\left(a^{3} + a^{2} b\right)} \tan\left(d x + c\right)^{2}}{a^{4} \tan\left(d x + c\right)^{7}}}{105 \, d}"," ",0,"1/105*(105*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*arctan((a + b)*tan(d*x + c)/sqrt((a + b)*a))/(sqrt((a + b)*a)*a^4) + (105*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*tan(d*x + c)^6 - 35*(a^3 + 2*a^2*b + a*b^2)*tan(d*x + c)^4 - 15*a^3 + 21*(a^3 + a^2*b)*tan(d*x + c)^2)/(a^4*tan(d*x + c)^7))/d","A",0
457,1,69,0,0.345015," ","integrate((a-a*sin(f*x+e)^2)^(1/2)*tan(f*x+e)^5,x, algorithm=""maxima"")","-\frac{3 \, \sqrt{-a \sin\left(f x + e\right)^{2} + a} a^{3} - \frac{6 \, {\left(a \sin\left(f x + e\right)^{2} - a\right)} a^{4} + a^{5}}{{\left(-a \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}}{3 \, a^{3} f}"," ",0,"-1/3*(3*sqrt(-a*sin(f*x + e)^2 + a)*a^3 - (6*(a*sin(f*x + e)^2 - a)*a^4 + a^5)/(-a*sin(f*x + e)^2 + a)^(3/2))/(a^3*f)","A",0
458,1,46,0,0.351183," ","integrate((a-a*sin(f*x+e)^2)^(1/2)*tan(f*x+e)^3,x, algorithm=""maxima"")","\frac{\sqrt{-a \sin\left(f x + e\right)^{2} + a} a^{2} + \frac{a^{3}}{\sqrt{-a \sin\left(f x + e\right)^{2} + a}}}{a^{2} f}"," ",0,"(sqrt(-a*sin(f*x + e)^2 + a)*a^2 + a^3/sqrt(-a*sin(f*x + e)^2 + a))/(a^2*f)","A",0
459,1,20,0,0.429146," ","integrate((a-a*sin(f*x+e)^2)^(1/2)*tan(f*x+e),x, algorithm=""maxima"")","-\frac{\sqrt{-a \sin\left(f x + e\right)^{2} + a}}{f}"," ",0,"-sqrt(-a*sin(f*x + e)^2 + a)/f","A",0
460,1,70,0,0.422799," ","integrate(cot(f*x+e)*(a-a*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{a} \log\left(\frac{2 \, \sqrt{-a \sin\left(f x + e\right)^{2} + a} \sqrt{a}}{{\left| \sin\left(f x + e\right) \right|}} + \frac{2 \, a}{{\left| \sin\left(f x + e\right) \right|}}\right) - \sqrt{-a \sin\left(f x + e\right)^{2} + a}}{f}"," ",0,"-(sqrt(a)*log(2*sqrt(-a*sin(f*x + e)^2 + a)*sqrt(a)/abs(sin(f*x + e)) + 2*a/abs(sin(f*x + e))) - sqrt(-a*sin(f*x + e)^2 + a))/f","A",0
461,1,99,0,0.417802," ","integrate(cot(f*x+e)^3*(a-a*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\frac{3 \, \sqrt{a} \log\left(\frac{2 \, \sqrt{-a \sin\left(f x + e\right)^{2} + a} \sqrt{a}}{{\left| \sin\left(f x + e\right) \right|}} + \frac{2 \, a}{{\left| \sin\left(f x + e\right) \right|}}\right) - 3 \, \sqrt{-a \sin\left(f x + e\right)^{2} + a} - \frac{{\left(-a \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}{a \sin\left(f x + e\right)^{2}}}{2 \, f}"," ",0,"1/2*(3*sqrt(a)*log(2*sqrt(-a*sin(f*x + e)^2 + a)*sqrt(a)/abs(sin(f*x + e)) + 2*a/abs(sin(f*x + e))) - 3*sqrt(-a*sin(f*x + e)^2 + a) - (-a*sin(f*x + e)^2 + a)^(3/2)/(a*sin(f*x + e)^2))/f","A",0
462,1,1955,0,1.502768," ","integrate((a-a*sin(f*x+e)^2)^(1/2)*tan(f*x+e)^6,x, algorithm=""maxima"")","\frac{{\left(8 \, {\left(\sin\left(9 \, f x + 9 \, e\right) + 4 \, \sin\left(7 \, f x + 7 \, e\right) + 6 \, \sin\left(5 \, f x + 5 \, e\right) + 4 \, \sin\left(3 \, f x + 3 \, e\right) + \sin\left(f x + e\right)\right)} \cos\left(10 \, f x + 10 \, e\right) - 20 \, {\left(3 \, \sin\left(8 \, f x + 8 \, e\right) + \sin\left(6 \, f x + 6 \, e\right) - \sin\left(4 \, f x + 4 \, e\right) - 3 \, \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(9 \, f x + 9 \, e\right) + 60 \, {\left(4 \, \sin\left(7 \, f x + 7 \, e\right) + 6 \, \sin\left(5 \, f x + 5 \, e\right) + 4 \, \sin\left(3 \, f x + 3 \, e\right) + \sin\left(f x + e\right)\right)} \cos\left(8 \, f x + 8 \, e\right) - 80 \, {\left(\sin\left(6 \, f x + 6 \, e\right) - \sin\left(4 \, f x + 4 \, e\right) - 3 \, \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(7 \, f x + 7 \, e\right) + 20 \, {\left(6 \, \sin\left(5 \, f x + 5 \, e\right) + 4 \, \sin\left(3 \, f x + 3 \, e\right) + \sin\left(f x + e\right)\right)} \cos\left(6 \, f x + 6 \, e\right) + 120 \, {\left(\sin\left(4 \, f x + 4 \, e\right) + 3 \, \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(5 \, f x + 5 \, e\right) - 20 \, {\left(4 \, \sin\left(3 \, f x + 3 \, e\right) + \sin\left(f x + e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 15 \, {\left(2 \, {\left(4 \, \cos\left(7 \, f x + 7 \, e\right) + 6 \, \cos\left(5 \, f x + 5 \, e\right) + 4 \, \cos\left(3 \, f x + 3 \, e\right) + \cos\left(f x + e\right)\right)} \cos\left(9 \, f x + 9 \, e\right) + \cos\left(9 \, f x + 9 \, e\right)^{2} + 8 \, {\left(6 \, \cos\left(5 \, f x + 5 \, e\right) + 4 \, \cos\left(3 \, f x + 3 \, e\right) + \cos\left(f x + e\right)\right)} \cos\left(7 \, f x + 7 \, e\right) + 16 \, \cos\left(7 \, f x + 7 \, e\right)^{2} + 12 \, {\left(4 \, \cos\left(3 \, f x + 3 \, e\right) + \cos\left(f x + e\right)\right)} \cos\left(5 \, f x + 5 \, e\right) + 36 \, \cos\left(5 \, f x + 5 \, e\right)^{2} + 16 \, \cos\left(3 \, f x + 3 \, e\right)^{2} + 8 \, \cos\left(3 \, f x + 3 \, e\right) \cos\left(f x + e\right) + \cos\left(f x + e\right)^{2} + 2 \, {\left(4 \, \sin\left(7 \, f x + 7 \, e\right) + 6 \, \sin\left(5 \, f x + 5 \, e\right) + 4 \, \sin\left(3 \, f x + 3 \, e\right) + \sin\left(f x + e\right)\right)} \sin\left(9 \, f x + 9 \, e\right) + \sin\left(9 \, f x + 9 \, e\right)^{2} + 8 \, {\left(6 \, \sin\left(5 \, f x + 5 \, e\right) + 4 \, \sin\left(3 \, f x + 3 \, e\right) + \sin\left(f x + e\right)\right)} \sin\left(7 \, f x + 7 \, e\right) + 16 \, \sin\left(7 \, f x + 7 \, e\right)^{2} + 12 \, {\left(4 \, \sin\left(3 \, f x + 3 \, e\right) + \sin\left(f x + e\right)\right)} \sin\left(5 \, f x + 5 \, e\right) + 36 \, \sin\left(5 \, f x + 5 \, e\right)^{2} + 16 \, \sin\left(3 \, f x + 3 \, e\right)^{2} + 8 \, \sin\left(3 \, f x + 3 \, e\right) \sin\left(f x + e\right) + \sin\left(f x + e\right)^{2}\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \sin\left(f x + e\right) + 1\right) - 15 \, {\left(2 \, {\left(4 \, \cos\left(7 \, f x + 7 \, e\right) + 6 \, \cos\left(5 \, f x + 5 \, e\right) + 4 \, \cos\left(3 \, f x + 3 \, e\right) + \cos\left(f x + e\right)\right)} \cos\left(9 \, f x + 9 \, e\right) + \cos\left(9 \, f x + 9 \, e\right)^{2} + 8 \, {\left(6 \, \cos\left(5 \, f x + 5 \, e\right) + 4 \, \cos\left(3 \, f x + 3 \, e\right) + \cos\left(f x + e\right)\right)} \cos\left(7 \, f x + 7 \, e\right) + 16 \, \cos\left(7 \, f x + 7 \, e\right)^{2} + 12 \, {\left(4 \, \cos\left(3 \, f x + 3 \, e\right) + \cos\left(f x + e\right)\right)} \cos\left(5 \, f x + 5 \, e\right) + 36 \, \cos\left(5 \, f x + 5 \, e\right)^{2} + 16 \, \cos\left(3 \, f x + 3 \, e\right)^{2} + 8 \, \cos\left(3 \, f x + 3 \, e\right) \cos\left(f x + e\right) + \cos\left(f x + e\right)^{2} + 2 \, {\left(4 \, \sin\left(7 \, f x + 7 \, e\right) + 6 \, \sin\left(5 \, f x + 5 \, e\right) + 4 \, \sin\left(3 \, f x + 3 \, e\right) + \sin\left(f x + e\right)\right)} \sin\left(9 \, f x + 9 \, e\right) + \sin\left(9 \, f x + 9 \, e\right)^{2} + 8 \, {\left(6 \, \sin\left(5 \, f x + 5 \, e\right) + 4 \, \sin\left(3 \, f x + 3 \, e\right) + \sin\left(f x + e\right)\right)} \sin\left(7 \, f x + 7 \, e\right) + 16 \, \sin\left(7 \, f x + 7 \, e\right)^{2} + 12 \, {\left(4 \, \sin\left(3 \, f x + 3 \, e\right) + \sin\left(f x + e\right)\right)} \sin\left(5 \, f x + 5 \, e\right) + 36 \, \sin\left(5 \, f x + 5 \, e\right)^{2} + 16 \, \sin\left(3 \, f x + 3 \, e\right)^{2} + 8 \, \sin\left(3 \, f x + 3 \, e\right) \sin\left(f x + e\right) + \sin\left(f x + e\right)^{2}\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} - 2 \, \sin\left(f x + e\right) + 1\right) - 8 \, {\left(\cos\left(9 \, f x + 9 \, e\right) + 4 \, \cos\left(7 \, f x + 7 \, e\right) + 6 \, \cos\left(5 \, f x + 5 \, e\right) + 4 \, \cos\left(3 \, f x + 3 \, e\right) + \cos\left(f x + e\right)\right)} \sin\left(10 \, f x + 10 \, e\right) + 4 \, {\left(15 \, \cos\left(8 \, f x + 8 \, e\right) + 5 \, \cos\left(6 \, f x + 6 \, e\right) - 5 \, \cos\left(4 \, f x + 4 \, e\right) - 15 \, \cos\left(2 \, f x + 2 \, e\right) - 2\right)} \sin\left(9 \, f x + 9 \, e\right) - 60 \, {\left(4 \, \cos\left(7 \, f x + 7 \, e\right) + 6 \, \cos\left(5 \, f x + 5 \, e\right) + 4 \, \cos\left(3 \, f x + 3 \, e\right) + \cos\left(f x + e\right)\right)} \sin\left(8 \, f x + 8 \, e\right) + 16 \, {\left(5 \, \cos\left(6 \, f x + 6 \, e\right) - 5 \, \cos\left(4 \, f x + 4 \, e\right) - 15 \, \cos\left(2 \, f x + 2 \, e\right) - 2\right)} \sin\left(7 \, f x + 7 \, e\right) - 20 \, {\left(6 \, \cos\left(5 \, f x + 5 \, e\right) + 4 \, \cos\left(3 \, f x + 3 \, e\right) + \cos\left(f x + e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) - 24 \, {\left(5 \, \cos\left(4 \, f x + 4 \, e\right) + 15 \, \cos\left(2 \, f x + 2 \, e\right) + 2\right)} \sin\left(5 \, f x + 5 \, e\right) + 20 \, {\left(4 \, \cos\left(3 \, f x + 3 \, e\right) + \cos\left(f x + e\right)\right)} \sin\left(4 \, f x + 4 \, e\right) - 16 \, {\left(15 \, \cos\left(2 \, f x + 2 \, e\right) + 2\right)} \sin\left(3 \, f x + 3 \, e\right) + 240 \, \cos\left(3 \, f x + 3 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 60 \, \cos\left(f x + e\right) \sin\left(2 \, f x + 2 \, e\right) - 60 \, \cos\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) - 8 \, \sin\left(f x + e\right)\right)} \sqrt{a}}{16 \, {\left(2 \, {\left(4 \, \cos\left(7 \, f x + 7 \, e\right) + 6 \, \cos\left(5 \, f x + 5 \, e\right) + 4 \, \cos\left(3 \, f x + 3 \, e\right) + \cos\left(f x + e\right)\right)} \cos\left(9 \, f x + 9 \, e\right) + \cos\left(9 \, f x + 9 \, e\right)^{2} + 8 \, {\left(6 \, \cos\left(5 \, f x + 5 \, e\right) + 4 \, \cos\left(3 \, f x + 3 \, e\right) + \cos\left(f x + e\right)\right)} \cos\left(7 \, f x + 7 \, e\right) + 16 \, \cos\left(7 \, f x + 7 \, e\right)^{2} + 12 \, {\left(4 \, \cos\left(3 \, f x + 3 \, e\right) + \cos\left(f x + e\right)\right)} \cos\left(5 \, f x + 5 \, e\right) + 36 \, \cos\left(5 \, f x + 5 \, e\right)^{2} + 16 \, \cos\left(3 \, f x + 3 \, e\right)^{2} + 8 \, \cos\left(3 \, f x + 3 \, e\right) \cos\left(f x + e\right) + \cos\left(f x + e\right)^{2} + 2 \, {\left(4 \, \sin\left(7 \, f x + 7 \, e\right) + 6 \, \sin\left(5 \, f x + 5 \, e\right) + 4 \, \sin\left(3 \, f x + 3 \, e\right) + \sin\left(f x + e\right)\right)} \sin\left(9 \, f x + 9 \, e\right) + \sin\left(9 \, f x + 9 \, e\right)^{2} + 8 \, {\left(6 \, \sin\left(5 \, f x + 5 \, e\right) + 4 \, \sin\left(3 \, f x + 3 \, e\right) + \sin\left(f x + e\right)\right)} \sin\left(7 \, f x + 7 \, e\right) + 16 \, \sin\left(7 \, f x + 7 \, e\right)^{2} + 12 \, {\left(4 \, \sin\left(3 \, f x + 3 \, e\right) + \sin\left(f x + e\right)\right)} \sin\left(5 \, f x + 5 \, e\right) + 36 \, \sin\left(5 \, f x + 5 \, e\right)^{2} + 16 \, \sin\left(3 \, f x + 3 \, e\right)^{2} + 8 \, \sin\left(3 \, f x + 3 \, e\right) \sin\left(f x + e\right) + \sin\left(f x + e\right)^{2}\right)} f}"," ",0,"1/16*(8*(sin(9*f*x + 9*e) + 4*sin(7*f*x + 7*e) + 6*sin(5*f*x + 5*e) + 4*sin(3*f*x + 3*e) + sin(f*x + e))*cos(10*f*x + 10*e) - 20*(3*sin(8*f*x + 8*e) + sin(6*f*x + 6*e) - sin(4*f*x + 4*e) - 3*sin(2*f*x + 2*e))*cos(9*f*x + 9*e) + 60*(4*sin(7*f*x + 7*e) + 6*sin(5*f*x + 5*e) + 4*sin(3*f*x + 3*e) + sin(f*x + e))*cos(8*f*x + 8*e) - 80*(sin(6*f*x + 6*e) - sin(4*f*x + 4*e) - 3*sin(2*f*x + 2*e))*cos(7*f*x + 7*e) + 20*(6*sin(5*f*x + 5*e) + 4*sin(3*f*x + 3*e) + sin(f*x + e))*cos(6*f*x + 6*e) + 120*(sin(4*f*x + 4*e) + 3*sin(2*f*x + 2*e))*cos(5*f*x + 5*e) - 20*(4*sin(3*f*x + 3*e) + sin(f*x + e))*cos(4*f*x + 4*e) + 15*(2*(4*cos(7*f*x + 7*e) + 6*cos(5*f*x + 5*e) + 4*cos(3*f*x + 3*e) + cos(f*x + e))*cos(9*f*x + 9*e) + cos(9*f*x + 9*e)^2 + 8*(6*cos(5*f*x + 5*e) + 4*cos(3*f*x + 3*e) + cos(f*x + e))*cos(7*f*x + 7*e) + 16*cos(7*f*x + 7*e)^2 + 12*(4*cos(3*f*x + 3*e) + cos(f*x + e))*cos(5*f*x + 5*e) + 36*cos(5*f*x + 5*e)^2 + 16*cos(3*f*x + 3*e)^2 + 8*cos(3*f*x + 3*e)*cos(f*x + e) + cos(f*x + e)^2 + 2*(4*sin(7*f*x + 7*e) + 6*sin(5*f*x + 5*e) + 4*sin(3*f*x + 3*e) + sin(f*x + e))*sin(9*f*x + 9*e) + sin(9*f*x + 9*e)^2 + 8*(6*sin(5*f*x + 5*e) + 4*sin(3*f*x + 3*e) + sin(f*x + e))*sin(7*f*x + 7*e) + 16*sin(7*f*x + 7*e)^2 + 12*(4*sin(3*f*x + 3*e) + sin(f*x + e))*sin(5*f*x + 5*e) + 36*sin(5*f*x + 5*e)^2 + 16*sin(3*f*x + 3*e)^2 + 8*sin(3*f*x + 3*e)*sin(f*x + e) + sin(f*x + e)^2)*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*sin(f*x + e) + 1) - 15*(2*(4*cos(7*f*x + 7*e) + 6*cos(5*f*x + 5*e) + 4*cos(3*f*x + 3*e) + cos(f*x + e))*cos(9*f*x + 9*e) + cos(9*f*x + 9*e)^2 + 8*(6*cos(5*f*x + 5*e) + 4*cos(3*f*x + 3*e) + cos(f*x + e))*cos(7*f*x + 7*e) + 16*cos(7*f*x + 7*e)^2 + 12*(4*cos(3*f*x + 3*e) + cos(f*x + e))*cos(5*f*x + 5*e) + 36*cos(5*f*x + 5*e)^2 + 16*cos(3*f*x + 3*e)^2 + 8*cos(3*f*x + 3*e)*cos(f*x + e) + cos(f*x + e)^2 + 2*(4*sin(7*f*x + 7*e) + 6*sin(5*f*x + 5*e) + 4*sin(3*f*x + 3*e) + sin(f*x + e))*sin(9*f*x + 9*e) + sin(9*f*x + 9*e)^2 + 8*(6*sin(5*f*x + 5*e) + 4*sin(3*f*x + 3*e) + sin(f*x + e))*sin(7*f*x + 7*e) + 16*sin(7*f*x + 7*e)^2 + 12*(4*sin(3*f*x + 3*e) + sin(f*x + e))*sin(5*f*x + 5*e) + 36*sin(5*f*x + 5*e)^2 + 16*sin(3*f*x + 3*e)^2 + 8*sin(3*f*x + 3*e)*sin(f*x + e) + sin(f*x + e)^2)*log(cos(f*x + e)^2 + sin(f*x + e)^2 - 2*sin(f*x + e) + 1) - 8*(cos(9*f*x + 9*e) + 4*cos(7*f*x + 7*e) + 6*cos(5*f*x + 5*e) + 4*cos(3*f*x + 3*e) + cos(f*x + e))*sin(10*f*x + 10*e) + 4*(15*cos(8*f*x + 8*e) + 5*cos(6*f*x + 6*e) - 5*cos(4*f*x + 4*e) - 15*cos(2*f*x + 2*e) - 2)*sin(9*f*x + 9*e) - 60*(4*cos(7*f*x + 7*e) + 6*cos(5*f*x + 5*e) + 4*cos(3*f*x + 3*e) + cos(f*x + e))*sin(8*f*x + 8*e) + 16*(5*cos(6*f*x + 6*e) - 5*cos(4*f*x + 4*e) - 15*cos(2*f*x + 2*e) - 2)*sin(7*f*x + 7*e) - 20*(6*cos(5*f*x + 5*e) + 4*cos(3*f*x + 3*e) + cos(f*x + e))*sin(6*f*x + 6*e) - 24*(5*cos(4*f*x + 4*e) + 15*cos(2*f*x + 2*e) + 2)*sin(5*f*x + 5*e) + 20*(4*cos(3*f*x + 3*e) + cos(f*x + e))*sin(4*f*x + 4*e) - 16*(15*cos(2*f*x + 2*e) + 2)*sin(3*f*x + 3*e) + 240*cos(3*f*x + 3*e)*sin(2*f*x + 2*e) + 60*cos(f*x + e)*sin(2*f*x + 2*e) - 60*cos(2*f*x + 2*e)*sin(f*x + e) - 8*sin(f*x + e))*sqrt(a)/((2*(4*cos(7*f*x + 7*e) + 6*cos(5*f*x + 5*e) + 4*cos(3*f*x + 3*e) + cos(f*x + e))*cos(9*f*x + 9*e) + cos(9*f*x + 9*e)^2 + 8*(6*cos(5*f*x + 5*e) + 4*cos(3*f*x + 3*e) + cos(f*x + e))*cos(7*f*x + 7*e) + 16*cos(7*f*x + 7*e)^2 + 12*(4*cos(3*f*x + 3*e) + cos(f*x + e))*cos(5*f*x + 5*e) + 36*cos(5*f*x + 5*e)^2 + 16*cos(3*f*x + 3*e)^2 + 8*cos(3*f*x + 3*e)*cos(f*x + e) + cos(f*x + e)^2 + 2*(4*sin(7*f*x + 7*e) + 6*sin(5*f*x + 5*e) + 4*sin(3*f*x + 3*e) + sin(f*x + e))*sin(9*f*x + 9*e) + sin(9*f*x + 9*e)^2 + 8*(6*sin(5*f*x + 5*e) + 4*sin(3*f*x + 3*e) + sin(f*x + e))*sin(7*f*x + 7*e) + 16*sin(7*f*x + 7*e)^2 + 12*(4*sin(3*f*x + 3*e) + sin(f*x + e))*sin(5*f*x + 5*e) + 36*sin(5*f*x + 5*e)^2 + 16*sin(3*f*x + 3*e)^2 + 8*sin(3*f*x + 3*e)*sin(f*x + e) + sin(f*x + e)^2)*f)","B",0
