1,-1,0,0,0.000000," ","integrate((d*sin(f*x+e))**n*(a+a*sin(f*x+e))**3*(A+B*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2,-1,0,0,0.000000," ","integrate((d*sin(f*x+e))**n*(a+a*sin(f*x+e))**2*(A+B*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3,-1,0,0,0.000000," ","integrate((d*sin(f*x+e))**n*(a+a*sin(f*x+e))*(A+B*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
4,-1,0,0,0.000000," ","integrate((d*sin(f*x+e))**n*(A+B*sin(f*x+e))/(a+a*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
5,-1,0,0,0.000000," ","integrate((d*sin(f*x+e))**n*(A+B*sin(f*x+e))/(a+a*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
6,-1,0,0,0.000000," ","integrate((d*sin(f*x+e))**n*(A+B*sin(f*x+e))/(a+a*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
7,-1,0,0,0.000000," ","integrate((d*sin(f*x+e))**n*(a+a*sin(f*x+e))**(5/2)*(A+B*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
8,-1,0,0,0.000000," ","integrate((d*sin(f*x+e))**n*(a+a*sin(f*x+e))**(3/2)*(A+B*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
9,0,0,0,0.000000," ","integrate((d*sin(f*x+e))**n*(a+a*sin(f*x+e))**(1/2)*(A+B*sin(f*x+e)),x)","\int \sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)} \left(d \sin{\left(e + f x \right)}\right)^{n} \left(A + B \sin{\left(e + f x \right)}\right)\, dx"," ",0,"Integral(sqrt(a*(sin(e + f*x) + 1))*(d*sin(e + f*x))**n*(A + B*sin(e + f*x)), x)","F",0
10,0,0,0,0.000000," ","integrate((d*sin(f*x+e))**n*(A+B*sin(f*x+e))/(a+a*sin(f*x+e))**(1/2),x)","\int \frac{\left(d \sin{\left(e + f x \right)}\right)^{n} \left(A + B \sin{\left(e + f x \right)}\right)}{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)}}\, dx"," ",0,"Integral((d*sin(e + f*x))**n*(A + B*sin(e + f*x))/sqrt(a*(sin(e + f*x) + 1)), x)","F",0
11,0,0,0,0.000000," ","integrate((d*sin(f*x+e))**n*(A+B*sin(f*x+e))/(a+a*sin(f*x+e))**(3/2),x)","\int \frac{\left(d \sin{\left(e + f x \right)}\right)^{n} \left(A + B \sin{\left(e + f x \right)}\right)}{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d*sin(e + f*x))**n*(A + B*sin(e + f*x))/(a*(sin(e + f*x) + 1))**(3/2), x)","F",0
12,0,0,0,0.000000," ","integrate((d*sin(f*x+e))**n*(a+a*sin(f*x+e))**m*(A+B*sin(f*x+e)),x)","\int \left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{m} \left(d \sin{\left(e + f x \right)}\right)^{n} \left(A + B \sin{\left(e + f x \right)}\right)\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**m*(d*sin(e + f*x))**n*(A + B*sin(e + f*x)), x)","F",0
13,0,0,0,0.000000," ","integrate((d*sin(f*x+e))**n*(a-a*sin(f*x+e))*(a+a*sin(f*x+e))**m,x)","- a \left(\int \left(- \left(d \sin{\left(e + f x \right)}\right)^{n} \left(a \sin{\left(e + f x \right)} + a\right)^{m}\right)\, dx + \int \left(d \sin{\left(e + f x \right)}\right)^{n} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}\, dx\right)"," ",0,"-a*(Integral(-(d*sin(e + f*x))**n*(a*sin(e + f*x) + a)**m, x) + Integral((d*sin(e + f*x))**n*(a*sin(e + f*x) + a)**m*sin(e + f*x), x))","F",0
14,-1,0,0,0.000000," ","integrate(sin(d*x+c)**n*(a+a*sin(d*x+c))**(-2-n)*(-1-n-(-2-n)*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
15,-1,0,0,0.000000," ","integrate(sin(d*x+c)**(-2-m)*(a+a*sin(d*x+c))**m*(1+m-m*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
16,-1,0,0,0.000000," ","integrate(sin(f*x+e)**2*(A+B*sin(f*x+e))/(a+b*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
17,1,853,0,7.881951," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**4,x)","\begin{cases} - \frac{9 A a c^{4} x \sin^{4}{\left(e + f x \right)}}{8} - \frac{9 A a c^{4} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + A a c^{4} x \sin^{2}{\left(e + f x \right)} - \frac{9 A a c^{4} x \cos^{4}{\left(e + f x \right)}}{8} + A a c^{4} x \cos^{2}{\left(e + f x \right)} + A a c^{4} x - \frac{A a c^{4} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{15 A a c^{4} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{4 A a c^{4} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{2 A a c^{4} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{9 A a c^{4} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{A a c^{4} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{8 A a c^{4} \cos^{5}{\left(e + f x \right)}}{15 f} - \frac{4 A a c^{4} \cos^{3}{\left(e + f x \right)}}{3 f} + \frac{3 A a c^{4} \cos{\left(e + f x \right)}}{f} + \frac{5 B a c^{4} x \sin^{6}{\left(e + f x \right)}}{16} + \frac{15 B a c^{4} x \sin^{4}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{16} + \frac{3 B a c^{4} x \sin^{4}{\left(e + f x \right)}}{4} + \frac{15 B a c^{4} x \sin^{2}{\left(e + f x \right)} \cos^{4}{\left(e + f x \right)}}{16} + \frac{3 B a c^{4} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{2} - \frac{3 B a c^{4} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{5 B a c^{4} x \cos^{6}{\left(e + f x \right)}}{16} + \frac{3 B a c^{4} x \cos^{4}{\left(e + f x \right)}}{4} - \frac{3 B a c^{4} x \cos^{2}{\left(e + f x \right)}}{2} - \frac{11 B a c^{4} \sin^{5}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{16 f} + \frac{3 B a c^{4} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{5 B a c^{4} \sin^{3}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{6 f} - \frac{5 B a c^{4} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{4 f} + \frac{4 B a c^{4} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{f} - \frac{2 B a c^{4} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{5 B a c^{4} \sin{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{16 f} - \frac{3 B a c^{4} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{4 f} + \frac{3 B a c^{4} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} + \frac{8 B a c^{4} \cos^{5}{\left(e + f x \right)}}{5 f} - \frac{4 B a c^{4} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{B a c^{4} \cos{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \left(A + B \sin{\left(e \right)}\right) \left(a \sin{\left(e \right)} + a\right) \left(- c \sin{\left(e \right)} + c\right)^{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-9*A*a*c**4*x*sin(e + f*x)**4/8 - 9*A*a*c**4*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + A*a*c**4*x*sin(e + f*x)**2 - 9*A*a*c**4*x*cos(e + f*x)**4/8 + A*a*c**4*x*cos(e + f*x)**2 + A*a*c**4*x - A*a*c**4*sin(e + f*x)**4*cos(e + f*x)/f + 15*A*a*c**4*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 4*A*a*c**4*sin(e + f*x)**2*cos(e + f*x)**3/(3*f) - 2*A*a*c**4*sin(e + f*x)**2*cos(e + f*x)/f + 9*A*a*c**4*sin(e + f*x)*cos(e + f*x)**3/(8*f) - A*a*c**4*sin(e + f*x)*cos(e + f*x)/f - 8*A*a*c**4*cos(e + f*x)**5/(15*f) - 4*A*a*c**4*cos(e + f*x)**3/(3*f) + 3*A*a*c**4*cos(e + f*x)/f + 5*B*a*c**4*x*sin(e + f*x)**6/16 + 15*B*a*c**4*x*sin(e + f*x)**4*cos(e + f*x)**2/16 + 3*B*a*c**4*x*sin(e + f*x)**4/4 + 15*B*a*c**4*x*sin(e + f*x)**2*cos(e + f*x)**4/16 + 3*B*a*c**4*x*sin(e + f*x)**2*cos(e + f*x)**2/2 - 3*B*a*c**4*x*sin(e + f*x)**2/2 + 5*B*a*c**4*x*cos(e + f*x)**6/16 + 3*B*a*c**4*x*cos(e + f*x)**4/4 - 3*B*a*c**4*x*cos(e + f*x)**2/2 - 11*B*a*c**4*sin(e + f*x)**5*cos(e + f*x)/(16*f) + 3*B*a*c**4*sin(e + f*x)**4*cos(e + f*x)/f - 5*B*a*c**4*sin(e + f*x)**3*cos(e + f*x)**3/(6*f) - 5*B*a*c**4*sin(e + f*x)**3*cos(e + f*x)/(4*f) + 4*B*a*c**4*sin(e + f*x)**2*cos(e + f*x)**3/f - 2*B*a*c**4*sin(e + f*x)**2*cos(e + f*x)/f - 5*B*a*c**4*sin(e + f*x)*cos(e + f*x)**5/(16*f) - 3*B*a*c**4*sin(e + f*x)*cos(e + f*x)**3/(4*f) + 3*B*a*c**4*sin(e + f*x)*cos(e + f*x)/(2*f) + 8*B*a*c**4*cos(e + f*x)**5/(5*f) - 4*B*a*c**4*cos(e + f*x)**3/(3*f) - B*a*c**4*cos(e + f*x)/f, Ne(f, 0)), (x*(A + B*sin(e))*(a*sin(e) + a)*(-c*sin(e) + c)**4, True))","A",0
18,1,486,0,4.093359," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**3,x)","\begin{cases} - \frac{3 A a c^{3} x \sin^{4}{\left(e + f x \right)}}{8} - \frac{3 A a c^{3} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} - \frac{3 A a c^{3} x \cos^{4}{\left(e + f x \right)}}{8} + A a c^{3} x + \frac{5 A a c^{3} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{2 A a c^{3} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{3 A a c^{3} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{4 A a c^{3} \cos^{3}{\left(e + f x \right)}}{3 f} + \frac{2 A a c^{3} \cos{\left(e + f x \right)}}{f} + \frac{3 B a c^{3} x \sin^{4}{\left(e + f x \right)}}{4} + \frac{3 B a c^{3} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{2} - B a c^{3} x \sin^{2}{\left(e + f x \right)} + \frac{3 B a c^{3} x \cos^{4}{\left(e + f x \right)}}{4} - B a c^{3} x \cos^{2}{\left(e + f x \right)} + \frac{B a c^{3} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{5 B a c^{3} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{4 f} + \frac{4 B a c^{3} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{3 B a c^{3} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{4 f} + \frac{B a c^{3} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{8 B a c^{3} \cos^{5}{\left(e + f x \right)}}{15 f} - \frac{B a c^{3} \cos{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \left(A + B \sin{\left(e \right)}\right) \left(a \sin{\left(e \right)} + a\right) \left(- c \sin{\left(e \right)} + c\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*A*a*c**3*x*sin(e + f*x)**4/8 - 3*A*a*c**3*x*sin(e + f*x)**2*cos(e + f*x)**2/4 - 3*A*a*c**3*x*cos(e + f*x)**4/8 + A*a*c**3*x + 5*A*a*c**3*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 2*A*a*c**3*sin(e + f*x)**2*cos(e + f*x)/f + 3*A*a*c**3*sin(e + f*x)*cos(e + f*x)**3/(8*f) - 4*A*a*c**3*cos(e + f*x)**3/(3*f) + 2*A*a*c**3*cos(e + f*x)/f + 3*B*a*c**3*x*sin(e + f*x)**4/4 + 3*B*a*c**3*x*sin(e + f*x)**2*cos(e + f*x)**2/2 - B*a*c**3*x*sin(e + f*x)**2 + 3*B*a*c**3*x*cos(e + f*x)**4/4 - B*a*c**3*x*cos(e + f*x)**2 + B*a*c**3*sin(e + f*x)**4*cos(e + f*x)/f - 5*B*a*c**3*sin(e + f*x)**3*cos(e + f*x)/(4*f) + 4*B*a*c**3*sin(e + f*x)**2*cos(e + f*x)**3/(3*f) - 3*B*a*c**3*sin(e + f*x)*cos(e + f*x)**3/(4*f) + B*a*c**3*sin(e + f*x)*cos(e + f*x)/f + 8*B*a*c**3*cos(e + f*x)**5/(15*f) - B*a*c**3*cos(e + f*x)/f, Ne(f, 0)), (x*(A + B*sin(e))*(a*sin(e) + a)*(-c*sin(e) + c)**3, True))","A",0
19,1,396,0,2.125981," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**2,x)","\begin{cases} - \frac{A a c^{2} x \sin^{2}{\left(e + f x \right)}}{2} - \frac{A a c^{2} x \cos^{2}{\left(e + f x \right)}}{2} + A a c^{2} x - \frac{A a c^{2} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{A a c^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{2 A a c^{2} \cos^{3}{\left(e + f x \right)}}{3 f} + \frac{A a c^{2} \cos{\left(e + f x \right)}}{f} + \frac{3 B a c^{2} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{3 B a c^{2} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} - \frac{B a c^{2} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{3 B a c^{2} x \cos^{4}{\left(e + f x \right)}}{8} - \frac{B a c^{2} x \cos^{2}{\left(e + f x \right)}}{2} - \frac{5 B a c^{2} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} + \frac{B a c^{2} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{3 B a c^{2} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} + \frac{B a c^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} + \frac{2 B a c^{2} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{B a c^{2} \cos{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \left(A + B \sin{\left(e \right)}\right) \left(a \sin{\left(e \right)} + a\right) \left(- c \sin{\left(e \right)} + c\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-A*a*c**2*x*sin(e + f*x)**2/2 - A*a*c**2*x*cos(e + f*x)**2/2 + A*a*c**2*x - A*a*c**2*sin(e + f*x)**2*cos(e + f*x)/f + A*a*c**2*sin(e + f*x)*cos(e + f*x)/(2*f) - 2*A*a*c**2*cos(e + f*x)**3/(3*f) + A*a*c**2*cos(e + f*x)/f + 3*B*a*c**2*x*sin(e + f*x)**4/8 + 3*B*a*c**2*x*sin(e + f*x)**2*cos(e + f*x)**2/4 - B*a*c**2*x*sin(e + f*x)**2/2 + 3*B*a*c**2*x*cos(e + f*x)**4/8 - B*a*c**2*x*cos(e + f*x)**2/2 - 5*B*a*c**2*sin(e + f*x)**3*cos(e + f*x)/(8*f) + B*a*c**2*sin(e + f*x)**2*cos(e + f*x)/f - 3*B*a*c**2*sin(e + f*x)*cos(e + f*x)**3/(8*f) + B*a*c**2*sin(e + f*x)*cos(e + f*x)/(2*f) + 2*B*a*c**2*cos(e + f*x)**3/(3*f) - B*a*c**2*cos(e + f*x)/f, Ne(f, 0)), (x*(A + B*sin(e))*(a*sin(e) + a)*(-c*sin(e) + c)**2, True))","A",0
20,1,138,0,0.787609," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c-c*sin(f*x+e)),x)","\begin{cases} - \frac{A a c x \sin^{2}{\left(e + f x \right)}}{2} - \frac{A a c x \cos^{2}{\left(e + f x \right)}}{2} + A a c x + \frac{A a c \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} + \frac{B a c \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{2 B a c \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{B a c \cos{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \left(A + B \sin{\left(e \right)}\right) \left(a \sin{\left(e \right)} + a\right) \left(- c \sin{\left(e \right)} + c\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((-A*a*c*x*sin(e + f*x)**2/2 - A*a*c*x*cos(e + f*x)**2/2 + A*a*c*x + A*a*c*sin(e + f*x)*cos(e + f*x)/(2*f) + B*a*c*sin(e + f*x)**2*cos(e + f*x)/f + 2*B*a*c*cos(e + f*x)**3/(3*f) - B*a*c*cos(e + f*x)/f, Ne(f, 0)), (x*(A + B*sin(e))*(a*sin(e) + a)*(-c*sin(e) + c), True))","A",0
21,1,828,0,4.033516," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c-c*sin(f*x+e)),x)","\begin{cases} - \frac{A a f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - c f} + \frac{A a f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - c f} - \frac{A a f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - c f} + \frac{A a f x}{c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - c f} - \frac{4 A a \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - c f} - \frac{4 A a}{c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - c f} - \frac{2 B a f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - c f} + \frac{2 B a f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - c f} - \frac{2 B a f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - c f} + \frac{2 B a f x}{c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - c f} - \frac{4 B a \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - c f} + \frac{2 B a \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - c f} - \frac{6 B a}{c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - c f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right) \left(a \sin{\left(e \right)} + a\right)}{- c \sin{\left(e \right)} + c} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-A*a*f*x*tan(e/2 + f*x/2)**3/(c*f*tan(e/2 + f*x/2)**3 - c*f*tan(e/2 + f*x/2)**2 + c*f*tan(e/2 + f*x/2) - c*f) + A*a*f*x*tan(e/2 + f*x/2)**2/(c*f*tan(e/2 + f*x/2)**3 - c*f*tan(e/2 + f*x/2)**2 + c*f*tan(e/2 + f*x/2) - c*f) - A*a*f*x*tan(e/2 + f*x/2)/(c*f*tan(e/2 + f*x/2)**3 - c*f*tan(e/2 + f*x/2)**2 + c*f*tan(e/2 + f*x/2) - c*f) + A*a*f*x/(c*f*tan(e/2 + f*x/2)**3 - c*f*tan(e/2 + f*x/2)**2 + c*f*tan(e/2 + f*x/2) - c*f) - 4*A*a*tan(e/2 + f*x/2)**2/(c*f*tan(e/2 + f*x/2)**3 - c*f*tan(e/2 + f*x/2)**2 + c*f*tan(e/2 + f*x/2) - c*f) - 4*A*a/(c*f*tan(e/2 + f*x/2)**3 - c*f*tan(e/2 + f*x/2)**2 + c*f*tan(e/2 + f*x/2) - c*f) - 2*B*a*f*x*tan(e/2 + f*x/2)**3/(c*f*tan(e/2 + f*x/2)**3 - c*f*tan(e/2 + f*x/2)**2 + c*f*tan(e/2 + f*x/2) - c*f) + 2*B*a*f*x*tan(e/2 + f*x/2)**2/(c*f*tan(e/2 + f*x/2)**3 - c*f*tan(e/2 + f*x/2)**2 + c*f*tan(e/2 + f*x/2) - c*f) - 2*B*a*f*x*tan(e/2 + f*x/2)/(c*f*tan(e/2 + f*x/2)**3 - c*f*tan(e/2 + f*x/2)**2 + c*f*tan(e/2 + f*x/2) - c*f) + 2*B*a*f*x/(c*f*tan(e/2 + f*x/2)**3 - c*f*tan(e/2 + f*x/2)**2 + c*f*tan(e/2 + f*x/2) - c*f) - 4*B*a*tan(e/2 + f*x/2)**2/(c*f*tan(e/2 + f*x/2)**3 - c*f*tan(e/2 + f*x/2)**2 + c*f*tan(e/2 + f*x/2) - c*f) + 2*B*a*tan(e/2 + f*x/2)/(c*f*tan(e/2 + f*x/2)**3 - c*f*tan(e/2 + f*x/2)**2 + c*f*tan(e/2 + f*x/2) - c*f) - 6*B*a/(c*f*tan(e/2 + f*x/2)**3 - c*f*tan(e/2 + f*x/2)**2 + c*f*tan(e/2 + f*x/2) - c*f), Ne(f, 0)), (x*(A + B*sin(e))*(a*sin(e) + a)/(-c*sin(e) + c), True))","A",0
22,1,700,0,8.107797," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**2,x)","\begin{cases} - \frac{6 A a \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 9 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 c^{2} f} - \frac{2 A a}{3 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 9 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 c^{2} f} + \frac{3 B a f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 9 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 c^{2} f} - \frac{9 B a f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 9 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 c^{2} f} + \frac{9 B a f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 9 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 c^{2} f} - \frac{3 B a f x}{3 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 9 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 c^{2} f} + \frac{6 B a \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 9 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 c^{2} f} - \frac{24 B a \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 9 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 c^{2} f} + \frac{10 B a}{3 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 9 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 c^{2} f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right) \left(a \sin{\left(e \right)} + a\right)}{\left(- c \sin{\left(e \right)} + c\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-6*A*a*tan(e/2 + f*x/2)**2/(3*c**2*f*tan(e/2 + f*x/2)**3 - 9*c**2*f*tan(e/2 + f*x/2)**2 + 9*c**2*f*tan(e/2 + f*x/2) - 3*c**2*f) - 2*A*a/(3*c**2*f*tan(e/2 + f*x/2)**3 - 9*c**2*f*tan(e/2 + f*x/2)**2 + 9*c**2*f*tan(e/2 + f*x/2) - 3*c**2*f) + 3*B*a*f*x*tan(e/2 + f*x/2)**3/(3*c**2*f*tan(e/2 + f*x/2)**3 - 9*c**2*f*tan(e/2 + f*x/2)**2 + 9*c**2*f*tan(e/2 + f*x/2) - 3*c**2*f) - 9*B*a*f*x*tan(e/2 + f*x/2)**2/(3*c**2*f*tan(e/2 + f*x/2)**3 - 9*c**2*f*tan(e/2 + f*x/2)**2 + 9*c**2*f*tan(e/2 + f*x/2) - 3*c**2*f) + 9*B*a*f*x*tan(e/2 + f*x/2)/(3*c**2*f*tan(e/2 + f*x/2)**3 - 9*c**2*f*tan(e/2 + f*x/2)**2 + 9*c**2*f*tan(e/2 + f*x/2) - 3*c**2*f) - 3*B*a*f*x/(3*c**2*f*tan(e/2 + f*x/2)**3 - 9*c**2*f*tan(e/2 + f*x/2)**2 + 9*c**2*f*tan(e/2 + f*x/2) - 3*c**2*f) + 6*B*a*tan(e/2 + f*x/2)**2/(3*c**2*f*tan(e/2 + f*x/2)**3 - 9*c**2*f*tan(e/2 + f*x/2)**2 + 9*c**2*f*tan(e/2 + f*x/2) - 3*c**2*f) - 24*B*a*tan(e/2 + f*x/2)/(3*c**2*f*tan(e/2 + f*x/2)**3 - 9*c**2*f*tan(e/2 + f*x/2)**2 + 9*c**2*f*tan(e/2 + f*x/2) - 3*c**2*f) + 10*B*a/(3*c**2*f*tan(e/2 + f*x/2)**3 - 9*c**2*f*tan(e/2 + f*x/2)**2 + 9*c**2*f*tan(e/2 + f*x/2) - 3*c**2*f), Ne(f, 0)), (x*(A + B*sin(e))*(a*sin(e) + a)/(-c*sin(e) + c)**2, True))","A",0
23,1,1035,0,15.780590," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**3,x)","\begin{cases} - \frac{30 A a \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 150 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} + \frac{30 A a \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 150 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} - \frac{50 A a \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 150 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} + \frac{10 A a \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 150 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} - \frac{8 A a}{15 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 150 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} - \frac{30 B a \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 150 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} - \frac{10 B a \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 150 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} - \frac{10 B a \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 150 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} + \frac{2 B a}{15 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 150 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right) \left(a \sin{\left(e \right)} + a\right)}{\left(- c \sin{\left(e \right)} + c\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-30*A*a*tan(e/2 + f*x/2)**4/(15*c**3*f*tan(e/2 + f*x/2)**5 - 75*c**3*f*tan(e/2 + f*x/2)**4 + 150*c**3*f*tan(e/2 + f*x/2)**3 - 150*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) + 30*A*a*tan(e/2 + f*x/2)**3/(15*c**3*f*tan(e/2 + f*x/2)**5 - 75*c**3*f*tan(e/2 + f*x/2)**4 + 150*c**3*f*tan(e/2 + f*x/2)**3 - 150*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) - 50*A*a*tan(e/2 + f*x/2)**2/(15*c**3*f*tan(e/2 + f*x/2)**5 - 75*c**3*f*tan(e/2 + f*x/2)**4 + 150*c**3*f*tan(e/2 + f*x/2)**3 - 150*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) + 10*A*a*tan(e/2 + f*x/2)/(15*c**3*f*tan(e/2 + f*x/2)**5 - 75*c**3*f*tan(e/2 + f*x/2)**4 + 150*c**3*f*tan(e/2 + f*x/2)**3 - 150*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) - 8*A*a/(15*c**3*f*tan(e/2 + f*x/2)**5 - 75*c**3*f*tan(e/2 + f*x/2)**4 + 150*c**3*f*tan(e/2 + f*x/2)**3 - 150*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) - 30*B*a*tan(e/2 + f*x/2)**3/(15*c**3*f*tan(e/2 + f*x/2)**5 - 75*c**3*f*tan(e/2 + f*x/2)**4 + 150*c**3*f*tan(e/2 + f*x/2)**3 - 150*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) - 10*B*a*tan(e/2 + f*x/2)**2/(15*c**3*f*tan(e/2 + f*x/2)**5 - 75*c**3*f*tan(e/2 + f*x/2)**4 + 150*c**3*f*tan(e/2 + f*x/2)**3 - 150*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) - 10*B*a*tan(e/2 + f*x/2)/(15*c**3*f*tan(e/2 + f*x/2)**5 - 75*c**3*f*tan(e/2 + f*x/2)**4 + 150*c**3*f*tan(e/2 + f*x/2)**3 - 150*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) + 2*B*a/(15*c**3*f*tan(e/2 + f*x/2)**5 - 75*c**3*f*tan(e/2 + f*x/2)**4 + 150*c**3*f*tan(e/2 + f*x/2)**3 - 150*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f), Ne(f, 0)), (x*(A + B*sin(e))*(a*sin(e) + a)/(-c*sin(e) + c)**3, True))","A",0