463,1,827,0,0.540176," ","integrate((a-a*sin(f*x+e)^2)^(1/2)*tan(f*x+e)^4,x, algorithm=""maxima"")","-\frac{{\left(2 \, {\left(\sin\left(5 \, f x + 5 \, e\right) + 2 \, \sin\left(3 \, f x + 3 \, e\right) + \sin\left(f x + e\right)\right)} \cos\left(6 \, f x + 6 \, e\right) - 6 \, {\left(\sin\left(4 \, f x + 4 \, e\right) - \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(5 \, f x + 5 \, e\right) + 6 \, {\left(2 \, \sin\left(3 \, f x + 3 \, e\right) + \sin\left(f x + e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + 3 \, {\left(2 \, {\left(2 \, \cos\left(3 \, f x + 3 \, e\right) + \cos\left(f x + e\right)\right)} \cos\left(5 \, f x + 5 \, e\right) + \cos\left(5 \, f x + 5 \, e\right)^{2} + 4 \, \cos\left(3 \, f x + 3 \, e\right)^{2} + 4 \, \cos\left(3 \, f x + 3 \, e\right) \cos\left(f x + e\right) + \cos\left(f x + e\right)^{2} + 2 \, {\left(2 \, \sin\left(3 \, f x + 3 \, e\right) + \sin\left(f x + e\right)\right)} \sin\left(5 \, f x + 5 \, e\right) + \sin\left(5 \, f x + 5 \, e\right)^{2} + 4 \, \sin\left(3 \, f x + 3 \, e\right)^{2} + 4 \, \sin\left(3 \, f x + 3 \, e\right) \sin\left(f x + e\right) + \sin\left(f x + e\right)^{2}\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \sin\left(f x + e\right) + 1\right) - 3 \, {\left(2 \, {\left(2 \, \cos\left(3 \, f x + 3 \, e\right) + \cos\left(f x + e\right)\right)} \cos\left(5 \, f x + 5 \, e\right) + \cos\left(5 \, f x + 5 \, e\right)^{2} + 4 \, \cos\left(3 \, f x + 3 \, e\right)^{2} + 4 \, \cos\left(3 \, f x + 3 \, e\right) \cos\left(f x + e\right) + \cos\left(f x + e\right)^{2} + 2 \, {\left(2 \, \sin\left(3 \, f x + 3 \, e\right) + \sin\left(f x + e\right)\right)} \sin\left(5 \, f x + 5 \, e\right) + \sin\left(5 \, f x + 5 \, e\right)^{2} + 4 \, \sin\left(3 \, f x + 3 \, e\right)^{2} + 4 \, \sin\left(3 \, f x + 3 \, e\right) \sin\left(f x + e\right) + \sin\left(f x + e\right)^{2}\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} - 2 \, \sin\left(f x + e\right) + 1\right) - 2 \, {\left(\cos\left(5 \, f x + 5 \, e\right) + 2 \, \cos\left(3 \, f x + 3 \, e\right) + \cos\left(f x + e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) + 2 \, {\left(3 \, \cos\left(4 \, f x + 4 \, e\right) - 3 \, \cos\left(2 \, f x + 2 \, e\right) - 1\right)} \sin\left(5 \, f x + 5 \, e\right) - 6 \, {\left(2 \, \cos\left(3 \, f x + 3 \, e\right) + \cos\left(f x + e\right)\right)} \sin\left(4 \, f x + 4 \, e\right) - 4 \, {\left(3 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \sin\left(3 \, f x + 3 \, e\right) + 12 \, \cos\left(3 \, f x + 3 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 6 \, \cos\left(f x + e\right) \sin\left(2 \, f x + 2 \, e\right) - 6 \, \cos\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) - 2 \, \sin\left(f x + e\right)\right)} \sqrt{a}}{4 \, {\left(2 \, {\left(2 \, \cos\left(3 \, f x + 3 \, e\right) + \cos\left(f x + e\right)\right)} \cos\left(5 \, f x + 5 \, e\right) + \cos\left(5 \, f x + 5 \, e\right)^{2} + 4 \, \cos\left(3 \, f x + 3 \, e\right)^{2} + 4 \, \cos\left(3 \, f x + 3 \, e\right) \cos\left(f x + e\right) + \cos\left(f x + e\right)^{2} + 2 \, {\left(2 \, \sin\left(3 \, f x + 3 \, e\right) + \sin\left(f x + e\right)\right)} \sin\left(5 \, f x + 5 \, e\right) + \sin\left(5 \, f x + 5 \, e\right)^{2} + 4 \, \sin\left(3 \, f x + 3 \, e\right)^{2} + 4 \, \sin\left(3 \, f x + 3 \, e\right) \sin\left(f x + e\right) + \sin\left(f x + e\right)^{2}\right)} f}"," ",0,"-1/4*(2*(sin(5*f*x + 5*e) + 2*sin(3*f*x + 3*e) + sin(f*x + e))*cos(6*f*x + 6*e) - 6*(sin(4*f*x + 4*e) - sin(2*f*x + 2*e))*cos(5*f*x + 5*e) + 6*(2*sin(3*f*x + 3*e) + sin(f*x + e))*cos(4*f*x + 4*e) + 3*(2*(2*cos(3*f*x + 3*e) + cos(f*x + e))*cos(5*f*x + 5*e) + cos(5*f*x + 5*e)^2 + 4*cos(3*f*x + 3*e)^2 + 4*cos(3*f*x + 3*e)*cos(f*x + e) + cos(f*x + e)^2 + 2*(2*sin(3*f*x + 3*e) + sin(f*x + e))*sin(5*f*x + 5*e) + sin(5*f*x + 5*e)^2 + 4*sin(3*f*x + 3*e)^2 + 4*sin(3*f*x + 3*e)*sin(f*x + e) + sin(f*x + e)^2)*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*sin(f*x + e) + 1) - 3*(2*(2*cos(3*f*x + 3*e) + cos(f*x + e))*cos(5*f*x + 5*e) + cos(5*f*x + 5*e)^2 + 4*cos(3*f*x + 3*e)^2 + 4*cos(3*f*x + 3*e)*cos(f*x + e) + cos(f*x + e)^2 + 2*(2*sin(3*f*x + 3*e) + sin(f*x + e))*sin(5*f*x + 5*e) + sin(5*f*x + 5*e)^2 + 4*sin(3*f*x + 3*e)^2 + 4*sin(3*f*x + 3*e)*sin(f*x + e) + sin(f*x + e)^2)*log(cos(f*x + e)^2 + sin(f*x + e)^2 - 2*sin(f*x + e) + 1) - 2*(cos(5*f*x + 5*e) + 2*cos(3*f*x + 3*e) + cos(f*x + e))*sin(6*f*x + 6*e) + 2*(3*cos(4*f*x + 4*e) - 3*cos(2*f*x + 2*e) - 1)*sin(5*f*x + 5*e) - 6*(2*cos(3*f*x + 3*e) + cos(f*x + e))*sin(4*f*x + 4*e) - 4*(3*cos(2*f*x + 2*e) + 1)*sin(3*f*x + 3*e) + 12*cos(3*f*x + 3*e)*sin(2*f*x + 2*e) + 6*cos(f*x + e)*sin(2*f*x + 2*e) - 6*cos(2*f*x + 2*e)*sin(f*x + e) - 2*sin(f*x + e))*sqrt(a)/((2*(2*cos(3*f*x + 3*e) + cos(f*x + e))*cos(5*f*x + 5*e) + cos(5*f*x + 5*e)^2 + 4*cos(3*f*x + 3*e)^2 + 4*cos(3*f*x + 3*e)*cos(f*x + e) + cos(f*x + e)^2 + 2*(2*sin(3*f*x + 3*e) + sin(f*x + e))*sin(5*f*x + 5*e) + sin(5*f*x + 5*e)^2 + 4*sin(3*f*x + 3*e)^2 + 4*sin(3*f*x + 3*e)*sin(f*x + e) + sin(f*x + e)^2)*f)","B",0
464,1,73,0,0.478041," ","integrate((a-a*sin(f*x+e)^2)^(1/2)*tan(f*x+e)^2,x, algorithm=""maxima"")","\frac{\sqrt{a} {\left(\log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \sin\left(f x + e\right) + 1\right) - \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} - 2 \, \sin\left(f x + e\right) + 1\right) - 2 \, \sin\left(f x + e\right)\right)}}{2 \, f}"," ",0,"1/2*sqrt(a)*(log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*sin(f*x + e) + 1) - log(cos(f*x + e)^2 + sin(f*x + e)^2 - 2*sin(f*x + e) + 1) - 2*sin(f*x + e))/f","A",0
465,1,42,0,0.421571," ","integrate(cot(f*x+e)^2*(a-a*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{a} \tan\left(f x + e\right)^{2} + \sqrt{a}}{\sqrt{\tan\left(f x + e\right)^{2} + 1} f \tan\left(f x + e\right)}"," ",0,"-(2*sqrt(a)*tan(f*x + e)^2 + sqrt(a))/(sqrt(tan(f*x + e)^2 + 1)*f*tan(f*x + e))","A",0
466,1,57,0,0.419791," ","integrate(cot(f*x+e)^4*(a-a*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\frac{8 \, \sqrt{a} \tan\left(f x + e\right)^{4} + 4 \, \sqrt{a} \tan\left(f x + e\right)^{2} - \sqrt{a}}{3 \, \sqrt{\tan\left(f x + e\right)^{2} + 1} f \tan\left(f x + e\right)^{3}}"," ",0,"1/3*(8*sqrt(a)*tan(f*x + e)^4 + 4*sqrt(a)*tan(f*x + e)^2 - sqrt(a))/(sqrt(tan(f*x + e)^2 + 1)*f*tan(f*x + e)^3)","A",0
467,1,68,0,0.424827," ","integrate(cot(f*x+e)^6*(a-a*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","-\frac{16 \, \sqrt{a} \tan\left(f x + e\right)^{6} + 8 \, \sqrt{a} \tan\left(f x + e\right)^{4} - 2 \, \sqrt{a} \tan\left(f x + e\right)^{2} + \sqrt{a}}{5 \, \sqrt{\tan\left(f x + e\right)^{2} + 1} f \tan\left(f x + e\right)^{5}}"," ",0,"-1/5*(16*sqrt(a)*tan(f*x + e)^6 + 8*sqrt(a)*tan(f*x + e)^4 - 2*sqrt(a)*tan(f*x + e)^2 + sqrt(a))/(sqrt(tan(f*x + e)^2 + 1)*f*tan(f*x + e)^5)","A",0
468,1,69,0,0.345363," ","integrate(tan(f*x+e)^5/(a-a*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\frac{15 \, {\left(a \sin\left(f x + e\right)^{2} - a\right)}^{2} a^{3} + 10 \, {\left(a \sin\left(f x + e\right)^{2} - a\right)} a^{4} + 3 \, a^{5}}{15 \, {\left(-a \sin\left(f x + e\right)^{2} + a\right)}^{\frac{5}{2}} a^{3} f}"," ",0,"1/15*(15*(a*sin(f*x + e)^2 - a)^2*a^3 + 10*(a*sin(f*x + e)^2 - a)*a^4 + 3*a^5)/((-a*sin(f*x + e)^2 + a)^(5/2)*a^3*f)","A",0
469,1,46,0,0.342032," ","integrate(tan(f*x+e)^3/(a-a*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\frac{3 \, {\left(a \sin\left(f x + e\right)^{2} - a\right)} a^{2} + a^{3}}{3 \, {\left(-a \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} a^{2} f}"," ",0,"1/3*(3*(a*sin(f*x + e)^2 - a)*a^2 + a^3)/((-a*sin(f*x + e)^2 + a)^(3/2)*a^2*f)","A",0
470,1,65,0,0.441337," ","integrate(tan(f*x+e)/(a-a*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\frac{\frac{\sqrt{-a \sin\left(f x + e\right)^{2} + a}}{a \sin\left(f x + e\right) + a} - \frac{\sqrt{-a \sin\left(f x + e\right)^{2} + a}}{a \sin\left(f x + e\right) - a}}{2 \, f}"," ",0,"1/2*(sqrt(-a*sin(f*x + e)^2 + a)/(a*sin(f*x + e) + a) - sqrt(-a*sin(f*x + e)^2 + a)/(a*sin(f*x + e) - a))/f","B",0
471,1,51,0,0.312454," ","integrate(cot(f*x+e)/(a-a*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","-\frac{\log\left(\frac{2 \, \sqrt{-a \sin\left(f x + e\right)^{2} + a} \sqrt{a}}{{\left| \sin\left(f x + e\right) \right|}} + \frac{2 \, a}{{\left| \sin\left(f x + e\right) \right|}}\right)}{\sqrt{a} f}"," ",0,"-log(2*sqrt(-a*sin(f*x + e)^2 + a)*sqrt(a)/abs(sin(f*x + e)) + 2*a/abs(sin(f*x + e)))/(sqrt(a)*f)","B",0
472,1,81,0,0.410372," ","integrate(cot(f*x+e)^3/(a-a*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\frac{\frac{\log\left(\frac{2 \, \sqrt{-a \sin\left(f x + e\right)^{2} + a} \sqrt{a}}{{\left| \sin\left(f x + e\right) \right|}} + \frac{2 \, a}{{\left| \sin\left(f x + e\right) \right|}}\right)}{\sqrt{a}} - \frac{\sqrt{-a \sin\left(f x + e\right)^{2} + a}}{a \sin\left(f x + e\right)^{2}}}{2 \, f}"," ",0,"1/2*(log(2*sqrt(-a*sin(f*x + e)^2 + a)*sqrt(a)/abs(sin(f*x + e)) + 2*a/abs(sin(f*x + e)))/sqrt(a) - sqrt(-a*sin(f*x + e)^2 + a)/(a*sin(f*x + e)^2))/f","A",0
473,1,1518,0,0.733206," ","integrate(tan(f*x+e)^4/(a-a*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","-\frac{4 \, {\left(5 \, \sin\left(7 \, f x + 7 \, e\right) - 3 \, \sin\left(5 \, f x + 5 \, e\right) + 3 \, \sin\left(3 \, f x + 3 \, e\right) - 5 \, \sin\left(f x + e\right)\right)} \cos\left(8 \, f x + 8 \, e\right) - 40 \, {\left(2 \, \sin\left(6 \, f x + 6 \, e\right) + 3 \, \sin\left(4 \, f x + 4 \, e\right) + 2 \, \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(7 \, f x + 7 \, e\right) - 16 \, {\left(3 \, \sin\left(5 \, f x + 5 \, e\right) - 3 \, \sin\left(3 \, f x + 3 \, e\right) + 5 \, \sin\left(f x + e\right)\right)} \cos\left(6 \, f x + 6 \, e\right) + 24 \, {\left(3 \, \sin\left(4 \, f x + 4 \, e\right) + 2 \, \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(5 \, f x + 5 \, e\right) + 24 \, {\left(3 \, \sin\left(3 \, f x + 3 \, e\right) - 5 \, \sin\left(f x + e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) - 3 \, {\left(2 \, {\left(4 \, \cos\left(6 \, f x + 6 \, e\right) + 6 \, \cos\left(4 \, f x + 4 \, e\right) + 4 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \cos\left(8 \, f x + 8 \, e\right) + \cos\left(8 \, f x + 8 \, e\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, f x + 4 \, e\right) + 4 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \cos\left(6 \, f x + 6 \, e\right) + 16 \, \cos\left(6 \, f x + 6 \, e\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \cos\left(4 \, f x + 4 \, e\right) + 36 \, \cos\left(4 \, f x + 4 \, e\right)^{2} + 16 \, \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, f x + 6 \, e\right) + 3 \, \sin\left(4 \, f x + 4 \, e\right) + 2 \, \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(8 \, f x + 8 \, e\right) + \sin\left(8 \, f x + 8 \, e\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, f x + 4 \, e\right) + 2 \, \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) + 16 \, \sin\left(6 \, f x + 6 \, e\right)^{2} + 36 \, \sin\left(4 \, f x + 4 \, e\right)^{2} + 48 \, \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 16 \, \sin\left(2 \, f x + 2 \, e\right)^{2} + 8 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \sin\left(f x + e\right) + 1\right) + 3 \, {\left(2 \, {\left(4 \, \cos\left(6 \, f x + 6 \, e\right) + 6 \, \cos\left(4 \, f x + 4 \, e\right) + 4 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \cos\left(8 \, f x + 8 \, e\right) + \cos\left(8 \, f x + 8 \, e\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, f x + 4 \, e\right) + 4 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \cos\left(6 \, f x + 6 \, e\right) + 16 \, \cos\left(6 \, f x + 6 \, e\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \cos\left(4 \, f x + 4 \, e\right) + 36 \, \cos\left(4 \, f x + 4 \, e\right)^{2} + 16 \, \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, f x + 6 \, e\right) + 3 \, \sin\left(4 \, f x + 4 \, e\right) + 2 \, \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(8 \, f x + 8 \, e\right) + \sin\left(8 \, f x + 8 \, e\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, f x + 4 \, e\right) + 2 \, \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) + 16 \, \sin\left(6 \, f x + 6 \, e\right)^{2} + 36 \, \sin\left(4 \, f x + 4 \, e\right)^{2} + 48 \, \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 16 \, \sin\left(2 \, f x + 2 \, e\right)^{2} + 8 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} - 2 \, \sin\left(f x + e\right) + 1\right) - 4 \, {\left(5 \, \cos\left(7 \, f x + 7 \, e\right) - 3 \, \cos\left(5 \, f x + 5 \, e\right) + 3 \, \cos\left(3 \, f x + 3 \, e\right) - 5 \, \cos\left(f x + e\right)\right)} \sin\left(8 \, f x + 8 \, e\right) + 20 \, {\left(4 \, \cos\left(6 \, f x + 6 \, e\right) + 6 \, \cos\left(4 \, f x + 4 \, e\right) + 4 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \sin\left(7 \, f x + 7 \, e\right) + 16 \, {\left(3 \, \cos\left(5 \, f x + 5 \, e\right) - 3 \, \cos\left(3 \, f x + 3 \, e\right) + 5 \, \cos\left(f x + e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) - 12 \, {\left(6 \, \cos\left(4 \, f x + 4 \, e\right) + 4 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \sin\left(5 \, f x + 5 \, e\right) - 24 \, {\left(3 \, \cos\left(3 \, f x + 3 \, e\right) - 5 \, \cos\left(f x + e\right)\right)} \sin\left(4 \, f x + 4 \, e\right) + 12 \, {\left(4 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \sin\left(3 \, f x + 3 \, e\right) - 48 \, \cos\left(3 \, f x + 3 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 80 \, \cos\left(f x + e\right) \sin\left(2 \, f x + 2 \, e\right) - 80 \, \cos\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) - 20 \, \sin\left(f x + e\right)}{16 \, {\left(2 \, {\left(4 \, \cos\left(6 \, f x + 6 \, e\right) + 6 \, \cos\left(4 \, f x + 4 \, e\right) + 4 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \cos\left(8 \, f x + 8 \, e\right) + \cos\left(8 \, f x + 8 \, e\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, f x + 4 \, e\right) + 4 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \cos\left(6 \, f x + 6 \, e\right) + 16 \, \cos\left(6 \, f x + 6 \, e\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \cos\left(4 \, f x + 4 \, e\right) + 36 \, \cos\left(4 \, f x + 4 \, e\right)^{2} + 16 \, \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, f x + 6 \, e\right) + 3 \, \sin\left(4 \, f x + 4 \, e\right) + 2 \, \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(8 \, f x + 8 \, e\right) + \sin\left(8 \, f x + 8 \, e\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, f x + 4 \, e\right) + 2 \, \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) + 16 \, \sin\left(6 \, f x + 6 \, e\right)^{2} + 36 \, \sin\left(4 \, f x + 4 \, e\right)^{2} + 48 \, \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 16 \, \sin\left(2 \, f x + 2 \, e\right)^{2} + 8 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \sqrt{a} f}"," ",0,"-1/16*(4*(5*sin(7*f*x + 7*e) - 3*sin(5*f*x + 5*e) + 3*sin(3*f*x + 3*e) - 5*sin(f*x + e))*cos(8*f*x + 8*e) - 40*(2*sin(6*f*x + 6*e) + 3*sin(4*f*x + 4*e) + 2*sin(2*f*x + 2*e))*cos(7*f*x + 7*e) - 16*(3*sin(5*f*x + 5*e) - 3*sin(3*f*x + 3*e) + 5*sin(f*x + e))*cos(6*f*x + 6*e) + 24*(3*sin(4*f*x + 4*e) + 2*sin(2*f*x + 2*e))*cos(5*f*x + 5*e) + 24*(3*sin(3*f*x + 3*e) - 5*sin(f*x + e))*cos(4*f*x + 4*e) - 3*(2*(4*cos(6*f*x + 6*e) + 6*cos(4*f*x + 4*e) + 4*cos(2*f*x + 2*e) + 1)*cos(8*f*x + 8*e) + cos(8*f*x + 8*e)^2 + 8*(6*cos(4*f*x + 4*e) + 4*cos(2*f*x + 2*e) + 1)*cos(6*f*x + 6*e) + 16*cos(6*f*x + 6*e)^2 + 12*(4*cos(2*f*x + 2*e) + 1)*cos(4*f*x + 4*e) + 36*cos(4*f*x + 4*e)^2 + 16*cos(2*f*x + 2*e)^2 + 4*(2*sin(6*f*x + 6*e) + 3*sin(4*f*x + 4*e) + 2*sin(2*f*x + 2*e))*sin(8*f*x + 8*e) + sin(8*f*x + 8*e)^2 + 16*(3*sin(4*f*x + 4*e) + 2*sin(2*f*x + 2*e))*sin(6*f*x + 6*e) + 16*sin(6*f*x + 6*e)^2 + 36*sin(4*f*x + 4*e)^2 + 48*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 16*sin(2*f*x + 2*e)^2 + 8*cos(2*f*x + 2*e) + 1)*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*sin(f*x + e) + 1) + 3*(2*(4*cos(6*f*x + 6*e) + 6*cos(4*f*x + 4*e) + 4*cos(2*f*x + 2*e) + 1)*cos(8*f*x + 8*e) + cos(8*f*x + 8*e)^2 + 8*(6*cos(4*f*x + 4*e) + 4*cos(2*f*x + 2*e) + 1)*cos(6*f*x + 6*e) + 16*cos(6*f*x + 6*e)^2 + 12*(4*cos(2*f*x + 2*e) + 1)*cos(4*f*x + 4*e) + 36*cos(4*f*x + 4*e)^2 + 16*cos(2*f*x + 2*e)^2 + 4*(2*sin(6*f*x + 6*e) + 3*sin(4*f*x + 4*e) + 2*sin(2*f*x + 2*e))*sin(8*f*x + 8*e) + sin(8*f*x + 8*e)^2 + 16*(3*sin(4*f*x + 4*e) + 2*sin(2*f*x + 2*e))*sin(6*f*x + 6*e) + 16*sin(6*f*x + 6*e)^2 + 36*sin(4*f*x + 4*e)^2 + 48*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 16*sin(2*f*x + 2*e)^2 + 8*cos(2*f*x + 2*e) + 1)*log(cos(f*x + e)^2 + sin(f*x + e)^2 - 2*sin(f*x + e) + 1) - 4*(5*cos(7*f*x + 7*e) - 3*cos(5*f*x + 5*e) + 3*cos(3*f*x + 3*e) - 5*cos(f*x + e))*sin(8*f*x + 8*e) + 20*(4*cos(6*f*x + 6*e) + 6*cos(4*f*x + 4*e) + 4*cos(2*f*x + 2*e) + 1)*sin(7*f*x + 7*e) + 16*(3*cos(5*f*x + 5*e) - 3*cos(3*f*x + 3*e) + 5*cos(f*x + e))*sin(6*f*x + 6*e) - 12*(6*cos(4*f*x + 4*e) + 4*cos(2*f*x + 2*e) + 1)*sin(5*f*x + 5*e) - 24*(3*cos(3*f*x + 3*e) - 5*cos(f*x + e))*sin(4*f*x + 4*e) + 12*(4*cos(2*f*x + 2*e) + 1)*sin(3*f*x + 3*e) - 48*cos(3*f*x + 3*e)*sin(2*f*x + 2*e) + 80*cos(f*x + e)*sin(2*f*x + 2*e) - 80*cos(2*f*x + 2*e)*sin(f*x + e) - 20*sin(f*x + e))/((2*(4*cos(6*f*x + 6*e) + 6*cos(4*f*x + 4*e) + 4*cos(2*f*x + 2*e) + 1)*cos(8*f*x + 8*e) + cos(8*f*x + 8*e)^2 + 8*(6*cos(4*f*x + 4*e) + 4*cos(2*f*x + 2*e) + 1)*cos(6*f*x + 6*e) + 16*cos(6*f*x + 6*e)^2 + 12*(4*cos(2*f*x + 2*e) + 1)*cos(4*f*x + 4*e) + 36*cos(4*f*x + 4*e)^2 + 16*cos(2*f*x + 2*e)^2 + 4*(2*sin(6*f*x + 6*e) + 3*sin(4*f*x + 4*e) + 2*sin(2*f*x + 2*e))*sin(8*f*x + 8*e) + sin(8*f*x + 8*e)^2 + 16*(3*sin(4*f*x + 4*e) + 2*sin(2*f*x + 2*e))*sin(6*f*x + 6*e) + 16*sin(6*f*x + 6*e)^2 + 36*sin(4*f*x + 4*e)^2 + 48*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 16*sin(2*f*x + 2*e)^2 + 8*cos(2*f*x + 2*e) + 1)*sqrt(a)*f)","B",0