24,1,1831,0,29.471649," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**4,x)","\begin{cases} - \frac{210 A a \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 735 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2205 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3675 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3675 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2205 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 735 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 c^{4} f} + \frac{420 A a \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 735 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2205 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3675 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3675 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2205 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 735 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 c^{4} f} - \frac{910 A a \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 735 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2205 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3675 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3675 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2205 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 735 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 c^{4} f} + \frac{700 A a \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 735 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2205 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3675 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3675 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2205 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 735 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 c^{4} f} - \frac{546 A a \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 735 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2205 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3675 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3675 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2205 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 735 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 c^{4} f} + \frac{112 A a \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 735 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2205 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3675 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3675 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2205 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 735 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 c^{4} f} - \frac{46 A a}{105 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 735 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2205 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3675 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3675 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2205 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 735 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 c^{4} f} - \frac{210 B a \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 735 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2205 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3675 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3675 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2205 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 735 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 c^{4} f} + \frac{70 B a \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 735 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2205 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3675 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3675 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2205 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 735 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 c^{4} f} - \frac{280 B a \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 735 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2205 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3675 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3675 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2205 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 735 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 c^{4} f} - \frac{70 B a \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 735 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2205 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3675 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3675 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2205 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 735 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 c^{4} f} + \frac{10 B a}{105 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 735 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2205 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3675 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3675 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2205 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 735 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 c^{4} f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right) \left(a \sin{\left(e \right)} + a\right)}{\left(- c \sin{\left(e \right)} + c\right)^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-210*A*a*tan(e/2 + f*x/2)**6/(105*c**4*f*tan(e/2 + f*x/2)**7 - 735*c**4*f*tan(e/2 + f*x/2)**6 + 2205*c**4*f*tan(e/2 + f*x/2)**5 - 3675*c**4*f*tan(e/2 + f*x/2)**4 + 3675*c**4*f*tan(e/2 + f*x/2)**3 - 2205*c**4*f*tan(e/2 + f*x/2)**2 + 735*c**4*f*tan(e/2 + f*x/2) - 105*c**4*f) + 420*A*a*tan(e/2 + f*x/2)**5/(105*c**4*f*tan(e/2 + f*x/2)**7 - 735*c**4*f*tan(e/2 + f*x/2)**6 + 2205*c**4*f*tan(e/2 + f*x/2)**5 - 3675*c**4*f*tan(e/2 + f*x/2)**4 + 3675*c**4*f*tan(e/2 + f*x/2)**3 - 2205*c**4*f*tan(e/2 + f*x/2)**2 + 735*c**4*f*tan(e/2 + f*x/2) - 105*c**4*f) - 910*A*a*tan(e/2 + f*x/2)**4/(105*c**4*f*tan(e/2 + f*x/2)**7 - 735*c**4*f*tan(e/2 + f*x/2)**6 + 2205*c**4*f*tan(e/2 + f*x/2)**5 - 3675*c**4*f*tan(e/2 + f*x/2)**4 + 3675*c**4*f*tan(e/2 + f*x/2)**3 - 2205*c**4*f*tan(e/2 + f*x/2)**2 + 735*c**4*f*tan(e/2 + f*x/2) - 105*c**4*f) + 700*A*a*tan(e/2 + f*x/2)**3/(105*c**4*f*tan(e/2 + f*x/2)**7 - 735*c**4*f*tan(e/2 + f*x/2)**6 + 2205*c**4*f*tan(e/2 + f*x/2)**5 - 3675*c**4*f*tan(e/2 + f*x/2)**4 + 3675*c**4*f*tan(e/2 + f*x/2)**3 - 2205*c**4*f*tan(e/2 + f*x/2)**2 + 735*c**4*f*tan(e/2 + f*x/2) - 105*c**4*f) - 546*A*a*tan(e/2 + f*x/2)**2/(105*c**4*f*tan(e/2 + f*x/2)**7 - 735*c**4*f*tan(e/2 + f*x/2)**6 + 2205*c**4*f*tan(e/2 + f*x/2)**5 - 3675*c**4*f*tan(e/2 + f*x/2)**4 + 3675*c**4*f*tan(e/2 + f*x/2)**3 - 2205*c**4*f*tan(e/2 + f*x/2)**2 + 735*c**4*f*tan(e/2 + f*x/2) - 105*c**4*f) + 112*A*a*tan(e/2 + f*x/2)/(105*c**4*f*tan(e/2 + f*x/2)**7 - 735*c**4*f*tan(e/2 + f*x/2)**6 + 2205*c**4*f*tan(e/2 + f*x/2)**5 - 3675*c**4*f*tan(e/2 + f*x/2)**4 + 3675*c**4*f*tan(e/2 + f*x/2)**3 - 2205*c**4*f*tan(e/2 + f*x/2)**2 + 735*c**4*f*tan(e/2 + f*x/2) - 105*c**4*f) - 46*A*a/(105*c**4*f*tan(e/2 + f*x/2)**7 - 735*c**4*f*tan(e/2 + f*x/2)**6 + 2205*c**4*f*tan(e/2 + f*x/2)**5 - 3675*c**4*f*tan(e/2 + f*x/2)**4 + 3675*c**4*f*tan(e/2 + f*x/2)**3 - 2205*c**4*f*tan(e/2 + f*x/2)**2 + 735*c**4*f*tan(e/2 + f*x/2) - 105*c**4*f) - 210*B*a*tan(e/2 + f*x/2)**5/(105*c**4*f*tan(e/2 + f*x/2)**7 - 735*c**4*f*tan(e/2 + f*x/2)**6 + 2205*c**4*f*tan(e/2 + f*x/2)**5 - 3675*c**4*f*tan(e/2 + f*x/2)**4 + 3675*c**4*f*tan(e/2 + f*x/2)**3 - 2205*c**4*f*tan(e/2 + f*x/2)**2 + 735*c**4*f*tan(e/2 + f*x/2) - 105*c**4*f) + 70*B*a*tan(e/2 + f*x/2)**4/(105*c**4*f*tan(e/2 + f*x/2)**7 - 735*c**4*f*tan(e/2 + f*x/2)**6 + 2205*c**4*f*tan(e/2 + f*x/2)**5 - 3675*c**4*f*tan(e/2 + f*x/2)**4 + 3675*c**4*f*tan(e/2 + f*x/2)**3 - 2205*c**4*f*tan(e/2 + f*x/2)**2 + 735*c**4*f*tan(e/2 + f*x/2) - 105*c**4*f) - 280*B*a*tan(e/2 + f*x/2)**3/(105*c**4*f*tan(e/2 + f*x/2)**7 - 735*c**4*f*tan(e/2 + f*x/2)**6 + 2205*c**4*f*tan(e/2 + f*x/2)**5 - 3675*c**4*f*tan(e/2 + f*x/2)**4 + 3675*c**4*f*tan(e/2 + f*x/2)**3 - 2205*c**4*f*tan(e/2 + f*x/2)**2 + 735*c**4*f*tan(e/2 + f*x/2) - 105*c**4*f) - 70*B*a*tan(e/2 + f*x/2)/(105*c**4*f*tan(e/2 + f*x/2)**7 - 735*c**4*f*tan(e/2 + f*x/2)**6 + 2205*c**4*f*tan(e/2 + f*x/2)**5 - 3675*c**4*f*tan(e/2 + f*x/2)**4 + 3675*c**4*f*tan(e/2 + f*x/2)**3 - 2205*c**4*f*tan(e/2 + f*x/2)**2 + 735*c**4*f*tan(e/2 + f*x/2) - 105*c**4*f) + 10*B*a/(105*c**4*f*tan(e/2 + f*x/2)**7 - 735*c**4*f*tan(e/2 + f*x/2)**6 + 2205*c**4*f*tan(e/2 + f*x/2)**5 - 3675*c**4*f*tan(e/2 + f*x/2)**4 + 3675*c**4*f*tan(e/2 + f*x/2)**3 - 2205*c**4*f*tan(e/2 + f*x/2)**2 + 735*c**4*f*tan(e/2 + f*x/2) - 105*c**4*f), Ne(f, 0)), (x*(A + B*sin(e))*(a*sin(e) + a)/(-c*sin(e) + c)**4, True))","A",0
25,1,3232,0,52.384151," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**5,x)","\begin{cases} - \frac{630 A a \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2835 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 26460 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39690 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 11340 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 c^{5} f} + \frac{1890 A a \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2835 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 26460 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39690 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 11340 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 c^{5} f} - \frac{5250 A a \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2835 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 26460 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39690 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 11340 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 c^{5} f} + \frac{6930 A a \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2835 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 26460 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39690 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 11340 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 c^{5} f} - \frac{7686 A a \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2835 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 26460 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39690 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 11340 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 c^{5} f} + \frac{4494 A a \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2835 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 26460 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39690 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 11340 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 c^{5} f} - \frac{2286 A a \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2835 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 26460 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39690 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 11340 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 c^{5} f} + \frac{414 A a \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2835 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 26460 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39690 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 11340 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 c^{5} f} - \frac{116 A a}{315 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2835 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 26460 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39690 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 11340 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 c^{5} f} - \frac{630 B a \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2835 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 26460 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39690 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 11340 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 c^{5} f} + \frac{630 B a \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2835 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 26460 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39690 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 11340 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 c^{5} f} - \frac{1890 B a \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2835 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 26460 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39690 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 11340 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 c^{5} f} + \frac{882 B a \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2835 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 26460 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39690 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 11340 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 c^{5} f} - \frac{1218 B a \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2835 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 26460 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39690 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 11340 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 c^{5} f} + \frac{162 B a \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2835 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 26460 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39690 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 11340 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 c^{5} f} - \frac{198 B a \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2835 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 26460 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39690 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 11340 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 c^{5} f} + \frac{22 B a}{315 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2835 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 26460 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39690 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 11340 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 c^{5} f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right) \left(a \sin{\left(e \right)} + a\right)}{\left(- c \sin{\left(e \right)} + c\right)^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-630*A*a*tan(e/2 + f*x/2)**8/(315*c**5*f*tan(e/2 + f*x/2)**9 - 2835*c**5*f*tan(e/2 + f*x/2)**8 + 11340*c**5*f*tan(e/2 + f*x/2)**7 - 26460*c**5*f*tan(e/2 + f*x/2)**6 + 39690*c**5*f*tan(e/2 + f*x/2)**5 - 39690*c**5*f*tan(e/2 + f*x/2)**4 + 26460*c**5*f*tan(e/2 + f*x/2)**3 - 11340*c**5*f*tan(e/2 + f*x/2)**2 + 2835*c**5*f*tan(e/2 + f*x/2) - 315*c**5*f) + 1890*A*a*tan(e/2 + f*x/2)**7/(315*c**5*f*tan(e/2 + f*x/2)**9 - 2835*c**5*f*tan(e/2 + f*x/2)**8 + 11340*c**5*f*tan(e/2 + f*x/2)**7 - 26460*c**5*f*tan(e/2 + f*x/2)**6 + 39690*c**5*f*tan(e/2 + f*x/2)**5 - 39690*c**5*f*tan(e/2 + f*x/2)**4 + 26460*c**5*f*tan(e/2 + f*x/2)**3 - 11340*c**5*f*tan(e/2 + f*x/2)**2 + 2835*c**5*f*tan(e/2 + f*x/2) - 315*c**5*f) - 5250*A*a*tan(e/2 + f*x/2)**6/(315*c**5*f*tan(e/2 + f*x/2)**9 - 2835*c**5*f*tan(e/2 + f*x/2)**8 + 11340*c**5*f*tan(e/2 + f*x/2)**7 - 26460*c**5*f*tan(e/2 + f*x/2)**6 + 39690*c**5*f*tan(e/2 + f*x/2)**5 - 39690*c**5*f*tan(e/2 + f*x/2)**4 + 26460*c**5*f*tan(e/2 + f*x/2)**3 - 11340*c**5*f*tan(e/2 + f*x/2)**2 + 2835*c**5*f*tan(e/2 + f*x/2) - 315*c**5*f) + 6930*A*a*tan(e/2 + f*x/2)**5/(315*c**5*f*tan(e/2 + f*x/2)**9 - 2835*c**5*f*tan(e/2 + f*x/2)**8 + 11340*c**5*f*tan(e/2 + f*x/2)**7 - 26460*c**5*f*tan(e/2 + f*x/2)**6 + 39690*c**5*f*tan(e/2 + f*x/2)**5 - 39690*c**5*f*tan(e/2 + f*x/2)**4 + 26460*c**5*f*tan(e/2 + f*x/2)**3 - 11340*c**5*f*tan(e/2 + f*x/2)**2 + 2835*c**5*f*tan(e/2 + f*x/2) - 315*c**5*f) - 7686*A*a*tan(e/2 + f*x/2)**4/(315*c**5*f*tan(e/2 + f*x/2)**9 - 2835*c**5*f*tan(e/2 + f*x/2)**8 + 11340*c**5*f*tan(e/2 + f*x/2)**7 - 26460*c**5*f*tan(e/2 + f*x/2)**6 + 39690*c**5*f*tan(e/2 + f*x/2)**5 - 39690*c**5*f*tan(e/2 + f*x/2)**4 + 26460*c**5*f*tan(e/2 + f*x/2)**3 - 11340*c**5*f*tan(e/2 + f*x/2)**2 + 2835*c**5*f*tan(e/2 + f*x/2) - 315*c**5*f) + 4494*A*a*tan(e/2 + f*x/2)**3/(315*c**5*f*tan(e/2 + f*x/2)**9 - 2835*c**5*f*tan(e/2 + f*x/2)**8 + 11340*c**5*f*tan(e/2 + f*x/2)**7 - 26460*c**5*f*tan(e/2 + f*x/2)**6 + 39690*c**5*f*tan(e/2 + f*x/2)**5 - 39690*c**5*f*tan(e/2 + f*x/2)**4 + 26460*c**5*f*tan(e/2 + f*x/2)**3 - 11340*c**5*f*tan(e/2 + f*x/2)**2 + 2835*c**5*f*tan(e/2 + f*x/2) - 315*c**5*f) - 2286*A*a*tan(e/2 + f*x/2)**2/(315*c**5*f*tan(e/2 + f*x/2)**9 - 2835*c**5*f*tan(e/2 + f*x/2)**8 + 11340*c**5*f*tan(e/2 + f*x/2)**7 - 26460*c**5*f*tan(e/2 + f*x/2)**6 + 39690*c**5*f*tan(e/2 + f*x/2)**5 - 39690*c**5*f*tan(e/2 + f*x/2)**4 + 26460*c**5*f*tan(e/2 + f*x/2)**3 - 11340*c**5*f*tan(e/2 + f*x/2)**2 + 2835*c**5*f*tan(e/2 + f*x/2) - 315*c**5*f) + 414*A*a*tan(e/2 + f*x/2)/(315*c**5*f*tan(e/2 + f*x/2)**9 - 2835*c**5*f*tan(e/2 + f*x/2)**8 + 11340*c**5*f*tan(e/2 + f*x/2)**7 - 26460*c**5*f*tan(e/2 + f*x/2)**6 + 39690*c**5*f*tan(e/2 + f*x/2)**5 - 39690*c**5*f*tan(e/2 + f*x/2)**4 + 26460*c**5*f*tan(e/2 + f*x/2)**3 - 11340*c**5*f*tan(e/2 + f*x/2)**2 + 2835*c**5*f*tan(e/2 + f*x/2) - 315*c**5*f) - 116*A*a/(315*c**5*f*tan(e/2 + f*x/2)**9 - 2835*c**5*f*tan(e/2 + f*x/2)**8 + 11340*c**5*f*tan(e/2 + f*x/2)**7 - 26460*c**5*f*tan(e/2 + f*x/2)**6 + 39690*c**5*f*tan(e/2 + f*x/2)**5 - 39690*c**5*f*tan(e/2 + f*x/2)**4 + 26460*c**5*f*tan(e/2 + f*x/2)**3 - 11340*c**5*f*tan(e/2 + f*x/2)**2 + 2835*c**5*f*tan(e/2 + f*x/2) - 315*c**5*f) - 630*B*a*tan(e/2 + f*x/2)**7/(315*c**5*f*tan(e/2 + f*x/2)**9 - 2835*c**5*f*tan(e/2 + f*x/2)**8 + 11340*c**5*f*tan(e/2 + f*x/2)**7 - 26460*c**5*f*tan(e/2 + f*x/2)**6 + 39690*c**5*f*tan(e/2 + f*x/2)**5 - 39690*c**5*f*tan(e/2 + f*x/2)**4 + 26460*c**5*f*tan(e/2 + f*x/2)**3 - 11340*c**5*f*tan(e/2 + f*x/2)**2 + 2835*c**5*f*tan(e/2 + f*x/2) - 315*c**5*f) + 630*B*a*tan(e/2 + f*x/2)**6/(315*c**5*f*tan(e/2 + f*x/2)**9 - 2835*c**5*f*tan(e/2 + f*x/2)**8 + 11340*c**5*f*tan(e/2 + f*x/2)**7 - 26460*c**5*f*tan(e/2 + f*x/2)**6 + 39690*c**5*f*tan(e/2 + f*x/2)**5 - 39690*c**5*f*tan(e/2 + f*x/2)**4 + 26460*c**5*f*tan(e/2 + f*x/2)**3 - 11340*c**5*f*tan(e/2 + f*x/2)**2 + 2835*c**5*f*tan(e/2 + f*x/2) - 315*c**5*f) - 1890*B*a*tan(e/2 + f*x/2)**5/(315*c**5*f*tan(e/2 + f*x/2)**9 - 2835*c**5*f*tan(e/2 + f*x/2)**8 + 11340*c**5*f*tan(e/2 + f*x/2)**7 - 26460*c**5*f*tan(e/2 + f*x/2)**6 + 39690*c**5*f*tan(e/2 + f*x/2)**5 - 39690*c**5*f*tan(e/2 + f*x/2)**4 + 26460*c**5*f*tan(e/2 + f*x/2)**3 - 11340*c**5*f*tan(e/2 + f*x/2)**2 + 2835*c**5*f*tan(e/2 + f*x/2) - 315*c**5*f) + 882*B*a*tan(e/2 + f*x/2)**4/(315*c**5*f*tan(e/2 + f*x/2)**9 - 2835*c**5*f*tan(e/2 + f*x/2)**8 + 11340*c**5*f*tan(e/2 + f*x/2)**7 - 26460*c**5*f*tan(e/2 + f*x/2)**6 + 39690*c**5*f*tan(e/2 + f*x/2)**5 - 39690*c**5*f*tan(e/2 + f*x/2)**4 + 26460*c**5*f*tan(e/2 + f*x/2)**3 - 11340*c**5*f*tan(e/2 + f*x/2)**2 + 2835*c**5*f*tan(e/2 + f*x/2) - 315*c**5*f) - 1218*B*a*tan(e/2 + f*x/2)**3/(315*c**5*f*tan(e/2 + f*x/2)**9 - 2835*c**5*f*tan(e/2 + f*x/2)**8 + 11340*c**5*f*tan(e/2 + f*x/2)**7 - 26460*c**5*f*tan(e/2 + f*x/2)**6 + 39690*c**5*f*tan(e/2 + f*x/2)**5 - 39690*c**5*f*tan(e/2 + f*x/2)**4 + 26460*c**5*f*tan(e/2 + f*x/2)**3 - 11340*c**5*f*tan(e/2 + f*x/2)**2 + 2835*c**5*f*tan(e/2 + f*x/2) - 315*c**5*f) + 162*B*a*tan(e/2 + f*x/2)**2/(315*c**5*f*tan(e/2 + f*x/2)**9 - 2835*c**5*f*tan(e/2 + f*x/2)**8 + 11340*c**5*f*tan(e/2 + f*x/2)**7 - 26460*c**5*f*tan(e/2 + f*x/2)**6 + 39690*c**5*f*tan(e/2 + f*x/2)**5 - 39690*c**5*f*tan(e/2 + f*x/2)**4 + 26460*c**5*f*tan(e/2 + f*x/2)**3 - 11340*c**5*f*tan(e/2 + f*x/2)**2 + 2835*c**5*f*tan(e/2 + f*x/2) - 315*c**5*f) - 198*B*a*tan(e/2 + f*x/2)/(315*c**5*f*tan(e/2 + f*x/2)**9 - 2835*c**5*f*tan(e/2 + f*x/2)**8 + 11340*c**5*f*tan(e/2 + f*x/2)**7 - 26460*c**5*f*tan(e/2 + f*x/2)**6 + 39690*c**5*f*tan(e/2 + f*x/2)**5 - 39690*c**5*f*tan(e/2 + f*x/2)**4 + 26460*c**5*f*tan(e/2 + f*x/2)**3 - 11340*c**5*f*tan(e/2 + f*x/2)**2 + 2835*c**5*f*tan(e/2 + f*x/2) - 315*c**5*f) + 22*B*a/(315*c**5*f*tan(e/2 + f*x/2)**9 - 2835*c**5*f*tan(e/2 + f*x/2)**8 + 11340*c**5*f*tan(e/2 + f*x/2)**7 - 26460*c**5*f*tan(e/2 + f*x/2)**6 + 39690*c**5*f*tan(e/2 + f*x/2)**5 - 39690*c**5*f*tan(e/2 + f*x/2)**4 + 26460*c**5*f*tan(e/2 + f*x/2)**3 - 11340*c**5*f*tan(e/2 + f*x/2)**2 + 2835*c**5*f*tan(e/2 + f*x/2) - 315*c**5*f), Ne(f, 0)), (x*(A + B*sin(e))*(a*sin(e) + a)/(-c*sin(e) + c)**5, True))","A",0
26,1,1586,0,25.001925," ","integrate((a+a*sin(f*x+e))**2*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**5,x)","\begin{cases} \frac{15 A a^{2} c^{5} x \sin^{6}{\left(e + f x \right)}}{16} + \frac{45 A a^{2} c^{5} x \sin^{4}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{16} - \frac{15 A a^{2} c^{5} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{45 A a^{2} c^{5} x \sin^{2}{\left(e + f x \right)} \cos^{4}{\left(e + f x \right)}}{16} - \frac{15 A a^{2} c^{5} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{A a^{2} c^{5} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{15 A a^{2} c^{5} x \cos^{6}{\left(e + f x \right)}}{16} - \frac{15 A a^{2} c^{5} x \cos^{4}{\left(e + f x \right)}}{8} + \frac{A a^{2} c^{5} x \cos^{2}{\left(e + f x \right)}}{2} + A a^{2} c^{5} x + \frac{A a^{2} c^{5} \sin^{6}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{33 A a^{2} c^{5} \sin^{5}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{16 f} + \frac{2 A a^{2} c^{5} \sin^{4}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{f} + \frac{A a^{2} c^{5} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{5 A a^{2} c^{5} \sin^{3}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{2 f} + \frac{25 A a^{2} c^{5} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} + \frac{8 A a^{2} c^{5} \sin^{2}{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{5 f} + \frac{4 A a^{2} c^{5} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{5 A a^{2} c^{5} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{15 A a^{2} c^{5} \sin{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{16 f} + \frac{15 A a^{2} c^{5} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{A a^{2} c^{5} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} + \frac{16 A a^{2} c^{5} \cos^{7}{\left(e + f x \right)}}{35 f} + \frac{8 A a^{2} c^{5} \cos^{5}{\left(e + f x \right)}}{15 f} - \frac{10 A a^{2} c^{5} \cos^{3}{\left(e + f x \right)}}{3 f} + \frac{3 A a^{2} c^{5} \cos{\left(e + f x \right)}}{f} - \frac{35 B a^{2} c^{5} x \sin^{8}{\left(e + f x \right)}}{128} - \frac{35 B a^{2} c^{5} x \sin^{6}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{32} - \frac{5 B a^{2} c^{5} x \sin^{6}{\left(e + f x \right)}}{16} - \frac{105 B a^{2} c^{5} x \sin^{4}{\left(e + f x \right)} \cos^{4}{\left(e + f x \right)}}{64} - \frac{15 B a^{2} c^{5} x \sin^{4}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{16} + \frac{15 B a^{2} c^{5} x \sin^{4}{\left(e + f x \right)}}{8} - \frac{35 B a^{2} c^{5} x \sin^{2}{\left(e + f x \right)} \cos^{6}{\left(e + f x \right)}}{32} - \frac{15 B a^{2} c^{5} x \sin^{2}{\left(e + f x \right)} \cos^{4}{\left(e + f x \right)}}{16} + \frac{15 B a^{2} c^{5} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} - \frac{3 B a^{2} c^{5} x \sin^{2}{\left(e + f x \right)}}{2} - \frac{35 B a^{2} c^{5} x \cos^{8}{\left(e + f x \right)}}{128} - \frac{5 B a^{2} c^{5} x \cos^{6}{\left(e + f x \right)}}{16} + \frac{15 B a^{2} c^{5} x \cos^{4}{\left(e + f x \right)}}{8} - \frac{3 B a^{2} c^{5} x \cos^{2}{\left(e + f x \right)}}{2} + \frac{93 B a^{2} c^{5} \sin^{7}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{128 f} - \frac{3 B a^{2} c^{5} \sin^{6}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{511 B a^{2} c^{5} \sin^{5}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{384 f} + \frac{11 B a^{2} c^{5} \sin^{5}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{16 f} - \frac{6 B a^{2} c^{5} \sin^{4}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{f} + \frac{5 B a^{2} c^{5} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{385 B a^{2} c^{5} \sin^{3}{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{384 f} + \frac{5 B a^{2} c^{5} \sin^{3}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{6 f} - \frac{25 B a^{2} c^{5} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{24 B a^{2} c^{5} \sin^{2}{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{5 f} + \frac{20 B a^{2} c^{5} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{B a^{2} c^{5} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{35 B a^{2} c^{5} \sin{\left(e + f x \right)} \cos^{7}{\left(e + f x \right)}}{128 f} + \frac{5 B a^{2} c^{5} \sin{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{16 f} - \frac{15 B a^{2} c^{5} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} + \frac{3 B a^{2} c^{5} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{48 B a^{2} c^{5} \cos^{7}{\left(e + f x \right)}}{35 f} + \frac{8 B a^{2} c^{5} \cos^{5}{\left(e + f x \right)}}{3 f} - \frac{2 B a^{2} c^{5} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{B a^{2} c^{5} \cos{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \left(A + B \sin{\left(e \right)}\right) \left(a \sin{\left(e \right)} + a\right)^{2} \left(- c \sin{\left(e \right)} + c\right)^{5} & \text{otherwise} \end{cases}"," ",0,"Piecewise((15*A*a**2*c**5*x*sin(e + f*x)**6/16 + 45*A*a**2*c**5*x*sin(e + f*x)**4*cos(e + f*x)**2/16 - 15*A*a**2*c**5*x*sin(e + f*x)**4/8 + 45*A*a**2*c**5*x*sin(e + f*x)**2*cos(e + f*x)**4/16 - 15*A*a**2*c**5*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + A*a**2*c**5*x*sin(e + f*x)**2/2 + 15*A*a**2*c**5*x*cos(e + f*x)**6/16 - 15*A*a**2*c**5*x*cos(e + f*x)**4/8 + A*a**2*c**5*x*cos(e + f*x)**2/2 + A*a**2*c**5*x + A*a**2*c**5*sin(e + f*x)**6*cos(e + f*x)/f - 33*A*a**2*c**5*sin(e + f*x)**5*cos(e + f*x)/(16*f) + 2*A*a**2*c**5*sin(e + f*x)**4*cos(e + f*x)**3/f + A*a**2*c**5*sin(e + f*x)**4*cos(e + f*x)/f - 5*A*a**2*c**5*sin(e + f*x)**3*cos(e + f*x)**3/(2*f) + 25*A*a**2*c**5*sin(e + f*x)**3*cos(e + f*x)/(8*f) + 8*A*a**2*c**5*sin(e + f*x)**2*cos(e + f*x)**5/(5*f) + 4*A*a**2*c**5*sin(e + f*x)**2*cos(e + f*x)**3/(3*f) - 5*A*a**2*c**5*sin(e + f*x)**2*cos(e + f*x)/f - 15*A*a**2*c**5*sin(e + f*x)*cos(e + f*x)**5/(16*f) + 15*A*a**2*c**5*sin(e + f*x)*cos(e + f*x)**3/(8*f) - A*a**2*c**5*sin(e + f*x)*cos(e + f*x)/(2*f) + 16*A*a**2*c**5*cos(e + f*x)**7/(35*f) + 8*A*a**2*c**5*cos(e + f*x)**5/(15*f) - 10*A*a**2*c**5*cos(e + f*x)**3/(3*f) + 3*A*a**2*c**5*cos(e + f*x)/f - 35*B*a**2*c**5*x*sin(e + f*x)**8/128 - 35*B*a**2*c**5*x*sin(e + f*x)**6*cos(e + f*x)**2/32 - 5*B*a**2*c**5*x*sin(e + f*x)**6/16 - 105*B*a**2*c**5*x*sin(e + f*x)**4*cos(e + f*x)**4/64 - 15*B*a**2*c**5*x*sin(e + f*x)**4*cos(e + f*x)**2/16 + 15*B*a**2*c**5*x*sin(e + f*x)**4/8 - 35*B*a**2*c**5*x*sin(e + f*x)**2*cos(e + f*x)**6/32 - 15*B*a**2*c**5*x*sin(e + f*x)**2*cos(e + f*x)**4/16 + 15*B*a**2*c**5*x*sin(e + f*x)**2*cos(e + f*x)**2/4 - 3*B*a**2*c**5*x*sin(e + f*x)**2/2 - 35*B*a**2*c**5*x*cos(e + f*x)**8/128 - 5*B*a**2*c**5*x*cos(e + f*x)**6/16 + 15*B*a**2*c**5*x*cos(e + f*x)**4/8 - 3*B*a**2*c**5*x*cos(e + f*x)**2/2 + 93*B*a**2*c**5*sin(e + f*x)**7*cos(e + f*x)/(128*f) - 3*B*a**2*c**5*sin(e + f*x)**6*cos(e + f*x)/f + 511*B*a**2*c**5*sin(e + f*x)**5*cos(e + f*x)**3/(384*f) + 11*B*a**2*c**5*sin(e + f*x)**5*cos(e + f*x)/(16*f) - 6*B*a**2*c**5*sin(e + f*x)**4*cos(e + f*x)**3/f + 5*B*a**2*c**5*sin(e + f*x)**4*cos(e + f*x)/f + 385*B*a**2*c**5*sin(e + f*x)**3*cos(e + f*x)**5/(384*f) + 5*B*a**2*c**5*sin(e + f*x)**3*cos(e + f*x)**3/(6*f) - 25*B*a**2*c**5*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 24*B*a**2*c**5*sin(e + f*x)**2*cos(e + f*x)**5/(5*f) + 20*B*a**2*c**5*sin(e + f*x)**2*cos(e + f*x)**3/(3*f) - B*a**2*c**5*sin(e + f*x)**2*cos(e + f*x)/f + 35*B*a**2*c**5*sin(e + f*x)*cos(e + f*x)**7/(128*f) + 5*B*a**2*c**5*sin(e + f*x)*cos(e + f*x)**5/(16*f) - 15*B*a**2*c**5*sin(e + f*x)*cos(e + f*x)**3/(8*f) + 3*B*a**2*c**5*sin(e + f*x)*cos(e + f*x)/(2*f) - 48*B*a**2*c**5*cos(e + f*x)**7/(35*f) + 8*B*a**2*c**5*cos(e + f*x)**5/(3*f) - 2*B*a**2*c**5*cos(e + f*x)**3/(3*f) - B*a**2*c**5*cos(e + f*x)/f, Ne(f, 0)), (x*(A + B*sin(e))*(a*sin(e) + a)**2*(-c*sin(e) + c)**5, True))","A",0
27,1,1210,0,15.016247," ","integrate((a+a*sin(f*x+e))**2*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**4,x)","\begin{cases} \frac{5 A a^{2} c^{4} x \sin^{6}{\left(e + f x \right)}}{16} + \frac{15 A a^{2} c^{4} x \sin^{4}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{16} - \frac{3 A a^{2} c^{4} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{15 A a^{2} c^{4} x \sin^{2}{\left(e + f x \right)} \cos^{4}{\left(e + f x \right)}}{16} - \frac{3 A a^{2} c^{4} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} - \frac{A a^{2} c^{4} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{5 A a^{2} c^{4} x \cos^{6}{\left(e + f x \right)}}{16} - \frac{3 A a^{2} c^{4} x \cos^{4}{\left(e + f x \right)}}{8} - \frac{A a^{2} c^{4} x \cos^{2}{\left(e + f x \right)}}{2} + A a^{2} c^{4} x - \frac{11 A a^{2} c^{4} \sin^{5}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{16 f} + \frac{2 A a^{2} c^{4} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{5 A a^{2} c^{4} \sin^{3}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{6 f} + \frac{5 A a^{2} c^{4} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} + \frac{8 A a^{2} c^{4} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{4 A a^{2} c^{4} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{5 A a^{2} c^{4} \sin{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{16 f} + \frac{3 A a^{2} c^{4} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} + \frac{A a^{2} c^{4} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} + \frac{16 A a^{2} c^{4} \cos^{5}{\left(e + f x \right)}}{15 f} - \frac{8 A a^{2} c^{4} \cos^{3}{\left(e + f x \right)}}{3 f} + \frac{2 A a^{2} c^{4} \cos{\left(e + f x \right)}}{f} - \frac{5 B a^{2} c^{4} x \sin^{6}{\left(e + f x \right)}}{8} - \frac{15 B a^{2} c^{4} x \sin^{4}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{8} + \frac{3 B a^{2} c^{4} x \sin^{4}{\left(e + f x \right)}}{2} - \frac{15 B a^{2} c^{4} x \sin^{2}{\left(e + f x \right)} \cos^{4}{\left(e + f x \right)}}{8} + 3 B a^{2} c^{4} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)} - B a^{2} c^{4} x \sin^{2}{\left(e + f x \right)} - \frac{5 B a^{2} c^{4} x \cos^{6}{\left(e + f x \right)}}{8} + \frac{3 B a^{2} c^{4} x \cos^{4}{\left(e + f x \right)}}{2} - B a^{2} c^{4} x \cos^{2}{\left(e + f x \right)} - \frac{B a^{2} c^{4} \sin^{6}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{11 B a^{2} c^{4} \sin^{5}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{2 B a^{2} c^{4} \sin^{4}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{f} + \frac{B a^{2} c^{4} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{5 B a^{2} c^{4} \sin^{3}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{5 B a^{2} c^{4} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{8 B a^{2} c^{4} \sin^{2}{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{5 f} + \frac{4 B a^{2} c^{4} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{3 f} + \frac{B a^{2} c^{4} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{5 B a^{2} c^{4} \sin{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{8 f} - \frac{3 B a^{2} c^{4} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{2 f} + \frac{B a^{2} c^{4} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{16 B a^{2} c^{4} \cos^{7}{\left(e + f x \right)}}{35 f} + \frac{8 B a^{2} c^{4} \cos^{5}{\left(e + f x \right)}}{15 f} + \frac{2 B a^{2} c^{4} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{B a^{2} c^{4} \cos{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \left(A + B \sin{\left(e \right)}\right) \left(a \sin{\left(e \right)} + a\right)^{2} \left(- c \sin{\left(e \right)} + c\right)^{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((5*A*a**2*c**4*x*sin(e + f*x)**6/16 + 15*A*a**2*c**4*x*sin(e + f*x)**4*cos(e + f*x)**2/16 - 3*A*a**2*c**4*x*sin(e + f*x)**4/8 + 15*A*a**2*c**4*x*sin(e + f*x)**2*cos(e + f*x)**4/16 - 3*A*a**2*c**4*x*sin(e + f*x)**2*cos(e + f*x)**2/4 - A*a**2*c**4*x*sin(e + f*x)**2/2 + 5*A*a**2*c**4*x*cos(e + f*x)**6/16 - 3*A*a**2*c**4*x*cos(e + f*x)**4/8 - A*a**2*c**4*x*cos(e + f*x)**2/2 + A*a**2*c**4*x - 11*A*a**2*c**4*sin(e + f*x)**5*cos(e + f*x)/(16*f) + 2*A*a**2*c**4*sin(e + f*x)**4*cos(e + f*x)/f - 5*A*a**2*c**4*sin(e + f*x)**3*cos(e + f*x)**3/(6*f) + 5*A*a**2*c**4*sin(e + f*x)**3*cos(e + f*x)/(8*f) + 8*A*a**2*c**4*sin(e + f*x)**2*cos(e + f*x)**3/(3*f) - 4*A*a**2*c**4*sin(e + f*x)**2*cos(e + f*x)/f - 5*A*a**2*c**4*sin(e + f*x)*cos(e + f*x)**5/(16*f) + 3*A*a**2*c**4*sin(e + f*x)*cos(e + f*x)**3/(8*f) + A*a**2*c**4*sin(e + f*x)*cos(e + f*x)/(2*f) + 16*A*a**2*c**4*cos(e + f*x)**5/(15*f) - 8*A*a**2*c**4*cos(e + f*x)**3/(3*f) + 2*A*a**2*c**4*cos(e + f*x)/f - 5*B*a**2*c**4*x*sin(e + f*x)**6/8 - 15*B*a**2*c**4*x*sin(e + f*x)**4*cos(e + f*x)**2/8 + 3*B*a**2*c**4*x*sin(e + f*x)**4/2 - 15*B*a**2*c**4*x*sin(e + f*x)**2*cos(e + f*x)**4/8 + 3*B*a**2*c**4*x*sin(e + f*x)**2*cos(e + f*x)**2 - B*a**2*c**4*x*sin(e + f*x)**2 - 5*B*a**2*c**4*x*cos(e + f*x)**6/8 + 3*B*a**2*c**4*x*cos(e + f*x)**4/2 - B*a**2*c**4*x*cos(e + f*x)**2 - B*a**2*c**4*sin(e + f*x)**6*cos(e + f*x)/f + 11*B*a**2*c**4*sin(e + f*x)**5*cos(e + f*x)/(8*f) - 2*B*a**2*c**4*sin(e + f*x)**4*cos(e + f*x)**3/f + B*a**2*c**4*sin(e + f*x)**4*cos(e + f*x)/f + 5*B*a**2*c**4*sin(e + f*x)**3*cos(e + f*x)**3/(3*f) - 5*B*a**2*c**4*sin(e + f*x)**3*cos(e + f*x)/(2*f) - 8*B*a**2*c**4*sin(e + f*x)**2*cos(e + f*x)**5/(5*f) + 4*B*a**2*c**4*sin(e + f*x)**2*cos(e + f*x)**3/(3*f) + B*a**2*c**4*sin(e + f*x)**2*cos(e + f*x)/f + 5*B*a**2*c**4*sin(e + f*x)*cos(e + f*x)**5/(8*f) - 3*B*a**2*c**4*sin(e + f*x)*cos(e + f*x)**3/(2*f) + B*a**2*c**4*sin(e + f*x)*cos(e + f*x)/f - 16*B*a**2*c**4*cos(e + f*x)**7/(35*f) + 8*B*a**2*c**4*cos(e + f*x)**5/(15*f) + 2*B*a**2*c**4*cos(e + f*x)**3/(3*f) - B*a**2*c**4*cos(e + f*x)/f, Ne(f, 0)), (x*(A + B*sin(e))*(a*sin(e) + a)**2*(-c*sin(e) + c)**4, True))","A",0
28,1,910,0,9.139006," ","integrate((a+a*sin(f*x+e))**2*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**3,x)","\begin{cases} \frac{3 A a^{2} c^{3} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{3 A a^{2} c^{3} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} - A a^{2} c^{3} x \sin^{2}{\left(e + f x \right)} + \frac{3 A a^{2} c^{3} x \cos^{4}{\left(e + f x \right)}}{8} - A a^{2} c^{3} x \cos^{2}{\left(e + f x \right)} + A a^{2} c^{3} x + \frac{A a^{2} c^{3} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{5 A a^{2} c^{3} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} + \frac{4 A a^{2} c^{3} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{2 A a^{2} c^{3} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{3 A a^{2} c^{3} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} + \frac{A a^{2} c^{3} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{8 A a^{2} c^{3} \cos^{5}{\left(e + f x \right)}}{15 f} - \frac{4 A a^{2} c^{3} \cos^{3}{\left(e + f x \right)}}{3 f} + \frac{A a^{2} c^{3} \cos{\left(e + f x \right)}}{f} - \frac{5 B a^{2} c^{3} x \sin^{6}{\left(e + f x \right)}}{16} - \frac{15 B a^{2} c^{3} x \sin^{4}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{16} + \frac{3 B a^{2} c^{3} x \sin^{4}{\left(e + f x \right)}}{4} - \frac{15 B a^{2} c^{3} x \sin^{2}{\left(e + f x \right)} \cos^{4}{\left(e + f x \right)}}{16} + \frac{3 B a^{2} c^{3} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{2} - \frac{B a^{2} c^{3} x \sin^{2}{\left(e + f x \right)}}{2} - \frac{5 B a^{2} c^{3} x \cos^{6}{\left(e + f x \right)}}{16} + \frac{3 B a^{2} c^{3} x \cos^{4}{\left(e + f x \right)}}{4} - \frac{B a^{2} c^{3} x \cos^{2}{\left(e + f x \right)}}{2} + \frac{11 B a^{2} c^{3} \sin^{5}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{16 f} - \frac{B a^{2} c^{3} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{5 B a^{2} c^{3} \sin^{3}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{6 f} - \frac{5 B a^{2} c^{3} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{4 f} - \frac{4 B a^{2} c^{3} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{3 f} + \frac{2 B a^{2} c^{3} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{5 B a^{2} c^{3} \sin{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{16 f} - \frac{3 B a^{2} c^{3} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{4 f} + \frac{B a^{2} c^{3} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{8 B a^{2} c^{3} \cos^{5}{\left(e + f x \right)}}{15 f} + \frac{4 B a^{2} c^{3} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{B a^{2} c^{3} \cos{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \left(A + B \sin{\left(e \right)}\right) \left(a \sin{\left(e \right)} + a\right)^{2} \left(- c \sin{\left(e \right)} + c\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*A*a**2*c**3*x*sin(e + f*x)**4/8 + 3*A*a**2*c**3*x*sin(e + f*x)**2*cos(e + f*x)**2/4 - A*a**2*c**3*x*sin(e + f*x)**2 + 3*A*a**2*c**3*x*cos(e + f*x)**4/8 - A*a**2*c**3*x*cos(e + f*x)**2 + A*a**2*c**3*x + A*a**2*c**3*sin(e + f*x)**4*cos(e + f*x)/f - 5*A*a**2*c**3*sin(e + f*x)**3*cos(e + f*x)/(8*f) + 4*A*a**2*c**3*sin(e + f*x)**2*cos(e + f*x)**3/(3*f) - 2*A*a**2*c**3*sin(e + f*x)**2*cos(e + f*x)/f - 3*A*a**2*c**3*sin(e + f*x)*cos(e + f*x)**3/(8*f) + A*a**2*c**3*sin(e + f*x)*cos(e + f*x)/f + 8*A*a**2*c**3*cos(e + f*x)**5/(15*f) - 4*A*a**2*c**3*cos(e + f*x)**3/(3*f) + A*a**2*c**3*cos(e + f*x)/f - 5*B*a**2*c**3*x*sin(e + f*x)**6/16 - 15*B*a**2*c**3*x*sin(e + f*x)**4*cos(e + f*x)**2/16 + 3*B*a**2*c**3*x*sin(e + f*x)**4/4 - 15*B*a**2*c**3*x*sin(e + f*x)**2*cos(e + f*x)**4/16 + 3*B*a**2*c**3*x*sin(e + f*x)**2*cos(e + f*x)**2/2 - B*a**2*c**3*x*sin(e + f*x)**2/2 - 5*B*a**2*c**3*x*cos(e + f*x)**6/16 + 3*B*a**2*c**3*x*cos(e + f*x)**4/4 - B*a**2*c**3*x*cos(e + f*x)**2/2 + 11*B*a**2*c**3*sin(e + f*x)**5*cos(e + f*x)/(16*f) - B*a**2*c**3*sin(e + f*x)**4*cos(e + f*x)/f + 5*B*a**2*c**3*sin(e + f*x)**3*cos(e + f*x)**3/(6*f) - 5*B*a**2*c**3*sin(e + f*x)**3*cos(e + f*x)/(4*f) - 4*B*a**2*c**3*sin(e + f*x)**2*cos(e + f*x)**3/(3*f) + 2*B*a**2*c**3*sin(e + f*x)**2*cos(e + f*x)/f + 5*B*a**2*c**3*sin(e + f*x)*cos(e + f*x)**5/(16*f) - 3*B*a**2*c**3*sin(e + f*x)*cos(e + f*x)**3/(4*f) + B*a**2*c**3*sin(e + f*x)*cos(e + f*x)/(2*f) - 8*B*a**2*c**3*cos(e + f*x)**5/(15*f) + 4*B*a**2*c**3*cos(e + f*x)**3/(3*f) - B*a**2*c**3*cos(e + f*x)/f, Ne(f, 0)), (x*(A + B*sin(e))*(a*sin(e) + a)**2*(-c*sin(e) + c)**3, True))","A",0
29,1,372,0,3.697202," ","integrate((a+a*sin(f*x+e))**2*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**2,x)","\begin{cases} \frac{3 A a^{2} c^{2} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{3 A a^{2} c^{2} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} - A a^{2} c^{2} x \sin^{2}{\left(e + f x \right)} + \frac{3 A a^{2} c^{2} x \cos^{4}{\left(e + f x \right)}}{8} - A a^{2} c^{2} x \cos^{2}{\left(e + f x \right)} + A a^{2} c^{2} x - \frac{5 A a^{2} c^{2} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{3 A a^{2} c^{2} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} + \frac{A a^{2} c^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{B a^{2} c^{2} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{4 B a^{2} c^{2} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{3 f} + \frac{2 B a^{2} c^{2} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{8 B a^{2} c^{2} \cos^{5}{\left(e + f x \right)}}{15 f} + \frac{4 B a^{2} c^{2} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{B a^{2} c^{2} \cos{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \left(A + B \sin{\left(e \right)}\right) \left(a \sin{\left(e \right)} + a\right)^{2} \left(- c \sin{\left(e \right)} + c\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*A*a**2*c**2*x*sin(e + f*x)**4/8 + 3*A*a**2*c**2*x*sin(e + f*x)**2*cos(e + f*x)**2/4 - A*a**2*c**2*x*sin(e + f*x)**2 + 3*A*a**2*c**2*x*cos(e + f*x)**4/8 - A*a**2*c**2*x*cos(e + f*x)**2 + A*a**2*c**2*x - 5*A*a**2*c**2*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 3*A*a**2*c**2*sin(e + f*x)*cos(e + f*x)**3/(8*f) + A*a**2*c**2*sin(e + f*x)*cos(e + f*x)/f - B*a**2*c**2*sin(e + f*x)**4*cos(e + f*x)/f - 4*B*a**2*c**2*sin(e + f*x)**2*cos(e + f*x)**3/(3*f) + 2*B*a**2*c**2*sin(e + f*x)**2*cos(e + f*x)/f - 8*B*a**2*c**2*cos(e + f*x)**5/(15*f) + 4*B*a**2*c**2*cos(e + f*x)**3/(3*f) - B*a**2*c**2*cos(e + f*x)/f, Ne(f, 0)), (x*(A + B*sin(e))*(a*sin(e) + a)**2*(-c*sin(e) + c)**2, True))","A",0
30,1,396,0,2.434042," ","integrate((a+a*sin(f*x+e))**2*(A+B*sin(f*x+e))*(c-c*sin(f*x+e)),x)","\begin{cases} - \frac{A a^{2} c x \sin^{2}{\left(e + f x \right)}}{2} - \frac{A a^{2} c x \cos^{2}{\left(e + f x \right)}}{2} + A a^{2} c x + \frac{A a^{2} c \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{A a^{2} c \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} + \frac{2 A a^{2} c \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{A a^{2} c \cos{\left(e + f x \right)}}{f} - \frac{3 B a^{2} c x \sin^{4}{\left(e + f x \right)}}{8} - \frac{3 B a^{2} c x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{B a^{2} c x \sin^{2}{\left(e + f x \right)}}{2} - \frac{3 B a^{2} c x \cos^{4}{\left(e + f x \right)}}{8} + \frac{B a^{2} c x \cos^{2}{\left(e + f x \right)}}{2} + \frac{5 B a^{2} c \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} + \frac{B a^{2} c \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{3 B a^{2} c \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{B a^{2} c \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} + \frac{2 B a^{2} c \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{B a^{2} c \cos{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \left(A + B \sin{\left(e \right)}\right) \left(a \sin{\left(e \right)} + a\right)^{2} \left(- c \sin{\left(e \right)} + c\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((-A*a**2*c*x*sin(e + f*x)**2/2 - A*a**2*c*x*cos(e + f*x)**2/2 + A*a**2*c*x + A*a**2*c*sin(e + f*x)**2*cos(e + f*x)/f + A*a**2*c*sin(e + f*x)*cos(e + f*x)/(2*f) + 2*A*a**2*c*cos(e + f*x)**3/(3*f) - A*a**2*c*cos(e + f*x)/f - 3*B*a**2*c*x*sin(e + f*x)**4/8 - 3*B*a**2*c*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + B*a**2*c*x*sin(e + f*x)**2/2 - 3*B*a**2*c*x*cos(e + f*x)**4/8 + B*a**2*c*x*cos(e + f*x)**2/2 + 5*B*a**2*c*sin(e + f*x)**3*cos(e + f*x)/(8*f) + B*a**2*c*sin(e + f*x)**2*cos(e + f*x)/f + 3*B*a**2*c*sin(e + f*x)*cos(e + f*x)**3/(8*f) - B*a**2*c*sin(e + f*x)*cos(e + f*x)/(2*f) + 2*B*a**2*c*cos(e + f*x)**3/(3*f) - B*a**2*c*cos(e + f*x)/f, Ne(f, 0)), (x*(A + B*sin(e))*(a*sin(e) + a)**2*(-c*sin(e) + c), True))","A",0