474,1,527,0,0.501878," ","integrate(tan(f*x+e)^2/(a-a*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\frac{4 \, {\left(\sin\left(3 \, f x + 3 \, e\right) - \sin\left(f x + e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) - {\left(2 \, {\left(2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \cos\left(4 \, f x + 4 \, e\right) + \cos\left(4 \, f x + 4 \, e\right)^{2} + 4 \, \cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \sin\left(f x + e\right) + 1\right) + {\left(2 \, {\left(2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \cos\left(4 \, f x + 4 \, e\right) + \cos\left(4 \, f x + 4 \, e\right)^{2} + 4 \, \cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} - 2 \, \sin\left(f x + e\right) + 1\right) - 4 \, {\left(\cos\left(3 \, f x + 3 \, e\right) - \cos\left(f x + e\right)\right)} \sin\left(4 \, f x + 4 \, e\right) + 4 \, {\left(2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \sin\left(3 \, f x + 3 \, e\right) - 8 \, \cos\left(3 \, f x + 3 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 8 \, \cos\left(f x + e\right) \sin\left(2 \, f x + 2 \, e\right) - 8 \, \cos\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) - 4 \, \sin\left(f x + e\right)}{4 \, {\left(2 \, {\left(2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \cos\left(4 \, f x + 4 \, e\right) + \cos\left(4 \, f x + 4 \, e\right)^{2} + 4 \, \cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \sqrt{a} f}"," ",0,"1/4*(4*(sin(3*f*x + 3*e) - sin(f*x + e))*cos(4*f*x + 4*e) - (2*(2*cos(2*f*x + 2*e) + 1)*cos(4*f*x + 4*e) + cos(4*f*x + 4*e)^2 + 4*cos(2*f*x + 2*e)^2 + sin(4*f*x + 4*e)^2 + 4*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*sin(2*f*x + 2*e)^2 + 4*cos(2*f*x + 2*e) + 1)*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*sin(f*x + e) + 1) + (2*(2*cos(2*f*x + 2*e) + 1)*cos(4*f*x + 4*e) + cos(4*f*x + 4*e)^2 + 4*cos(2*f*x + 2*e)^2 + sin(4*f*x + 4*e)^2 + 4*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*sin(2*f*x + 2*e)^2 + 4*cos(2*f*x + 2*e) + 1)*log(cos(f*x + e)^2 + sin(f*x + e)^2 - 2*sin(f*x + e) + 1) - 4*(cos(3*f*x + 3*e) - cos(f*x + e))*sin(4*f*x + 4*e) + 4*(2*cos(2*f*x + 2*e) + 1)*sin(3*f*x + 3*e) - 8*cos(3*f*x + 3*e)*sin(2*f*x + 2*e) + 8*cos(f*x + e)*sin(2*f*x + 2*e) - 8*cos(2*f*x + 2*e)*sin(f*x + e) - 4*sin(f*x + e))/((2*(2*cos(2*f*x + 2*e) + 1)*cos(4*f*x + 4*e) + cos(4*f*x + 4*e)^2 + 4*cos(2*f*x + 2*e)^2 + sin(4*f*x + 4*e)^2 + 4*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 4*sin(2*f*x + 2*e)^2 + 4*cos(2*f*x + 2*e) + 1)*sqrt(a)*f)","B",0
475,1,90,0,0.484226," ","integrate(cot(f*x+e)^2/(a-a*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(\cos\left(f x + e\right) \sin\left(2 \, f x + 2 \, e\right) - \cos\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) + \sin\left(f x + e\right)\right)} \sqrt{a}}{{\left(a \cos\left(2 \, f x + 2 \, e\right)^{2} + a \sin\left(2 \, f x + 2 \, e\right)^{2} - 2 \, a \cos\left(2 \, f x + 2 \, e\right) + a\right)} f}"," ",0,"-2*(cos(f*x + e)*sin(2*f*x + 2*e) - cos(2*f*x + 2*e)*sin(f*x + e) + sin(f*x + e))*sqrt(a)/((a*cos(2*f*x + 2*e)^2 + a*sin(2*f*x + 2*e)^2 - 2*a*cos(2*f*x + 2*e) + a)*f)","B",0
476,1,525,0,0.500753," ","integrate(cot(f*x+e)^4/(a-a*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","-\frac{2 \, {\left({\left(3 \, \sin\left(5 \, f x + 5 \, e\right) - 2 \, \sin\left(3 \, f x + 3 \, e\right) + 3 \, \sin\left(f x + e\right)\right)} \cos\left(6 \, f x + 6 \, e\right) + 9 \, {\left(\sin\left(4 \, f x + 4 \, e\right) - \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(5 \, f x + 5 \, e\right) + 3 \, {\left(2 \, \sin\left(3 \, f x + 3 \, e\right) - 3 \, \sin\left(f x + e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) - {\left(3 \, \cos\left(5 \, f x + 5 \, e\right) - 2 \, \cos\left(3 \, f x + 3 \, e\right) + 3 \, \cos\left(f x + e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) - 3 \, {\left(3 \, \cos\left(4 \, f x + 4 \, e\right) - 3 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \sin\left(5 \, f x + 5 \, e\right) - 3 \, {\left(2 \, \cos\left(3 \, f x + 3 \, e\right) - 3 \, \cos\left(f x + e\right)\right)} \sin\left(4 \, f x + 4 \, e\right) - 2 \, {\left(3 \, \cos\left(2 \, f x + 2 \, e\right) - 1\right)} \sin\left(3 \, f x + 3 \, e\right) + 6 \, \cos\left(3 \, f x + 3 \, e\right) \sin\left(2 \, f x + 2 \, e\right) - 9 \, \cos\left(f x + e\right) \sin\left(2 \, f x + 2 \, e\right) + 9 \, \cos\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) - 3 \, \sin\left(f x + e\right)\right)} \sqrt{a}}{3 \, {\left(a \cos\left(6 \, f x + 6 \, e\right)^{2} + 9 \, a \cos\left(4 \, f x + 4 \, e\right)^{2} + 9 \, a \cos\left(2 \, f x + 2 \, e\right)^{2} + a \sin\left(6 \, f x + 6 \, e\right)^{2} + 9 \, a \sin\left(4 \, f x + 4 \, e\right)^{2} - 18 \, a \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 9 \, a \sin\left(2 \, f x + 2 \, e\right)^{2} - 2 \, {\left(3 \, a \cos\left(4 \, f x + 4 \, e\right) - 3 \, a \cos\left(2 \, f x + 2 \, e\right) + a\right)} \cos\left(6 \, f x + 6 \, e\right) - 6 \, {\left(3 \, a \cos\left(2 \, f x + 2 \, e\right) - a\right)} \cos\left(4 \, f x + 4 \, e\right) - 6 \, a \cos\left(2 \, f x + 2 \, e\right) - 6 \, {\left(a \sin\left(4 \, f x + 4 \, e\right) - a \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) + a\right)} f}"," ",0,"-2/3*((3*sin(5*f*x + 5*e) - 2*sin(3*f*x + 3*e) + 3*sin(f*x + e))*cos(6*f*x + 6*e) + 9*(sin(4*f*x + 4*e) - sin(2*f*x + 2*e))*cos(5*f*x + 5*e) + 3*(2*sin(3*f*x + 3*e) - 3*sin(f*x + e))*cos(4*f*x + 4*e) - (3*cos(5*f*x + 5*e) - 2*cos(3*f*x + 3*e) + 3*cos(f*x + e))*sin(6*f*x + 6*e) - 3*(3*cos(4*f*x + 4*e) - 3*cos(2*f*x + 2*e) + 1)*sin(5*f*x + 5*e) - 3*(2*cos(3*f*x + 3*e) - 3*cos(f*x + e))*sin(4*f*x + 4*e) - 2*(3*cos(2*f*x + 2*e) - 1)*sin(3*f*x + 3*e) + 6*cos(3*f*x + 3*e)*sin(2*f*x + 2*e) - 9*cos(f*x + e)*sin(2*f*x + 2*e) + 9*cos(2*f*x + 2*e)*sin(f*x + e) - 3*sin(f*x + e))*sqrt(a)/((a*cos(6*f*x + 6*e)^2 + 9*a*cos(4*f*x + 4*e)^2 + 9*a*cos(2*f*x + 2*e)^2 + a*sin(6*f*x + 6*e)^2 + 9*a*sin(4*f*x + 4*e)^2 - 18*a*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 9*a*sin(2*f*x + 2*e)^2 - 2*(3*a*cos(4*f*x + 4*e) - 3*a*cos(2*f*x + 2*e) + a)*cos(6*f*x + 6*e) - 6*(3*a*cos(2*f*x + 2*e) - a)*cos(4*f*x + 4*e) - 6*a*cos(2*f*x + 2*e) - 6*(a*sin(4*f*x + 4*e) - a*sin(2*f*x + 2*e))*sin(6*f*x + 6*e) + a)*f)","B",0
477,1,1236,0,0.509148," ","integrate(cot(f*x+e)^6/(a-a*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left({\left(15 \, \sin\left(9 \, f x + 9 \, e\right) - 20 \, \sin\left(7 \, f x + 7 \, e\right) + 58 \, \sin\left(5 \, f x + 5 \, e\right) - 20 \, \sin\left(3 \, f x + 3 \, e\right) + 15 \, \sin\left(f x + e\right)\right)} \cos\left(10 \, f x + 10 \, e\right) + 75 \, {\left(\sin\left(8 \, f x + 8 \, e\right) - 2 \, \sin\left(6 \, f x + 6 \, e\right) + 2 \, \sin\left(4 \, f x + 4 \, e\right) - \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(9 \, f x + 9 \, e\right) + 5 \, {\left(20 \, \sin\left(7 \, f x + 7 \, e\right) - 58 \, \sin\left(5 \, f x + 5 \, e\right) + 20 \, \sin\left(3 \, f x + 3 \, e\right) - 15 \, \sin\left(f x + e\right)\right)} \cos\left(8 \, f x + 8 \, e\right) + 100 \, {\left(2 \, \sin\left(6 \, f x + 6 \, e\right) - 2 \, \sin\left(4 \, f x + 4 \, e\right) + \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(7 \, f x + 7 \, e\right) + 10 \, {\left(58 \, \sin\left(5 \, f x + 5 \, e\right) - 20 \, \sin\left(3 \, f x + 3 \, e\right) + 15 \, \sin\left(f x + e\right)\right)} \cos\left(6 \, f x + 6 \, e\right) + 290 \, {\left(2 \, \sin\left(4 \, f x + 4 \, e\right) - \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(5 \, f x + 5 \, e\right) + 50 \, {\left(4 \, \sin\left(3 \, f x + 3 \, e\right) - 3 \, \sin\left(f x + e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) - {\left(15 \, \cos\left(9 \, f x + 9 \, e\right) - 20 \, \cos\left(7 \, f x + 7 \, e\right) + 58 \, \cos\left(5 \, f x + 5 \, e\right) - 20 \, \cos\left(3 \, f x + 3 \, e\right) + 15 \, \cos\left(f x + e\right)\right)} \sin\left(10 \, f x + 10 \, e\right) - 15 \, {\left(5 \, \cos\left(8 \, f x + 8 \, e\right) - 10 \, \cos\left(6 \, f x + 6 \, e\right) + 10 \, \cos\left(4 \, f x + 4 \, e\right) - 5 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \sin\left(9 \, f x + 9 \, e\right) - 5 \, {\left(20 \, \cos\left(7 \, f x + 7 \, e\right) - 58 \, \cos\left(5 \, f x + 5 \, e\right) + 20 \, \cos\left(3 \, f x + 3 \, e\right) - 15 \, \cos\left(f x + e\right)\right)} \sin\left(8 \, f x + 8 \, e\right) - 20 \, {\left(10 \, \cos\left(6 \, f x + 6 \, e\right) - 10 \, \cos\left(4 \, f x + 4 \, e\right) + 5 \, \cos\left(2 \, f x + 2 \, e\right) - 1\right)} \sin\left(7 \, f x + 7 \, e\right) - 10 \, {\left(58 \, \cos\left(5 \, f x + 5 \, e\right) - 20 \, \cos\left(3 \, f x + 3 \, e\right) + 15 \, \cos\left(f x + e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) - 58 \, {\left(10 \, \cos\left(4 \, f x + 4 \, e\right) - 5 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \sin\left(5 \, f x + 5 \, e\right) - 50 \, {\left(4 \, \cos\left(3 \, f x + 3 \, e\right) - 3 \, \cos\left(f x + e\right)\right)} \sin\left(4 \, f x + 4 \, e\right) - 20 \, {\left(5 \, \cos\left(2 \, f x + 2 \, e\right) - 1\right)} \sin\left(3 \, f x + 3 \, e\right) + 100 \, \cos\left(3 \, f x + 3 \, e\right) \sin\left(2 \, f x + 2 \, e\right) - 75 \, \cos\left(f x + e\right) \sin\left(2 \, f x + 2 \, e\right) + 75 \, \cos\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) - 15 \, \sin\left(f x + e\right)\right)} \sqrt{a}}{15 \, {\left(a \cos\left(10 \, f x + 10 \, e\right)^{2} + 25 \, a \cos\left(8 \, f x + 8 \, e\right)^{2} + 100 \, a \cos\left(6 \, f x + 6 \, e\right)^{2} + 100 \, a \cos\left(4 \, f x + 4 \, e\right)^{2} + 25 \, a \cos\left(2 \, f x + 2 \, e\right)^{2} + a \sin\left(10 \, f x + 10 \, e\right)^{2} + 25 \, a \sin\left(8 \, f x + 8 \, e\right)^{2} + 100 \, a \sin\left(6 \, f x + 6 \, e\right)^{2} + 100 \, a \sin\left(4 \, f x + 4 \, e\right)^{2} - 100 \, a \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 25 \, a \sin\left(2 \, f x + 2 \, e\right)^{2} - 2 \, {\left(5 \, a \cos\left(8 \, f x + 8 \, e\right) - 10 \, a \cos\left(6 \, f x + 6 \, e\right) + 10 \, a \cos\left(4 \, f x + 4 \, e\right) - 5 \, a \cos\left(2 \, f x + 2 \, e\right) + a\right)} \cos\left(10 \, f x + 10 \, e\right) - 10 \, {\left(10 \, a \cos\left(6 \, f x + 6 \, e\right) - 10 \, a \cos\left(4 \, f x + 4 \, e\right) + 5 \, a \cos\left(2 \, f x + 2 \, e\right) - a\right)} \cos\left(8 \, f x + 8 \, e\right) - 20 \, {\left(10 \, a \cos\left(4 \, f x + 4 \, e\right) - 5 \, a \cos\left(2 \, f x + 2 \, e\right) + a\right)} \cos\left(6 \, f x + 6 \, e\right) - 20 \, {\left(5 \, a \cos\left(2 \, f x + 2 \, e\right) - a\right)} \cos\left(4 \, f x + 4 \, e\right) - 10 \, a \cos\left(2 \, f x + 2 \, e\right) - 10 \, {\left(a \sin\left(8 \, f x + 8 \, e\right) - 2 \, a \sin\left(6 \, f x + 6 \, e\right) + 2 \, a \sin\left(4 \, f x + 4 \, e\right) - a \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(10 \, f x + 10 \, e\right) - 50 \, {\left(2 \, a \sin\left(6 \, f x + 6 \, e\right) - 2 \, a \sin\left(4 \, f x + 4 \, e\right) + a \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(8 \, f x + 8 \, e\right) - 100 \, {\left(2 \, a \sin\left(4 \, f x + 4 \, e\right) - a \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) + a\right)} f}"," ",0,"2/15*((15*sin(9*f*x + 9*e) - 20*sin(7*f*x + 7*e) + 58*sin(5*f*x + 5*e) - 20*sin(3*f*x + 3*e) + 15*sin(f*x + e))*cos(10*f*x + 10*e) + 75*(sin(8*f*x + 8*e) - 2*sin(6*f*x + 6*e) + 2*sin(4*f*x + 4*e) - sin(2*f*x + 2*e))*cos(9*f*x + 9*e) + 5*(20*sin(7*f*x + 7*e) - 58*sin(5*f*x + 5*e) + 20*sin(3*f*x + 3*e) - 15*sin(f*x + e))*cos(8*f*x + 8*e) + 100*(2*sin(6*f*x + 6*e) - 2*sin(4*f*x + 4*e) + sin(2*f*x + 2*e))*cos(7*f*x + 7*e) + 10*(58*sin(5*f*x + 5*e) - 20*sin(3*f*x + 3*e) + 15*sin(f*x + e))*cos(6*f*x + 6*e) + 290*(2*sin(4*f*x + 4*e) - sin(2*f*x + 2*e))*cos(5*f*x + 5*e) + 50*(4*sin(3*f*x + 3*e) - 3*sin(f*x + e))*cos(4*f*x + 4*e) - (15*cos(9*f*x + 9*e) - 20*cos(7*f*x + 7*e) + 58*cos(5*f*x + 5*e) - 20*cos(3*f*x + 3*e) + 15*cos(f*x + e))*sin(10*f*x + 10*e) - 15*(5*cos(8*f*x + 8*e) - 10*cos(6*f*x + 6*e) + 10*cos(4*f*x + 4*e) - 5*cos(2*f*x + 2*e) + 1)*sin(9*f*x + 9*e) - 5*(20*cos(7*f*x + 7*e) - 58*cos(5*f*x + 5*e) + 20*cos(3*f*x + 3*e) - 15*cos(f*x + e))*sin(8*f*x + 8*e) - 20*(10*cos(6*f*x + 6*e) - 10*cos(4*f*x + 4*e) + 5*cos(2*f*x + 2*e) - 1)*sin(7*f*x + 7*e) - 10*(58*cos(5*f*x + 5*e) - 20*cos(3*f*x + 3*e) + 15*cos(f*x + e))*sin(6*f*x + 6*e) - 58*(10*cos(4*f*x + 4*e) - 5*cos(2*f*x + 2*e) + 1)*sin(5*f*x + 5*e) - 50*(4*cos(3*f*x + 3*e) - 3*cos(f*x + e))*sin(4*f*x + 4*e) - 20*(5*cos(2*f*x + 2*e) - 1)*sin(3*f*x + 3*e) + 100*cos(3*f*x + 3*e)*sin(2*f*x + 2*e) - 75*cos(f*x + e)*sin(2*f*x + 2*e) + 75*cos(2*f*x + 2*e)*sin(f*x + e) - 15*sin(f*x + e))*sqrt(a)/((a*cos(10*f*x + 10*e)^2 + 25*a*cos(8*f*x + 8*e)^2 + 100*a*cos(6*f*x + 6*e)^2 + 100*a*cos(4*f*x + 4*e)^2 + 25*a*cos(2*f*x + 2*e)^2 + a*sin(10*f*x + 10*e)^2 + 25*a*sin(8*f*x + 8*e)^2 + 100*a*sin(6*f*x + 6*e)^2 + 100*a*sin(4*f*x + 4*e)^2 - 100*a*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 25*a*sin(2*f*x + 2*e)^2 - 2*(5*a*cos(8*f*x + 8*e) - 10*a*cos(6*f*x + 6*e) + 10*a*cos(4*f*x + 4*e) - 5*a*cos(2*f*x + 2*e) + a)*cos(10*f*x + 10*e) - 10*(10*a*cos(6*f*x + 6*e) - 10*a*cos(4*f*x + 4*e) + 5*a*cos(2*f*x + 2*e) - a)*cos(8*f*x + 8*e) - 20*(10*a*cos(4*f*x + 4*e) - 5*a*cos(2*f*x + 2*e) + a)*cos(6*f*x + 6*e) - 20*(5*a*cos(2*f*x + 2*e) - a)*cos(4*f*x + 4*e) - 10*a*cos(2*f*x + 2*e) - 10*(a*sin(8*f*x + 8*e) - 2*a*sin(6*f*x + 6*e) + 2*a*sin(4*f*x + 4*e) - a*sin(2*f*x + 2*e))*sin(10*f*x + 10*e) - 50*(2*a*sin(6*f*x + 6*e) - 2*a*sin(4*f*x + 4*e) + a*sin(2*f*x + 2*e))*sin(8*f*x + 8*e) - 100*(2*a*sin(4*f*x + 4*e) - a*sin(2*f*x + 2*e))*sin(6*f*x + 6*e) + a)*f)","B",0
478,1,69,0,0.332920," ","integrate(tan(f*x+e)^5/(a-a*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\frac{35 \, {\left(a \sin\left(f x + e\right)^{2} - a\right)}^{2} a^{3} + 42 \, {\left(a \sin\left(f x + e\right)^{2} - a\right)} a^{4} + 15 \, a^{5}}{105 \, {\left(-a \sin\left(f x + e\right)^{2} + a\right)}^{\frac{7}{2}} a^{3} f}"," ",0,"1/105*(35*(a*sin(f*x + e)^2 - a)^2*a^3 + 42*(a*sin(f*x + e)^2 - a)*a^4 + 15*a^5)/((-a*sin(f*x + e)^2 + a)^(7/2)*a^3*f)","A",0
479,1,48,0,0.346454," ","integrate(tan(f*x+e)^3/(a-a*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\frac{5 \, {\left(a \sin\left(f x + e\right)^{2} - a\right)} a^{2} + 3 \, a^{3}}{15 \, {\left(-a \sin\left(f x + e\right)^{2} + a\right)}^{\frac{5}{2}} a^{2} f}"," ",0,"1/15*(5*(a*sin(f*x + e)^2 - a)*a^2 + 3*a^3)/((-a*sin(f*x + e)^2 + a)^(5/2)*a^2*f)","A",0
480,1,95,0,0.438129," ","integrate(tan(f*x+e)/(a-a*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\frac{\frac{1}{\sqrt{-a \sin\left(f x + e\right)^{2} + a} a \sin\left(f x + e\right) + \sqrt{-a \sin\left(f x + e\right)^{2} + a} a} - \frac{1}{\sqrt{-a \sin\left(f x + e\right)^{2} + a} a \sin\left(f x + e\right) - \sqrt{-a \sin\left(f x + e\right)^{2} + a} a}}{6 \, f}"," ",0,"1/6*(1/(sqrt(-a*sin(f*x + e)^2 + a)*a*sin(f*x + e) + sqrt(-a*sin(f*x + e)^2 + a)*a) - 1/(sqrt(-a*sin(f*x + e)^2 + a)*a*sin(f*x + e) - sqrt(-a*sin(f*x + e)^2 + a)*a))/f","B",0
481,1,73,0,0.328492," ","integrate(cot(f*x+e)/(a-a*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","-\frac{\frac{\log\left(\frac{2 \, \sqrt{-a \sin\left(f x + e\right)^{2} + a} \sqrt{a}}{{\left| \sin\left(f x + e\right) \right|}} + \frac{2 \, a}{{\left| \sin\left(f x + e\right) \right|}}\right)}{a^{\frac{3}{2}}} - \frac{1}{\sqrt{-a \sin\left(f x + e\right)^{2} + a} a}}{f}"," ",0,"-(log(2*sqrt(-a*sin(f*x + e)^2 + a)*sqrt(a)/abs(sin(f*x + e)) + 2*a/abs(sin(f*x + e)))/a^(3/2) - 1/(sqrt(-a*sin(f*x + e)^2 + a)*a))/f","A",0
482,1,100,0,0.330683," ","integrate(cot(f*x+e)^3/(a-a*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","-\frac{\frac{\log\left(\frac{2 \, \sqrt{-a \sin\left(f x + e\right)^{2} + a} \sqrt{a}}{{\left| \sin\left(f x + e\right) \right|}} + \frac{2 \, a}{{\left| \sin\left(f x + e\right) \right|}}\right)}{a^{\frac{3}{2}}} - \frac{1}{\sqrt{-a \sin\left(f x + e\right)^{2} + a} a} + \frac{1}{\sqrt{-a \sin\left(f x + e\right)^{2} + a} a \sin\left(f x + e\right)^{2}}}{2 \, f}"," ",0,"-1/2*(log(2*sqrt(-a*sin(f*x + e)^2 + a)*sqrt(a)/abs(sin(f*x + e)) + 2*a/abs(sin(f*x + e)))/a^(3/2) - 1/(sqrt(-a*sin(f*x + e)^2 + a)*a) + 1/(sqrt(-a*sin(f*x + e)^2 + a)*a*sin(f*x + e)^2))/f","A",0
483,1,1532,0,0.727172," ","integrate(tan(f*x+e)^2/(a-a*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","-\frac{4 \, {\left(\sin\left(7 \, f x + 7 \, e\right) - 7 \, \sin\left(5 \, f x + 5 \, e\right) + 7 \, \sin\left(3 \, f x + 3 \, e\right) - \sin\left(f x + e\right)\right)} \cos\left(8 \, f x + 8 \, e\right) - 8 \, {\left(2 \, \sin\left(6 \, f x + 6 \, e\right) + 3 \, \sin\left(4 \, f x + 4 \, e\right) + 2 \, \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(7 \, f x + 7 \, e\right) - 16 \, {\left(7 \, \sin\left(5 \, f x + 5 \, e\right) - 7 \, \sin\left(3 \, f x + 3 \, e\right) + \sin\left(f x + e\right)\right)} \cos\left(6 \, f x + 6 \, e\right) + 56 \, {\left(3 \, \sin\left(4 \, f x + 4 \, e\right) + 2 \, \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(5 \, f x + 5 \, e\right) + 24 \, {\left(7 \, \sin\left(3 \, f x + 3 \, e\right) - \sin\left(f x + e\right)\right)} \cos\left(4 \, f x + 4 \, e\right) + {\left(2 \, {\left(4 \, \cos\left(6 \, f x + 6 \, e\right) + 6 \, \cos\left(4 \, f x + 4 \, e\right) + 4 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \cos\left(8 \, f x + 8 \, e\right) + \cos\left(8 \, f x + 8 \, e\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, f x + 4 \, e\right) + 4 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \cos\left(6 \, f x + 6 \, e\right) + 16 \, \cos\left(6 \, f x + 6 \, e\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \cos\left(4 \, f x + 4 \, e\right) + 36 \, \cos\left(4 \, f x + 4 \, e\right)^{2} + 16 \, \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, f x + 6 \, e\right) + 3 \, \sin\left(4 \, f x + 4 \, e\right) + 2 \, \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(8 \, f x + 8 \, e\right) + \sin\left(8 \, f x + 8 \, e\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, f x + 4 \, e\right) + 2 \, \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) + 16 \, \sin\left(6 \, f x + 6 \, e\right)^{2} + 36 \, \sin\left(4 \, f x + 4 \, e\right)^{2} + 48 \, \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 16 \, \sin\left(2 \, f x + 2 \, e\right)^{2} + 8 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \sin\left(f x + e\right) + 1\right) - {\left(2 \, {\left(4 \, \cos\left(6 \, f x + 6 \, e\right) + 6 \, \cos\left(4 \, f x + 4 \, e\right) + 4 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \cos\left(8 \, f x + 8 \, e\right) + \cos\left(8 \, f x + 8 \, e\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, f x + 4 \, e\right) + 4 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \cos\left(6 \, f x + 6 \, e\right) + 16 \, \cos\left(6 \, f x + 6 \, e\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \cos\left(4 \, f x + 4 \, e\right) + 36 \, \cos\left(4 \, f x + 4 \, e\right)^{2} + 16 \, \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, f x + 6 \, e\right) + 3 \, \sin\left(4 \, f x + 4 \, e\right) + 2 \, \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(8 \, f x + 8 \, e\right) + \sin\left(8 \, f x + 8 \, e\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, f x + 4 \, e\right) + 2 \, \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) + 16 \, \sin\left(6 \, f x + 6 \, e\right)^{2} + 36 \, \sin\left(4 \, f x + 4 \, e\right)^{2} + 48 \, \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 16 \, \sin\left(2 \, f x + 2 \, e\right)^{2} + 8 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} - 2 \, \sin\left(f x + e\right) + 1\right) - 4 \, {\left(\cos\left(7 \, f x + 7 \, e\right) - 7 \, \cos\left(5 \, f x + 5 \, e\right) + 7 \, \cos\left(3 \, f x + 3 \, e\right) - \cos\left(f x + e\right)\right)} \sin\left(8 \, f x + 8 \, e\right) + 4 \, {\left(4 \, \cos\left(6 \, f x + 6 \, e\right) + 6 \, \cos\left(4 \, f x + 4 \, e\right) + 4 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \sin\left(7 \, f x + 7 \, e\right) + 16 \, {\left(7 \, \cos\left(5 \, f x + 5 \, e\right) - 7 \, \cos\left(3 \, f x + 3 \, e\right) + \cos\left(f x + e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) - 28 \, {\left(6 \, \cos\left(4 \, f x + 4 \, e\right) + 4 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \sin\left(5 \, f x + 5 \, e\right) - 24 \, {\left(7 \, \cos\left(3 \, f x + 3 \, e\right) - \cos\left(f x + e\right)\right)} \sin\left(4 \, f x + 4 \, e\right) + 28 \, {\left(4 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \sin\left(3 \, f x + 3 \, e\right) - 112 \, \cos\left(3 \, f x + 3 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 16 \, \cos\left(f x + e\right) \sin\left(2 \, f x + 2 \, e\right) - 16 \, \cos\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) - 4 \, \sin\left(f x + e\right)}{16 \, {\left(a \cos\left(8 \, f x + 8 \, e\right)^{2} + 16 \, a \cos\left(6 \, f x + 6 \, e\right)^{2} + 36 \, a \cos\left(4 \, f x + 4 \, e\right)^{2} + 16 \, a \cos\left(2 \, f x + 2 \, e\right)^{2} + a \sin\left(8 \, f x + 8 \, e\right)^{2} + 16 \, a \sin\left(6 \, f x + 6 \, e\right)^{2} + 36 \, a \sin\left(4 \, f x + 4 \, e\right)^{2} + 48 \, a \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 16 \, a \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(4 \, a \cos\left(6 \, f x + 6 \, e\right) + 6 \, a \cos\left(4 \, f x + 4 \, e\right) + 4 \, a \cos\left(2 \, f x + 2 \, e\right) + a\right)} \cos\left(8 \, f x + 8 \, e\right) + 8 \, {\left(6 \, a \cos\left(4 \, f x + 4 \, e\right) + 4 \, a \cos\left(2 \, f x + 2 \, e\right) + a\right)} \cos\left(6 \, f x + 6 \, e\right) + 12 \, {\left(4 \, a \cos\left(2 \, f x + 2 \, e\right) + a\right)} \cos\left(4 \, f x + 4 \, e\right) + 8 \, a \cos\left(2 \, f x + 2 \, e\right) + 4 \, {\left(2 \, a \sin\left(6 \, f x + 6 \, e\right) + 3 \, a \sin\left(4 \, f x + 4 \, e\right) + 2 \, a \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(8 \, f x + 8 \, e\right) + 16 \, {\left(3 \, a \sin\left(4 \, f x + 4 \, e\right) + 2 \, a \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) + a\right)} \sqrt{a} f}"," ",0,"-1/16*(4*(sin(7*f*x + 7*e) - 7*sin(5*f*x + 5*e) + 7*sin(3*f*x + 3*e) - sin(f*x + e))*cos(8*f*x + 8*e) - 8*(2*sin(6*f*x + 6*e) + 3*sin(4*f*x + 4*e) + 2*sin(2*f*x + 2*e))*cos(7*f*x + 7*e) - 16*(7*sin(5*f*x + 5*e) - 7*sin(3*f*x + 3*e) + sin(f*x + e))*cos(6*f*x + 6*e) + 56*(3*sin(4*f*x + 4*e) + 2*sin(2*f*x + 2*e))*cos(5*f*x + 5*e) + 24*(7*sin(3*f*x + 3*e) - sin(f*x + e))*cos(4*f*x + 4*e) + (2*(4*cos(6*f*x + 6*e) + 6*cos(4*f*x + 4*e) + 4*cos(2*f*x + 2*e) + 1)*cos(8*f*x + 8*e) + cos(8*f*x + 8*e)^2 + 8*(6*cos(4*f*x + 4*e) + 4*cos(2*f*x + 2*e) + 1)*cos(6*f*x + 6*e) + 16*cos(6*f*x + 6*e)^2 + 12*(4*cos(2*f*x + 2*e) + 1)*cos(4*f*x + 4*e) + 36*cos(4*f*x + 4*e)^2 + 16*cos(2*f*x + 2*e)^2 + 4*(2*sin(6*f*x + 6*e) + 3*sin(4*f*x + 4*e) + 2*sin(2*f*x + 2*e))*sin(8*f*x + 8*e) + sin(8*f*x + 8*e)^2 + 16*(3*sin(4*f*x + 4*e) + 2*sin(2*f*x + 2*e))*sin(6*f*x + 6*e) + 16*sin(6*f*x + 6*e)^2 + 36*sin(4*f*x + 4*e)^2 + 48*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 16*sin(2*f*x + 2*e)^2 + 8*cos(2*f*x + 2*e) + 1)*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*sin(f*x + e) + 1) - (2*(4*cos(6*f*x + 6*e) + 6*cos(4*f*x + 4*e) + 4*cos(2*f*x + 2*e) + 1)*cos(8*f*x + 8*e) + cos(8*f*x + 8*e)^2 + 8*(6*cos(4*f*x + 4*e) + 4*cos(2*f*x + 2*e) + 1)*cos(6*f*x + 6*e) + 16*cos(6*f*x + 6*e)^2 + 12*(4*cos(2*f*x + 2*e) + 1)*cos(4*f*x + 4*e) + 36*cos(4*f*x + 4*e)^2 + 16*cos(2*f*x + 2*e)^2 + 4*(2*sin(6*f*x + 6*e) + 3*sin(4*f*x + 4*e) + 2*sin(2*f*x + 2*e))*sin(8*f*x + 8*e) + sin(8*f*x + 8*e)^2 + 16*(3*sin(4*f*x + 4*e) + 2*sin(2*f*x + 2*e))*sin(6*f*x + 6*e) + 16*sin(6*f*x + 6*e)^2 + 36*sin(4*f*x + 4*e)^2 + 48*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 16*sin(2*f*x + 2*e)^2 + 8*cos(2*f*x + 2*e) + 1)*log(cos(f*x + e)^2 + sin(f*x + e)^2 - 2*sin(f*x + e) + 1) - 4*(cos(7*f*x + 7*e) - 7*cos(5*f*x + 5*e) + 7*cos(3*f*x + 3*e) - cos(f*x + e))*sin(8*f*x + 8*e) + 4*(4*cos(6*f*x + 6*e) + 6*cos(4*f*x + 4*e) + 4*cos(2*f*x + 2*e) + 1)*sin(7*f*x + 7*e) + 16*(7*cos(5*f*x + 5*e) - 7*cos(3*f*x + 3*e) + cos(f*x + e))*sin(6*f*x + 6*e) - 28*(6*cos(4*f*x + 4*e) + 4*cos(2*f*x + 2*e) + 1)*sin(5*f*x + 5*e) - 24*(7*cos(3*f*x + 3*e) - cos(f*x + e))*sin(4*f*x + 4*e) + 28*(4*cos(2*f*x + 2*e) + 1)*sin(3*f*x + 3*e) - 112*cos(3*f*x + 3*e)*sin(2*f*x + 2*e) + 16*cos(f*x + e)*sin(2*f*x + 2*e) - 16*cos(2*f*x + 2*e)*sin(f*x + e) - 4*sin(f*x + e))/((a*cos(8*f*x + 8*e)^2 + 16*a*cos(6*f*x + 6*e)^2 + 36*a*cos(4*f*x + 4*e)^2 + 16*a*cos(2*f*x + 2*e)^2 + a*sin(8*f*x + 8*e)^2 + 16*a*sin(6*f*x + 6*e)^2 + 36*a*sin(4*f*x + 4*e)^2 + 48*a*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 16*a*sin(2*f*x + 2*e)^2 + 2*(4*a*cos(6*f*x + 6*e) + 6*a*cos(4*f*x + 4*e) + 4*a*cos(2*f*x + 2*e) + a)*cos(8*f*x + 8*e) + 8*(6*a*cos(4*f*x + 4*e) + 4*a*cos(2*f*x + 2*e) + a)*cos(6*f*x + 6*e) + 12*(4*a*cos(2*f*x + 2*e) + a)*cos(4*f*x + 4*e) + 8*a*cos(2*f*x + 2*e) + 4*(2*a*sin(6*f*x + 6*e) + 3*a*sin(4*f*x + 4*e) + 2*a*sin(2*f*x + 2*e))*sin(8*f*x + 8*e) + 16*(3*a*sin(4*f*x + 4*e) + 2*a*sin(2*f*x + 2*e))*sin(6*f*x + 6*e) + a)*sqrt(a)*f)","B",0
484,1,220,0,0.499437," ","integrate(cot(f*x+e)^2/(a-a*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\frac{{\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} - 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \sin\left(f x + e\right) + 1\right) - {\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} - 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} - 2 \, \sin\left(f x + e\right) + 1\right) - 4 \, \cos\left(f x + e\right) \sin\left(2 \, f x + 2 \, e\right) + 4 \, \cos\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) - 4 \, \sin\left(f x + e\right)}{2 \, {\left(a \cos\left(2 \, f x + 2 \, e\right)^{2} + a \sin\left(2 \, f x + 2 \, e\right)^{2} - 2 \, a \cos\left(2 \, f x + 2 \, e\right) + a\right)} \sqrt{a} f}"," ",0,"1/2*((cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 - 2*cos(2*f*x + 2*e) + 1)*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*sin(f*x + e) + 1) - (cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 - 2*cos(2*f*x + 2*e) + 1)*log(cos(f*x + e)^2 + sin(f*x + e)^2 - 2*sin(f*x + e) + 1) - 4*cos(f*x + e)*sin(2*f*x + 2*e) + 4*cos(2*f*x + 2*e)*sin(f*x + e) - 4*sin(f*x + e))/((a*cos(2*f*x + 2*e)^2 + a*sin(2*f*x + 2*e)^2 - 2*a*cos(2*f*x + 2*e) + a)*sqrt(a)*f)","B",0
485,1,382,0,0.492269," ","integrate(cot(f*x+e)^4/(a-a*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\frac{8 \, {\left(\cos\left(3 \, f x + 3 \, e\right) \sin\left(6 \, f x + 6 \, e\right) - 3 \, \cos\left(3 \, f x + 3 \, e\right) \sin\left(4 \, f x + 4 \, e\right) - {\left(3 \, \cos\left(2 \, f x + 2 \, e\right) - 1\right)} \sin\left(3 \, f x + 3 \, e\right) - \cos\left(6 \, f x + 6 \, e\right) \sin\left(3 \, f x + 3 \, e\right) + 3 \, \cos\left(4 \, f x + 4 \, e\right) \sin\left(3 \, f x + 3 \, e\right) + 3 \, \cos\left(3 \, f x + 3 \, e\right) \sin\left(2 \, f x + 2 \, e\right)\right)} \sqrt{a}}{3 \, {\left(a^{2} \cos\left(6 \, f x + 6 \, e\right)^{2} + 9 \, a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + 9 \, a^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + a^{2} \sin\left(6 \, f x + 6 \, e\right)^{2} + 9 \, a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} - 18 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 9 \, a^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} - 6 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2} - 2 \, {\left(3 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) - 3 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2}\right)} \cos\left(6 \, f x + 6 \, e\right) - 6 \, {\left(3 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) - a^{2}\right)} \cos\left(4 \, f x + 4 \, e\right) - 6 \, {\left(a^{2} \sin\left(4 \, f x + 4 \, e\right) - a^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right)\right)} f}"," ",0,"8/3*(cos(3*f*x + 3*e)*sin(6*f*x + 6*e) - 3*cos(3*f*x + 3*e)*sin(4*f*x + 4*e) - (3*cos(2*f*x + 2*e) - 1)*sin(3*f*x + 3*e) - cos(6*f*x + 6*e)*sin(3*f*x + 3*e) + 3*cos(4*f*x + 4*e)*sin(3*f*x + 3*e) + 3*cos(3*f*x + 3*e)*sin(2*f*x + 2*e))*sqrt(a)/((a^2*cos(6*f*x + 6*e)^2 + 9*a^2*cos(4*f*x + 4*e)^2 + 9*a^2*cos(2*f*x + 2*e)^2 + a^2*sin(6*f*x + 6*e)^2 + 9*a^2*sin(4*f*x + 4*e)^2 - 18*a^2*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 9*a^2*sin(2*f*x + 2*e)^2 - 6*a^2*cos(2*f*x + 2*e) + a^2 - 2*(3*a^2*cos(4*f*x + 4*e) - 3*a^2*cos(2*f*x + 2*e) + a^2)*cos(6*f*x + 6*e) - 6*(3*a^2*cos(2*f*x + 2*e) - a^2)*cos(4*f*x + 4*e) - 6*(a^2*sin(4*f*x + 4*e) - a^2*sin(2*f*x + 2*e))*sin(6*f*x + 6*e))*f)","B",0
486,1,1063,0,0.511293," ","integrate(cot(f*x+e)^6/(a-a*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\frac{8 \, {\left({\left(5 \, \sin\left(7 \, f x + 7 \, e\right) + 2 \, \sin\left(5 \, f x + 5 \, e\right) + 5 \, \sin\left(3 \, f x + 3 \, e\right)\right)} \cos\left(10 \, f x + 10 \, e\right) - 5 \, {\left(5 \, \sin\left(7 \, f x + 7 \, e\right) + 2 \, \sin\left(5 \, f x + 5 \, e\right) + 5 \, \sin\left(3 \, f x + 3 \, e\right)\right)} \cos\left(8 \, f x + 8 \, e\right) - 25 \, {\left(2 \, \sin\left(6 \, f x + 6 \, e\right) - 2 \, \sin\left(4 \, f x + 4 \, e\right) + \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(7 \, f x + 7 \, e\right) + 10 \, {\left(2 \, \sin\left(5 \, f x + 5 \, e\right) + 5 \, \sin\left(3 \, f x + 3 \, e\right)\right)} \cos\left(6 \, f x + 6 \, e\right) + 10 \, {\left(2 \, \sin\left(4 \, f x + 4 \, e\right) - \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(5 \, f x + 5 \, e\right) - {\left(5 \, \cos\left(7 \, f x + 7 \, e\right) + 2 \, \cos\left(5 \, f x + 5 \, e\right) + 5 \, \cos\left(3 \, f x + 3 \, e\right)\right)} \sin\left(10 \, f x + 10 \, e\right) + 5 \, {\left(5 \, \cos\left(7 \, f x + 7 \, e\right) + 2 \, \cos\left(5 \, f x + 5 \, e\right) + 5 \, \cos\left(3 \, f x + 3 \, e\right)\right)} \sin\left(8 \, f x + 8 \, e\right) + 5 \, {\left(10 \, \cos\left(6 \, f x + 6 \, e\right) - 10 \, \cos\left(4 \, f x + 4 \, e\right) + 5 \, \cos\left(2 \, f x + 2 \, e\right) - 1\right)} \sin\left(7 \, f x + 7 \, e\right) - 10 \, {\left(2 \, \cos\left(5 \, f x + 5 \, e\right) + 5 \, \cos\left(3 \, f x + 3 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) - 2 \, {\left(10 \, \cos\left(4 \, f x + 4 \, e\right) - 5 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \sin\left(5 \, f x + 5 \, e\right) + 50 \, \cos\left(3 \, f x + 3 \, e\right) \sin\left(4 \, f x + 4 \, e\right) + 5 \, {\left(5 \, \cos\left(2 \, f x + 2 \, e\right) - 1\right)} \sin\left(3 \, f x + 3 \, e\right) - 50 \, \cos\left(4 \, f x + 4 \, e\right) \sin\left(3 \, f x + 3 \, e\right) - 25 \, \cos\left(3 \, f x + 3 \, e\right) \sin\left(2 \, f x + 2 \, e\right)\right)} \sqrt{a}}{15 \, {\left(a^{2} \cos\left(10 \, f x + 10 \, e\right)^{2} + 25 \, a^{2} \cos\left(8 \, f x + 8 \, e\right)^{2} + 100 \, a^{2} \cos\left(6 \, f x + 6 \, e\right)^{2} + 100 \, a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + 25 \, a^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + a^{2} \sin\left(10 \, f x + 10 \, e\right)^{2} + 25 \, a^{2} \sin\left(8 \, f x + 8 \, e\right)^{2} + 100 \, a^{2} \sin\left(6 \, f x + 6 \, e\right)^{2} + 100 \, a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} - 100 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 25 \, a^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} - 10 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2} - 2 \, {\left(5 \, a^{2} \cos\left(8 \, f x + 8 \, e\right) - 10 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) + 10 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) - 5 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2}\right)} \cos\left(10 \, f x + 10 \, e\right) - 10 \, {\left(10 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) - 10 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) + 5 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) - a^{2}\right)} \cos\left(8 \, f x + 8 \, e\right) - 20 \, {\left(10 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) - 5 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2}\right)} \cos\left(6 \, f x + 6 \, e\right) - 20 \, {\left(5 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) - a^{2}\right)} \cos\left(4 \, f x + 4 \, e\right) - 10 \, {\left(a^{2} \sin\left(8 \, f x + 8 \, e\right) - 2 \, a^{2} \sin\left(6 \, f x + 6 \, e\right) + 2 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) - a^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(10 \, f x + 10 \, e\right) - 50 \, {\left(2 \, a^{2} \sin\left(6 \, f x + 6 \, e\right) - 2 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + a^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(8 \, f x + 8 \, e\right) - 100 \, {\left(2 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) - a^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right)\right)} f}"," ",0,"8/15*((5*sin(7*f*x + 7*e) + 2*sin(5*f*x + 5*e) + 5*sin(3*f*x + 3*e))*cos(10*f*x + 10*e) - 5*(5*sin(7*f*x + 7*e) + 2*sin(5*f*x + 5*e) + 5*sin(3*f*x + 3*e))*cos(8*f*x + 8*e) - 25*(2*sin(6*f*x + 6*e) - 2*sin(4*f*x + 4*e) + sin(2*f*x + 2*e))*cos(7*f*x + 7*e) + 10*(2*sin(5*f*x + 5*e) + 5*sin(3*f*x + 3*e))*cos(6*f*x + 6*e) + 10*(2*sin(4*f*x + 4*e) - sin(2*f*x + 2*e))*cos(5*f*x + 5*e) - (5*cos(7*f*x + 7*e) + 2*cos(5*f*x + 5*e) + 5*cos(3*f*x + 3*e))*sin(10*f*x + 10*e) + 5*(5*cos(7*f*x + 7*e) + 2*cos(5*f*x + 5*e) + 5*cos(3*f*x + 3*e))*sin(8*f*x + 8*e) + 5*(10*cos(6*f*x + 6*e) - 10*cos(4*f*x + 4*e) + 5*cos(2*f*x + 2*e) - 1)*sin(7*f*x + 7*e) - 10*(2*cos(5*f*x + 5*e) + 5*cos(3*f*x + 3*e))*sin(6*f*x + 6*e) - 2*(10*cos(4*f*x + 4*e) - 5*cos(2*f*x + 2*e) + 1)*sin(5*f*x + 5*e) + 50*cos(3*f*x + 3*e)*sin(4*f*x + 4*e) + 5*(5*cos(2*f*x + 2*e) - 1)*sin(3*f*x + 3*e) - 50*cos(4*f*x + 4*e)*sin(3*f*x + 3*e) - 25*cos(3*f*x + 3*e)*sin(2*f*x + 2*e))*sqrt(a)/((a^2*cos(10*f*x + 10*e)^2 + 25*a^2*cos(8*f*x + 8*e)^2 + 100*a^2*cos(6*f*x + 6*e)^2 + 100*a^2*cos(4*f*x + 4*e)^2 + 25*a^2*cos(2*f*x + 2*e)^2 + a^2*sin(10*f*x + 10*e)^2 + 25*a^2*sin(8*f*x + 8*e)^2 + 100*a^2*sin(6*f*x + 6*e)^2 + 100*a^2*sin(4*f*x + 4*e)^2 - 100*a^2*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 25*a^2*sin(2*f*x + 2*e)^2 - 10*a^2*cos(2*f*x + 2*e) + a^2 - 2*(5*a^2*cos(8*f*x + 8*e) - 10*a^2*cos(6*f*x + 6*e) + 10*a^2*cos(4*f*x + 4*e) - 5*a^2*cos(2*f*x + 2*e) + a^2)*cos(10*f*x + 10*e) - 10*(10*a^2*cos(6*f*x + 6*e) - 10*a^2*cos(4*f*x + 4*e) + 5*a^2*cos(2*f*x + 2*e) - a^2)*cos(8*f*x + 8*e) - 20*(10*a^2*cos(4*f*x + 4*e) - 5*a^2*cos(2*f*x + 2*e) + a^2)*cos(6*f*x + 6*e) - 20*(5*a^2*cos(2*f*x + 2*e) - a^2)*cos(4*f*x + 4*e) - 10*(a^2*sin(8*f*x + 8*e) - 2*a^2*sin(6*f*x + 6*e) + 2*a^2*sin(4*f*x + 4*e) - a^2*sin(2*f*x + 2*e))*sin(10*f*x + 10*e) - 50*(2*a^2*sin(6*f*x + 6*e) - 2*a^2*sin(4*f*x + 4*e) + a^2*sin(2*f*x + 2*e))*sin(8*f*x + 8*e) - 100*(2*a^2*sin(4*f*x + 4*e) - a^2*sin(2*f*x + 2*e))*sin(6*f*x + 6*e))*f)","B",0