31,1,2365,0,8.092222," ","integrate((a+a*sin(f*x+e))**2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e)),x)","\begin{cases} - \frac{6 A a^{2} f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2 c f} + \frac{6 A a^{2} f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2 c f} - \frac{12 A a^{2} f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2 c f} + \frac{12 A a^{2} f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2 c f} - \frac{6 A a^{2} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2 c f} + \frac{6 A a^{2} f x}{2 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2 c f} - \frac{16 A a^{2} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2 c f} + \frac{4 A a^{2} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2 c f} - \frac{36 A a^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2 c f} + \frac{4 A a^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2 c f} - \frac{20 A a^{2}}{2 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2 c f} - \frac{9 B a^{2} f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2 c f} + \frac{9 B a^{2} f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2 c f} - \frac{18 B a^{2} f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2 c f} + \frac{18 B a^{2} f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2 c f} - \frac{9 B a^{2} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2 c f} + \frac{9 B a^{2} f x}{2 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2 c f} - \frac{18 B a^{2} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2 c f} + \frac{14 B a^{2} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2 c f} - \frac{42 B a^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2 c f} + \frac{10 B a^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2 c f} - \frac{28 B a^{2}}{2 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2 c f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right) \left(a \sin{\left(e \right)} + a\right)^{2}}{- c \sin{\left(e \right)} + c} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-6*A*a**2*f*x*tan(e/2 + f*x/2)**5/(2*c*f*tan(e/2 + f*x/2)**5 - 2*c*f*tan(e/2 + f*x/2)**4 + 4*c*f*tan(e/2 + f*x/2)**3 - 4*c*f*tan(e/2 + f*x/2)**2 + 2*c*f*tan(e/2 + f*x/2) - 2*c*f) + 6*A*a**2*f*x*tan(e/2 + f*x/2)**4/(2*c*f*tan(e/2 + f*x/2)**5 - 2*c*f*tan(e/2 + f*x/2)**4 + 4*c*f*tan(e/2 + f*x/2)**3 - 4*c*f*tan(e/2 + f*x/2)**2 + 2*c*f*tan(e/2 + f*x/2) - 2*c*f) - 12*A*a**2*f*x*tan(e/2 + f*x/2)**3/(2*c*f*tan(e/2 + f*x/2)**5 - 2*c*f*tan(e/2 + f*x/2)**4 + 4*c*f*tan(e/2 + f*x/2)**3 - 4*c*f*tan(e/2 + f*x/2)**2 + 2*c*f*tan(e/2 + f*x/2) - 2*c*f) + 12*A*a**2*f*x*tan(e/2 + f*x/2)**2/(2*c*f*tan(e/2 + f*x/2)**5 - 2*c*f*tan(e/2 + f*x/2)**4 + 4*c*f*tan(e/2 + f*x/2)**3 - 4*c*f*tan(e/2 + f*x/2)**2 + 2*c*f*tan(e/2 + f*x/2) - 2*c*f) - 6*A*a**2*f*x*tan(e/2 + f*x/2)/(2*c*f*tan(e/2 + f*x/2)**5 - 2*c*f*tan(e/2 + f*x/2)**4 + 4*c*f*tan(e/2 + f*x/2)**3 - 4*c*f*tan(e/2 + f*x/2)**2 + 2*c*f*tan(e/2 + f*x/2) - 2*c*f) + 6*A*a**2*f*x/(2*c*f*tan(e/2 + f*x/2)**5 - 2*c*f*tan(e/2 + f*x/2)**4 + 4*c*f*tan(e/2 + f*x/2)**3 - 4*c*f*tan(e/2 + f*x/2)**2 + 2*c*f*tan(e/2 + f*x/2) - 2*c*f) - 16*A*a**2*tan(e/2 + f*x/2)**4/(2*c*f*tan(e/2 + f*x/2)**5 - 2*c*f*tan(e/2 + f*x/2)**4 + 4*c*f*tan(e/2 + f*x/2)**3 - 4*c*f*tan(e/2 + f*x/2)**2 + 2*c*f*tan(e/2 + f*x/2) - 2*c*f) + 4*A*a**2*tan(e/2 + f*x/2)**3/(2*c*f*tan(e/2 + f*x/2)**5 - 2*c*f*tan(e/2 + f*x/2)**4 + 4*c*f*tan(e/2 + f*x/2)**3 - 4*c*f*tan(e/2 + f*x/2)**2 + 2*c*f*tan(e/2 + f*x/2) - 2*c*f) - 36*A*a**2*tan(e/2 + f*x/2)**2/(2*c*f*tan(e/2 + f*x/2)**5 - 2*c*f*tan(e/2 + f*x/2)**4 + 4*c*f*tan(e/2 + f*x/2)**3 - 4*c*f*tan(e/2 + f*x/2)**2 + 2*c*f*tan(e/2 + f*x/2) - 2*c*f) + 4*A*a**2*tan(e/2 + f*x/2)/(2*c*f*tan(e/2 + f*x/2)**5 - 2*c*f*tan(e/2 + f*x/2)**4 + 4*c*f*tan(e/2 + f*x/2)**3 - 4*c*f*tan(e/2 + f*x/2)**2 + 2*c*f*tan(e/2 + f*x/2) - 2*c*f) - 20*A*a**2/(2*c*f*tan(e/2 + f*x/2)**5 - 2*c*f*tan(e/2 + f*x/2)**4 + 4*c*f*tan(e/2 + f*x/2)**3 - 4*c*f*tan(e/2 + f*x/2)**2 + 2*c*f*tan(e/2 + f*x/2) - 2*c*f) - 9*B*a**2*f*x*tan(e/2 + f*x/2)**5/(2*c*f*tan(e/2 + f*x/2)**5 - 2*c*f*tan(e/2 + f*x/2)**4 + 4*c*f*tan(e/2 + f*x/2)**3 - 4*c*f*tan(e/2 + f*x/2)**2 + 2*c*f*tan(e/2 + f*x/2) - 2*c*f) + 9*B*a**2*f*x*tan(e/2 + f*x/2)**4/(2*c*f*tan(e/2 + f*x/2)**5 - 2*c*f*tan(e/2 + f*x/2)**4 + 4*c*f*tan(e/2 + f*x/2)**3 - 4*c*f*tan(e/2 + f*x/2)**2 + 2*c*f*tan(e/2 + f*x/2) - 2*c*f) - 18*B*a**2*f*x*tan(e/2 + f*x/2)**3/(2*c*f*tan(e/2 + f*x/2)**5 - 2*c*f*tan(e/2 + f*x/2)**4 + 4*c*f*tan(e/2 + f*x/2)**3 - 4*c*f*tan(e/2 + f*x/2)**2 + 2*c*f*tan(e/2 + f*x/2) - 2*c*f) + 18*B*a**2*f*x*tan(e/2 + f*x/2)**2/(2*c*f*tan(e/2 + f*x/2)**5 - 2*c*f*tan(e/2 + f*x/2)**4 + 4*c*f*tan(e/2 + f*x/2)**3 - 4*c*f*tan(e/2 + f*x/2)**2 + 2*c*f*tan(e/2 + f*x/2) - 2*c*f) - 9*B*a**2*f*x*tan(e/2 + f*x/2)/(2*c*f*tan(e/2 + f*x/2)**5 - 2*c*f*tan(e/2 + f*x/2)**4 + 4*c*f*tan(e/2 + f*x/2)**3 - 4*c*f*tan(e/2 + f*x/2)**2 + 2*c*f*tan(e/2 + f*x/2) - 2*c*f) + 9*B*a**2*f*x/(2*c*f*tan(e/2 + f*x/2)**5 - 2*c*f*tan(e/2 + f*x/2)**4 + 4*c*f*tan(e/2 + f*x/2)**3 - 4*c*f*tan(e/2 + f*x/2)**2 + 2*c*f*tan(e/2 + f*x/2) - 2*c*f) - 18*B*a**2*tan(e/2 + f*x/2)**4/(2*c*f*tan(e/2 + f*x/2)**5 - 2*c*f*tan(e/2 + f*x/2)**4 + 4*c*f*tan(e/2 + f*x/2)**3 - 4*c*f*tan(e/2 + f*x/2)**2 + 2*c*f*tan(e/2 + f*x/2) - 2*c*f) + 14*B*a**2*tan(e/2 + f*x/2)**3/(2*c*f*tan(e/2 + f*x/2)**5 - 2*c*f*tan(e/2 + f*x/2)**4 + 4*c*f*tan(e/2 + f*x/2)**3 - 4*c*f*tan(e/2 + f*x/2)**2 + 2*c*f*tan(e/2 + f*x/2) - 2*c*f) - 42*B*a**2*tan(e/2 + f*x/2)**2/(2*c*f*tan(e/2 + f*x/2)**5 - 2*c*f*tan(e/2 + f*x/2)**4 + 4*c*f*tan(e/2 + f*x/2)**3 - 4*c*f*tan(e/2 + f*x/2)**2 + 2*c*f*tan(e/2 + f*x/2) - 2*c*f) + 10*B*a**2*tan(e/2 + f*x/2)/(2*c*f*tan(e/2 + f*x/2)**5 - 2*c*f*tan(e/2 + f*x/2)**4 + 4*c*f*tan(e/2 + f*x/2)**3 - 4*c*f*tan(e/2 + f*x/2)**2 + 2*c*f*tan(e/2 + f*x/2) - 2*c*f) - 28*B*a**2/(2*c*f*tan(e/2 + f*x/2)**5 - 2*c*f*tan(e/2 + f*x/2)**4 + 4*c*f*tan(e/2 + f*x/2)**3 - 4*c*f*tan(e/2 + f*x/2)**2 + 2*c*f*tan(e/2 + f*x/2) - 2*c*f), Ne(f, 0)), (x*(A + B*sin(e))*(a*sin(e) + a)**2/(-c*sin(e) + c), True))","A",0
32,1,2474,0,16.122654," ","integrate((a+a*sin(f*x+e))**2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**2,x)","\begin{cases} \frac{3 A a^{2} f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 9 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 12 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 c^{2} f} - \frac{9 A a^{2} f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 9 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 12 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 c^{2} f} + \frac{12 A a^{2} f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 9 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 12 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 c^{2} f} - \frac{12 A a^{2} f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 9 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 12 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 c^{2} f} + \frac{9 A a^{2} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 9 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 12 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 c^{2} f} - \frac{3 A a^{2} f x}{3 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 9 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 12 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 c^{2} f} - \frac{24 A a^{2} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 9 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 12 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 c^{2} f} + \frac{8 A a^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 9 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 12 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 c^{2} f} - \frac{24 A a^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 9 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 12 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 c^{2} f} + \frac{8 A a^{2}}{3 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 9 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 12 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 c^{2} f} + \frac{12 B a^{2} f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 9 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 12 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 c^{2} f} - \frac{36 B a^{2} f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 9 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 12 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 c^{2} f} + \frac{48 B a^{2} f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 9 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 12 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 c^{2} f} - \frac{48 B a^{2} f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 9 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 12 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 c^{2} f} + \frac{36 B a^{2} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 9 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 12 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 c^{2} f} - \frac{12 B a^{2} f x}{3 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 9 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 12 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 c^{2} f} + \frac{24 B a^{2} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 9 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 12 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 c^{2} f} - \frac{78 B a^{2} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 9 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 12 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 c^{2} f} + \frac{74 B a^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 9 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 12 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 c^{2} f} - \frac{90 B a^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 9 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 12 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 c^{2} f} + \frac{38 B a^{2}}{3 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 9 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 12 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 c^{2} f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right) \left(a \sin{\left(e \right)} + a\right)^{2}}{\left(- c \sin{\left(e \right)} + c\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*A*a**2*f*x*tan(e/2 + f*x/2)**5/(3*c**2*f*tan(e/2 + f*x/2)**5 - 9*c**2*f*tan(e/2 + f*x/2)**4 + 12*c**2*f*tan(e/2 + f*x/2)**3 - 12*c**2*f*tan(e/2 + f*x/2)**2 + 9*c**2*f*tan(e/2 + f*x/2) - 3*c**2*f) - 9*A*a**2*f*x*tan(e/2 + f*x/2)**4/(3*c**2*f*tan(e/2 + f*x/2)**5 - 9*c**2*f*tan(e/2 + f*x/2)**4 + 12*c**2*f*tan(e/2 + f*x/2)**3 - 12*c**2*f*tan(e/2 + f*x/2)**2 + 9*c**2*f*tan(e/2 + f*x/2) - 3*c**2*f) + 12*A*a**2*f*x*tan(e/2 + f*x/2)**3/(3*c**2*f*tan(e/2 + f*x/2)**5 - 9*c**2*f*tan(e/2 + f*x/2)**4 + 12*c**2*f*tan(e/2 + f*x/2)**3 - 12*c**2*f*tan(e/2 + f*x/2)**2 + 9*c**2*f*tan(e/2 + f*x/2) - 3*c**2*f) - 12*A*a**2*f*x*tan(e/2 + f*x/2)**2/(3*c**2*f*tan(e/2 + f*x/2)**5 - 9*c**2*f*tan(e/2 + f*x/2)**4 + 12*c**2*f*tan(e/2 + f*x/2)**3 - 12*c**2*f*tan(e/2 + f*x/2)**2 + 9*c**2*f*tan(e/2 + f*x/2) - 3*c**2*f) + 9*A*a**2*f*x*tan(e/2 + f*x/2)/(3*c**2*f*tan(e/2 + f*x/2)**5 - 9*c**2*f*tan(e/2 + f*x/2)**4 + 12*c**2*f*tan(e/2 + f*x/2)**3 - 12*c**2*f*tan(e/2 + f*x/2)**2 + 9*c**2*f*tan(e/2 + f*x/2) - 3*c**2*f) - 3*A*a**2*f*x/(3*c**2*f*tan(e/2 + f*x/2)**5 - 9*c**2*f*tan(e/2 + f*x/2)**4 + 12*c**2*f*tan(e/2 + f*x/2)**3 - 12*c**2*f*tan(e/2 + f*x/2)**2 + 9*c**2*f*tan(e/2 + f*x/2) - 3*c**2*f) - 24*A*a**2*tan(e/2 + f*x/2)**3/(3*c**2*f*tan(e/2 + f*x/2)**5 - 9*c**2*f*tan(e/2 + f*x/2)**4 + 12*c**2*f*tan(e/2 + f*x/2)**3 - 12*c**2*f*tan(e/2 + f*x/2)**2 + 9*c**2*f*tan(e/2 + f*x/2) - 3*c**2*f) + 8*A*a**2*tan(e/2 + f*x/2)**2/(3*c**2*f*tan(e/2 + f*x/2)**5 - 9*c**2*f*tan(e/2 + f*x/2)**4 + 12*c**2*f*tan(e/2 + f*x/2)**3 - 12*c**2*f*tan(e/2 + f*x/2)**2 + 9*c**2*f*tan(e/2 + f*x/2) - 3*c**2*f) - 24*A*a**2*tan(e/2 + f*x/2)/(3*c**2*f*tan(e/2 + f*x/2)**5 - 9*c**2*f*tan(e/2 + f*x/2)**4 + 12*c**2*f*tan(e/2 + f*x/2)**3 - 12*c**2*f*tan(e/2 + f*x/2)**2 + 9*c**2*f*tan(e/2 + f*x/2) - 3*c**2*f) + 8*A*a**2/(3*c**2*f*tan(e/2 + f*x/2)**5 - 9*c**2*f*tan(e/2 + f*x/2)**4 + 12*c**2*f*tan(e/2 + f*x/2)**3 - 12*c**2*f*tan(e/2 + f*x/2)**2 + 9*c**2*f*tan(e/2 + f*x/2) - 3*c**2*f) + 12*B*a**2*f*x*tan(e/2 + f*x/2)**5/(3*c**2*f*tan(e/2 + f*x/2)**5 - 9*c**2*f*tan(e/2 + f*x/2)**4 + 12*c**2*f*tan(e/2 + f*x/2)**3 - 12*c**2*f*tan(e/2 + f*x/2)**2 + 9*c**2*f*tan(e/2 + f*x/2) - 3*c**2*f) - 36*B*a**2*f*x*tan(e/2 + f*x/2)**4/(3*c**2*f*tan(e/2 + f*x/2)**5 - 9*c**2*f*tan(e/2 + f*x/2)**4 + 12*c**2*f*tan(e/2 + f*x/2)**3 - 12*c**2*f*tan(e/2 + f*x/2)**2 + 9*c**2*f*tan(e/2 + f*x/2) - 3*c**2*f) + 48*B*a**2*f*x*tan(e/2 + f*x/2)**3/(3*c**2*f*tan(e/2 + f*x/2)**5 - 9*c**2*f*tan(e/2 + f*x/2)**4 + 12*c**2*f*tan(e/2 + f*x/2)**3 - 12*c**2*f*tan(e/2 + f*x/2)**2 + 9*c**2*f*tan(e/2 + f*x/2) - 3*c**2*f) - 48*B*a**2*f*x*tan(e/2 + f*x/2)**2/(3*c**2*f*tan(e/2 + f*x/2)**5 - 9*c**2*f*tan(e/2 + f*x/2)**4 + 12*c**2*f*tan(e/2 + f*x/2)**3 - 12*c**2*f*tan(e/2 + f*x/2)**2 + 9*c**2*f*tan(e/2 + f*x/2) - 3*c**2*f) + 36*B*a**2*f*x*tan(e/2 + f*x/2)/(3*c**2*f*tan(e/2 + f*x/2)**5 - 9*c**2*f*tan(e/2 + f*x/2)**4 + 12*c**2*f*tan(e/2 + f*x/2)**3 - 12*c**2*f*tan(e/2 + f*x/2)**2 + 9*c**2*f*tan(e/2 + f*x/2) - 3*c**2*f) - 12*B*a**2*f*x/(3*c**2*f*tan(e/2 + f*x/2)**5 - 9*c**2*f*tan(e/2 + f*x/2)**4 + 12*c**2*f*tan(e/2 + f*x/2)**3 - 12*c**2*f*tan(e/2 + f*x/2)**2 + 9*c**2*f*tan(e/2 + f*x/2) - 3*c**2*f) + 24*B*a**2*tan(e/2 + f*x/2)**4/(3*c**2*f*tan(e/2 + f*x/2)**5 - 9*c**2*f*tan(e/2 + f*x/2)**4 + 12*c**2*f*tan(e/2 + f*x/2)**3 - 12*c**2*f*tan(e/2 + f*x/2)**2 + 9*c**2*f*tan(e/2 + f*x/2) - 3*c**2*f) - 78*B*a**2*tan(e/2 + f*x/2)**3/(3*c**2*f*tan(e/2 + f*x/2)**5 - 9*c**2*f*tan(e/2 + f*x/2)**4 + 12*c**2*f*tan(e/2 + f*x/2)**3 - 12*c**2*f*tan(e/2 + f*x/2)**2 + 9*c**2*f*tan(e/2 + f*x/2) - 3*c**2*f) + 74*B*a**2*tan(e/2 + f*x/2)**2/(3*c**2*f*tan(e/2 + f*x/2)**5 - 9*c**2*f*tan(e/2 + f*x/2)**4 + 12*c**2*f*tan(e/2 + f*x/2)**3 - 12*c**2*f*tan(e/2 + f*x/2)**2 + 9*c**2*f*tan(e/2 + f*x/2) - 3*c**2*f) - 90*B*a**2*tan(e/2 + f*x/2)/(3*c**2*f*tan(e/2 + f*x/2)**5 - 9*c**2*f*tan(e/2 + f*x/2)**4 + 12*c**2*f*tan(e/2 + f*x/2)**3 - 12*c**2*f*tan(e/2 + f*x/2)**2 + 9*c**2*f*tan(e/2 + f*x/2) - 3*c**2*f) + 38*B*a**2/(3*c**2*f*tan(e/2 + f*x/2)**5 - 9*c**2*f*tan(e/2 + f*x/2)**4 + 12*c**2*f*tan(e/2 + f*x/2)**3 - 12*c**2*f*tan(e/2 + f*x/2)**2 + 9*c**2*f*tan(e/2 + f*x/2) - 3*c**2*f), Ne(f, 0)), (x*(A + B*sin(e))*(a*sin(e) + a)**2/(-c*sin(e) + c)**2, True))","A",0
33,1,1647,0,26.922610," ","integrate((a+a*sin(f*x+e))**2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**3,x)","\begin{cases} - \frac{30 A a^{2} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 150 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} - \frac{60 A a^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 150 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} - \frac{6 A a^{2}}{15 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 150 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} - \frac{15 B a^{2} f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 150 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} + \frac{75 B a^{2} f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 150 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} - \frac{150 B a^{2} f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 150 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} + \frac{150 B a^{2} f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 150 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} - \frac{75 B a^{2} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 150 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} + \frac{15 B a^{2} f x}{15 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 150 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} - \frac{30 B a^{2} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 150 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} + \frac{120 B a^{2} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 150 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} - \frac{340 B a^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 150 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} + \frac{200 B a^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 150 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} - \frac{46 B a^{2}}{15 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 150 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right) \left(a \sin{\left(e \right)} + a\right)^{2}}{\left(- c \sin{\left(e \right)} + c\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-30*A*a**2*tan(e/2 + f*x/2)**4/(15*c**3*f*tan(e/2 + f*x/2)**5 - 75*c**3*f*tan(e/2 + f*x/2)**4 + 150*c**3*f*tan(e/2 + f*x/2)**3 - 150*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) - 60*A*a**2*tan(e/2 + f*x/2)**2/(15*c**3*f*tan(e/2 + f*x/2)**5 - 75*c**3*f*tan(e/2 + f*x/2)**4 + 150*c**3*f*tan(e/2 + f*x/2)**3 - 150*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) - 6*A*a**2/(15*c**3*f*tan(e/2 + f*x/2)**5 - 75*c**3*f*tan(e/2 + f*x/2)**4 + 150*c**3*f*tan(e/2 + f*x/2)**3 - 150*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) - 15*B*a**2*f*x*tan(e/2 + f*x/2)**5/(15*c**3*f*tan(e/2 + f*x/2)**5 - 75*c**3*f*tan(e/2 + f*x/2)**4 + 150*c**3*f*tan(e/2 + f*x/2)**3 - 150*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) + 75*B*a**2*f*x*tan(e/2 + f*x/2)**4/(15*c**3*f*tan(e/2 + f*x/2)**5 - 75*c**3*f*tan(e/2 + f*x/2)**4 + 150*c**3*f*tan(e/2 + f*x/2)**3 - 150*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) - 150*B*a**2*f*x*tan(e/2 + f*x/2)**3/(15*c**3*f*tan(e/2 + f*x/2)**5 - 75*c**3*f*tan(e/2 + f*x/2)**4 + 150*c**3*f*tan(e/2 + f*x/2)**3 - 150*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) + 150*B*a**2*f*x*tan(e/2 + f*x/2)**2/(15*c**3*f*tan(e/2 + f*x/2)**5 - 75*c**3*f*tan(e/2 + f*x/2)**4 + 150*c**3*f*tan(e/2 + f*x/2)**3 - 150*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) - 75*B*a**2*f*x*tan(e/2 + f*x/2)/(15*c**3*f*tan(e/2 + f*x/2)**5 - 75*c**3*f*tan(e/2 + f*x/2)**4 + 150*c**3*f*tan(e/2 + f*x/2)**3 - 150*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) + 15*B*a**2*f*x/(15*c**3*f*tan(e/2 + f*x/2)**5 - 75*c**3*f*tan(e/2 + f*x/2)**4 + 150*c**3*f*tan(e/2 + f*x/2)**3 - 150*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) - 30*B*a**2*tan(e/2 + f*x/2)**4/(15*c**3*f*tan(e/2 + f*x/2)**5 - 75*c**3*f*tan(e/2 + f*x/2)**4 + 150*c**3*f*tan(e/2 + f*x/2)**3 - 150*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) + 120*B*a**2*tan(e/2 + f*x/2)**3/(15*c**3*f*tan(e/2 + f*x/2)**5 - 75*c**3*f*tan(e/2 + f*x/2)**4 + 150*c**3*f*tan(e/2 + f*x/2)**3 - 150*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) - 340*B*a**2*tan(e/2 + f*x/2)**2/(15*c**3*f*tan(e/2 + f*x/2)**5 - 75*c**3*f*tan(e/2 + f*x/2)**4 + 150*c**3*f*tan(e/2 + f*x/2)**3 - 150*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) + 200*B*a**2*tan(e/2 + f*x/2)/(15*c**3*f*tan(e/2 + f*x/2)**5 - 75*c**3*f*tan(e/2 + f*x/2)**4 + 150*c**3*f*tan(e/2 + f*x/2)**3 - 150*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) - 46*B*a**2/(15*c**3*f*tan(e/2 + f*x/2)**5 - 75*c**3*f*tan(e/2 + f*x/2)**4 + 150*c**3*f*tan(e/2 + f*x/2)**3 - 150*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f), Ne(f, 0)), (x*(A + B*sin(e))*(a*sin(e) + a)**2/(-c*sin(e) + c)**3, True))","A",0
34,1,2008,0,45.068197," ","integrate((a+a*sin(f*x+e))**2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**4,x)","\begin{cases} - \frac{70 A a^{2} \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{35 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 245 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 735 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1225 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1225 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 735 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 245 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 35 c^{4} f} + \frac{70 A a^{2} \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{35 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 245 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 735 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1225 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1225 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 735 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 245 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 35 c^{4} f} - \frac{280 A a^{2} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{35 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 245 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 735 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1225 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1225 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 735 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 245 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 35 c^{4} f} + \frac{140 A a^{2} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{35 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 245 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 735 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1225 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1225 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 735 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 245 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 35 c^{4} f} - \frac{182 A a^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{35 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 245 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 735 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1225 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1225 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 735 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 245 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 35 c^{4} f} + \frac{14 A a^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{35 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 245 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 735 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1225 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1225 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 735 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 245 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 35 c^{4} f} - \frac{12 A a^{2}}{35 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 245 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 735 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1225 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1225 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 735 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 245 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 35 c^{4} f} - \frac{70 B a^{2} \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{35 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 245 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 735 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1225 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1225 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 735 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 245 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 35 c^{4} f} - \frac{70 B a^{2} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{35 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 245 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 735 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1225 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1225 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 735 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 245 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 35 c^{4} f} - \frac{140 B a^{2} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{35 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 245 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 735 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1225 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1225 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 735 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 245 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 35 c^{4} f} - \frac{28 B a^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{35 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 245 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 735 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1225 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1225 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 735 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 245 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 35 c^{4} f} - \frac{14 B a^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{35 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 245 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 735 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1225 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1225 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 735 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 245 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 35 c^{4} f} + \frac{2 B a^{2}}{35 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 245 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 735 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1225 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1225 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 735 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 245 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 35 c^{4} f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right) \left(a \sin{\left(e \right)} + a\right)^{2}}{\left(- c \sin{\left(e \right)} + c\right)^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-70*A*a**2*tan(e/2 + f*x/2)**6/(35*c**4*f*tan(e/2 + f*x/2)**7 - 245*c**4*f*tan(e/2 + f*x/2)**6 + 735*c**4*f*tan(e/2 + f*x/2)**5 - 1225*c**4*f*tan(e/2 + f*x/2)**4 + 1225*c**4*f*tan(e/2 + f*x/2)**3 - 735*c**4*f*tan(e/2 + f*x/2)**2 + 245*c**4*f*tan(e/2 + f*x/2) - 35*c**4*f) + 70*A*a**2*tan(e/2 + f*x/2)**5/(35*c**4*f*tan(e/2 + f*x/2)**7 - 245*c**4*f*tan(e/2 + f*x/2)**6 + 735*c**4*f*tan(e/2 + f*x/2)**5 - 1225*c**4*f*tan(e/2 + f*x/2)**4 + 1225*c**4*f*tan(e/2 + f*x/2)**3 - 735*c**4*f*tan(e/2 + f*x/2)**2 + 245*c**4*f*tan(e/2 + f*x/2) - 35*c**4*f) - 280*A*a**2*tan(e/2 + f*x/2)**4/(35*c**4*f*tan(e/2 + f*x/2)**7 - 245*c**4*f*tan(e/2 + f*x/2)**6 + 735*c**4*f*tan(e/2 + f*x/2)**5 - 1225*c**4*f*tan(e/2 + f*x/2)**4 + 1225*c**4*f*tan(e/2 + f*x/2)**3 - 735*c**4*f*tan(e/2 + f*x/2)**2 + 245*c**4*f*tan(e/2 + f*x/2) - 35*c**4*f) + 140*A*a**2*tan(e/2 + f*x/2)**3/(35*c**4*f*tan(e/2 + f*x/2)**7 - 245*c**4*f*tan(e/2 + f*x/2)**6 + 735*c**4*f*tan(e/2 + f*x/2)**5 - 1225*c**4*f*tan(e/2 + f*x/2)**4 + 1225*c**4*f*tan(e/2 + f*x/2)**3 - 735*c**4*f*tan(e/2 + f*x/2)**2 + 245*c**4*f*tan(e/2 + f*x/2) - 35*c**4*f) - 182*A*a**2*tan(e/2 + f*x/2)**2/(35*c**4*f*tan(e/2 + f*x/2)**7 - 245*c**4*f*tan(e/2 + f*x/2)**6 + 735*c**4*f*tan(e/2 + f*x/2)**5 - 1225*c**4*f*tan(e/2 + f*x/2)**4 + 1225*c**4*f*tan(e/2 + f*x/2)**3 - 735*c**4*f*tan(e/2 + f*x/2)**2 + 245*c**4*f*tan(e/2 + f*x/2) - 35*c**4*f) + 14*A*a**2*tan(e/2 + f*x/2)/(35*c**4*f*tan(e/2 + f*x/2)**7 - 245*c**4*f*tan(e/2 + f*x/2)**6 + 735*c**4*f*tan(e/2 + f*x/2)**5 - 1225*c**4*f*tan(e/2 + f*x/2)**4 + 1225*c**4*f*tan(e/2 + f*x/2)**3 - 735*c**4*f*tan(e/2 + f*x/2)**2 + 245*c**4*f*tan(e/2 + f*x/2) - 35*c**4*f) - 12*A*a**2/(35*c**4*f*tan(e/2 + f*x/2)**7 - 245*c**4*f*tan(e/2 + f*x/2)**6 + 735*c**4*f*tan(e/2 + f*x/2)**5 - 1225*c**4*f*tan(e/2 + f*x/2)**4 + 1225*c**4*f*tan(e/2 + f*x/2)**3 - 735*c**4*f*tan(e/2 + f*x/2)**2 + 245*c**4*f*tan(e/2 + f*x/2) - 35*c**4*f) - 70*B*a**2*tan(e/2 + f*x/2)**5/(35*c**4*f*tan(e/2 + f*x/2)**7 - 245*c**4*f*tan(e/2 + f*x/2)**6 + 735*c**4*f*tan(e/2 + f*x/2)**5 - 1225*c**4*f*tan(e/2 + f*x/2)**4 + 1225*c**4*f*tan(e/2 + f*x/2)**3 - 735*c**4*f*tan(e/2 + f*x/2)**2 + 245*c**4*f*tan(e/2 + f*x/2) - 35*c**4*f) - 70*B*a**2*tan(e/2 + f*x/2)**4/(35*c**4*f*tan(e/2 + f*x/2)**7 - 245*c**4*f*tan(e/2 + f*x/2)**6 + 735*c**4*f*tan(e/2 + f*x/2)**5 - 1225*c**4*f*tan(e/2 + f*x/2)**4 + 1225*c**4*f*tan(e/2 + f*x/2)**3 - 735*c**4*f*tan(e/2 + f*x/2)**2 + 245*c**4*f*tan(e/2 + f*x/2) - 35*c**4*f) - 140*B*a**2*tan(e/2 + f*x/2)**3/(35*c**4*f*tan(e/2 + f*x/2)**7 - 245*c**4*f*tan(e/2 + f*x/2)**6 + 735*c**4*f*tan(e/2 + f*x/2)**5 - 1225*c**4*f*tan(e/2 + f*x/2)**4 + 1225*c**4*f*tan(e/2 + f*x/2)**3 - 735*c**4*f*tan(e/2 + f*x/2)**2 + 245*c**4*f*tan(e/2 + f*x/2) - 35*c**4*f) - 28*B*a**2*tan(e/2 + f*x/2)**2/(35*c**4*f*tan(e/2 + f*x/2)**7 - 245*c**4*f*tan(e/2 + f*x/2)**6 + 735*c**4*f*tan(e/2 + f*x/2)**5 - 1225*c**4*f*tan(e/2 + f*x/2)**4 + 1225*c**4*f*tan(e/2 + f*x/2)**3 - 735*c**4*f*tan(e/2 + f*x/2)**2 + 245*c**4*f*tan(e/2 + f*x/2) - 35*c**4*f) - 14*B*a**2*tan(e/2 + f*x/2)/(35*c**4*f*tan(e/2 + f*x/2)**7 - 245*c**4*f*tan(e/2 + f*x/2)**6 + 735*c**4*f*tan(e/2 + f*x/2)**5 - 1225*c**4*f*tan(e/2 + f*x/2)**4 + 1225*c**4*f*tan(e/2 + f*x/2)**3 - 735*c**4*f*tan(e/2 + f*x/2)**2 + 245*c**4*f*tan(e/2 + f*x/2) - 35*c**4*f) + 2*B*a**2/(35*c**4*f*tan(e/2 + f*x/2)**7 - 245*c**4*f*tan(e/2 + f*x/2)**6 + 735*c**4*f*tan(e/2 + f*x/2)**5 - 1225*c**4*f*tan(e/2 + f*x/2)**4 + 1225*c**4*f*tan(e/2 + f*x/2)**3 - 735*c**4*f*tan(e/2 + f*x/2)**2 + 245*c**4*f*tan(e/2 + f*x/2) - 35*c**4*f), Ne(f, 0)), (x*(A + B*sin(e))*(a*sin(e) + a)**2/(-c*sin(e) + c)**4, True))","A",0
35,1,3262,0,78.088470," ","integrate((a+a*sin(f*x+e))**2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**5,x)","\begin{cases} - \frac{630 A a^{2} \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2835 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 26460 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39690 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 11340 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 c^{5} f} + \frac{1260 A a^{2} \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2835 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 26460 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39690 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 11340 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 c^{5} f} - \frac{4620 A a^{2} \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2835 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 26460 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39690 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 11340 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 c^{5} f} + \frac{5040 A a^{2} \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2835 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 26460 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39690 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 11340 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 c^{5} f} - \frac{6804 A a^{2} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2835 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 26460 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39690 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 11340 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 c^{5} f} + \frac{3276 A a^{2} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2835 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 26460 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39690 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 11340 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 c^{5} f} - \frac{2124 A a^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2835 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 26460 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39690 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 11340 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 c^{5} f} + \frac{216 A a^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2835 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 26460 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39690 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 11340 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 c^{5} f} - \frac{94 A a^{2}}{315 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2835 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 26460 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39690 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 11340 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 c^{5} f} - \frac{630 B a^{2} \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2835 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 26460 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39690 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 11340 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 c^{5} f} - \frac{210 B a^{2} \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2835 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 26460 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39690 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 11340 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 c^{5} f} - \frac{1890 B a^{2} \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2835 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 26460 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39690 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 11340 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 c^{5} f} - \frac{126 B a^{2} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2835 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 26460 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39690 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 11340 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 c^{5} f} - \frac{1386 B a^{2} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2835 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 26460 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39690 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 11340 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 c^{5} f} - \frac{126 B a^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2835 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 26460 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39690 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 11340 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 c^{5} f} - \frac{126 B a^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2835 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 26460 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39690 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 11340 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 c^{5} f} + \frac{14 B a^{2}}{315 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2835 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 26460 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39690 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 11340 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 c^{5} f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right) \left(a \sin{\left(e \right)} + a\right)^{2}}{\left(- c \sin{\left(e \right)} + c\right)^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-630*A*a**2*tan(e/2 + f*x/2)**8/(315*c**5*f*tan(e/2 + f*x/2)**9 - 2835*c**5*f*tan(e/2 + f*x/2)**8 + 11340*c**5*f*tan(e/2 + f*x/2)**7 - 26460*c**5*f*tan(e/2 + f*x/2)**6 + 39690*c**5*f*tan(e/2 + f*x/2)**5 - 39690*c**5*f*tan(e/2 + f*x/2)**4 + 26460*c**5*f*tan(e/2 + f*x/2)**3 - 11340*c**5*f*tan(e/2 + f*x/2)**2 + 2835*c**5*f*tan(e/2 + f*x/2) - 315*c**5*f) + 1260*A*a**2*tan(e/2 + f*x/2)**7/(315*c**5*f*tan(e/2 + f*x/2)**9 - 2835*c**5*f*tan(e/2 + f*x/2)**8 + 11340*c**5*f*tan(e/2 + f*x/2)**7 - 26460*c**5*f*tan(e/2 + f*x/2)**6 + 39690*c**5*f*tan(e/2 + f*x/2)**5 - 39690*c**5*f*tan(e/2 + f*x/2)**4 + 26460*c**5*f*tan(e/2 + f*x/2)**3 - 11340*c**5*f*tan(e/2 + f*x/2)**2 + 2835*c**5*f*tan(e/2 + f*x/2) - 315*c**5*f) - 4620*A*a**2*tan(e/2 + f*x/2)**6/(315*c**5*f*tan(e/2 + f*x/2)**9 - 2835*c**5*f*tan(e/2 + f*x/2)**8 + 11340*c**5*f*tan(e/2 + f*x/2)**7 - 26460*c**5*f*tan(e/2 + f*x/2)**6 + 39690*c**5*f*tan(e/2 + f*x/2)**5 - 39690*c**5*f*tan(e/2 + f*x/2)**4 + 26460*c**5*f*tan(e/2 + f*x/2)**3 - 11340*c**5*f*tan(e/2 + f*x/2)**2 + 2835*c**5*f*tan(e/2 + f*x/2) - 315*c**5*f) + 5040*A*a**2*tan(e/2 + f*x/2)**5/(315*c**5*f*tan(e/2 + f*x/2)**9 - 2835*c**5*f*tan(e/2 + f*x/2)**8 + 11340*c**5*f*tan(e/2 + f*x/2)**7 - 26460*c**5*f*tan(e/2 + f*x/2)**6 + 39690*c**5*f*tan(e/2 + f*x/2)**5 - 39690*c**5*f*tan(e/2 + f*x/2)**4 + 26460*c**5*f*tan(e/2 + f*x/2)**3 - 11340*c**5*f*tan(e/2 + f*x/2)**2 + 2835*c**5*f*tan(e/2 + f*x/2) - 315*c**5*f) - 6804*A*a**2*tan(e/2 + f*x/2)**4/(315*c**5*f*tan(e/2 + f*x/2)**9 - 2835*c**5*f*tan(e/2 + f*x/2)**8 + 11340*c**5*f*tan(e/2 + f*x/2)**7 - 26460*c**5*f*tan(e/2 + f*x/2)**6 + 39690*c**5*f*tan(e/2 + f*x/2)**5 - 39690*c**5*f*tan(e/2 + f*x/2)**4 + 26460*c**5*f*tan(e/2 + f*x/2)**3 - 11340*c**5*f*tan(e/2 + f*x/2)**2 + 2835*c**5*f*tan(e/2 + f*x/2) - 315*c**5*f) + 3276*A*a**2*tan(e/2 + f*x/2)**3/(315*c**5*f*tan(e/2 + f*x/2)**9 - 2835*c**5*f*tan(e/2 + f*x/2)**8 + 11340*c**5*f*tan(e/2 + f*x/2)**7 - 26460*c**5*f*tan(e/2 + f*x/2)**6 + 39690*c**5*f*tan(e/2 + f*x/2)**5 - 39690*c**5*f*tan(e/2 + f*x/2)**4 + 26460*c**5*f*tan(e/2 + f*x/2)**3 - 11340*c**5*f*tan(e/2 + f*x/2)**2 + 2835*c**5*f*tan(e/2 + f*x/2) - 315*c**5*f) - 2124*A*a**2*tan(e/2 + f*x/2)**2/(315*c**5*f*tan(e/2 + f*x/2)**9 - 2835*c**5*f*tan(e/2 + f*x/2)**8 + 11340*c**5*f*tan(e/2 + f*x/2)**7 - 26460*c**5*f*tan(e/2 + f*x/2)**6 + 39690*c**5*f*tan(e/2 + f*x/2)**5 - 39690*c**5*f*tan(e/2 + f*x/2)**4 + 26460*c**5*f*tan(e/2 + f*x/2)**3 - 11340*c**5*f*tan(e/2 + f*x/2)**2 + 2835*c**5*f*tan(e/2 + f*x/2) - 315*c**5*f) + 216*A*a**2*tan(e/2 + f*x/2)/(315*c**5*f*tan(e/2 + f*x/2)**9 - 2835*c**5*f*tan(e/2 + f*x/2)**8 + 11340*c**5*f*tan(e/2 + f*x/2)**7 - 26460*c**5*f*tan(e/2 + f*x/2)**6 + 39690*c**5*f*tan(e/2 + f*x/2)**5 - 39690*c**5*f*tan(e/2 + f*x/2)**4 + 26460*c**5*f*tan(e/2 + f*x/2)**3 - 11340*c**5*f*tan(e/2 + f*x/2)**2 + 2835*c**5*f*tan(e/2 + f*x/2) - 315*c**5*f) - 94*A*a**2/(315*c**5*f*tan(e/2 + f*x/2)**9 - 2835*c**5*f*tan(e/2 + f*x/2)**8 + 11340*c**5*f*tan(e/2 + f*x/2)**7 - 26460*c**5*f*tan(e/2 + f*x/2)**6 + 39690*c**5*f*tan(e/2 + f*x/2)**5 - 39690*c**5*f*tan(e/2 + f*x/2)**4 + 26460*c**5*f*tan(e/2 + f*x/2)**3 - 11340*c**5*f*tan(e/2 + f*x/2)**2 + 2835*c**5*f*tan(e/2 + f*x/2) - 315*c**5*f) - 630*B*a**2*tan(e/2 + f*x/2)**7/(315*c**5*f*tan(e/2 + f*x/2)**9 - 2835*c**5*f*tan(e/2 + f*x/2)**8 + 11340*c**5*f*tan(e/2 + f*x/2)**7 - 26460*c**5*f*tan(e/2 + f*x/2)**6 + 39690*c**5*f*tan(e/2 + f*x/2)**5 - 39690*c**5*f*tan(e/2 + f*x/2)**4 + 26460*c**5*f*tan(e/2 + f*x/2)**3 - 11340*c**5*f*tan(e/2 + f*x/2)**2 + 2835*c**5*f*tan(e/2 + f*x/2) - 315*c**5*f) - 210*B*a**2*tan(e/2 + f*x/2)**6/(315*c**5*f*tan(e/2 + f*x/2)**9 - 2835*c**5*f*tan(e/2 + f*x/2)**8 + 11340*c**5*f*tan(e/2 + f*x/2)**7 - 26460*c**5*f*tan(e/2 + f*x/2)**6 + 39690*c**5*f*tan(e/2 + f*x/2)**5 - 39690*c**5*f*tan(e/2 + f*x/2)**4 + 26460*c**5*f*tan(e/2 + f*x/2)**3 - 11340*c**5*f*tan(e/2 + f*x/2)**2 + 2835*c**5*f*tan(e/2 + f*x/2) - 315*c**5*f) - 1890*B*a**2*tan(e/2 + f*x/2)**5/(315*c**5*f*tan(e/2 + f*x/2)**9 - 2835*c**5*f*tan(e/2 + f*x/2)**8 + 11340*c**5*f*tan(e/2 + f*x/2)**7 - 26460*c**5*f*tan(e/2 + f*x/2)**6 + 39690*c**5*f*tan(e/2 + f*x/2)**5 - 39690*c**5*f*tan(e/2 + f*x/2)**4 + 26460*c**5*f*tan(e/2 + f*x/2)**3 - 11340*c**5*f*tan(e/2 + f*x/2)**2 + 2835*c**5*f*tan(e/2 + f*x/2) - 315*c**5*f) - 126*B*a**2*tan(e/2 + f*x/2)**4/(315*c**5*f*tan(e/2 + f*x/2)**9 - 2835*c**5*f*tan(e/2 + f*x/2)**8 + 11340*c**5*f*tan(e/2 + f*x/2)**7 - 26460*c**5*f*tan(e/2 + f*x/2)**6 + 39690*c**5*f*tan(e/2 + f*x/2)**5 - 39690*c**5*f*tan(e/2 + f*x/2)**4 + 26460*c**5*f*tan(e/2 + f*x/2)**3 - 11340*c**5*f*tan(e/2 + f*x/2)**2 + 2835*c**5*f*tan(e/2 + f*x/2) - 315*c**5*f) - 1386*B*a**2*tan(e/2 + f*x/2)**3/(315*c**5*f*tan(e/2 + f*x/2)**9 - 2835*c**5*f*tan(e/2 + f*x/2)**8 + 11340*c**5*f*tan(e/2 + f*x/2)**7 - 26460*c**5*f*tan(e/2 + f*x/2)**6 + 39690*c**5*f*tan(e/2 + f*x/2)**5 - 39690*c**5*f*tan(e/2 + f*x/2)**4 + 26460*c**5*f*tan(e/2 + f*x/2)**3 - 11340*c**5*f*tan(e/2 + f*x/2)**2 + 2835*c**5*f*tan(e/2 + f*x/2) - 315*c**5*f) - 126*B*a**2*tan(e/2 + f*x/2)**2/(315*c**5*f*tan(e/2 + f*x/2)**9 - 2835*c**5*f*tan(e/2 + f*x/2)**8 + 11340*c**5*f*tan(e/2 + f*x/2)**7 - 26460*c**5*f*tan(e/2 + f*x/2)**6 + 39690*c**5*f*tan(e/2 + f*x/2)**5 - 39690*c**5*f*tan(e/2 + f*x/2)**4 + 26460*c**5*f*tan(e/2 + f*x/2)**3 - 11340*c**5*f*tan(e/2 + f*x/2)**2 + 2835*c**5*f*tan(e/2 + f*x/2) - 315*c**5*f) - 126*B*a**2*tan(e/2 + f*x/2)/(315*c**5*f*tan(e/2 + f*x/2)**9 - 2835*c**5*f*tan(e/2 + f*x/2)**8 + 11340*c**5*f*tan(e/2 + f*x/2)**7 - 26460*c**5*f*tan(e/2 + f*x/2)**6 + 39690*c**5*f*tan(e/2 + f*x/2)**5 - 39690*c**5*f*tan(e/2 + f*x/2)**4 + 26460*c**5*f*tan(e/2 + f*x/2)**3 - 11340*c**5*f*tan(e/2 + f*x/2)**2 + 2835*c**5*f*tan(e/2 + f*x/2) - 315*c**5*f) + 14*B*a**2/(315*c**5*f*tan(e/2 + f*x/2)**9 - 2835*c**5*f*tan(e/2 + f*x/2)**8 + 11340*c**5*f*tan(e/2 + f*x/2)**7 - 26460*c**5*f*tan(e/2 + f*x/2)**6 + 39690*c**5*f*tan(e/2 + f*x/2)**5 - 39690*c**5*f*tan(e/2 + f*x/2)**4 + 26460*c**5*f*tan(e/2 + f*x/2)**3 - 11340*c**5*f*tan(e/2 + f*x/2)**2 + 2835*c**5*f*tan(e/2 + f*x/2) - 315*c**5*f), Ne(f, 0)), (x*(A + B*sin(e))*(a*sin(e) + a)**2/(-c*sin(e) + c)**5, True))","A",0