487,1,2026,0,0.535420," ","integrate(cot(f*x+e)^8/(a-a*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","-\frac{8 \, {\left({\left(35 \, \sin\left(11 \, f x + 11 \, e\right) + 28 \, \sin\left(9 \, f x + 9 \, e\right) + 114 \, \sin\left(7 \, f x + 7 \, e\right) + 28 \, \sin\left(5 \, f x + 5 \, e\right) + 35 \, \sin\left(3 \, f x + 3 \, e\right)\right)} \cos\left(14 \, f x + 14 \, e\right) - 7 \, {\left(35 \, \sin\left(11 \, f x + 11 \, e\right) + 28 \, \sin\left(9 \, f x + 9 \, e\right) + 114 \, \sin\left(7 \, f x + 7 \, e\right) + 28 \, \sin\left(5 \, f x + 5 \, e\right) + 35 \, \sin\left(3 \, f x + 3 \, e\right)\right)} \cos\left(12 \, f x + 12 \, e\right) - 245 \, {\left(3 \, \sin\left(10 \, f x + 10 \, e\right) - 5 \, \sin\left(8 \, f x + 8 \, e\right) + 5 \, \sin\left(6 \, f x + 6 \, e\right) - 3 \, \sin\left(4 \, f x + 4 \, e\right) + \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(11 \, f x + 11 \, e\right) + 21 \, {\left(28 \, \sin\left(9 \, f x + 9 \, e\right) + 114 \, \sin\left(7 \, f x + 7 \, e\right) + 28 \, \sin\left(5 \, f x + 5 \, e\right) + 35 \, \sin\left(3 \, f x + 3 \, e\right)\right)} \cos\left(10 \, f x + 10 \, e\right) + 196 \, {\left(5 \, \sin\left(8 \, f x + 8 \, e\right) - 5 \, \sin\left(6 \, f x + 6 \, e\right) + 3 \, \sin\left(4 \, f x + 4 \, e\right) - \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(9 \, f x + 9 \, e\right) - 35 \, {\left(114 \, \sin\left(7 \, f x + 7 \, e\right) + 28 \, \sin\left(5 \, f x + 5 \, e\right) + 35 \, \sin\left(3 \, f x + 3 \, e\right)\right)} \cos\left(8 \, f x + 8 \, e\right) - 798 \, {\left(5 \, \sin\left(6 \, f x + 6 \, e\right) - 3 \, \sin\left(4 \, f x + 4 \, e\right) + \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(7 \, f x + 7 \, e\right) + 245 \, {\left(4 \, \sin\left(5 \, f x + 5 \, e\right) + 5 \, \sin\left(3 \, f x + 3 \, e\right)\right)} \cos\left(6 \, f x + 6 \, e\right) + 196 \, {\left(3 \, \sin\left(4 \, f x + 4 \, e\right) - \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(5 \, f x + 5 \, e\right) - {\left(35 \, \cos\left(11 \, f x + 11 \, e\right) + 28 \, \cos\left(9 \, f x + 9 \, e\right) + 114 \, \cos\left(7 \, f x + 7 \, e\right) + 28 \, \cos\left(5 \, f x + 5 \, e\right) + 35 \, \cos\left(3 \, f x + 3 \, e\right)\right)} \sin\left(14 \, f x + 14 \, e\right) + 7 \, {\left(35 \, \cos\left(11 \, f x + 11 \, e\right) + 28 \, \cos\left(9 \, f x + 9 \, e\right) + 114 \, \cos\left(7 \, f x + 7 \, e\right) + 28 \, \cos\left(5 \, f x + 5 \, e\right) + 35 \, \cos\left(3 \, f x + 3 \, e\right)\right)} \sin\left(12 \, f x + 12 \, e\right) + 35 \, {\left(21 \, \cos\left(10 \, f x + 10 \, e\right) - 35 \, \cos\left(8 \, f x + 8 \, e\right) + 35 \, \cos\left(6 \, f x + 6 \, e\right) - 21 \, \cos\left(4 \, f x + 4 \, e\right) + 7 \, \cos\left(2 \, f x + 2 \, e\right) - 1\right)} \sin\left(11 \, f x + 11 \, e\right) - 21 \, {\left(28 \, \cos\left(9 \, f x + 9 \, e\right) + 114 \, \cos\left(7 \, f x + 7 \, e\right) + 28 \, \cos\left(5 \, f x + 5 \, e\right) + 35 \, \cos\left(3 \, f x + 3 \, e\right)\right)} \sin\left(10 \, f x + 10 \, e\right) - 28 \, {\left(35 \, \cos\left(8 \, f x + 8 \, e\right) - 35 \, \cos\left(6 \, f x + 6 \, e\right) + 21 \, \cos\left(4 \, f x + 4 \, e\right) - 7 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \sin\left(9 \, f x + 9 \, e\right) + 35 \, {\left(114 \, \cos\left(7 \, f x + 7 \, e\right) + 28 \, \cos\left(5 \, f x + 5 \, e\right) + 35 \, \cos\left(3 \, f x + 3 \, e\right)\right)} \sin\left(8 \, f x + 8 \, e\right) + 114 \, {\left(35 \, \cos\left(6 \, f x + 6 \, e\right) - 21 \, \cos\left(4 \, f x + 4 \, e\right) + 7 \, \cos\left(2 \, f x + 2 \, e\right) - 1\right)} \sin\left(7 \, f x + 7 \, e\right) - 245 \, {\left(4 \, \cos\left(5 \, f x + 5 \, e\right) + 5 \, \cos\left(3 \, f x + 3 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right) - 28 \, {\left(21 \, \cos\left(4 \, f x + 4 \, e\right) - 7 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \sin\left(5 \, f x + 5 \, e\right) + 735 \, \cos\left(3 \, f x + 3 \, e\right) \sin\left(4 \, f x + 4 \, e\right) + 35 \, {\left(7 \, \cos\left(2 \, f x + 2 \, e\right) - 1\right)} \sin\left(3 \, f x + 3 \, e\right) - 735 \, \cos\left(4 \, f x + 4 \, e\right) \sin\left(3 \, f x + 3 \, e\right) - 245 \, \cos\left(3 \, f x + 3 \, e\right) \sin\left(2 \, f x + 2 \, e\right)\right)} \sqrt{a}}{105 \, {\left(a^{2} \cos\left(14 \, f x + 14 \, e\right)^{2} + 49 \, a^{2} \cos\left(12 \, f x + 12 \, e\right)^{2} + 441 \, a^{2} \cos\left(10 \, f x + 10 \, e\right)^{2} + 1225 \, a^{2} \cos\left(8 \, f x + 8 \, e\right)^{2} + 1225 \, a^{2} \cos\left(6 \, f x + 6 \, e\right)^{2} + 441 \, a^{2} \cos\left(4 \, f x + 4 \, e\right)^{2} + 49 \, a^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + a^{2} \sin\left(14 \, f x + 14 \, e\right)^{2} + 49 \, a^{2} \sin\left(12 \, f x + 12 \, e\right)^{2} + 441 \, a^{2} \sin\left(10 \, f x + 10 \, e\right)^{2} + 1225 \, a^{2} \sin\left(8 \, f x + 8 \, e\right)^{2} + 1225 \, a^{2} \sin\left(6 \, f x + 6 \, e\right)^{2} + 441 \, a^{2} \sin\left(4 \, f x + 4 \, e\right)^{2} - 294 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) \sin\left(2 \, f x + 2 \, e\right) + 49 \, a^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} - 14 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2} - 2 \, {\left(7 \, a^{2} \cos\left(12 \, f x + 12 \, e\right) - 21 \, a^{2} \cos\left(10 \, f x + 10 \, e\right) + 35 \, a^{2} \cos\left(8 \, f x + 8 \, e\right) - 35 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) + 21 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) - 7 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2}\right)} \cos\left(14 \, f x + 14 \, e\right) - 14 \, {\left(21 \, a^{2} \cos\left(10 \, f x + 10 \, e\right) - 35 \, a^{2} \cos\left(8 \, f x + 8 \, e\right) + 35 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) - 21 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) + 7 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) - a^{2}\right)} \cos\left(12 \, f x + 12 \, e\right) - 42 \, {\left(35 \, a^{2} \cos\left(8 \, f x + 8 \, e\right) - 35 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) + 21 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) - 7 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2}\right)} \cos\left(10 \, f x + 10 \, e\right) - 70 \, {\left(35 \, a^{2} \cos\left(6 \, f x + 6 \, e\right) - 21 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) + 7 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) - a^{2}\right)} \cos\left(8 \, f x + 8 \, e\right) - 70 \, {\left(21 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) - 7 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + a^{2}\right)} \cos\left(6 \, f x + 6 \, e\right) - 42 \, {\left(7 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) - a^{2}\right)} \cos\left(4 \, f x + 4 \, e\right) - 14 \, {\left(a^{2} \sin\left(12 \, f x + 12 \, e\right) - 3 \, a^{2} \sin\left(10 \, f x + 10 \, e\right) + 5 \, a^{2} \sin\left(8 \, f x + 8 \, e\right) - 5 \, a^{2} \sin\left(6 \, f x + 6 \, e\right) + 3 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) - a^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(14 \, f x + 14 \, e\right) - 98 \, {\left(3 \, a^{2} \sin\left(10 \, f x + 10 \, e\right) - 5 \, a^{2} \sin\left(8 \, f x + 8 \, e\right) + 5 \, a^{2} \sin\left(6 \, f x + 6 \, e\right) - 3 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + a^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(12 \, f x + 12 \, e\right) - 294 \, {\left(5 \, a^{2} \sin\left(8 \, f x + 8 \, e\right) - 5 \, a^{2} \sin\left(6 \, f x + 6 \, e\right) + 3 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) - a^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(10 \, f x + 10 \, e\right) - 490 \, {\left(5 \, a^{2} \sin\left(6 \, f x + 6 \, e\right) - 3 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + a^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(8 \, f x + 8 \, e\right) - 490 \, {\left(3 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) - a^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(6 \, f x + 6 \, e\right)\right)} f}"," ",0,"-8/105*((35*sin(11*f*x + 11*e) + 28*sin(9*f*x + 9*e) + 114*sin(7*f*x + 7*e) + 28*sin(5*f*x + 5*e) + 35*sin(3*f*x + 3*e))*cos(14*f*x + 14*e) - 7*(35*sin(11*f*x + 11*e) + 28*sin(9*f*x + 9*e) + 114*sin(7*f*x + 7*e) + 28*sin(5*f*x + 5*e) + 35*sin(3*f*x + 3*e))*cos(12*f*x + 12*e) - 245*(3*sin(10*f*x + 10*e) - 5*sin(8*f*x + 8*e) + 5*sin(6*f*x + 6*e) - 3*sin(4*f*x + 4*e) + sin(2*f*x + 2*e))*cos(11*f*x + 11*e) + 21*(28*sin(9*f*x + 9*e) + 114*sin(7*f*x + 7*e) + 28*sin(5*f*x + 5*e) + 35*sin(3*f*x + 3*e))*cos(10*f*x + 10*e) + 196*(5*sin(8*f*x + 8*e) - 5*sin(6*f*x + 6*e) + 3*sin(4*f*x + 4*e) - sin(2*f*x + 2*e))*cos(9*f*x + 9*e) - 35*(114*sin(7*f*x + 7*e) + 28*sin(5*f*x + 5*e) + 35*sin(3*f*x + 3*e))*cos(8*f*x + 8*e) - 798*(5*sin(6*f*x + 6*e) - 3*sin(4*f*x + 4*e) + sin(2*f*x + 2*e))*cos(7*f*x + 7*e) + 245*(4*sin(5*f*x + 5*e) + 5*sin(3*f*x + 3*e))*cos(6*f*x + 6*e) + 196*(3*sin(4*f*x + 4*e) - sin(2*f*x + 2*e))*cos(5*f*x + 5*e) - (35*cos(11*f*x + 11*e) + 28*cos(9*f*x + 9*e) + 114*cos(7*f*x + 7*e) + 28*cos(5*f*x + 5*e) + 35*cos(3*f*x + 3*e))*sin(14*f*x + 14*e) + 7*(35*cos(11*f*x + 11*e) + 28*cos(9*f*x + 9*e) + 114*cos(7*f*x + 7*e) + 28*cos(5*f*x + 5*e) + 35*cos(3*f*x + 3*e))*sin(12*f*x + 12*e) + 35*(21*cos(10*f*x + 10*e) - 35*cos(8*f*x + 8*e) + 35*cos(6*f*x + 6*e) - 21*cos(4*f*x + 4*e) + 7*cos(2*f*x + 2*e) - 1)*sin(11*f*x + 11*e) - 21*(28*cos(9*f*x + 9*e) + 114*cos(7*f*x + 7*e) + 28*cos(5*f*x + 5*e) + 35*cos(3*f*x + 3*e))*sin(10*f*x + 10*e) - 28*(35*cos(8*f*x + 8*e) - 35*cos(6*f*x + 6*e) + 21*cos(4*f*x + 4*e) - 7*cos(2*f*x + 2*e) + 1)*sin(9*f*x + 9*e) + 35*(114*cos(7*f*x + 7*e) + 28*cos(5*f*x + 5*e) + 35*cos(3*f*x + 3*e))*sin(8*f*x + 8*e) + 114*(35*cos(6*f*x + 6*e) - 21*cos(4*f*x + 4*e) + 7*cos(2*f*x + 2*e) - 1)*sin(7*f*x + 7*e) - 245*(4*cos(5*f*x + 5*e) + 5*cos(3*f*x + 3*e))*sin(6*f*x + 6*e) - 28*(21*cos(4*f*x + 4*e) - 7*cos(2*f*x + 2*e) + 1)*sin(5*f*x + 5*e) + 735*cos(3*f*x + 3*e)*sin(4*f*x + 4*e) + 35*(7*cos(2*f*x + 2*e) - 1)*sin(3*f*x + 3*e) - 735*cos(4*f*x + 4*e)*sin(3*f*x + 3*e) - 245*cos(3*f*x + 3*e)*sin(2*f*x + 2*e))*sqrt(a)/((a^2*cos(14*f*x + 14*e)^2 + 49*a^2*cos(12*f*x + 12*e)^2 + 441*a^2*cos(10*f*x + 10*e)^2 + 1225*a^2*cos(8*f*x + 8*e)^2 + 1225*a^2*cos(6*f*x + 6*e)^2 + 441*a^2*cos(4*f*x + 4*e)^2 + 49*a^2*cos(2*f*x + 2*e)^2 + a^2*sin(14*f*x + 14*e)^2 + 49*a^2*sin(12*f*x + 12*e)^2 + 441*a^2*sin(10*f*x + 10*e)^2 + 1225*a^2*sin(8*f*x + 8*e)^2 + 1225*a^2*sin(6*f*x + 6*e)^2 + 441*a^2*sin(4*f*x + 4*e)^2 - 294*a^2*sin(4*f*x + 4*e)*sin(2*f*x + 2*e) + 49*a^2*sin(2*f*x + 2*e)^2 - 14*a^2*cos(2*f*x + 2*e) + a^2 - 2*(7*a^2*cos(12*f*x + 12*e) - 21*a^2*cos(10*f*x + 10*e) + 35*a^2*cos(8*f*x + 8*e) - 35*a^2*cos(6*f*x + 6*e) + 21*a^2*cos(4*f*x + 4*e) - 7*a^2*cos(2*f*x + 2*e) + a^2)*cos(14*f*x + 14*e) - 14*(21*a^2*cos(10*f*x + 10*e) - 35*a^2*cos(8*f*x + 8*e) + 35*a^2*cos(6*f*x + 6*e) - 21*a^2*cos(4*f*x + 4*e) + 7*a^2*cos(2*f*x + 2*e) - a^2)*cos(12*f*x + 12*e) - 42*(35*a^2*cos(8*f*x + 8*e) - 35*a^2*cos(6*f*x + 6*e) + 21*a^2*cos(4*f*x + 4*e) - 7*a^2*cos(2*f*x + 2*e) + a^2)*cos(10*f*x + 10*e) - 70*(35*a^2*cos(6*f*x + 6*e) - 21*a^2*cos(4*f*x + 4*e) + 7*a^2*cos(2*f*x + 2*e) - a^2)*cos(8*f*x + 8*e) - 70*(21*a^2*cos(4*f*x + 4*e) - 7*a^2*cos(2*f*x + 2*e) + a^2)*cos(6*f*x + 6*e) - 42*(7*a^2*cos(2*f*x + 2*e) - a^2)*cos(4*f*x + 4*e) - 14*(a^2*sin(12*f*x + 12*e) - 3*a^2*sin(10*f*x + 10*e) + 5*a^2*sin(8*f*x + 8*e) - 5*a^2*sin(6*f*x + 6*e) + 3*a^2*sin(4*f*x + 4*e) - a^2*sin(2*f*x + 2*e))*sin(14*f*x + 14*e) - 98*(3*a^2*sin(10*f*x + 10*e) - 5*a^2*sin(8*f*x + 8*e) + 5*a^2*sin(6*f*x + 6*e) - 3*a^2*sin(4*f*x + 4*e) + a^2*sin(2*f*x + 2*e))*sin(12*f*x + 12*e) - 294*(5*a^2*sin(8*f*x + 8*e) - 5*a^2*sin(6*f*x + 6*e) + 3*a^2*sin(4*f*x + 4*e) - a^2*sin(2*f*x + 2*e))*sin(10*f*x + 10*e) - 490*(5*a^2*sin(6*f*x + 6*e) - 3*a^2*sin(4*f*x + 4*e) + a^2*sin(2*f*x + 2*e))*sin(8*f*x + 8*e) - 490*(3*a^2*sin(4*f*x + 4*e) - a^2*sin(2*f*x + 2*e))*sin(6*f*x + 6*e))*f)","B",0
488,1,230,0,0.438183," ","integrate((a+b*sin(f*x+e)^2)^(1/2)*tan(f*x+e)^5,x, algorithm=""maxima"")","-\frac{16 \, \sqrt{b \sin\left(f x + e\right)^{2} + a} b^{3} + \frac{{\left(8 \, a^{2} b^{3} + 24 \, a b^{4} + 15 \, b^{5}\right)} \log\left(\frac{\sqrt{b \sin\left(f x + e\right)^{2} + a} - \sqrt{a + b}}{\sqrt{b \sin\left(f x + e\right)^{2} + a} + \sqrt{a + b}}\right)}{{\left(a + b\right)}^{\frac{3}{2}}} - \frac{2 \, {\left({\left(8 \, a b^{4} + 9 \, b^{5}\right)} {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} - {\left(8 \, a^{2} b^{4} + 15 \, a b^{5} + 7 \, b^{6}\right)} \sqrt{b \sin\left(f x + e\right)^{2} + a}\right)}}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{2} {\left(a + b\right)} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 2 \, {\left(b \sin\left(f x + e\right)^{2} + a\right)} {\left(a^{2} + 2 \, a b + b^{2}\right)}}}{16 \, b^{3} f}"," ",0,"-1/16*(16*sqrt(b*sin(f*x + e)^2 + a)*b^3 + (8*a^2*b^3 + 24*a*b^4 + 15*b^5)*log((sqrt(b*sin(f*x + e)^2 + a) - sqrt(a + b))/(sqrt(b*sin(f*x + e)^2 + a) + sqrt(a + b)))/(a + b)^(3/2) - 2*((8*a*b^4 + 9*b^5)*(b*sin(f*x + e)^2 + a)^(3/2) - (8*a^2*b^4 + 15*a*b^5 + 7*b^6)*sqrt(b*sin(f*x + e)^2 + a))/((b*sin(f*x + e)^2 + a)^2*(a + b) + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 2*(b*sin(f*x + e)^2 + a)*(a^2 + 2*a*b + b^2)))/(b^3*f)","A",0
489,1,127,0,0.442755," ","integrate((a+b*sin(f*x+e)^2)^(1/2)*tan(f*x+e)^3,x, algorithm=""maxima"")","\frac{4 \, \sqrt{b \sin\left(f x + e\right)^{2} + a} b^{2} - \frac{2 \, \sqrt{b \sin\left(f x + e\right)^{2} + a} b^{3}}{b \sin\left(f x + e\right)^{2} - b} + \frac{{\left(2 \, a b^{2} + 3 \, b^{3}\right)} \log\left(\frac{\sqrt{b \sin\left(f x + e\right)^{2} + a} - \sqrt{a + b}}{\sqrt{b \sin\left(f x + e\right)^{2} + a} + \sqrt{a + b}}\right)}{\sqrt{a + b}}}{4 \, b^{2} f}"," ",0,"1/4*(4*sqrt(b*sin(f*x + e)^2 + a)*b^2 - 2*sqrt(b*sin(f*x + e)^2 + a)*b^3/(b*sin(f*x + e)^2 - b) + (2*a*b^2 + 3*b^3)*log((sqrt(b*sin(f*x + e)^2 + a) - sqrt(a + b))/(sqrt(b*sin(f*x + e)^2 + a) + sqrt(a + b)))/sqrt(a + b))/(b^2*f)","A",0
490,1,122,0,0.441499," ","integrate((a+b*sin(f*x+e)^2)^(1/2)*tan(f*x+e),x, algorithm=""maxima"")","-\frac{\sqrt{a + b} \operatorname{arsinh}\left(\frac{b \sin\left(f x + e\right)}{\sqrt{a b} {\left(\sin\left(f x + e\right) + 1\right)}} - \frac{a}{\sqrt{a b} {\left(\sin\left(f x + e\right) + 1\right)}}\right) - \sqrt{a + b} \operatorname{arsinh}\left(-\frac{b \sin\left(f x + e\right)}{\sqrt{a b} {\left(\sin\left(f x + e\right) - 1\right)}} - \frac{a}{\sqrt{a b} {\left(\sin\left(f x + e\right) - 1\right)}}\right) + 2 \, \sqrt{b \sin\left(f x + e\right)^{2} + a}}{2 \, f}"," ",0,"-1/2*(sqrt(a + b)*arcsinh(b*sin(f*x + e)/(sqrt(a*b)*(sin(f*x + e) + 1)) - a/(sqrt(a*b)*(sin(f*x + e) + 1))) - sqrt(a + b)*arcsinh(-b*sin(f*x + e)/(sqrt(a*b)*(sin(f*x + e) - 1)) - a/(sqrt(a*b)*(sin(f*x + e) - 1))) + 2*sqrt(b*sin(f*x + e)^2 + a))/f","B",0