36,1,4816,0,125.915421," ","integrate((a+a*sin(f*x+e))**2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**6,x)","\begin{cases} - \frac{6930 A a^{2} \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3465 c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 38115 c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 190575 c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 571725 c^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1143450 c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1600830 c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1600830 c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1143450 c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 571725 c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 190575 c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 38115 c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3465 c^{6} f} + \frac{20790 A a^{2} \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3465 c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 38115 c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 190575 c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 571725 c^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1143450 c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1600830 c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1600830 c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1143450 c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 571725 c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 190575 c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 38115 c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3465 c^{6} f} - \frac{83160 A a^{2} \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3465 c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 38115 c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 190575 c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 571725 c^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1143450 c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1600830 c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1600830 c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1143450 c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 571725 c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 190575 c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 38115 c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3465 c^{6} f} + \frac{138600 A a^{2} \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3465 c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 38115 c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 190575 c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 571725 c^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1143450 c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1600830 c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1600830 c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1143450 c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 571725 c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 190575 c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 38115 c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3465 c^{6} f} - \frac{224532 A a^{2} \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3465 c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 38115 c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 190575 c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 571725 c^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1143450 c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1600830 c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1600830 c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1143450 c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 571725 c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 190575 c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 38115 c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3465 c^{6} f} + \frac{196812 A a^{2} \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3465 c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 38115 c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 190575 c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 571725 c^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1143450 c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1600830 c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1600830 c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1143450 c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 571725 c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 190575 c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 38115 c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3465 c^{6} f} - \frac{162360 A a^{2} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3465 c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 38115 c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 190575 c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 571725 c^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1143450 c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1600830 c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1600830 c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1143450 c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 571725 c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 190575 c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 38115 c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3465 c^{6} f} + \frac{67320 A a^{2} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3465 c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 38115 c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 190575 c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 571725 c^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1143450 c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1600830 c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1600830 c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1143450 c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 571725 c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 190575 c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 38115 c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3465 c^{6} f} - \frac{29370 A a^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3465 c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 38115 c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 190575 c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 571725 c^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1143450 c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1600830 c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1600830 c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1143450 c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 571725 c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 190575 c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 38115 c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3465 c^{6} f} + \frac{3102 A a^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3465 c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 38115 c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 190575 c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 571725 c^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1143450 c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1600830 c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1600830 c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1143450 c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 571725 c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 190575 c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 38115 c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3465 c^{6} f} - \frac{912 A a^{2}}{3465 c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 38115 c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 190575 c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 571725 c^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1143450 c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1600830 c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1600830 c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1143450 c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 571725 c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 190575 c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 38115 c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3465 c^{6} f} - \frac{6930 B a^{2} \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3465 c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 38115 c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 190575 c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 571725 c^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1143450 c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1600830 c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1600830 c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1143450 c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 571725 c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 190575 c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 38115 c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3465 c^{6} f} + \frac{2310 B a^{2} \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3465 c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 38115 c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 190575 c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 571725 c^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1143450 c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1600830 c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1600830 c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1143450 c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 571725 c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 190575 c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 38115 c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3465 c^{6} f} - \frac{32340 B a^{2} \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3465 c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 38115 c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 190575 c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 571725 c^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1143450 c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1600830 c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1600830 c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1143450 c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 571725 c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 190575 c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 38115 c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3465 c^{6} f} + \frac{12012 B a^{2} \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3465 c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 38115 c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 190575 c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 571725 c^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1143450 c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1600830 c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1600830 c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1143450 c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 571725 c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 190575 c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 38115 c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3465 c^{6} f} - \frac{44352 B a^{2} \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3465 c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 38115 c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 190575 c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 571725 c^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1143450 c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1600830 c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1600830 c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1143450 c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 571725 c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 190575 c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 38115 c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3465 c^{6} f} + \frac{7920 B a^{2} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3465 c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 38115 c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 190575 c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 571725 c^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1143450 c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1600830 c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1600830 c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1143450 c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 571725 c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 190575 c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 38115 c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3465 c^{6} f} - \frac{17820 B a^{2} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3465 c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 38115 c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 190575 c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 571725 c^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1143450 c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1600830 c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1600830 c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1143450 c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 571725 c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 190575 c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 38115 c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3465 c^{6} f} - \frac{220 B a^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3465 c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 38115 c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 190575 c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 571725 c^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1143450 c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1600830 c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1600830 c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1143450 c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 571725 c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 190575 c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 38115 c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3465 c^{6} f} - \frac{1342 B a^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3465 c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 38115 c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 190575 c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 571725 c^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1143450 c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1600830 c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1600830 c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1143450 c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 571725 c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 190575 c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 38115 c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3465 c^{6} f} + \frac{122 B a^{2}}{3465 c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 38115 c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 190575 c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 571725 c^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1143450 c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1600830 c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1600830 c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1143450 c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 571725 c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 190575 c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 38115 c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3465 c^{6} f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right) \left(a \sin{\left(e \right)} + a\right)^{2}}{\left(- c \sin{\left(e \right)} + c\right)^{6}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-6930*A*a**2*tan(e/2 + f*x/2)**10/(3465*c**6*f*tan(e/2 + f*x/2)**11 - 38115*c**6*f*tan(e/2 + f*x/2)**10 + 190575*c**6*f*tan(e/2 + f*x/2)**9 - 571725*c**6*f*tan(e/2 + f*x/2)**8 + 1143450*c**6*f*tan(e/2 + f*x/2)**7 - 1600830*c**6*f*tan(e/2 + f*x/2)**6 + 1600830*c**6*f*tan(e/2 + f*x/2)**5 - 1143450*c**6*f*tan(e/2 + f*x/2)**4 + 571725*c**6*f*tan(e/2 + f*x/2)**3 - 190575*c**6*f*tan(e/2 + f*x/2)**2 + 38115*c**6*f*tan(e/2 + f*x/2) - 3465*c**6*f) + 20790*A*a**2*tan(e/2 + f*x/2)**9/(3465*c**6*f*tan(e/2 + f*x/2)**11 - 38115*c**6*f*tan(e/2 + f*x/2)**10 + 190575*c**6*f*tan(e/2 + f*x/2)**9 - 571725*c**6*f*tan(e/2 + f*x/2)**8 + 1143450*c**6*f*tan(e/2 + f*x/2)**7 - 1600830*c**6*f*tan(e/2 + f*x/2)**6 + 1600830*c**6*f*tan(e/2 + f*x/2)**5 - 1143450*c**6*f*tan(e/2 + f*x/2)**4 + 571725*c**6*f*tan(e/2 + f*x/2)**3 - 190575*c**6*f*tan(e/2 + f*x/2)**2 + 38115*c**6*f*tan(e/2 + f*x/2) - 3465*c**6*f) - 83160*A*a**2*tan(e/2 + f*x/2)**8/(3465*c**6*f*tan(e/2 + f*x/2)**11 - 38115*c**6*f*tan(e/2 + f*x/2)**10 + 190575*c**6*f*tan(e/2 + f*x/2)**9 - 571725*c**6*f*tan(e/2 + f*x/2)**8 + 1143450*c**6*f*tan(e/2 + f*x/2)**7 - 1600830*c**6*f*tan(e/2 + f*x/2)**6 + 1600830*c**6*f*tan(e/2 + f*x/2)**5 - 1143450*c**6*f*tan(e/2 + f*x/2)**4 + 571725*c**6*f*tan(e/2 + f*x/2)**3 - 190575*c**6*f*tan(e/2 + f*x/2)**2 + 38115*c**6*f*tan(e/2 + f*x/2) - 3465*c**6*f) + 138600*A*a**2*tan(e/2 + f*x/2)**7/(3465*c**6*f*tan(e/2 + f*x/2)**11 - 38115*c**6*f*tan(e/2 + f*x/2)**10 + 190575*c**6*f*tan(e/2 + f*x/2)**9 - 571725*c**6*f*tan(e/2 + f*x/2)**8 + 1143450*c**6*f*tan(e/2 + f*x/2)**7 - 1600830*c**6*f*tan(e/2 + f*x/2)**6 + 1600830*c**6*f*tan(e/2 + f*x/2)**5 - 1143450*c**6*f*tan(e/2 + f*x/2)**4 + 571725*c**6*f*tan(e/2 + f*x/2)**3 - 190575*c**6*f*tan(e/2 + f*x/2)**2 + 38115*c**6*f*tan(e/2 + f*x/2) - 3465*c**6*f) - 224532*A*a**2*tan(e/2 + f*x/2)**6/(3465*c**6*f*tan(e/2 + f*x/2)**11 - 38115*c**6*f*tan(e/2 + f*x/2)**10 + 190575*c**6*f*tan(e/2 + f*x/2)**9 - 571725*c**6*f*tan(e/2 + f*x/2)**8 + 1143450*c**6*f*tan(e/2 + f*x/2)**7 - 1600830*c**6*f*tan(e/2 + f*x/2)**6 + 1600830*c**6*f*tan(e/2 + f*x/2)**5 - 1143450*c**6*f*tan(e/2 + f*x/2)**4 + 571725*c**6*f*tan(e/2 + f*x/2)**3 - 190575*c**6*f*tan(e/2 + f*x/2)**2 + 38115*c**6*f*tan(e/2 + f*x/2) - 3465*c**6*f) + 196812*A*a**2*tan(e/2 + f*x/2)**5/(3465*c**6*f*tan(e/2 + f*x/2)**11 - 38115*c**6*f*tan(e/2 + f*x/2)**10 + 190575*c**6*f*tan(e/2 + f*x/2)**9 - 571725*c**6*f*tan(e/2 + f*x/2)**8 + 1143450*c**6*f*tan(e/2 + f*x/2)**7 - 1600830*c**6*f*tan(e/2 + f*x/2)**6 + 1600830*c**6*f*tan(e/2 + f*x/2)**5 - 1143450*c**6*f*tan(e/2 + f*x/2)**4 + 571725*c**6*f*tan(e/2 + f*x/2)**3 - 190575*c**6*f*tan(e/2 + f*x/2)**2 + 38115*c**6*f*tan(e/2 + f*x/2) - 3465*c**6*f) - 162360*A*a**2*tan(e/2 + f*x/2)**4/(3465*c**6*f*tan(e/2 + f*x/2)**11 - 38115*c**6*f*tan(e/2 + f*x/2)**10 + 190575*c**6*f*tan(e/2 + f*x/2)**9 - 571725*c**6*f*tan(e/2 + f*x/2)**8 + 1143450*c**6*f*tan(e/2 + f*x/2)**7 - 1600830*c**6*f*tan(e/2 + f*x/2)**6 + 1600830*c**6*f*tan(e/2 + f*x/2)**5 - 1143450*c**6*f*tan(e/2 + f*x/2)**4 + 571725*c**6*f*tan(e/2 + f*x/2)**3 - 190575*c**6*f*tan(e/2 + f*x/2)**2 + 38115*c**6*f*tan(e/2 + f*x/2) - 3465*c**6*f) + 67320*A*a**2*tan(e/2 + f*x/2)**3/(3465*c**6*f*tan(e/2 + f*x/2)**11 - 38115*c**6*f*tan(e/2 + f*x/2)**10 + 190575*c**6*f*tan(e/2 + f*x/2)**9 - 571725*c**6*f*tan(e/2 + f*x/2)**8 + 1143450*c**6*f*tan(e/2 + f*x/2)**7 - 1600830*c**6*f*tan(e/2 + f*x/2)**6 + 1600830*c**6*f*tan(e/2 + f*x/2)**5 - 1143450*c**6*f*tan(e/2 + f*x/2)**4 + 571725*c**6*f*tan(e/2 + f*x/2)**3 - 190575*c**6*f*tan(e/2 + f*x/2)**2 + 38115*c**6*f*tan(e/2 + f*x/2) - 3465*c**6*f) - 29370*A*a**2*tan(e/2 + f*x/2)**2/(3465*c**6*f*tan(e/2 + f*x/2)**11 - 38115*c**6*f*tan(e/2 + f*x/2)**10 + 190575*c**6*f*tan(e/2 + f*x/2)**9 - 571725*c**6*f*tan(e/2 + f*x/2)**8 + 1143450*c**6*f*tan(e/2 + f*x/2)**7 - 1600830*c**6*f*tan(e/2 + f*x/2)**6 + 1600830*c**6*f*tan(e/2 + f*x/2)**5 - 1143450*c**6*f*tan(e/2 + f*x/2)**4 + 571725*c**6*f*tan(e/2 + f*x/2)**3 - 190575*c**6*f*tan(e/2 + f*x/2)**2 + 38115*c**6*f*tan(e/2 + f*x/2) - 3465*c**6*f) + 3102*A*a**2*tan(e/2 + f*x/2)/(3465*c**6*f*tan(e/2 + f*x/2)**11 - 38115*c**6*f*tan(e/2 + f*x/2)**10 + 190575*c**6*f*tan(e/2 + f*x/2)**9 - 571725*c**6*f*tan(e/2 + f*x/2)**8 + 1143450*c**6*f*tan(e/2 + f*x/2)**7 - 1600830*c**6*f*tan(e/2 + f*x/2)**6 + 1600830*c**6*f*tan(e/2 + f*x/2)**5 - 1143450*c**6*f*tan(e/2 + f*x/2)**4 + 571725*c**6*f*tan(e/2 + f*x/2)**3 - 190575*c**6*f*tan(e/2 + f*x/2)**2 + 38115*c**6*f*tan(e/2 + f*x/2) - 3465*c**6*f) - 912*A*a**2/(3465*c**6*f*tan(e/2 + f*x/2)**11 - 38115*c**6*f*tan(e/2 + f*x/2)**10 + 190575*c**6*f*tan(e/2 + f*x/2)**9 - 571725*c**6*f*tan(e/2 + f*x/2)**8 + 1143450*c**6*f*tan(e/2 + f*x/2)**7 - 1600830*c**6*f*tan(e/2 + f*x/2)**6 + 1600830*c**6*f*tan(e/2 + f*x/2)**5 - 1143450*c**6*f*tan(e/2 + f*x/2)**4 + 571725*c**6*f*tan(e/2 + f*x/2)**3 - 190575*c**6*f*tan(e/2 + f*x/2)**2 + 38115*c**6*f*tan(e/2 + f*x/2) - 3465*c**6*f) - 6930*B*a**2*tan(e/2 + f*x/2)**9/(3465*c**6*f*tan(e/2 + f*x/2)**11 - 38115*c**6*f*tan(e/2 + f*x/2)**10 + 190575*c**6*f*tan(e/2 + f*x/2)**9 - 571725*c**6*f*tan(e/2 + f*x/2)**8 + 1143450*c**6*f*tan(e/2 + f*x/2)**7 - 1600830*c**6*f*tan(e/2 + f*x/2)**6 + 1600830*c**6*f*tan(e/2 + f*x/2)**5 - 1143450*c**6*f*tan(e/2 + f*x/2)**4 + 571725*c**6*f*tan(e/2 + f*x/2)**3 - 190575*c**6*f*tan(e/2 + f*x/2)**2 + 38115*c**6*f*tan(e/2 + f*x/2) - 3465*c**6*f) + 2310*B*a**2*tan(e/2 + f*x/2)**8/(3465*c**6*f*tan(e/2 + f*x/2)**11 - 38115*c**6*f*tan(e/2 + f*x/2)**10 + 190575*c**6*f*tan(e/2 + f*x/2)**9 - 571725*c**6*f*tan(e/2 + f*x/2)**8 + 1143450*c**6*f*tan(e/2 + f*x/2)**7 - 1600830*c**6*f*tan(e/2 + f*x/2)**6 + 1600830*c**6*f*tan(e/2 + f*x/2)**5 - 1143450*c**6*f*tan(e/2 + f*x/2)**4 + 571725*c**6*f*tan(e/2 + f*x/2)**3 - 190575*c**6*f*tan(e/2 + f*x/2)**2 + 38115*c**6*f*tan(e/2 + f*x/2) - 3465*c**6*f) - 32340*B*a**2*tan(e/2 + f*x/2)**7/(3465*c**6*f*tan(e/2 + f*x/2)**11 - 38115*c**6*f*tan(e/2 + f*x/2)**10 + 190575*c**6*f*tan(e/2 + f*x/2)**9 - 571725*c**6*f*tan(e/2 + f*x/2)**8 + 1143450*c**6*f*tan(e/2 + f*x/2)**7 - 1600830*c**6*f*tan(e/2 + f*x/2)**6 + 1600830*c**6*f*tan(e/2 + f*x/2)**5 - 1143450*c**6*f*tan(e/2 + f*x/2)**4 + 571725*c**6*f*tan(e/2 + f*x/2)**3 - 190575*c**6*f*tan(e/2 + f*x/2)**2 + 38115*c**6*f*tan(e/2 + f*x/2) - 3465*c**6*f) + 12012*B*a**2*tan(e/2 + f*x/2)**6/(3465*c**6*f*tan(e/2 + f*x/2)**11 - 38115*c**6*f*tan(e/2 + f*x/2)**10 + 190575*c**6*f*tan(e/2 + f*x/2)**9 - 571725*c**6*f*tan(e/2 + f*x/2)**8 + 1143450*c**6*f*tan(e/2 + f*x/2)**7 - 1600830*c**6*f*tan(e/2 + f*x/2)**6 + 1600830*c**6*f*tan(e/2 + f*x/2)**5 - 1143450*c**6*f*tan(e/2 + f*x/2)**4 + 571725*c**6*f*tan(e/2 + f*x/2)**3 - 190575*c**6*f*tan(e/2 + f*x/2)**2 + 38115*c**6*f*tan(e/2 + f*x/2) - 3465*c**6*f) - 44352*B*a**2*tan(e/2 + f*x/2)**5/(3465*c**6*f*tan(e/2 + f*x/2)**11 - 38115*c**6*f*tan(e/2 + f*x/2)**10 + 190575*c**6*f*tan(e/2 + f*x/2)**9 - 571725*c**6*f*tan(e/2 + f*x/2)**8 + 1143450*c**6*f*tan(e/2 + f*x/2)**7 - 1600830*c**6*f*tan(e/2 + f*x/2)**6 + 1600830*c**6*f*tan(e/2 + f*x/2)**5 - 1143450*c**6*f*tan(e/2 + f*x/2)**4 + 571725*c**6*f*tan(e/2 + f*x/2)**3 - 190575*c**6*f*tan(e/2 + f*x/2)**2 + 38115*c**6*f*tan(e/2 + f*x/2) - 3465*c**6*f) + 7920*B*a**2*tan(e/2 + f*x/2)**4/(3465*c**6*f*tan(e/2 + f*x/2)**11 - 38115*c**6*f*tan(e/2 + f*x/2)**10 + 190575*c**6*f*tan(e/2 + f*x/2)**9 - 571725*c**6*f*tan(e/2 + f*x/2)**8 + 1143450*c**6*f*tan(e/2 + f*x/2)**7 - 1600830*c**6*f*tan(e/2 + f*x/2)**6 + 1600830*c**6*f*tan(e/2 + f*x/2)**5 - 1143450*c**6*f*tan(e/2 + f*x/2)**4 + 571725*c**6*f*tan(e/2 + f*x/2)**3 - 190575*c**6*f*tan(e/2 + f*x/2)**2 + 38115*c**6*f*tan(e/2 + f*x/2) - 3465*c**6*f) - 17820*B*a**2*tan(e/2 + f*x/2)**3/(3465*c**6*f*tan(e/2 + f*x/2)**11 - 38115*c**6*f*tan(e/2 + f*x/2)**10 + 190575*c**6*f*tan(e/2 + f*x/2)**9 - 571725*c**6*f*tan(e/2 + f*x/2)**8 + 1143450*c**6*f*tan(e/2 + f*x/2)**7 - 1600830*c**6*f*tan(e/2 + f*x/2)**6 + 1600830*c**6*f*tan(e/2 + f*x/2)**5 - 1143450*c**6*f*tan(e/2 + f*x/2)**4 + 571725*c**6*f*tan(e/2 + f*x/2)**3 - 190575*c**6*f*tan(e/2 + f*x/2)**2 + 38115*c**6*f*tan(e/2 + f*x/2) - 3465*c**6*f) - 220*B*a**2*tan(e/2 + f*x/2)**2/(3465*c**6*f*tan(e/2 + f*x/2)**11 - 38115*c**6*f*tan(e/2 + f*x/2)**10 + 190575*c**6*f*tan(e/2 + f*x/2)**9 - 571725*c**6*f*tan(e/2 + f*x/2)**8 + 1143450*c**6*f*tan(e/2 + f*x/2)**7 - 1600830*c**6*f*tan(e/2 + f*x/2)**6 + 1600830*c**6*f*tan(e/2 + f*x/2)**5 - 1143450*c**6*f*tan(e/2 + f*x/2)**4 + 571725*c**6*f*tan(e/2 + f*x/2)**3 - 190575*c**6*f*tan(e/2 + f*x/2)**2 + 38115*c**6*f*tan(e/2 + f*x/2) - 3465*c**6*f) - 1342*B*a**2*tan(e/2 + f*x/2)/(3465*c**6*f*tan(e/2 + f*x/2)**11 - 38115*c**6*f*tan(e/2 + f*x/2)**10 + 190575*c**6*f*tan(e/2 + f*x/2)**9 - 571725*c**6*f*tan(e/2 + f*x/2)**8 + 1143450*c**6*f*tan(e/2 + f*x/2)**7 - 1600830*c**6*f*tan(e/2 + f*x/2)**6 + 1600830*c**6*f*tan(e/2 + f*x/2)**5 - 1143450*c**6*f*tan(e/2 + f*x/2)**4 + 571725*c**6*f*tan(e/2 + f*x/2)**3 - 190575*c**6*f*tan(e/2 + f*x/2)**2 + 38115*c**6*f*tan(e/2 + f*x/2) - 3465*c**6*f) + 122*B*a**2/(3465*c**6*f*tan(e/2 + f*x/2)**11 - 38115*c**6*f*tan(e/2 + f*x/2)**10 + 190575*c**6*f*tan(e/2 + f*x/2)**9 - 571725*c**6*f*tan(e/2 + f*x/2)**8 + 1143450*c**6*f*tan(e/2 + f*x/2)**7 - 1600830*c**6*f*tan(e/2 + f*x/2)**6 + 1600830*c**6*f*tan(e/2 + f*x/2)**5 - 1143450*c**6*f*tan(e/2 + f*x/2)**4 + 571725*c**6*f*tan(e/2 + f*x/2)**3 - 190575*c**6*f*tan(e/2 + f*x/2)**2 + 38115*c**6*f*tan(e/2 + f*x/2) - 3465*c**6*f), Ne(f, 0)), (x*(A + B*sin(e))*(a*sin(e) + a)**2/(-c*sin(e) + c)**6, True))","A",0
37,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
38,1,1948,0,52.761658," ","integrate((a+a*sin(f*x+e))**3*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**6,x)","\begin{cases} - \frac{105 A a^{3} c^{6} x \sin^{8}{\left(e + f x \right)}}{128} - \frac{105 A a^{3} c^{6} x \sin^{6}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{32} + \frac{5 A a^{3} c^{6} x \sin^{6}{\left(e + f x \right)}}{2} - \frac{315 A a^{3} c^{6} x \sin^{4}{\left(e + f x \right)} \cos^{4}{\left(e + f x \right)}}{64} + \frac{15 A a^{3} c^{6} x \sin^{4}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{2} - \frac{9 A a^{3} c^{6} x \sin^{4}{\left(e + f x \right)}}{4} - \frac{105 A a^{3} c^{6} x \sin^{2}{\left(e + f x \right)} \cos^{6}{\left(e + f x \right)}}{32} + \frac{15 A a^{3} c^{6} x \sin^{2}{\left(e + f x \right)} \cos^{4}{\left(e + f x \right)}}{2} - \frac{9 A a^{3} c^{6} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{2} - \frac{105 A a^{3} c^{6} x \cos^{8}{\left(e + f x \right)}}{128} + \frac{5 A a^{3} c^{6} x \cos^{6}{\left(e + f x \right)}}{2} - \frac{9 A a^{3} c^{6} x \cos^{4}{\left(e + f x \right)}}{4} + A a^{3} c^{6} x - \frac{A a^{3} c^{6} \sin^{8}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{279 A a^{3} c^{6} \sin^{7}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{128 f} - \frac{8 A a^{3} c^{6} \sin^{6}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{3 f} + \frac{511 A a^{3} c^{6} \sin^{5}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{128 f} - \frac{11 A a^{3} c^{6} \sin^{5}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{16 A a^{3} c^{6} \sin^{4}{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{5 f} + \frac{6 A a^{3} c^{6} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{385 A a^{3} c^{6} \sin^{3}{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{128 f} - \frac{20 A a^{3} c^{6} \sin^{3}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{3 f} + \frac{15 A a^{3} c^{6} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{4 f} - \frac{64 A a^{3} c^{6} \sin^{2}{\left(e + f x \right)} \cos^{7}{\left(e + f x \right)}}{35 f} + \frac{8 A a^{3} c^{6} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{f} - \frac{8 A a^{3} c^{6} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{105 A a^{3} c^{6} \sin{\left(e + f x \right)} \cos^{7}{\left(e + f x \right)}}{128 f} - \frac{5 A a^{3} c^{6} \sin{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{2 f} + \frac{9 A a^{3} c^{6} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{4 f} - \frac{128 A a^{3} c^{6} \cos^{9}{\left(e + f x \right)}}{315 f} + \frac{16 A a^{3} c^{6} \cos^{5}{\left(e + f x \right)}}{5 f} - \frac{16 A a^{3} c^{6} \cos^{3}{\left(e + f x \right)}}{3 f} + \frac{3 A a^{3} c^{6} \cos{\left(e + f x \right)}}{f} + \frac{63 B a^{3} c^{6} x \sin^{10}{\left(e + f x \right)}}{256} + \frac{315 B a^{3} c^{6} x \sin^{8}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{256} + \frac{315 B a^{3} c^{6} x \sin^{6}{\left(e + f x \right)} \cos^{4}{\left(e + f x \right)}}{128} - \frac{15 B a^{3} c^{6} x \sin^{6}{\left(e + f x \right)}}{8} + \frac{315 B a^{3} c^{6} x \sin^{4}{\left(e + f x \right)} \cos^{6}{\left(e + f x \right)}}{128} - \frac{45 B a^{3} c^{6} x \sin^{4}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{8} + 3 B a^{3} c^{6} x \sin^{4}{\left(e + f x \right)} + \frac{315 B a^{3} c^{6} x \sin^{2}{\left(e + f x \right)} \cos^{8}{\left(e + f x \right)}}{256} - \frac{45 B a^{3} c^{6} x \sin^{2}{\left(e + f x \right)} \cos^{4}{\left(e + f x \right)}}{8} + 6 B a^{3} c^{6} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)} - \frac{3 B a^{3} c^{6} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{63 B a^{3} c^{6} x \cos^{10}{\left(e + f x \right)}}{256} - \frac{15 B a^{3} c^{6} x \cos^{6}{\left(e + f x \right)}}{8} + 3 B a^{3} c^{6} x \cos^{4}{\left(e + f x \right)} - \frac{3 B a^{3} c^{6} x \cos^{2}{\left(e + f x \right)}}{2} - \frac{193 B a^{3} c^{6} \sin^{9}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{256 f} + \frac{3 B a^{3} c^{6} \sin^{8}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{237 B a^{3} c^{6} \sin^{7}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{128 f} + \frac{8 B a^{3} c^{6} \sin^{6}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{f} - \frac{8 B a^{3} c^{6} \sin^{6}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{21 B a^{3} c^{6} \sin^{5}{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{10 f} + \frac{33 B a^{3} c^{6} \sin^{5}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} + \frac{48 B a^{3} c^{6} \sin^{4}{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{5 f} - \frac{16 B a^{3} c^{6} \sin^{4}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{f} + \frac{6 B a^{3} c^{6} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{147 B a^{3} c^{6} \sin^{3}{\left(e + f x \right)} \cos^{7}{\left(e + f x \right)}}{128 f} + \frac{5 B a^{3} c^{6} \sin^{3}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{f} - \frac{5 B a^{3} c^{6} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{192 B a^{3} c^{6} \sin^{2}{\left(e + f x \right)} \cos^{7}{\left(e + f x \right)}}{35 f} - \frac{64 B a^{3} c^{6} \sin^{2}{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{5 f} + \frac{8 B a^{3} c^{6} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{f} - \frac{63 B a^{3} c^{6} \sin{\left(e + f x \right)} \cos^{9}{\left(e + f x \right)}}{256 f} + \frac{15 B a^{3} c^{6} \sin{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{8 f} - \frac{3 B a^{3} c^{6} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{f} + \frac{3 B a^{3} c^{6} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} + \frac{128 B a^{3} c^{6} \cos^{9}{\left(e + f x \right)}}{105 f} - \frac{128 B a^{3} c^{6} \cos^{7}{\left(e + f x \right)}}{35 f} + \frac{16 B a^{3} c^{6} \cos^{5}{\left(e + f x \right)}}{5 f} - \frac{B a^{3} c^{6} \cos{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \left(A + B \sin{\left(e \right)}\right) \left(a \sin{\left(e \right)} + a\right)^{3} \left(- c \sin{\left(e \right)} + c\right)^{6} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-105*A*a**3*c**6*x*sin(e + f*x)**8/128 - 105*A*a**3*c**6*x*sin(e + f*x)**6*cos(e + f*x)**2/32 + 5*A*a**3*c**6*x*sin(e + f*x)**6/2 - 315*A*a**3*c**6*x*sin(e + f*x)**4*cos(e + f*x)**4/64 + 15*A*a**3*c**6*x*sin(e + f*x)**4*cos(e + f*x)**2/2 - 9*A*a**3*c**6*x*sin(e + f*x)**4/4 - 105*A*a**3*c**6*x*sin(e + f*x)**2*cos(e + f*x)**6/32 + 15*A*a**3*c**6*x*sin(e + f*x)**2*cos(e + f*x)**4/2 - 9*A*a**3*c**6*x*sin(e + f*x)**2*cos(e + f*x)**2/2 - 105*A*a**3*c**6*x*cos(e + f*x)**8/128 + 5*A*a**3*c**6*x*cos(e + f*x)**6/2 - 9*A*a**3*c**6*x*cos(e + f*x)**4/4 + A*a**3*c**6*x - A*a**3*c**6*sin(e + f*x)**8*cos(e + f*x)/f + 279*A*a**3*c**6*sin(e + f*x)**7*cos(e + f*x)/(128*f) - 8*A*a**3*c**6*sin(e + f*x)**6*cos(e + f*x)**3/(3*f) + 511*A*a**3*c**6*sin(e + f*x)**5*cos(e + f*x)**3/(128*f) - 11*A*a**3*c**6*sin(e + f*x)**5*cos(e + f*x)/(2*f) - 16*A*a**3*c**6*sin(e + f*x)**4*cos(e + f*x)**5/(5*f) + 6*A*a**3*c**6*sin(e + f*x)**4*cos(e + f*x)/f + 385*A*a**3*c**6*sin(e + f*x)**3*cos(e + f*x)**5/(128*f) - 20*A*a**3*c**6*sin(e + f*x)**3*cos(e + f*x)**3/(3*f) + 15*A*a**3*c**6*sin(e + f*x)**3*cos(e + f*x)/(4*f) - 64*A*a**3*c**6*sin(e + f*x)**2*cos(e + f*x)**7/(35*f) + 8*A*a**3*c**6*sin(e + f*x)**2*cos(e + f*x)**3/f - 8*A*a**3*c**6*sin(e + f*x)**2*cos(e + f*x)/f + 105*A*a**3*c**6*sin(e + f*x)*cos(e + f*x)**7/(128*f) - 5*A*a**3*c**6*sin(e + f*x)*cos(e + f*x)**5/(2*f) + 9*A*a**3*c**6*sin(e + f*x)*cos(e + f*x)**3/(4*f) - 128*A*a**3*c**6*cos(e + f*x)**9/(315*f) + 16*A*a**3*c**6*cos(e + f*x)**5/(5*f) - 16*A*a**3*c**6*cos(e + f*x)**3/(3*f) + 3*A*a**3*c**6*cos(e + f*x)/f + 63*B*a**3*c**6*x*sin(e + f*x)**10/256 + 315*B*a**3*c**6*x*sin(e + f*x)**8*cos(e + f*x)**2/256 + 315*B*a**3*c**6*x*sin(e + f*x)**6*cos(e + f*x)**4/128 - 15*B*a**3*c**6*x*sin(e + f*x)**6/8 + 315*B*a**3*c**6*x*sin(e + f*x)**4*cos(e + f*x)**6/128 - 45*B*a**3*c**6*x*sin(e + f*x)**4*cos(e + f*x)**2/8 + 3*B*a**3*c**6*x*sin(e + f*x)**4 + 315*B*a**3*c**6*x*sin(e + f*x)**2*cos(e + f*x)**8/256 - 45*B*a**3*c**6*x*sin(e + f*x)**2*cos(e + f*x)**4/8 + 6*B*a**3*c**6*x*sin(e + f*x)**2*cos(e + f*x)**2 - 3*B*a**3*c**6*x*sin(e + f*x)**2/2 + 63*B*a**3*c**6*x*cos(e + f*x)**10/256 - 15*B*a**3*c**6*x*cos(e + f*x)**6/8 + 3*B*a**3*c**6*x*cos(e + f*x)**4 - 3*B*a**3*c**6*x*cos(e + f*x)**2/2 - 193*B*a**3*c**6*sin(e + f*x)**9*cos(e + f*x)/(256*f) + 3*B*a**3*c**6*sin(e + f*x)**8*cos(e + f*x)/f - 237*B*a**3*c**6*sin(e + f*x)**7*cos(e + f*x)**3/(128*f) + 8*B*a**3*c**6*sin(e + f*x)**6*cos(e + f*x)**3/f - 8*B*a**3*c**6*sin(e + f*x)**6*cos(e + f*x)/f - 21*B*a**3*c**6*sin(e + f*x)**5*cos(e + f*x)**5/(10*f) + 33*B*a**3*c**6*sin(e + f*x)**5*cos(e + f*x)/(8*f) + 48*B*a**3*c**6*sin(e + f*x)**4*cos(e + f*x)**5/(5*f) - 16*B*a**3*c**6*sin(e + f*x)**4*cos(e + f*x)**3/f + 6*B*a**3*c**6*sin(e + f*x)**4*cos(e + f*x)/f - 147*B*a**3*c**6*sin(e + f*x)**3*cos(e + f*x)**7/(128*f) + 5*B*a**3*c**6*sin(e + f*x)**3*cos(e + f*x)**3/f - 5*B*a**3*c**6*sin(e + f*x)**3*cos(e + f*x)/f + 192*B*a**3*c**6*sin(e + f*x)**2*cos(e + f*x)**7/(35*f) - 64*B*a**3*c**6*sin(e + f*x)**2*cos(e + f*x)**5/(5*f) + 8*B*a**3*c**6*sin(e + f*x)**2*cos(e + f*x)**3/f - 63*B*a**3*c**6*sin(e + f*x)*cos(e + f*x)**9/(256*f) + 15*B*a**3*c**6*sin(e + f*x)*cos(e + f*x)**5/(8*f) - 3*B*a**3*c**6*sin(e + f*x)*cos(e + f*x)**3/f + 3*B*a**3*c**6*sin(e + f*x)*cos(e + f*x)/(2*f) + 128*B*a**3*c**6*cos(e + f*x)**9/(105*f) - 128*B*a**3*c**6*cos(e + f*x)**7/(35*f) + 16*B*a**3*c**6*cos(e + f*x)**5/(5*f) - B*a**3*c**6*cos(e + f*x)/f, Ne(f, 0)), (x*(A + B*sin(e))*(a*sin(e) + a)**3*(-c*sin(e) + c)**6, True))","A",0
39,1,1753,0,37.384070," ","integrate((a+a*sin(f*x+e))**3*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**5,x)","\begin{cases} - \frac{35 A a^{3} c^{5} x \sin^{8}{\left(e + f x \right)}}{128} - \frac{35 A a^{3} c^{5} x \sin^{6}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{32} + \frac{5 A a^{3} c^{5} x \sin^{6}{\left(e + f x \right)}}{8} - \frac{105 A a^{3} c^{5} x \sin^{4}{\left(e + f x \right)} \cos^{4}{\left(e + f x \right)}}{64} + \frac{15 A a^{3} c^{5} x \sin^{4}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{8} - \frac{35 A a^{3} c^{5} x \sin^{2}{\left(e + f x \right)} \cos^{6}{\left(e + f x \right)}}{32} + \frac{15 A a^{3} c^{5} x \sin^{2}{\left(e + f x \right)} \cos^{4}{\left(e + f x \right)}}{8} - A a^{3} c^{5} x \sin^{2}{\left(e + f x \right)} - \frac{35 A a^{3} c^{5} x \cos^{8}{\left(e + f x \right)}}{128} + \frac{5 A a^{3} c^{5} x \cos^{6}{\left(e + f x \right)}}{8} - A a^{3} c^{5} x \cos^{2}{\left(e + f x \right)} + A a^{3} c^{5} x + \frac{93 A a^{3} c^{5} \sin^{7}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{128 f} - \frac{2 A a^{3} c^{5} \sin^{6}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{511 A a^{3} c^{5} \sin^{5}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{384 f} - \frac{11 A a^{3} c^{5} \sin^{5}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{4 A a^{3} c^{5} \sin^{4}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{f} + \frac{6 A a^{3} c^{5} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{385 A a^{3} c^{5} \sin^{3}{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{384 f} - \frac{5 A a^{3} c^{5} \sin^{3}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{16 A a^{3} c^{5} \sin^{2}{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{5 f} + \frac{8 A a^{3} c^{5} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{f} - \frac{6 A a^{3} c^{5} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{35 A a^{3} c^{5} \sin{\left(e + f x \right)} \cos^{7}{\left(e + f x \right)}}{128 f} - \frac{5 A a^{3} c^{5} \sin{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{8 f} + \frac{A a^{3} c^{5} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{32 A a^{3} c^{5} \cos^{7}{\left(e + f x \right)}}{35 f} + \frac{16 A a^{3} c^{5} \cos^{5}{\left(e + f x \right)}}{5 f} - \frac{4 A a^{3} c^{5} \cos^{3}{\left(e + f x \right)}}{f} + \frac{2 A a^{3} c^{5} \cos{\left(e + f x \right)}}{f} + \frac{35 B a^{3} c^{5} x \sin^{8}{\left(e + f x \right)}}{64} + \frac{35 B a^{3} c^{5} x \sin^{6}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{16} - \frac{15 B a^{3} c^{5} x \sin^{6}{\left(e + f x \right)}}{8} + \frac{105 B a^{3} c^{5} x \sin^{4}{\left(e + f x \right)} \cos^{4}{\left(e + f x \right)}}{32} - \frac{45 B a^{3} c^{5} x \sin^{4}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{8} + \frac{9 B a^{3} c^{5} x \sin^{4}{\left(e + f x \right)}}{4} + \frac{35 B a^{3} c^{5} x \sin^{2}{\left(e + f x \right)} \cos^{6}{\left(e + f x \right)}}{16} - \frac{45 B a^{3} c^{5} x \sin^{2}{\left(e + f x \right)} \cos^{4}{\left(e + f x \right)}}{8} + \frac{9 B a^{3} c^{5} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{2} - B a^{3} c^{5} x \sin^{2}{\left(e + f x \right)} + \frac{35 B a^{3} c^{5} x \cos^{8}{\left(e + f x \right)}}{64} - \frac{15 B a^{3} c^{5} x \cos^{6}{\left(e + f x \right)}}{8} + \frac{9 B a^{3} c^{5} x \cos^{4}{\left(e + f x \right)}}{4} - B a^{3} c^{5} x \cos^{2}{\left(e + f x \right)} + \frac{B a^{3} c^{5} \sin^{8}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{93 B a^{3} c^{5} \sin^{7}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{64 f} + \frac{8 B a^{3} c^{5} \sin^{6}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{2 B a^{3} c^{5} \sin^{6}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{511 B a^{3} c^{5} \sin^{5}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{192 f} + \frac{33 B a^{3} c^{5} \sin^{5}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} + \frac{16 B a^{3} c^{5} \sin^{4}{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{5 f} - \frac{4 B a^{3} c^{5} \sin^{4}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{f} - \frac{385 B a^{3} c^{5} \sin^{3}{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{192 f} + \frac{5 B a^{3} c^{5} \sin^{3}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{f} - \frac{15 B a^{3} c^{5} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{4 f} + \frac{64 B a^{3} c^{5} \sin^{2}{\left(e + f x \right)} \cos^{7}{\left(e + f x \right)}}{35 f} - \frac{16 B a^{3} c^{5} \sin^{2}{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{5 f} + \frac{2 B a^{3} c^{5} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{35 B a^{3} c^{5} \sin{\left(e + f x \right)} \cos^{7}{\left(e + f x \right)}}{64 f} + \frac{15 B a^{3} c^{5} \sin{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{8 f} - \frac{9 B a^{3} c^{5} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{4 f} + \frac{B a^{3} c^{5} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{128 B a^{3} c^{5} \cos^{9}{\left(e + f x \right)}}{315 f} - \frac{32 B a^{3} c^{5} \cos^{7}{\left(e + f x \right)}}{35 f} + \frac{4 B a^{3} c^{5} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{B a^{3} c^{5} \cos{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \left(A + B \sin{\left(e \right)}\right) \left(a \sin{\left(e \right)} + a\right)^{3} \left(- c \sin{\left(e \right)} + c\right)^{5} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-35*A*a**3*c**5*x*sin(e + f*x)**8/128 - 35*A*a**3*c**5*x*sin(e + f*x)**6*cos(e + f*x)**2/32 + 5*A*a**3*c**5*x*sin(e + f*x)**6/8 - 105*A*a**3*c**5*x*sin(e + f*x)**4*cos(e + f*x)**4/64 + 15*A*a**3*c**5*x*sin(e + f*x)**4*cos(e + f*x)**2/8 - 35*A*a**3*c**5*x*sin(e + f*x)**2*cos(e + f*x)**6/32 + 15*A*a**3*c**5*x*sin(e + f*x)**2*cos(e + f*x)**4/8 - A*a**3*c**5*x*sin(e + f*x)**2 - 35*A*a**3*c**5*x*cos(e + f*x)**8/128 + 5*A*a**3*c**5*x*cos(e + f*x)**6/8 - A*a**3*c**5*x*cos(e + f*x)**2 + A*a**3*c**5*x + 93*A*a**3*c**5*sin(e + f*x)**7*cos(e + f*x)/(128*f) - 2*A*a**3*c**5*sin(e + f*x)**6*cos(e + f*x)/f + 511*A*a**3*c**5*sin(e + f*x)**5*cos(e + f*x)**3/(384*f) - 11*A*a**3*c**5*sin(e + f*x)**5*cos(e + f*x)/(8*f) - 4*A*a**3*c**5*sin(e + f*x)**4*cos(e + f*x)**3/f + 6*A*a**3*c**5*sin(e + f*x)**4*cos(e + f*x)/f + 385*A*a**3*c**5*sin(e + f*x)**3*cos(e + f*x)**5/(384*f) - 5*A*a**3*c**5*sin(e + f*x)**3*cos(e + f*x)**3/(3*f) - 16*A*a**3*c**5*sin(e + f*x)**2*cos(e + f*x)**5/(5*f) + 8*A*a**3*c**5*sin(e + f*x)**2*cos(e + f*x)**3/f - 6*A*a**3*c**5*sin(e + f*x)**2*cos(e + f*x)/f + 35*A*a**3*c**5*sin(e + f*x)*cos(e + f*x)**7/(128*f) - 5*A*a**3*c**5*sin(e + f*x)*cos(e + f*x)**5/(8*f) + A*a**3*c**5*sin(e + f*x)*cos(e + f*x)/f - 32*A*a**3*c**5*cos(e + f*x)**7/(35*f) + 16*A*a**3*c**5*cos(e + f*x)**5/(5*f) - 4*A*a**3*c**5*cos(e + f*x)**3/f + 2*A*a**3*c**5*cos(e + f*x)/f + 35*B*a**3*c**5*x*sin(e + f*x)**8/64 + 35*B*a**3*c**5*x*sin(e + f*x)**6*cos(e + f*x)**2/16 - 15*B*a**3*c**5*x*sin(e + f*x)**6/8 + 105*B*a**3*c**5*x*sin(e + f*x)**4*cos(e + f*x)**4/32 - 45*B*a**3*c**5*x*sin(e + f*x)**4*cos(e + f*x)**2/8 + 9*B*a**3*c**5*x*sin(e + f*x)**4/4 + 35*B*a**3*c**5*x*sin(e + f*x)**2*cos(e + f*x)**6/16 - 45*B*a**3*c**5*x*sin(e + f*x)**2*cos(e + f*x)**4/8 + 9*B*a**3*c**5*x*sin(e + f*x)**2*cos(e + f*x)**2/2 - B*a**3*c**5*x*sin(e + f*x)**2 + 35*B*a**3*c**5*x*cos(e + f*x)**8/64 - 15*B*a**3*c**5*x*cos(e + f*x)**6/8 + 9*B*a**3*c**5*x*cos(e + f*x)**4/4 - B*a**3*c**5*x*cos(e + f*x)**2 + B*a**3*c**5*sin(e + f*x)**8*cos(e + f*x)/f - 93*B*a**3*c**5*sin(e + f*x)**7*cos(e + f*x)/(64*f) + 8*B*a**3*c**5*sin(e + f*x)**6*cos(e + f*x)**3/(3*f) - 2*B*a**3*c**5*sin(e + f*x)**6*cos(e + f*x)/f - 511*B*a**3*c**5*sin(e + f*x)**5*cos(e + f*x)**3/(192*f) + 33*B*a**3*c**5*sin(e + f*x)**5*cos(e + f*x)/(8*f) + 16*B*a**3*c**5*sin(e + f*x)**4*cos(e + f*x)**5/(5*f) - 4*B*a**3*c**5*sin(e + f*x)**4*cos(e + f*x)**3/f - 385*B*a**3*c**5*sin(e + f*x)**3*cos(e + f*x)**5/(192*f) + 5*B*a**3*c**5*sin(e + f*x)**3*cos(e + f*x)**3/f - 15*B*a**3*c**5*sin(e + f*x)**3*cos(e + f*x)/(4*f) + 64*B*a**3*c**5*sin(e + f*x)**2*cos(e + f*x)**7/(35*f) - 16*B*a**3*c**5*sin(e + f*x)**2*cos(e + f*x)**5/(5*f) + 2*B*a**3*c**5*sin(e + f*x)**2*cos(e + f*x)/f - 35*B*a**3*c**5*sin(e + f*x)*cos(e + f*x)**7/(64*f) + 15*B*a**3*c**5*sin(e + f*x)*cos(e + f*x)**5/(8*f) - 9*B*a**3*c**5*sin(e + f*x)*cos(e + f*x)**3/(4*f) + B*a**3*c**5*sin(e + f*x)*cos(e + f*x)/f + 128*B*a**3*c**5*cos(e + f*x)**9/(315*f) - 32*B*a**3*c**5*cos(e + f*x)**7/(35*f) + 4*B*a**3*c**5*cos(e + f*x)**3/(3*f) - B*a**3*c**5*cos(e + f*x)/f, Ne(f, 0)), (x*(A + B*sin(e))*(a*sin(e) + a)**3*(-c*sin(e) + c)**5, True))","A",0