491,1,43,0,0.337021," ","integrate(cot(f*x+e)*(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{a} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| \sin\left(f x + e\right) \right|}}\right) - \sqrt{b \sin\left(f x + e\right)^{2} + a}}{f}"," ",0,"-(sqrt(a)*arcsinh(a/(sqrt(a*b)*abs(sin(f*x + e)))) - sqrt(b*sin(f*x + e)^2 + a))/f","A",0
492,1,113,0,0.346288," ","integrate(cot(f*x+e)^3*(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\frac{2 \, \sqrt{a} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| \sin\left(f x + e\right) \right|}}\right) - \frac{b \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| \sin\left(f x + e\right) \right|}}\right)}{\sqrt{a}} - 2 \, \sqrt{b \sin\left(f x + e\right)^{2} + a} + \frac{\sqrt{b \sin\left(f x + e\right)^{2} + a} b}{a} - \frac{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}{a \sin\left(f x + e\right)^{2}}}{2 \, f}"," ",0,"1/2*(2*sqrt(a)*arcsinh(a/(sqrt(a*b)*abs(sin(f*x + e)))) - b*arcsinh(a/(sqrt(a*b)*abs(sin(f*x + e))))/sqrt(a) - 2*sqrt(b*sin(f*x + e)^2 + a) + sqrt(b*sin(f*x + e)^2 + a)*b/a - (b*sin(f*x + e)^2 + a)^(3/2)/(a*sin(f*x + e)^2))/f","A",0
493,1,215,0,0.377117," ","integrate(cot(f*x+e)^5*(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","-\frac{8 \, \sqrt{a} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| \sin\left(f x + e\right) \right|}}\right) - \frac{8 \, b \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| \sin\left(f x + e\right) \right|}}\right)}{\sqrt{a}} - \frac{b^{2} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| \sin\left(f x + e\right) \right|}}\right)}{a^{\frac{3}{2}}} - 8 \, \sqrt{b \sin\left(f x + e\right)^{2} + a} + \frac{8 \, \sqrt{b \sin\left(f x + e\right)^{2} + a} b}{a} + \frac{\sqrt{b \sin\left(f x + e\right)^{2} + a} b^{2}}{a^{2}} - \frac{8 \, {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}{a \sin\left(f x + e\right)^{2}} - \frac{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} b}{a^{2} \sin\left(f x + e\right)^{2}} + \frac{2 \, {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}{a \sin\left(f x + e\right)^{4}}}{8 \, f}"," ",0,"-1/8*(8*sqrt(a)*arcsinh(a/(sqrt(a*b)*abs(sin(f*x + e)))) - 8*b*arcsinh(a/(sqrt(a*b)*abs(sin(f*x + e))))/sqrt(a) - b^2*arcsinh(a/(sqrt(a*b)*abs(sin(f*x + e))))/a^(3/2) - 8*sqrt(b*sin(f*x + e)^2 + a) + 8*sqrt(b*sin(f*x + e)^2 + a)*b/a + sqrt(b*sin(f*x + e)^2 + a)*b^2/a^2 - 8*(b*sin(f*x + e)^2 + a)^(3/2)/(a*sin(f*x + e)^2) - (b*sin(f*x + e)^2 + a)^(3/2)*b/(a^2*sin(f*x + e)^2) + 2*(b*sin(f*x + e)^2 + a)^(3/2)/(a*sin(f*x + e)^4))/f","A",0
494,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e)^2)^(1/2)*tan(f*x+e)^4,x, algorithm=""maxima"")","\int \sqrt{b \sin\left(f x + e\right)^{2} + a} \tan\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e)^2 + a)*tan(f*x + e)^4, x)","F",0
495,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e)^2)^(1/2)*tan(f*x+e)^2,x, algorithm=""maxima"")","\int \sqrt{b \sin\left(f x + e\right)^{2} + a} \tan\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e)^2 + a)*tan(f*x + e)^2, x)","F",0
496,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sin\left(f x + e\right)^{2} + a}\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e)^2 + a), x)","F",0
497,0,0,0,0.000000," ","integrate(cot(f*x+e)^2*(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sin\left(f x + e\right)^{2} + a} \cot\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e)^2 + a)*cot(f*x + e)^2, x)","F",0
498,0,0,0,0.000000," ","integrate(cot(f*x+e)^4*(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sin\left(f x + e\right)^{2} + a} \cot\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e)^2 + a)*cot(f*x + e)^4, x)","F",0
499,1,238,0,0.429159," ","integrate((a+b*sin(f*x+e)^2)^(3/2)*tan(f*x+e)^5,x, algorithm=""maxima"")","-\frac{16 \, {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} b^{3} + 48 \, {\left(a b^{3} + 3 \, b^{4}\right)} \sqrt{b \sin\left(f x + e\right)^{2} + a} + \frac{3 \, {\left(8 \, a^{2} b^{3} + 40 \, a b^{4} + 35 \, b^{5}\right)} \log\left(\frac{\sqrt{b \sin\left(f x + e\right)^{2} + a} - \sqrt{a + b}}{\sqrt{b \sin\left(f x + e\right)^{2} + a} + \sqrt{a + b}}\right)}{\sqrt{a + b}} - \frac{6 \, {\left({\left(8 \, a b^{4} + 13 \, b^{5}\right)} {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} - {\left(8 \, a^{2} b^{4} + 19 \, a b^{5} + 11 \, b^{6}\right)} \sqrt{b \sin\left(f x + e\right)^{2} + a}\right)}}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{2} - 2 \, {\left(b \sin\left(f x + e\right)^{2} + a\right)} {\left(a + b\right)} + a^{2} + 2 \, a b + b^{2}}}{48 \, b^{3} f}"," ",0,"-1/48*(16*(b*sin(f*x + e)^2 + a)^(3/2)*b^3 + 48*(a*b^3 + 3*b^4)*sqrt(b*sin(f*x + e)^2 + a) + 3*(8*a^2*b^3 + 40*a*b^4 + 35*b^5)*log((sqrt(b*sin(f*x + e)^2 + a) - sqrt(a + b))/(sqrt(b*sin(f*x + e)^2 + a) + sqrt(a + b)))/sqrt(a + b) - 6*((8*a*b^4 + 13*b^5)*(b*sin(f*x + e)^2 + a)^(3/2) - (8*a^2*b^4 + 19*a*b^5 + 11*b^6)*sqrt(b*sin(f*x + e)^2 + a))/((b*sin(f*x + e)^2 + a)^2 - 2*(b*sin(f*x + e)^2 + a)*(a + b) + a^2 + 2*a*b + b^2))/(b^3*f)","A",0
500,1,169,0,0.421462," ","integrate((a+b*sin(f*x+e)^2)^(3/2)*tan(f*x+e)^3,x, algorithm=""maxima"")","\frac{4 \, {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} b^{2} + 12 \, {\left(a b^{2} + 2 \, b^{3}\right)} \sqrt{b \sin\left(f x + e\right)^{2} + a} + \frac{3 \, {\left(2 \, a^{2} b^{2} + 7 \, a b^{3} + 5 \, b^{4}\right)} \log\left(\frac{\sqrt{b \sin\left(f x + e\right)^{2} + a} - \sqrt{a + b}}{\sqrt{b \sin\left(f x + e\right)^{2} + a} + \sqrt{a + b}}\right)}{\sqrt{a + b}} - \frac{6 \, {\left(a b^{3} + b^{4}\right)} \sqrt{b \sin\left(f x + e\right)^{2} + a}}{b \sin\left(f x + e\right)^{2} - b}}{12 \, b^{2} f}"," ",0,"1/12*(4*(b*sin(f*x + e)^2 + a)^(3/2)*b^2 + 12*(a*b^2 + 2*b^3)*sqrt(b*sin(f*x + e)^2 + a) + 3*(2*a^2*b^2 + 7*a*b^3 + 5*b^4)*log((sqrt(b*sin(f*x + e)^2 + a) - sqrt(a + b))/(sqrt(b*sin(f*x + e)^2 + a) + sqrt(a + b)))/sqrt(a + b) - 6*(a*b^3 + b^4)*sqrt(b*sin(f*x + e)^2 + a)/(b*sin(f*x + e)^2 - b))/(b^2*f)","A",0
501,1,157,0,0.459430," ","integrate((a+b*sin(f*x+e)^2)^(3/2)*tan(f*x+e),x, algorithm=""maxima"")","-\frac{3 \, {\left(a + b\right)}^{\frac{3}{2}} \operatorname{arsinh}\left(\frac{b \sin\left(f x + e\right)}{\sqrt{a b} {\left(\sin\left(f x + e\right) + 1\right)}} - \frac{a}{\sqrt{a b} {\left(\sin\left(f x + e\right) + 1\right)}}\right) - 3 \, {\left(a + b\right)}^{\frac{3}{2}} \operatorname{arsinh}\left(-\frac{b \sin\left(f x + e\right)}{\sqrt{a b} {\left(\sin\left(f x + e\right) - 1\right)}} - \frac{a}{\sqrt{a b} {\left(\sin\left(f x + e\right) - 1\right)}}\right) + 2 \, {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} + 6 \, \sqrt{b \sin\left(f x + e\right)^{2} + a} a + 6 \, \sqrt{b \sin\left(f x + e\right)^{2} + a} b}{6 \, f}"," ",0,"-1/6*(3*(a + b)^(3/2)*arcsinh(b*sin(f*x + e)/(sqrt(a*b)*(sin(f*x + e) + 1)) - a/(sqrt(a*b)*(sin(f*x + e) + 1))) - 3*(a + b)^(3/2)*arcsinh(-b*sin(f*x + e)/(sqrt(a*b)*(sin(f*x + e) - 1)) - a/(sqrt(a*b)*(sin(f*x + e) - 1))) + 2*(b*sin(f*x + e)^2 + a)^(3/2) + 6*sqrt(b*sin(f*x + e)^2 + a)*a + 6*sqrt(b*sin(f*x + e)^2 + a)*b)/f","B",0
502,1,61,0,0.313826," ","integrate(cot(f*x+e)*(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","-\frac{3 \, a^{\frac{3}{2}} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| \sin\left(f x + e\right) \right|}}\right) - {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} - 3 \, \sqrt{b \sin\left(f x + e\right)^{2} + a} a}{3 \, f}"," ",0,"-1/3*(3*a^(3/2)*arcsinh(a/(sqrt(a*b)*abs(sin(f*x + e)))) - (b*sin(f*x + e)^2 + a)^(3/2) - 3*sqrt(b*sin(f*x + e)^2 + a)*a)/f","A",0
503,1,148,0,0.333008," ","integrate(cot(f*x+e)^3*(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\frac{6 \, a^{\frac{3}{2}} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| \sin\left(f x + e\right) \right|}}\right) - 9 \, \sqrt{a} b \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| \sin\left(f x + e\right) \right|}}\right) - 2 \, {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} - 6 \, \sqrt{b \sin\left(f x + e\right)^{2} + a} a + 9 \, \sqrt{b \sin\left(f x + e\right)^{2} + a} b + \frac{3 \, {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} b}{a} - \frac{3 \, {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{5}{2}}}{a \sin\left(f x + e\right)^{2}}}{6 \, f}"," ",0,"1/6*(6*a^(3/2)*arcsinh(a/(sqrt(a*b)*abs(sin(f*x + e)))) - 9*sqrt(a)*b*arcsinh(a/(sqrt(a*b)*abs(sin(f*x + e)))) - 2*(b*sin(f*x + e)^2 + a)^(3/2) - 6*sqrt(b*sin(f*x + e)^2 + a)*a + 9*sqrt(b*sin(f*x + e)^2 + a)*b + 3*(b*sin(f*x + e)^2 + a)^(3/2)*b/a - 3*(b*sin(f*x + e)^2 + a)^(5/2)/(a*sin(f*x + e)^2))/f","A",0
504,1,272,0,0.332010," ","integrate(cot(f*x+e)^5*(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","-\frac{24 \, a^{\frac{3}{2}} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| \sin\left(f x + e\right) \right|}}\right) - 72 \, \sqrt{a} b \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| \sin\left(f x + e\right) \right|}}\right) + \frac{9 \, b^{2} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| \sin\left(f x + e\right) \right|}}\right)}{\sqrt{a}} - 8 \, {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} - 24 \, \sqrt{b \sin\left(f x + e\right)^{2} + a} a + 72 \, \sqrt{b \sin\left(f x + e\right)^{2} + a} b + \frac{24 \, {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} b}{a} - \frac{3 \, {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} b^{2}}{a^{2}} - \frac{9 \, \sqrt{b \sin\left(f x + e\right)^{2} + a} b^{2}}{a} - \frac{24 \, {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{5}{2}}}{a \sin\left(f x + e\right)^{2}} + \frac{3 \, {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{5}{2}} b}{a^{2} \sin\left(f x + e\right)^{2}} + \frac{6 \, {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{5}{2}}}{a \sin\left(f x + e\right)^{4}}}{24 \, f}"," ",0,"-1/24*(24*a^(3/2)*arcsinh(a/(sqrt(a*b)*abs(sin(f*x + e)))) - 72*sqrt(a)*b*arcsinh(a/(sqrt(a*b)*abs(sin(f*x + e)))) + 9*b^2*arcsinh(a/(sqrt(a*b)*abs(sin(f*x + e))))/sqrt(a) - 8*(b*sin(f*x + e)^2 + a)^(3/2) - 24*sqrt(b*sin(f*x + e)^2 + a)*a + 72*sqrt(b*sin(f*x + e)^2 + a)*b + 24*(b*sin(f*x + e)^2 + a)^(3/2)*b/a - 3*(b*sin(f*x + e)^2 + a)^(3/2)*b^2/a^2 - 9*sqrt(b*sin(f*x + e)^2 + a)*b^2/a - 24*(b*sin(f*x + e)^2 + a)^(5/2)/(a*sin(f*x + e)^2) + 3*(b*sin(f*x + e)^2 + a)^(5/2)*b/(a^2*sin(f*x + e)^2) + 6*(b*sin(f*x + e)^2 + a)^(5/2)/(a*sin(f*x + e)^4))/f","A",0
505,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e)^2)^(3/2)*tan(f*x+e)^4,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \tan\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^(3/2)*tan(f*x + e)^4, x)","F",0
506,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e)^2)^(3/2)*tan(f*x+e)^2,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \tan\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^(3/2)*tan(f*x + e)^2, x)","F",0
507,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^(3/2), x)","F",0
508,0,0,0,0.000000," ","integrate(cot(f*x+e)^2*(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \cot\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^(3/2)*cot(f*x + e)^2, x)","F",0
509,0,0,0,0.000000," ","integrate(cot(f*x+e)^4*(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \cot\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^(3/2)*cot(f*x + e)^4, x)","F",0
510,1,248,0,0.420879," ","integrate(tan(f*x+e)^5/(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","-\frac{\frac{{\left(8 \, a^{2} b^{3} + 8 \, a b^{4} + 3 \, b^{5}\right)} \log\left(\frac{\sqrt{b \sin\left(f x + e\right)^{2} + a} - \sqrt{a + b}}{\sqrt{b \sin\left(f x + e\right)^{2} + a} + \sqrt{a + b}}\right)}{{\left(a^{2} + 2 \, a b + b^{2}\right)} \sqrt{a + b}} - \frac{2 \, {\left({\left(8 \, a b^{4} + 5 \, b^{5}\right)} {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} - {\left(8 \, a^{2} b^{4} + 11 \, a b^{5} + 3 \, b^{6}\right)} \sqrt{b \sin\left(f x + e\right)^{2} + a}\right)}}{a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4} + {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{2} {\left(a^{2} + 2 \, a b + b^{2}\right)} - 2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} {\left(b \sin\left(f x + e\right)^{2} + a\right)}}}{16 \, b^{3} f}"," ",0,"-1/16*((8*a^2*b^3 + 8*a*b^4 + 3*b^5)*log((sqrt(b*sin(f*x + e)^2 + a) - sqrt(a + b))/(sqrt(b*sin(f*x + e)^2 + a) + sqrt(a + b)))/((a^2 + 2*a*b + b^2)*sqrt(a + b)) - 2*((8*a*b^4 + 5*b^5)*(b*sin(f*x + e)^2 + a)^(3/2) - (8*a^2*b^4 + 11*a*b^5 + 3*b^6)*sqrt(b*sin(f*x + e)^2 + a))/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4 + (b*sin(f*x + e)^2 + a)^2*(a^2 + 2*a*b + b^2) - 2*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*(b*sin(f*x + e)^2 + a)))/(b^3*f)","B",0
511,1,124,0,0.540267," ","integrate(tan(f*x+e)^3/(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","-\frac{\frac{2 \, \sqrt{b \sin\left(f x + e\right)^{2} + a} b^{3}}{{\left(b \sin\left(f x + e\right)^{2} + a\right)} {\left(a + b\right)} - a^{2} - 2 \, a b - b^{2}} - \frac{{\left(2 \, a b^{2} + b^{3}\right)} \log\left(\frac{\sqrt{b \sin\left(f x + e\right)^{2} + a} - \sqrt{a + b}}{\sqrt{b \sin\left(f x + e\right)^{2} + a} + \sqrt{a + b}}\right)}{{\left(a + b\right)}^{\frac{3}{2}}}}{4 \, b^{2} f}"," ",0,"-1/4*(2*sqrt(b*sin(f*x + e)^2 + a)*b^3/((b*sin(f*x + e)^2 + a)*(a + b) - a^2 - 2*a*b - b^2) - (2*a*b^2 + b^3)*log((sqrt(b*sin(f*x + e)^2 + a) - sqrt(a + b))/(sqrt(b*sin(f*x + e)^2 + a) + sqrt(a + b)))/(a + b)^(3/2))/(b^2*f)","A",0
512,1,106,0,0.415244," ","integrate(tan(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","-\frac{\frac{\operatorname{arsinh}\left(\frac{b \sin\left(f x + e\right)}{\sqrt{a b} {\left(\sin\left(f x + e\right) + 1\right)}} - \frac{a}{\sqrt{a b} {\left(\sin\left(f x + e\right) + 1\right)}}\right)}{\sqrt{a + b}} - \frac{\operatorname{arsinh}\left(-\frac{b \sin\left(f x + e\right)}{\sqrt{a b} {\left(\sin\left(f x + e\right) - 1\right)}} - \frac{a}{\sqrt{a b} {\left(\sin\left(f x + e\right) - 1\right)}}\right)}{\sqrt{a + b}}}{2 \, f}"," ",0,"-1/2*(arcsinh(b*sin(f*x + e)/(sqrt(a*b)*(sin(f*x + e) + 1)) - a/(sqrt(a*b)*(sin(f*x + e) + 1)))/sqrt(a + b) - arcsinh(-b*sin(f*x + e)/(sqrt(a*b)*(sin(f*x + e) - 1)) - a/(sqrt(a*b)*(sin(f*x + e) - 1)))/sqrt(a + b))/f","B",0
513,1,25,0,0.312295," ","integrate(cot(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","-\frac{\operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| \sin\left(f x + e\right) \right|}}\right)}{\sqrt{a} f}"," ",0,"-arcsinh(a/(sqrt(a*b)*abs(sin(f*x + e))))/(sqrt(a)*f)","A",0
514,1,77,0,0.300486," ","integrate(cot(f*x+e)^3/(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\frac{\frac{2 \, \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| \sin\left(f x + e\right) \right|}}\right)}{\sqrt{a}} + \frac{b \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| \sin\left(f x + e\right) \right|}}\right)}{a^{\frac{3}{2}}} - \frac{\sqrt{b \sin\left(f x + e\right)^{2} + a}}{a \sin\left(f x + e\right)^{2}}}{2 \, f}"," ",0,"1/2*(2*arcsinh(a/(sqrt(a*b)*abs(sin(f*x + e))))/sqrt(a) + b*arcsinh(a/(sqrt(a*b)*abs(sin(f*x + e))))/a^(3/2) - sqrt(b*sin(f*x + e)^2 + a)/(a*sin(f*x + e)^2))/f","A",0
515,1,158,0,0.318059," ","integrate(cot(f*x+e)^5/(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","-\frac{\frac{8 \, \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| \sin\left(f x + e\right) \right|}}\right)}{\sqrt{a}} + \frac{8 \, b \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| \sin\left(f x + e\right) \right|}}\right)}{a^{\frac{3}{2}}} + \frac{3 \, b^{2} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| \sin\left(f x + e\right) \right|}}\right)}{a^{\frac{5}{2}}} - \frac{8 \, \sqrt{b \sin\left(f x + e\right)^{2} + a}}{a \sin\left(f x + e\right)^{2}} - \frac{3 \, \sqrt{b \sin\left(f x + e\right)^{2} + a} b}{a^{2} \sin\left(f x + e\right)^{2}} + \frac{2 \, \sqrt{b \sin\left(f x + e\right)^{2} + a}}{a \sin\left(f x + e\right)^{4}}}{8 \, f}"," ",0,"-1/8*(8*arcsinh(a/(sqrt(a*b)*abs(sin(f*x + e))))/sqrt(a) + 8*b*arcsinh(a/(sqrt(a*b)*abs(sin(f*x + e))))/a^(3/2) + 3*b^2*arcsinh(a/(sqrt(a*b)*abs(sin(f*x + e))))/a^(5/2) - 8*sqrt(b*sin(f*x + e)^2 + a)/(a*sin(f*x + e)^2) - 3*sqrt(b*sin(f*x + e)^2 + a)*b/(a^2*sin(f*x + e)^2) + 2*sqrt(b*sin(f*x + e)^2 + a)/(a*sin(f*x + e)^4))/f","A",0
516,-1,0,0,0.000000," ","integrate(tan(f*x+e)^4/(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
517,0,0,0,0.000000," ","integrate(tan(f*x+e)^2/(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\tan\left(f x + e\right)^{2}}{\sqrt{b \sin\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(tan(f*x + e)^2/sqrt(b*sin(f*x + e)^2 + a), x)","F",0
518,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \sin\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(1/sqrt(b*sin(f*x + e)^2 + a), x)","F",0
519,0,0,0,0.000000," ","integrate(cot(f*x+e)^2/(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\cot\left(f x + e\right)^{2}}{\sqrt{b \sin\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(cot(f*x + e)^2/sqrt(b*sin(f*x + e)^2 + a), x)","F",0
520,-1,0,0,0.000000," ","integrate(cot(f*x+e)^4/(a+b*sin(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
521,1,334,0,0.793351," ","integrate(tan(f*x+e)^5/(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","-\frac{\frac{{\left(8 \, a^{2} b^{3} - 8 \, a b^{4} - b^{5}\right)} \log\left(\frac{\sqrt{b \sin\left(f x + e\right)^{2} + a} - \sqrt{a + b}}{\sqrt{b \sin\left(f x + e\right)^{2} + a} + \sqrt{a + b}}\right)}{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sqrt{a + b}} + \frac{2 \, {\left(8 \, a^{4} b^{3} + 16 \, a^{3} b^{4} + 8 \, a^{2} b^{5} + {\left(8 \, a^{2} b^{3} - 8 \, a b^{4} - b^{5}\right)} {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{2} - {\left(16 \, a^{3} b^{3} + 8 \, a^{2} b^{4} - 7 \, a b^{5} + b^{6}\right)} {\left(b \sin\left(f x + e\right)^{2} + a\right)}\right)}}{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{5}{2}} - 2 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} + {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \sqrt{b \sin\left(f x + e\right)^{2} + a}}}{16 \, b^{3} f}"," ",0,"-1/16*((8*a^2*b^3 - 8*a*b^4 - b^5)*log((sqrt(b*sin(f*x + e)^2 + a) - sqrt(a + b))/(sqrt(b*sin(f*x + e)^2 + a) + sqrt(a + b)))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sqrt(a + b)) + 2*(8*a^4*b^3 + 16*a^3*b^4 + 8*a^2*b^5 + (8*a^2*b^3 - 8*a*b^4 - b^5)*(b*sin(f*x + e)^2 + a)^2 - (16*a^3*b^3 + 8*a^2*b^4 - 7*a*b^5 + b^6)*(b*sin(f*x + e)^2 + a))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*(b*sin(f*x + e)^2 + a)^(5/2) - 2*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*(b*sin(f*x + e)^2 + a)^(3/2) + (a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*sqrt(b*sin(f*x + e)^2 + a)))/(b^3*f)","B",0
522,1,193,0,1.065554," ","integrate(tan(f*x+e)^3/(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\frac{\frac{{\left(2 \, a b^{2} - b^{3}\right)} \log\left(\frac{\sqrt{b \sin\left(f x + e\right)^{2} + a} - \sqrt{a + b}}{\sqrt{b \sin\left(f x + e\right)^{2} + a} + \sqrt{a + b}}\right)}{{\left(a^{2} + 2 \, a b + b^{2}\right)} \sqrt{a + b}} - \frac{2 \, {\left(2 \, a^{2} b^{2} + 2 \, a b^{3} - {\left(2 \, a b^{2} - b^{3}\right)} {\left(b \sin\left(f x + e\right)^{2} + a\right)}\right)}}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} {\left(a^{2} + 2 \, a b + b^{2}\right)} - {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sqrt{b \sin\left(f x + e\right)^{2} + a}}}{4 \, b^{2} f}"," ",0,"1/4*((2*a*b^2 - b^3)*log((sqrt(b*sin(f*x + e)^2 + a) - sqrt(a + b))/(sqrt(b*sin(f*x + e)^2 + a) + sqrt(a + b)))/((a^2 + 2*a*b + b^2)*sqrt(a + b)) - 2*(2*a^2*b^2 + 2*a*b^3 - (2*a*b^2 - b^3)*(b*sin(f*x + e)^2 + a))/((b*sin(f*x + e)^2 + a)^(3/2)*(a^2 + 2*a*b + b^2) - (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sqrt(b*sin(f*x + e)^2 + a)))/(b^2*f)","A",0
523,1,143,0,0.656151," ","integrate(tan(f*x+e)/(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","-\frac{\frac{\operatorname{arsinh}\left(\frac{b \sin\left(f x + e\right)}{\sqrt{a b} {\left(\sin\left(f x + e\right) + 1\right)}} - \frac{a}{\sqrt{a b} {\left(\sin\left(f x + e\right) + 1\right)}}\right)}{{\left(a + b\right)}^{\frac{3}{2}}} - \frac{\operatorname{arsinh}\left(-\frac{b \sin\left(f x + e\right)}{\sqrt{a b} {\left(\sin\left(f x + e\right) - 1\right)}} - \frac{a}{\sqrt{a b} {\left(\sin\left(f x + e\right) - 1\right)}}\right)}{{\left(a + b\right)}^{\frac{3}{2}}} + \frac{2}{\sqrt{b \sin\left(f x + e\right)^{2} + a} a + \sqrt{b \sin\left(f x + e\right)^{2} + a} b}}{2 \, f}"," ",0,"-1/2*(arcsinh(b*sin(f*x + e)/(sqrt(a*b)*(sin(f*x + e) + 1)) - a/(sqrt(a*b)*(sin(f*x + e) + 1)))/(a + b)^(3/2) - arcsinh(-b*sin(f*x + e)/(sqrt(a*b)*(sin(f*x + e) - 1)) - a/(sqrt(a*b)*(sin(f*x + e) - 1)))/(a + b)^(3/2) + 2/(sqrt(b*sin(f*x + e)^2 + a)*a + sqrt(b*sin(f*x + e)^2 + a)*b))/f","B",0
524,1,46,0,0.302241," ","integrate(cot(f*x+e)/(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","-\frac{\frac{\operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| \sin\left(f x + e\right) \right|}}\right)}{a^{\frac{3}{2}}} - \frac{1}{\sqrt{b \sin\left(f x + e\right)^{2} + a} a}}{f}"," ",0,"-(arcsinh(a/(sqrt(a*b)*abs(sin(f*x + e))))/a^(3/2) - 1/(sqrt(b*sin(f*x + e)^2 + a)*a))/f","A",0
525,1,117,0,0.506297," ","integrate(cot(f*x+e)^3/(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\frac{\frac{2 \, \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| \sin\left(f x + e\right) \right|}}\right)}{a^{\frac{3}{2}}} + \frac{3 \, b \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| \sin\left(f x + e\right) \right|}}\right)}{a^{\frac{5}{2}}} - \frac{2}{\sqrt{b \sin\left(f x + e\right)^{2} + a} a} - \frac{3 \, b}{\sqrt{b \sin\left(f x + e\right)^{2} + a} a^{2}} - \frac{1}{\sqrt{b \sin\left(f x + e\right)^{2} + a} a \sin\left(f x + e\right)^{2}}}{2 \, f}"," ",0,"1/2*(2*arcsinh(a/(sqrt(a*b)*abs(sin(f*x + e))))/a^(3/2) + 3*b*arcsinh(a/(sqrt(a*b)*abs(sin(f*x + e))))/a^(5/2) - 2/(sqrt(b*sin(f*x + e)^2 + a)*a) - 3*b/(sqrt(b*sin(f*x + e)^2 + a)*a^2) - 1/(sqrt(b*sin(f*x + e)^2 + a)*a*sin(f*x + e)^2))/f","A",0
526,1,219,0,0.331427," ","integrate(cot(f*x+e)^5/(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","-\frac{\frac{8 \, \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| \sin\left(f x + e\right) \right|}}\right)}{a^{\frac{3}{2}}} + \frac{24 \, b \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| \sin\left(f x + e\right) \right|}}\right)}{a^{\frac{5}{2}}} + \frac{15 \, b^{2} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| \sin\left(f x + e\right) \right|}}\right)}{a^{\frac{7}{2}}} - \frac{8}{\sqrt{b \sin\left(f x + e\right)^{2} + a} a} - \frac{24 \, b}{\sqrt{b \sin\left(f x + e\right)^{2} + a} a^{2}} - \frac{15 \, b^{2}}{\sqrt{b \sin\left(f x + e\right)^{2} + a} a^{3}} - \frac{8}{\sqrt{b \sin\left(f x + e\right)^{2} + a} a \sin\left(f x + e\right)^{2}} - \frac{5 \, b}{\sqrt{b \sin\left(f x + e\right)^{2} + a} a^{2} \sin\left(f x + e\right)^{2}} + \frac{2}{\sqrt{b \sin\left(f x + e\right)^{2} + a} a \sin\left(f x + e\right)^{4}}}{8 \, f}"," ",0,"-1/8*(8*arcsinh(a/(sqrt(a*b)*abs(sin(f*x + e))))/a^(3/2) + 24*b*arcsinh(a/(sqrt(a*b)*abs(sin(f*x + e))))/a^(5/2) + 15*b^2*arcsinh(a/(sqrt(a*b)*abs(sin(f*x + e))))/a^(7/2) - 8/(sqrt(b*sin(f*x + e)^2 + a)*a) - 24*b/(sqrt(b*sin(f*x + e)^2 + a)*a^2) - 15*b^2/(sqrt(b*sin(f*x + e)^2 + a)*a^3) - 8/(sqrt(b*sin(f*x + e)^2 + a)*a*sin(f*x + e)^2) - 5*b/(sqrt(b*sin(f*x + e)^2 + a)*a^2*sin(f*x + e)^2) + 2/(sqrt(b*sin(f*x + e)^2 + a)*a*sin(f*x + e)^4))/f","A",0
527,-1,0,0,0.000000," ","integrate(tan(f*x+e)^4/(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
528,0,0,0,0.000000," ","integrate(tan(f*x+e)^2/(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\tan\left(f x + e\right)^{2}}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(tan(f*x + e)^2/(b*sin(f*x + e)^2 + a)^(3/2), x)","F",0
529,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^(-3/2), x)","F",0
530,-1,0,0,0.000000," ","integrate(cot(f*x+e)^2/(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
531,-1,0,0,0.000000," ","integrate(cot(f*x+e)^4/(a+b*sin(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
532,1,424,0,0.657180," ","integrate(tan(f*x+e)^5/(a+b*sin(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","-\frac{\frac{3 \, {\left(8 \, a^{2} b^{3} - 24 \, a b^{4} + 3 \, b^{5}\right)} \log\left(\frac{\sqrt{b \sin\left(f x + e\right)^{2} + a} - \sqrt{a + b}}{\sqrt{b \sin\left(f x + e\right)^{2} + a} + \sqrt{a + b}}\right)}{{\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \sqrt{a + b}} + \frac{2 \, {\left(8 \, a^{5} b^{3} + 24 \, a^{4} b^{4} + 24 \, a^{3} b^{5} + 8 \, a^{2} b^{6} + 3 \, {\left(8 \, a^{2} b^{3} - 24 \, a b^{4} + 3 \, b^{5}\right)} {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{3} - 5 \, {\left(8 \, a^{3} b^{3} - 16 \, a^{2} b^{4} - 21 \, a b^{5} + 3 \, b^{6}\right)} {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{2} + 8 \, {\left(a^{4} b^{3} - 4 \, a^{3} b^{4} - 11 \, a^{2} b^{5} - 6 \, a b^{6}\right)} {\left(b \sin\left(f x + e\right)^{2} + a\right)}\right)}}{{\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{7}{2}} - 2 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{5}{2}} + {\left(a^{6} + 6 \, a^{5} b + 15 \, a^{4} b^{2} + 20 \, a^{3} b^{3} + 15 \, a^{2} b^{4} + 6 \, a b^{5} + b^{6}\right)} {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}}{48 \, b^{3} f}"," ",0,"-1/48*(3*(8*a^2*b^3 - 24*a*b^4 + 3*b^5)*log((sqrt(b*sin(f*x + e)^2 + a) - sqrt(a + b))/(sqrt(b*sin(f*x + e)^2 + a) + sqrt(a + b)))/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*sqrt(a + b)) + 2*(8*a^5*b^3 + 24*a^4*b^4 + 24*a^3*b^5 + 8*a^2*b^6 + 3*(8*a^2*b^3 - 24*a*b^4 + 3*b^5)*(b*sin(f*x + e)^2 + a)^3 - 5*(8*a^3*b^3 - 16*a^2*b^4 - 21*a*b^5 + 3*b^6)*(b*sin(f*x + e)^2 + a)^2 + 8*(a^4*b^3 - 4*a^3*b^4 - 11*a^2*b^5 - 6*a*b^6)*(b*sin(f*x + e)^2 + a))/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*(b*sin(f*x + e)^2 + a)^(7/2) - 2*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*(b*sin(f*x + e)^2 + a)^(5/2) + (a^6 + 6*a^5*b + 15*a^4*b^2 + 20*a^3*b^3 + 15*a^2*b^4 + 6*a*b^5 + b^6)*(b*sin(f*x + e)^2 + a)^(3/2)))/(b^3*f)","B",0
533,1,262,0,0.783409," ","integrate(tan(f*x+e)^3/(a+b*sin(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\frac{\frac{3 \, {\left(2 \, a b^{2} - 3 \, b^{3}\right)} \log\left(\frac{\sqrt{b \sin\left(f x + e\right)^{2} + a} - \sqrt{a + b}}{\sqrt{b \sin\left(f x + e\right)^{2} + a} + \sqrt{a + b}}\right)}{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sqrt{a + b}} - \frac{2 \, {\left(2 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + 2 \, a b^{4} - 3 \, {\left(2 \, a b^{2} - 3 \, b^{3}\right)} {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{2} + 2 \, {\left(2 \, a^{2} b^{2} - a b^{3} - 3 \, b^{4}\right)} {\left(b \sin\left(f x + e\right)^{2} + a\right)}\right)}}{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{5}{2}} - {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}}{12 \, b^{2} f}"," ",0,"1/12*(3*(2*a*b^2 - 3*b^3)*log((sqrt(b*sin(f*x + e)^2 + a) - sqrt(a + b))/(sqrt(b*sin(f*x + e)^2 + a) + sqrt(a + b)))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sqrt(a + b)) - 2*(2*a^3*b^2 + 4*a^2*b^3 + 2*a*b^4 - 3*(2*a*b^2 - 3*b^3)*(b*sin(f*x + e)^2 + a)^2 + 2*(2*a^2*b^2 - a*b^3 - 3*b^4)*(b*sin(f*x + e)^2 + a))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*(b*sin(f*x + e)^2 + a)^(5/2) - (a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*(b*sin(f*x + e)^2 + a)^(3/2)))/(b^2*f)","A",0
534,1,203,0,0.774193," ","integrate(tan(f*x+e)/(a+b*sin(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","-\frac{\frac{2}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} a + {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} b} + \frac{6}{\sqrt{b \sin\left(f x + e\right)^{2} + a} a^{2} + 2 \, \sqrt{b \sin\left(f x + e\right)^{2} + a} a b + \sqrt{b \sin\left(f x + e\right)^{2} + a} b^{2}} + \frac{3 \, \operatorname{arsinh}\left(\frac{b \sin\left(f x + e\right)}{\sqrt{a b} {\left(\sin\left(f x + e\right) + 1\right)}} - \frac{a}{\sqrt{a b} {\left(\sin\left(f x + e\right) + 1\right)}}\right)}{{\left(a + b\right)}^{\frac{5}{2}}} - \frac{3 \, \operatorname{arsinh}\left(-\frac{b \sin\left(f x + e\right)}{\sqrt{a b} {\left(\sin\left(f x + e\right) - 1\right)}} - \frac{a}{\sqrt{a b} {\left(\sin\left(f x + e\right) - 1\right)}}\right)}{{\left(a + b\right)}^{\frac{5}{2}}}}{6 \, f}"," ",0,"-1/6*(2/((b*sin(f*x + e)^2 + a)^(3/2)*a + (b*sin(f*x + e)^2 + a)^(3/2)*b) + 6/(sqrt(b*sin(f*x + e)^2 + a)*a^2 + 2*sqrt(b*sin(f*x + e)^2 + a)*a*b + sqrt(b*sin(f*x + e)^2 + a)*b^2) + 3*arcsinh(b*sin(f*x + e)/(sqrt(a*b)*(sin(f*x + e) + 1)) - a/(sqrt(a*b)*(sin(f*x + e) + 1)))/(a + b)^(5/2) - 3*arcsinh(-b*sin(f*x + e)/(sqrt(a*b)*(sin(f*x + e) - 1)) - a/(sqrt(a*b)*(sin(f*x + e) - 1)))/(a + b)^(5/2))/f","B",0
535,1,66,0,0.383037," ","integrate(cot(f*x+e)/(a+b*sin(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","-\frac{\frac{3 \, \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| \sin\left(f x + e\right) \right|}}\right)}{a^{\frac{5}{2}}} - \frac{3}{\sqrt{b \sin\left(f x + e\right)^{2} + a} a^{2}} - \frac{1}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} a}}{3 \, f}"," ",0,"-1/3*(3*arcsinh(a/(sqrt(a*b)*abs(sin(f*x + e))))/a^(5/2) - 3/(sqrt(b*sin(f*x + e)^2 + a)*a^2) - 1/((b*sin(f*x + e)^2 + a)^(3/2)*a))/f","A",0
536,1,156,0,0.441489," ","integrate(cot(f*x+e)^3/(a+b*sin(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\frac{\frac{6 \, \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| \sin\left(f x + e\right) \right|}}\right)}{a^{\frac{5}{2}}} + \frac{15 \, b \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| \sin\left(f x + e\right) \right|}}\right)}{a^{\frac{7}{2}}} - \frac{6}{\sqrt{b \sin\left(f x + e\right)^{2} + a} a^{2}} - \frac{2}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} a} - \frac{15 \, b}{\sqrt{b \sin\left(f x + e\right)^{2} + a} a^{3}} - \frac{5 \, b}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} a^{2}} - \frac{3}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} a \sin\left(f x + e\right)^{2}}}{6 \, f}"," ",0,"1/6*(6*arcsinh(a/(sqrt(a*b)*abs(sin(f*x + e))))/a^(5/2) + 15*b*arcsinh(a/(sqrt(a*b)*abs(sin(f*x + e))))/a^(7/2) - 6/(sqrt(b*sin(f*x + e)^2 + a)*a^2) - 2/((b*sin(f*x + e)^2 + a)^(3/2)*a) - 15*b/(sqrt(b*sin(f*x + e)^2 + a)*a^3) - 5*b/((b*sin(f*x + e)^2 + a)^(3/2)*a^2) - 3/((b*sin(f*x + e)^2 + a)^(3/2)*a*sin(f*x + e)^2))/f","A",0
537,1,280,0,0.402957," ","integrate(cot(f*x+e)^5/(a+b*sin(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","-\frac{\frac{24 \, \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| \sin\left(f x + e\right) \right|}}\right)}{a^{\frac{5}{2}}} + \frac{120 \, b \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| \sin\left(f x + e\right) \right|}}\right)}{a^{\frac{7}{2}}} + \frac{105 \, b^{2} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| \sin\left(f x + e\right) \right|}}\right)}{a^{\frac{9}{2}}} - \frac{24}{\sqrt{b \sin\left(f x + e\right)^{2} + a} a^{2}} - \frac{8}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} a} - \frac{120 \, b}{\sqrt{b \sin\left(f x + e\right)^{2} + a} a^{3}} - \frac{40 \, b}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} a^{2}} - \frac{105 \, b^{2}}{\sqrt{b \sin\left(f x + e\right)^{2} + a} a^{4}} - \frac{35 \, b^{2}}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} a^{3}} - \frac{24}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} a \sin\left(f x + e\right)^{2}} - \frac{21 \, b}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} a^{2} \sin\left(f x + e\right)^{2}} + \frac{6}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} a \sin\left(f x + e\right)^{4}}}{24 \, f}"," ",0,"-1/24*(24*arcsinh(a/(sqrt(a*b)*abs(sin(f*x + e))))/a^(5/2) + 120*b*arcsinh(a/(sqrt(a*b)*abs(sin(f*x + e))))/a^(7/2) + 105*b^2*arcsinh(a/(sqrt(a*b)*abs(sin(f*x + e))))/a^(9/2) - 24/(sqrt(b*sin(f*x + e)^2 + a)*a^2) - 8/((b*sin(f*x + e)^2 + a)^(3/2)*a) - 120*b/(sqrt(b*sin(f*x + e)^2 + a)*a^3) - 40*b/((b*sin(f*x + e)^2 + a)^(3/2)*a^2) - 105*b^2/(sqrt(b*sin(f*x + e)^2 + a)*a^4) - 35*b^2/((b*sin(f*x + e)^2 + a)^(3/2)*a^3) - 24/((b*sin(f*x + e)^2 + a)^(3/2)*a*sin(f*x + e)^2) - 21*b/((b*sin(f*x + e)^2 + a)^(3/2)*a^2*sin(f*x + e)^2) + 6/((b*sin(f*x + e)^2 + a)^(3/2)*a*sin(f*x + e)^4))/f","A",0
538,-1,0,0,0.000000," ","integrate(tan(f*x+e)^4/(a+b*sin(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
539,-1,0,0,0.000000," ","integrate(tan(f*x+e)^2/(a+b*sin(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
540,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sin\left(f x + e\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^(-5/2), x)","F",0
541,-1,0,0,0.000000," ","integrate(cot(f*x+e)^2/(a+b*sin(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
542,-1,0,0,0.000000," ","integrate(cot(f*x+e)^4/(a+b*sin(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
543,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e)^2)^p*(d*tan(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{p} \left(d \tan\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^p*(d*tan(f*x + e))^m, x)","F",0
544,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c)^2)^p*tan(d*x+c)^3,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right)^{2} + a\right)}^{p} \tan\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*sin(d*x + c)^2 + a)^p*tan(d*x + c)^3, x)","F",0
545,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c)^2)^p*tan(d*x+c),x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right)^{2} + a\right)}^{p} \tan\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sin(d*x + c)^2 + a)^p*tan(d*x + c), x)","F",0
546,0,0,0,0.000000," ","integrate(cot(d*x+c)*(a+b*sin(d*x+c)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right)^{2} + a\right)}^{p} \cot\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sin(d*x + c)^2 + a)^p*cot(d*x + c), x)","F",0
547,0,0,0,0.000000," ","integrate(cot(d*x+c)^3*(a+b*sin(d*x+c)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right)^{2} + a\right)}^{p} \cot\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*sin(d*x + c)^2 + a)^p*cot(d*x + c)^3, x)","F",0
548,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c)^2)^p*tan(d*x+c)^4,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right)^{2} + a\right)}^{p} \tan\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*sin(d*x + c)^2 + a)^p*tan(d*x + c)^4, x)","F",0
549,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c)^2)^p*tan(d*x+c)^2,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right)^{2} + a\right)}^{p} \tan\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sin(d*x + c)^2 + a)^p*tan(d*x + c)^2, x)","F",0
550,0,0,0,0.000000," ","integrate(cot(d*x+c)^2*(a+b*sin(d*x+c)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right)^{2} + a\right)}^{p} \cot\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sin(d*x + c)^2 + a)^p*cot(d*x + c)^2, x)","F",0
551,0,0,0,0.000000," ","integrate(cot(d*x+c)^4*(a+b*sin(d*x+c)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right)^{2} + a\right)}^{p} \cot\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*sin(d*x + c)^2 + a)^p*cot(d*x + c)^4, x)","F",0
552,1,152,0,1.004013," ","integrate(cot(x)^3/(a+b*sin(x)^3),x, algorithm=""maxima"")","-\frac{\sqrt{3} {\left(b {\left(3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}} - \frac{2 \, a}{b}\right)} + 2 \, a\right)} \arctan\left(-\frac{\sqrt{3} {\left(\left(\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, \sin\left(x\right)\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{9 \, a^{2}} + \frac{{\left(2 \, \left(\frac{a}{b}\right)^{\frac{2}{3}} + 1\right)} \log\left(\sin\left(x\right)^{2} - \left(\frac{a}{b}\right)^{\frac{1}{3}} \sin\left(x\right) + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \, a \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{{\left(\left(\frac{a}{b}\right)^{\frac{2}{3}} - 1\right)} \log\left(\left(\frac{a}{b}\right)^{\frac{1}{3}} + \sin\left(x\right)\right)}{3 \, a \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{\log\left(\sin\left(x\right)\right)}{a} - \frac{1}{2 \, a \sin\left(x\right)^{2}}"," ",0,"-1/9*sqrt(3)*(b*(3*(a/b)^(1/3) - 2*a/b) + 2*a)*arctan(-1/3*sqrt(3)*((a/b)^(1/3) - 2*sin(x))/(a/b)^(1/3))/a^2 + 1/6*(2*(a/b)^(2/3) + 1)*log(sin(x)^2 - (a/b)^(1/3)*sin(x) + (a/b)^(2/3))/(a*(a/b)^(2/3)) + 1/3*((a/b)^(2/3) - 1)*log((a/b)^(1/3) + sin(x))/(a*(a/b)^(2/3)) - log(sin(x))/a - 1/2/(a*sin(x)^2)","A",0
553,1,52,0,0.558955," ","integrate(cot(x)*(a+b*sin(x)^3)^(1/2),x, algorithm=""maxima"")","\frac{1}{3} \, \sqrt{a} \log\left(\frac{\sqrt{b \sin\left(x\right)^{3} + a} - \sqrt{a}}{\sqrt{b \sin\left(x\right)^{3} + a} + \sqrt{a}}\right) + \frac{2}{3} \, \sqrt{b \sin\left(x\right)^{3} + a}"," ",0,"1/3*sqrt(a)*log((sqrt(b*sin(x)^3 + a) - sqrt(a))/(sqrt(b*sin(x)^3 + a) + sqrt(a))) + 2/3*sqrt(b*sin(x)^3 + a)","A",0
554,1,39,0,1.066181," ","integrate(cot(x)/(a+b*sin(x)^3)^(1/2),x, algorithm=""maxima"")","\frac{\log\left(\frac{\sqrt{b \sin\left(x\right)^{3} + a} - \sqrt{a}}{\sqrt{b \sin\left(x\right)^{3} + a} + \sqrt{a}}\right)}{3 \, \sqrt{a}}"," ",0,"1/3*log((sqrt(b*sin(x)^3 + a) - sqrt(a))/(sqrt(b*sin(x)^3 + a) + sqrt(a)))/sqrt(a)","A",0
555,1,68,0,0.611202," ","integrate(cot(d*x+c)*(a+b*sin(d*x+c)^4)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{a} \log\left(\frac{\sqrt{b \sin\left(d x + c\right)^{4} + a} - \sqrt{a}}{\sqrt{b \sin\left(d x + c\right)^{4} + a} + \sqrt{a}}\right) + 2 \, \sqrt{b \sin\left(d x + c\right)^{4} + a}}{4 \, d}"," ",0,"1/4*(sqrt(a)*log((sqrt(b*sin(d*x + c)^4 + a) - sqrt(a))/(sqrt(b*sin(d*x + c)^4 + a) + sqrt(a))) + 2*sqrt(b*sin(d*x + c)^4 + a))/d","A",0
556,0,0,0,0.000000," ","integrate(tan(d*x+c)^3/(a+b*sin(d*x+c)^4)^(1/2),x, algorithm=""maxima"")","\int \frac{\tan\left(d x + c\right)^{3}}{\sqrt{b \sin\left(d x + c\right)^{4} + a}}\,{d x}"," ",0,"integrate(tan(d*x + c)^3/sqrt(b*sin(d*x + c)^4 + a), x)","F",0
557,0,0,0,0.000000," ","integrate(tan(d*x+c)/(a+b*sin(d*x+c)^4)^(1/2),x, algorithm=""maxima"")","\int \frac{\tan\left(d x + c\right)}{\sqrt{b \sin\left(d x + c\right)^{4} + a}}\,{d x}"," ",0,"integrate(tan(d*x + c)/sqrt(b*sin(d*x + c)^4 + a), x)","F",0
558,1,50,0,0.683781," ","integrate(cot(d*x+c)/(a+b*sin(d*x+c)^4)^(1/2),x, algorithm=""maxima"")","\frac{\log\left(\frac{\sqrt{b \sin\left(d x + c\right)^{4} + a} - \sqrt{a}}{\sqrt{b \sin\left(d x + c\right)^{4} + a} + \sqrt{a}}\right)}{4 \, \sqrt{a} d}"," ",0,"1/4*log((sqrt(b*sin(d*x + c)^4 + a) - sqrt(a))/(sqrt(b*sin(d*x + c)^4 + a) + sqrt(a)))/(sqrt(a)*d)","A",0
559,1,79,0,1.964399," ","integrate(cot(d*x+c)^3/(a+b*sin(d*x+c)^4)^(1/2),x, algorithm=""maxima"")","-\frac{\frac{\log\left(\frac{\sqrt{b \sin\left(d x + c\right)^{4} + a} - \sqrt{a}}{\sqrt{b \sin\left(d x + c\right)^{4} + a} + \sqrt{a}}\right)}{\sqrt{a}} + \frac{2 \, \sqrt{b \sin\left(d x + c\right)^{4} + a}}{a \sin\left(d x + c\right)^{2}}}{4 \, d}"," ",0,"-1/4*(log((sqrt(b*sin(d*x + c)^4 + a) - sqrt(a))/(sqrt(b*sin(d*x + c)^4 + a) + sqrt(a)))/sqrt(a) + 2*sqrt(b*sin(d*x + c)^4 + a)/(a*sin(d*x + c)^2))/d","A",0
560,1,166,0,0.687778," ","integrate(cot(d*x+c)^5/(a+b*sin(d*x+c)^4)^(1/2),x, algorithm=""maxima"")","-\frac{\frac{2 \, \sqrt{b \sin\left(d x + c\right)^{4} + a} b}{{\left(b \sin\left(d x + c\right)^{4} + a\right)} a - a^{2}} - \frac{2 \, \log\left(\frac{\sqrt{b \sin\left(d x + c\right)^{4} + a} - \sqrt{a}}{\sqrt{b \sin\left(d x + c\right)^{4} + a} + \sqrt{a}}\right)}{\sqrt{a}} + \frac{b \log\left(\frac{\sqrt{b \sin\left(d x + c\right)^{4} + a} - \sqrt{a}}{\sqrt{b \sin\left(d x + c\right)^{4} + a} + \sqrt{a}}\right)}{a^{\frac{3}{2}}} - \frac{8 \, \sqrt{b \sin\left(d x + c\right)^{4} + a}}{a \sin\left(d x + c\right)^{2}}}{8 \, d}"," ",0,"-1/8*(2*sqrt(b*sin(d*x + c)^4 + a)*b/((b*sin(d*x + c)^4 + a)*a - a^2) - 2*log((sqrt(b*sin(d*x + c)^4 + a) - sqrt(a))/(sqrt(b*sin(d*x + c)^4 + a) + sqrt(a)))/sqrt(a) + b*log((sqrt(b*sin(d*x + c)^4 + a) - sqrt(a))/(sqrt(b*sin(d*x + c)^4 + a) + sqrt(a)))/a^(3/2) - 8*sqrt(b*sin(d*x + c)^4 + a)/(a*sin(d*x + c)^2))/d","A",0
561,0,0,0,0.000000," ","integrate(tan(d*x+c)^2/(a+b*sin(d*x+c)^4)^(1/2),x, algorithm=""maxima"")","\int \frac{\tan\left(d x + c\right)^{2}}{\sqrt{b \sin\left(d x + c\right)^{4} + a}}\,{d x}"," ",0,"integrate(tan(d*x + c)^2/sqrt(b*sin(d*x + c)^4 + a), x)","F",0
562,0,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c)^4)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \sin\left(d x + c\right)^{4} + a}}\,{d x}"," ",0,"integrate(1/sqrt(b*sin(d*x + c)^4 + a), x)","F",0
563,0,0,0,0.000000," ","integrate(cot(d*x+c)^2/(a+b*sin(d*x+c)^4)^(1/2),x, algorithm=""maxima"")","\int \frac{\cot\left(d x + c\right)^{2}}{\sqrt{b \sin\left(d x + c\right)^{4} + a}}\,{d x}"," ",0,"integrate(cot(d*x + c)^2/sqrt(b*sin(d*x + c)^4 + a), x)","F",0
564,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c)^4)^p*tan(d*x+c)^m,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right)^{4} + a\right)}^{p} \tan\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((b*sin(d*x + c)^4 + a)^p*tan(d*x + c)^m, x)","F",0
565,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c)^4)^p*tan(d*x+c)^3,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right)^{4} + a\right)}^{p} \tan\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*sin(d*x + c)^4 + a)^p*tan(d*x + c)^3, x)","F",0
566,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c)^4)^p*tan(d*x+c),x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right)^{4} + a\right)}^{p} \tan\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sin(d*x + c)^4 + a)^p*tan(d*x + c), x)","F",0
567,0,0,0,0.000000," ","integrate(cot(d*x+c)*(a+b*sin(d*x+c)^4)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right)^{4} + a\right)}^{p} \cot\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sin(d*x + c)^4 + a)^p*cot(d*x + c), x)","F",0
568,0,0,0,0.000000," ","integrate(cot(d*x+c)^3*(a+b*sin(d*x+c)^4)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right)^{4} + a\right)}^{p} \cot\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*sin(d*x + c)^4 + a)^p*cot(d*x + c)^3, x)","F",0
569,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c)^4)^p*tan(d*x+c)^4,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right)^{4} + a\right)}^{p} \tan\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*sin(d*x + c)^4 + a)^p*tan(d*x + c)^4, x)","F",0
570,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c)^4)^p*tan(d*x+c)^2,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right)^{4} + a\right)}^{p} \tan\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sin(d*x + c)^4 + a)^p*tan(d*x + c)^2, x)","F",0
571,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c)^4)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right)^{4} + a\right)}^{p}\,{d x}"," ",0,"integrate((b*sin(d*x + c)^4 + a)^p, x)","F",0
572,0,0,0,0.000000," ","integrate(cot(d*x+c)^2*(a+b*sin(d*x+c)^4)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right)^{4} + a\right)}^{p} \cot\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sin(d*x + c)^4 + a)^p*cot(d*x + c)^2, x)","F",0
573,0,0,0,0.000000," ","integrate(cot(d*x+c)^4*(a+b*sin(d*x+c)^4)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right)^{4} + a\right)}^{p} \cot\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*sin(d*x + c)^4 + a)^p*cot(d*x + c)^4, x)","F",0
574,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c)^n)^3*tan(d*x+c)^m,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right)^{n} + a\right)}^{3} \tan\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((b*sin(d*x + c)^n + a)^3*tan(d*x + c)^m, x)","F",0
575,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c)^n)^2*tan(d*x+c)^m,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right)^{n} + a\right)}^{2} \tan\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((b*sin(d*x + c)^n + a)^2*tan(d*x + c)^m, x)","F",0
576,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c)^n)*tan(d*x+c)^m,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right)^{n} + a\right)} \tan\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((b*sin(d*x + c)^n + a)*tan(d*x + c)^m, x)","F",0
577,0,0,0,0.000000," ","integrate(tan(d*x+c)^m/(a+b*sin(d*x+c)^n),x, algorithm=""maxima"")","\int \frac{\tan\left(d x + c\right)^{m}}{b \sin\left(d x + c\right)^{n} + a}\,{d x}"," ",0,"integrate(tan(d*x + c)^m/(b*sin(d*x + c)^n + a), x)","F",0
578,0,0,0,0.000000," ","integrate(tan(d*x+c)^m/(a+b*sin(d*x+c)^n)^2,x, algorithm=""maxima"")","\int \frac{\tan\left(d x + c\right)^{m}}{{\left(b \sin\left(d x + c\right)^{n} + a\right)}^{2}}\,{d x}"," ",0,"integrate(tan(d*x + c)^m/(b*sin(d*x + c)^n + a)^2, x)","F",0
579,1,57,0,0.889852," ","integrate(cot(x)*(a+b*sin(x)^n)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{a} \log\left(\frac{\sqrt{b \sin\left(x\right)^{n} + a} - \sqrt{a}}{\sqrt{b \sin\left(x\right)^{n} + a} + \sqrt{a}}\right)}{n} + \frac{2 \, \sqrt{b \sin\left(x\right)^{n} + a}}{n}"," ",0,"sqrt(a)*log((sqrt(b*sin(x)^n + a) - sqrt(a))/(sqrt(b*sin(x)^n + a) + sqrt(a)))/n + 2*sqrt(b*sin(x)^n + a)/n","A",0
580,1,41,0,0.809845," ","integrate(cot(x)/(a+b*sin(x)^n)^(1/2),x, algorithm=""maxima"")","\frac{\log\left(\frac{\sqrt{b \sin\left(x\right)^{n} + a} - \sqrt{a}}{\sqrt{b \sin\left(x\right)^{n} + a} + \sqrt{a}}\right)}{\sqrt{a} n}"," ",0,"log((sqrt(b*sin(x)^n + a) - sqrt(a))/(sqrt(b*sin(x)^n + a) + sqrt(a)))/(sqrt(a)*n)","A",0
581,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c)^n)^p*tan(d*x+c)^m,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right)^{n} + a\right)}^{p} \tan\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((b*sin(d*x + c)^n + a)^p*tan(d*x + c)^m, x)","F",0
582,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c)^n)^p*tan(d*x+c)^3,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right)^{n} + a\right)}^{p} \tan\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*sin(d*x + c)^n + a)^p*tan(d*x + c)^3, x)","F",0
583,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c)^n)^p*tan(d*x+c),x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right)^{n} + a\right)}^{p} \tan\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sin(d*x + c)^n + a)^p*tan(d*x + c), x)","F",0
584,0,0,0,0.000000," ","integrate(cot(d*x+c)*(a+b*sin(d*x+c)^n)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right)^{n} + a\right)}^{p} \cot\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sin(d*x + c)^n + a)^p*cot(d*x + c), x)","F",0
585,0,0,0,0.000000," ","integrate(cot(d*x+c)^3*(a+b*sin(d*x+c)^n)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right)^{n} + a\right)}^{p} \cot\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*sin(d*x + c)^n + a)^p*cot(d*x + c)^3, x)","F",0
586,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c)^n)^p*tan(d*x+c)^4,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right)^{n} + a\right)}^{p} \tan\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*sin(d*x + c)^n + a)^p*tan(d*x + c)^4, x)","F",0
587,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c)^n)^p*tan(d*x+c)^2,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right)^{n} + a\right)}^{p} \tan\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sin(d*x + c)^n + a)^p*tan(d*x + c)^2, x)","F",0
588,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c)^n)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right)^{n} + a\right)}^{p}\,{d x}"," ",0,"integrate((b*sin(d*x + c)^n + a)^p, x)","F",0
589,0,0,0,0.000000," ","integrate(cot(d*x+c)^2*(a+b*sin(d*x+c)^n)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right)^{n} + a\right)}^{p} \cot\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sin(d*x + c)^n + a)^p*cot(d*x + c)^2, x)","F",0
590,0,0,0,0.000000," ","integrate(cot(d*x+c)^4*(a+b*sin(d*x+c)^n)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right)^{n} + a\right)}^{p} \cot\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*sin(d*x + c)^n + a)^p*cot(d*x + c)^4, x)","F",0
591,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e)^2)/(g*cos(f*x+e))^(5/2)/(d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{b \sin\left(f x + e\right)^{2} + a}{\left(g \cos\left(f x + e\right)\right)^{\frac{5}{2}} \sqrt{d \sin\left(f x + e\right)}}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)/((g*cos(f*x + e))^(5/2)*sqrt(d*sin(f*x + e))), x)","F",0
592,0,0,0,0.000000," ","integrate((c*cos(f*x+e))^m*(d*sin(f*x+e))^n*(a+b*sin(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right)^{2} + a\right)}^{p} \left(c \cos\left(f x + e\right)\right)^{m} \left(d \sin\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((b*sin(f*x + e)^2 + a)^p*(c*cos(f*x + e))^m*(d*sin(f*x + e))^n, x)","F",0
593,0,0,0,0.000000," ","integrate((a+(c*cos(f*x+e)+b*sin(f*x+e))^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{{\left(c \cos\left(f x + e\right) + b \sin\left(f x + e\right)\right)}^{2} + a}\,{d x}"," ",0,"integrate(sqrt((c*cos(f*x + e) + b*sin(f*x + e))^2 + a), x)","F",0
594,0,0,0,0.000000," ","integrate(1/(a+(c*cos(f*x+e)+b*sin(f*x+e))^2)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{{\left(c \cos\left(f x + e\right) + b \sin\left(f x + e\right)\right)}^{2} + a}}\,{d x}"," ",0,"integrate(1/sqrt((c*cos(f*x + e) + b*sin(f*x + e))^2 + a), x)","F",0