40,1,1579,0,23.432017," ","integrate((a+a*sin(f*x+e))**3*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**4,x)","\begin{cases} - \frac{5 A a^{3} c^{4} x \sin^{6}{\left(e + f x \right)}}{16} - \frac{15 A a^{3} c^{4} x \sin^{4}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{16} + \frac{9 A a^{3} c^{4} x \sin^{4}{\left(e + f x \right)}}{8} - \frac{15 A a^{3} c^{4} x \sin^{2}{\left(e + f x \right)} \cos^{4}{\left(e + f x \right)}}{16} + \frac{9 A a^{3} c^{4} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} - \frac{3 A a^{3} c^{4} x \sin^{2}{\left(e + f x \right)}}{2} - \frac{5 A a^{3} c^{4} x \cos^{6}{\left(e + f x \right)}}{16} + \frac{9 A a^{3} c^{4} x \cos^{4}{\left(e + f x \right)}}{8} - \frac{3 A a^{3} c^{4} x \cos^{2}{\left(e + f x \right)}}{2} + A a^{3} c^{4} x - \frac{A a^{3} c^{4} \sin^{6}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{11 A a^{3} c^{4} \sin^{5}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{16 f} - \frac{2 A a^{3} c^{4} \sin^{4}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{f} + \frac{3 A a^{3} c^{4} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{5 A a^{3} c^{4} \sin^{3}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{6 f} - \frac{15 A a^{3} c^{4} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{8 A a^{3} c^{4} \sin^{2}{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{5 f} + \frac{4 A a^{3} c^{4} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{f} - \frac{3 A a^{3} c^{4} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{5 A a^{3} c^{4} \sin{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{16 f} - \frac{9 A a^{3} c^{4} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} + \frac{3 A a^{3} c^{4} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{16 A a^{3} c^{4} \cos^{7}{\left(e + f x \right)}}{35 f} + \frac{8 A a^{3} c^{4} \cos^{5}{\left(e + f x \right)}}{5 f} - \frac{2 A a^{3} c^{4} \cos^{3}{\left(e + f x \right)}}{f} + \frac{A a^{3} c^{4} \cos{\left(e + f x \right)}}{f} + \frac{35 B a^{3} c^{4} x \sin^{8}{\left(e + f x \right)}}{128} + \frac{35 B a^{3} c^{4} x \sin^{6}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{32} - \frac{15 B a^{3} c^{4} x \sin^{6}{\left(e + f x \right)}}{16} + \frac{105 B a^{3} c^{4} x \sin^{4}{\left(e + f x \right)} \cos^{4}{\left(e + f x \right)}}{64} - \frac{45 B a^{3} c^{4} x \sin^{4}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{16} + \frac{9 B a^{3} c^{4} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{35 B a^{3} c^{4} x \sin^{2}{\left(e + f x \right)} \cos^{6}{\left(e + f x \right)}}{32} - \frac{45 B a^{3} c^{4} x \sin^{2}{\left(e + f x \right)} \cos^{4}{\left(e + f x \right)}}{16} + \frac{9 B a^{3} c^{4} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} - \frac{B a^{3} c^{4} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{35 B a^{3} c^{4} x \cos^{8}{\left(e + f x \right)}}{128} - \frac{15 B a^{3} c^{4} x \cos^{6}{\left(e + f x \right)}}{16} + \frac{9 B a^{3} c^{4} x \cos^{4}{\left(e + f x \right)}}{8} - \frac{B a^{3} c^{4} x \cos^{2}{\left(e + f x \right)}}{2} - \frac{93 B a^{3} c^{4} \sin^{7}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{128 f} + \frac{B a^{3} c^{4} \sin^{6}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{511 B a^{3} c^{4} \sin^{5}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{384 f} + \frac{33 B a^{3} c^{4} \sin^{5}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{16 f} + \frac{2 B a^{3} c^{4} \sin^{4}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{f} - \frac{3 B a^{3} c^{4} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{385 B a^{3} c^{4} \sin^{3}{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{384 f} + \frac{5 B a^{3} c^{4} \sin^{3}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{2 f} - \frac{15 B a^{3} c^{4} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} + \frac{8 B a^{3} c^{4} \sin^{2}{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{5 f} - \frac{4 B a^{3} c^{4} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{f} + \frac{3 B a^{3} c^{4} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{35 B a^{3} c^{4} \sin{\left(e + f x \right)} \cos^{7}{\left(e + f x \right)}}{128 f} + \frac{15 B a^{3} c^{4} \sin{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{16 f} - \frac{9 B a^{3} c^{4} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} + \frac{B a^{3} c^{4} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} + \frac{16 B a^{3} c^{4} \cos^{7}{\left(e + f x \right)}}{35 f} - \frac{8 B a^{3} c^{4} \cos^{5}{\left(e + f x \right)}}{5 f} + \frac{2 B a^{3} c^{4} \cos^{3}{\left(e + f x \right)}}{f} - \frac{B a^{3} c^{4} \cos{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \left(A + B \sin{\left(e \right)}\right) \left(a \sin{\left(e \right)} + a\right)^{3} \left(- c \sin{\left(e \right)} + c\right)^{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-5*A*a**3*c**4*x*sin(e + f*x)**6/16 - 15*A*a**3*c**4*x*sin(e + f*x)**4*cos(e + f*x)**2/16 + 9*A*a**3*c**4*x*sin(e + f*x)**4/8 - 15*A*a**3*c**4*x*sin(e + f*x)**2*cos(e + f*x)**4/16 + 9*A*a**3*c**4*x*sin(e + f*x)**2*cos(e + f*x)**2/4 - 3*A*a**3*c**4*x*sin(e + f*x)**2/2 - 5*A*a**3*c**4*x*cos(e + f*x)**6/16 + 9*A*a**3*c**4*x*cos(e + f*x)**4/8 - 3*A*a**3*c**4*x*cos(e + f*x)**2/2 + A*a**3*c**4*x - A*a**3*c**4*sin(e + f*x)**6*cos(e + f*x)/f + 11*A*a**3*c**4*sin(e + f*x)**5*cos(e + f*x)/(16*f) - 2*A*a**3*c**4*sin(e + f*x)**4*cos(e + f*x)**3/f + 3*A*a**3*c**4*sin(e + f*x)**4*cos(e + f*x)/f + 5*A*a**3*c**4*sin(e + f*x)**3*cos(e + f*x)**3/(6*f) - 15*A*a**3*c**4*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 8*A*a**3*c**4*sin(e + f*x)**2*cos(e + f*x)**5/(5*f) + 4*A*a**3*c**4*sin(e + f*x)**2*cos(e + f*x)**3/f - 3*A*a**3*c**4*sin(e + f*x)**2*cos(e + f*x)/f + 5*A*a**3*c**4*sin(e + f*x)*cos(e + f*x)**5/(16*f) - 9*A*a**3*c**4*sin(e + f*x)*cos(e + f*x)**3/(8*f) + 3*A*a**3*c**4*sin(e + f*x)*cos(e + f*x)/(2*f) - 16*A*a**3*c**4*cos(e + f*x)**7/(35*f) + 8*A*a**3*c**4*cos(e + f*x)**5/(5*f) - 2*A*a**3*c**4*cos(e + f*x)**3/f + A*a**3*c**4*cos(e + f*x)/f + 35*B*a**3*c**4*x*sin(e + f*x)**8/128 + 35*B*a**3*c**4*x*sin(e + f*x)**6*cos(e + f*x)**2/32 - 15*B*a**3*c**4*x*sin(e + f*x)**6/16 + 105*B*a**3*c**4*x*sin(e + f*x)**4*cos(e + f*x)**4/64 - 45*B*a**3*c**4*x*sin(e + f*x)**4*cos(e + f*x)**2/16 + 9*B*a**3*c**4*x*sin(e + f*x)**4/8 + 35*B*a**3*c**4*x*sin(e + f*x)**2*cos(e + f*x)**6/32 - 45*B*a**3*c**4*x*sin(e + f*x)**2*cos(e + f*x)**4/16 + 9*B*a**3*c**4*x*sin(e + f*x)**2*cos(e + f*x)**2/4 - B*a**3*c**4*x*sin(e + f*x)**2/2 + 35*B*a**3*c**4*x*cos(e + f*x)**8/128 - 15*B*a**3*c**4*x*cos(e + f*x)**6/16 + 9*B*a**3*c**4*x*cos(e + f*x)**4/8 - B*a**3*c**4*x*cos(e + f*x)**2/2 - 93*B*a**3*c**4*sin(e + f*x)**7*cos(e + f*x)/(128*f) + B*a**3*c**4*sin(e + f*x)**6*cos(e + f*x)/f - 511*B*a**3*c**4*sin(e + f*x)**5*cos(e + f*x)**3/(384*f) + 33*B*a**3*c**4*sin(e + f*x)**5*cos(e + f*x)/(16*f) + 2*B*a**3*c**4*sin(e + f*x)**4*cos(e + f*x)**3/f - 3*B*a**3*c**4*sin(e + f*x)**4*cos(e + f*x)/f - 385*B*a**3*c**4*sin(e + f*x)**3*cos(e + f*x)**5/(384*f) + 5*B*a**3*c**4*sin(e + f*x)**3*cos(e + f*x)**3/(2*f) - 15*B*a**3*c**4*sin(e + f*x)**3*cos(e + f*x)/(8*f) + 8*B*a**3*c**4*sin(e + f*x)**2*cos(e + f*x)**5/(5*f) - 4*B*a**3*c**4*sin(e + f*x)**2*cos(e + f*x)**3/f + 3*B*a**3*c**4*sin(e + f*x)**2*cos(e + f*x)/f - 35*B*a**3*c**4*sin(e + f*x)*cos(e + f*x)**7/(128*f) + 15*B*a**3*c**4*sin(e + f*x)*cos(e + f*x)**5/(16*f) - 9*B*a**3*c**4*sin(e + f*x)*cos(e + f*x)**3/(8*f) + B*a**3*c**4*sin(e + f*x)*cos(e + f*x)/(2*f) + 16*B*a**3*c**4*cos(e + f*x)**7/(35*f) - 8*B*a**3*c**4*cos(e + f*x)**5/(5*f) + 2*B*a**3*c**4*cos(e + f*x)**3/f - B*a**3*c**4*cos(e + f*x)/f, Ne(f, 0)), (x*(A + B*sin(e))*(a*sin(e) + a)**3*(-c*sin(e) + c)**4, True))","A",0
41,1,682,0,10.351328," ","integrate((a+a*sin(f*x+e))**3*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**3,x)","\begin{cases} - \frac{5 A a^{3} c^{3} x \sin^{6}{\left(e + f x \right)}}{16} - \frac{15 A a^{3} c^{3} x \sin^{4}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{16} + \frac{9 A a^{3} c^{3} x \sin^{4}{\left(e + f x \right)}}{8} - \frac{15 A a^{3} c^{3} x \sin^{2}{\left(e + f x \right)} \cos^{4}{\left(e + f x \right)}}{16} + \frac{9 A a^{3} c^{3} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} - \frac{3 A a^{3} c^{3} x \sin^{2}{\left(e + f x \right)}}{2} - \frac{5 A a^{3} c^{3} x \cos^{6}{\left(e + f x \right)}}{16} + \frac{9 A a^{3} c^{3} x \cos^{4}{\left(e + f x \right)}}{8} - \frac{3 A a^{3} c^{3} x \cos^{2}{\left(e + f x \right)}}{2} + A a^{3} c^{3} x + \frac{11 A a^{3} c^{3} \sin^{5}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{16 f} + \frac{5 A a^{3} c^{3} \sin^{3}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{6 f} - \frac{15 A a^{3} c^{3} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} + \frac{5 A a^{3} c^{3} \sin{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{16 f} - \frac{9 A a^{3} c^{3} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} + \frac{3 A a^{3} c^{3} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} + \frac{B a^{3} c^{3} \sin^{6}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{2 B a^{3} c^{3} \sin^{4}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{f} - \frac{3 B a^{3} c^{3} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{8 B a^{3} c^{3} \sin^{2}{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{5 f} - \frac{4 B a^{3} c^{3} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{f} + \frac{3 B a^{3} c^{3} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{16 B a^{3} c^{3} \cos^{7}{\left(e + f x \right)}}{35 f} - \frac{8 B a^{3} c^{3} \cos^{5}{\left(e + f x \right)}}{5 f} + \frac{2 B a^{3} c^{3} \cos^{3}{\left(e + f x \right)}}{f} - \frac{B a^{3} c^{3} \cos{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \left(A + B \sin{\left(e \right)}\right) \left(a \sin{\left(e \right)} + a\right)^{3} \left(- c \sin{\left(e \right)} + c\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-5*A*a**3*c**3*x*sin(e + f*x)**6/16 - 15*A*a**3*c**3*x*sin(e + f*x)**4*cos(e + f*x)**2/16 + 9*A*a**3*c**3*x*sin(e + f*x)**4/8 - 15*A*a**3*c**3*x*sin(e + f*x)**2*cos(e + f*x)**4/16 + 9*A*a**3*c**3*x*sin(e + f*x)**2*cos(e + f*x)**2/4 - 3*A*a**3*c**3*x*sin(e + f*x)**2/2 - 5*A*a**3*c**3*x*cos(e + f*x)**6/16 + 9*A*a**3*c**3*x*cos(e + f*x)**4/8 - 3*A*a**3*c**3*x*cos(e + f*x)**2/2 + A*a**3*c**3*x + 11*A*a**3*c**3*sin(e + f*x)**5*cos(e + f*x)/(16*f) + 5*A*a**3*c**3*sin(e + f*x)**3*cos(e + f*x)**3/(6*f) - 15*A*a**3*c**3*sin(e + f*x)**3*cos(e + f*x)/(8*f) + 5*A*a**3*c**3*sin(e + f*x)*cos(e + f*x)**5/(16*f) - 9*A*a**3*c**3*sin(e + f*x)*cos(e + f*x)**3/(8*f) + 3*A*a**3*c**3*sin(e + f*x)*cos(e + f*x)/(2*f) + B*a**3*c**3*sin(e + f*x)**6*cos(e + f*x)/f + 2*B*a**3*c**3*sin(e + f*x)**4*cos(e + f*x)**3/f - 3*B*a**3*c**3*sin(e + f*x)**4*cos(e + f*x)/f + 8*B*a**3*c**3*sin(e + f*x)**2*cos(e + f*x)**5/(5*f) - 4*B*a**3*c**3*sin(e + f*x)**2*cos(e + f*x)**3/f + 3*B*a**3*c**3*sin(e + f*x)**2*cos(e + f*x)/f + 16*B*a**3*c**3*cos(e + f*x)**7/(35*f) - 8*B*a**3*c**3*cos(e + f*x)**5/(5*f) + 2*B*a**3*c**3*cos(e + f*x)**3/f - B*a**3*c**3*cos(e + f*x)/f, Ne(f, 0)), (x*(A + B*sin(e))*(a*sin(e) + a)**3*(-c*sin(e) + c)**3, True))","A",0
42,1,910,0,8.100754," ","integrate((a+a*sin(f*x+e))**3*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**2,x)","\begin{cases} \frac{3 A a^{3} c^{2} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{3 A a^{3} c^{2} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} - A a^{3} c^{2} x \sin^{2}{\left(e + f x \right)} + \frac{3 A a^{3} c^{2} x \cos^{4}{\left(e + f x \right)}}{8} - A a^{3} c^{2} x \cos^{2}{\left(e + f x \right)} + A a^{3} c^{2} x - \frac{A a^{3} c^{2} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{5 A a^{3} c^{2} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{4 A a^{3} c^{2} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{3 f} + \frac{2 A a^{3} c^{2} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{3 A a^{3} c^{2} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} + \frac{A a^{3} c^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{8 A a^{3} c^{2} \cos^{5}{\left(e + f x \right)}}{15 f} + \frac{4 A a^{3} c^{2} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{A a^{3} c^{2} \cos{\left(e + f x \right)}}{f} + \frac{5 B a^{3} c^{2} x \sin^{6}{\left(e + f x \right)}}{16} + \frac{15 B a^{3} c^{2} x \sin^{4}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{16} - \frac{3 B a^{3} c^{2} x \sin^{4}{\left(e + f x \right)}}{4} + \frac{15 B a^{3} c^{2} x \sin^{2}{\left(e + f x \right)} \cos^{4}{\left(e + f x \right)}}{16} - \frac{3 B a^{3} c^{2} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{2} + \frac{B a^{3} c^{2} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{5 B a^{3} c^{2} x \cos^{6}{\left(e + f x \right)}}{16} - \frac{3 B a^{3} c^{2} x \cos^{4}{\left(e + f x \right)}}{4} + \frac{B a^{3} c^{2} x \cos^{2}{\left(e + f x \right)}}{2} - \frac{11 B a^{3} c^{2} \sin^{5}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{16 f} - \frac{B a^{3} c^{2} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{5 B a^{3} c^{2} \sin^{3}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{6 f} + \frac{5 B a^{3} c^{2} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{4 f} - \frac{4 B a^{3} c^{2} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{3 f} + \frac{2 B a^{3} c^{2} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{5 B a^{3} c^{2} \sin{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{16 f} + \frac{3 B a^{3} c^{2} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{4 f} - \frac{B a^{3} c^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{8 B a^{3} c^{2} \cos^{5}{\left(e + f x \right)}}{15 f} + \frac{4 B a^{3} c^{2} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{B a^{3} c^{2} \cos{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \left(A + B \sin{\left(e \right)}\right) \left(a \sin{\left(e \right)} + a\right)^{3} \left(- c \sin{\left(e \right)} + c\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*A*a**3*c**2*x*sin(e + f*x)**4/8 + 3*A*a**3*c**2*x*sin(e + f*x)**2*cos(e + f*x)**2/4 - A*a**3*c**2*x*sin(e + f*x)**2 + 3*A*a**3*c**2*x*cos(e + f*x)**4/8 - A*a**3*c**2*x*cos(e + f*x)**2 + A*a**3*c**2*x - A*a**3*c**2*sin(e + f*x)**4*cos(e + f*x)/f - 5*A*a**3*c**2*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 4*A*a**3*c**2*sin(e + f*x)**2*cos(e + f*x)**3/(3*f) + 2*A*a**3*c**2*sin(e + f*x)**2*cos(e + f*x)/f - 3*A*a**3*c**2*sin(e + f*x)*cos(e + f*x)**3/(8*f) + A*a**3*c**2*sin(e + f*x)*cos(e + f*x)/f - 8*A*a**3*c**2*cos(e + f*x)**5/(15*f) + 4*A*a**3*c**2*cos(e + f*x)**3/(3*f) - A*a**3*c**2*cos(e + f*x)/f + 5*B*a**3*c**2*x*sin(e + f*x)**6/16 + 15*B*a**3*c**2*x*sin(e + f*x)**4*cos(e + f*x)**2/16 - 3*B*a**3*c**2*x*sin(e + f*x)**4/4 + 15*B*a**3*c**2*x*sin(e + f*x)**2*cos(e + f*x)**4/16 - 3*B*a**3*c**2*x*sin(e + f*x)**2*cos(e + f*x)**2/2 + B*a**3*c**2*x*sin(e + f*x)**2/2 + 5*B*a**3*c**2*x*cos(e + f*x)**6/16 - 3*B*a**3*c**2*x*cos(e + f*x)**4/4 + B*a**3*c**2*x*cos(e + f*x)**2/2 - 11*B*a**3*c**2*sin(e + f*x)**5*cos(e + f*x)/(16*f) - B*a**3*c**2*sin(e + f*x)**4*cos(e + f*x)/f - 5*B*a**3*c**2*sin(e + f*x)**3*cos(e + f*x)**3/(6*f) + 5*B*a**3*c**2*sin(e + f*x)**3*cos(e + f*x)/(4*f) - 4*B*a**3*c**2*sin(e + f*x)**2*cos(e + f*x)**3/(3*f) + 2*B*a**3*c**2*sin(e + f*x)**2*cos(e + f*x)/f - 5*B*a**3*c**2*sin(e + f*x)*cos(e + f*x)**5/(16*f) + 3*B*a**3*c**2*sin(e + f*x)*cos(e + f*x)**3/(4*f) - B*a**3*c**2*sin(e + f*x)*cos(e + f*x)/(2*f) - 8*B*a**3*c**2*cos(e + f*x)**5/(15*f) + 4*B*a**3*c**2*cos(e + f*x)**3/(3*f) - B*a**3*c**2*cos(e + f*x)/f, Ne(f, 0)), (x*(A + B*sin(e))*(a*sin(e) + a)**3*(-c*sin(e) + c)**2, True))","A",0
43,1,486,0,4.211128," ","integrate((a+a*sin(f*x+e))**3*(A+B*sin(f*x+e))*(c-c*sin(f*x+e)),x)","\begin{cases} - \frac{3 A a^{3} c x \sin^{4}{\left(e + f x \right)}}{8} - \frac{3 A a^{3} c x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} - \frac{3 A a^{3} c x \cos^{4}{\left(e + f x \right)}}{8} + A a^{3} c x + \frac{5 A a^{3} c \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} + \frac{2 A a^{3} c \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{3 A a^{3} c \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} + \frac{4 A a^{3} c \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{2 A a^{3} c \cos{\left(e + f x \right)}}{f} - \frac{3 B a^{3} c x \sin^{4}{\left(e + f x \right)}}{4} - \frac{3 B a^{3} c x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{2} + B a^{3} c x \sin^{2}{\left(e + f x \right)} - \frac{3 B a^{3} c x \cos^{4}{\left(e + f x \right)}}{4} + B a^{3} c x \cos^{2}{\left(e + f x \right)} + \frac{B a^{3} c \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{5 B a^{3} c \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{4 f} + \frac{4 B a^{3} c \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{3 f} + \frac{3 B a^{3} c \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{4 f} - \frac{B a^{3} c \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{8 B a^{3} c \cos^{5}{\left(e + f x \right)}}{15 f} - \frac{B a^{3} c \cos{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \left(A + B \sin{\left(e \right)}\right) \left(a \sin{\left(e \right)} + a\right)^{3} \left(- c \sin{\left(e \right)} + c\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*A*a**3*c*x*sin(e + f*x)**4/8 - 3*A*a**3*c*x*sin(e + f*x)**2*cos(e + f*x)**2/4 - 3*A*a**3*c*x*cos(e + f*x)**4/8 + A*a**3*c*x + 5*A*a**3*c*sin(e + f*x)**3*cos(e + f*x)/(8*f) + 2*A*a**3*c*sin(e + f*x)**2*cos(e + f*x)/f + 3*A*a**3*c*sin(e + f*x)*cos(e + f*x)**3/(8*f) + 4*A*a**3*c*cos(e + f*x)**3/(3*f) - 2*A*a**3*c*cos(e + f*x)/f - 3*B*a**3*c*x*sin(e + f*x)**4/4 - 3*B*a**3*c*x*sin(e + f*x)**2*cos(e + f*x)**2/2 + B*a**3*c*x*sin(e + f*x)**2 - 3*B*a**3*c*x*cos(e + f*x)**4/4 + B*a**3*c*x*cos(e + f*x)**2 + B*a**3*c*sin(e + f*x)**4*cos(e + f*x)/f + 5*B*a**3*c*sin(e + f*x)**3*cos(e + f*x)/(4*f) + 4*B*a**3*c*sin(e + f*x)**2*cos(e + f*x)**3/(3*f) + 3*B*a**3*c*sin(e + f*x)*cos(e + f*x)**3/(4*f) - B*a**3*c*sin(e + f*x)*cos(e + f*x)/f + 8*B*a**3*c*cos(e + f*x)**5/(15*f) - B*a**3*c*cos(e + f*x)/f, Ne(f, 0)), (x*(A + B*sin(e))*(a*sin(e) + a)**3*(-c*sin(e) + c), True))","A",0
44,1,4255,0,15.993125," ","integrate((a+a*sin(f*x+e))**3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e)),x)","\begin{cases} - \frac{45 A a^{3} f x \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f} + \frac{45 A a^{3} f x \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f} - \frac{135 A a^{3} f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f} + \frac{135 A a^{3} f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f} - \frac{135 A a^{3} f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f} + \frac{135 A a^{3} f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f} - \frac{45 A a^{3} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f} + \frac{45 A a^{3} f x}{6 c f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f} - \frac{102 A a^{3} \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f} + \frac{54 A a^{3} \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f} - \frac{336 A a^{3} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f} + \frac{96 A a^{3} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f} - \frac{378 A a^{3} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f} + \frac{42 A a^{3} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f} - \frac{144 A a^{3}}{6 c f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f} - \frac{60 B a^{3} f x \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f} + \frac{60 B a^{3} f x \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f} - \frac{180 B a^{3} f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f} + \frac{180 B a^{3} f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f} - \frac{180 B a^{3} f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f} + \frac{180 B a^{3} f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f} - \frac{60 B a^{3} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f} + \frac{60 B a^{3} f x}{6 c f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f} - \frac{120 B a^{3} \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f} + \frac{108 B a^{3} \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f} - \frac{372 B a^{3} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f} + \frac{192 B a^{3} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f} - \frac{456 B a^{3} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f} + \frac{68 B a^{3} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f} - \frac{188 B a^{3}}{6 c f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right) \left(a \sin{\left(e \right)} + a\right)^{3}}{- c \sin{\left(e \right)} + c} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-45*A*a**3*f*x*tan(e/2 + f*x/2)**7/(6*c*f*tan(e/2 + f*x/2)**7 - 6*c*f*tan(e/2 + f*x/2)**6 + 18*c*f*tan(e/2 + f*x/2)**5 - 18*c*f*tan(e/2 + f*x/2)**4 + 18*c*f*tan(e/2 + f*x/2)**3 - 18*c*f*tan(e/2 + f*x/2)**2 + 6*c*f*tan(e/2 + f*x/2) - 6*c*f) + 45*A*a**3*f*x*tan(e/2 + f*x/2)**6/(6*c*f*tan(e/2 + f*x/2)**7 - 6*c*f*tan(e/2 + f*x/2)**6 + 18*c*f*tan(e/2 + f*x/2)**5 - 18*c*f*tan(e/2 + f*x/2)**4 + 18*c*f*tan(e/2 + f*x/2)**3 - 18*c*f*tan(e/2 + f*x/2)**2 + 6*c*f*tan(e/2 + f*x/2) - 6*c*f) - 135*A*a**3*f*x*tan(e/2 + f*x/2)**5/(6*c*f*tan(e/2 + f*x/2)**7 - 6*c*f*tan(e/2 + f*x/2)**6 + 18*c*f*tan(e/2 + f*x/2)**5 - 18*c*f*tan(e/2 + f*x/2)**4 + 18*c*f*tan(e/2 + f*x/2)**3 - 18*c*f*tan(e/2 + f*x/2)**2 + 6*c*f*tan(e/2 + f*x/2) - 6*c*f) + 135*A*a**3*f*x*tan(e/2 + f*x/2)**4/(6*c*f*tan(e/2 + f*x/2)**7 - 6*c*f*tan(e/2 + f*x/2)**6 + 18*c*f*tan(e/2 + f*x/2)**5 - 18*c*f*tan(e/2 + f*x/2)**4 + 18*c*f*tan(e/2 + f*x/2)**3 - 18*c*f*tan(e/2 + f*x/2)**2 + 6*c*f*tan(e/2 + f*x/2) - 6*c*f) - 135*A*a**3*f*x*tan(e/2 + f*x/2)**3/(6*c*f*tan(e/2 + f*x/2)**7 - 6*c*f*tan(e/2 + f*x/2)**6 + 18*c*f*tan(e/2 + f*x/2)**5 - 18*c*f*tan(e/2 + f*x/2)**4 + 18*c*f*tan(e/2 + f*x/2)**3 - 18*c*f*tan(e/2 + f*x/2)**2 + 6*c*f*tan(e/2 + f*x/2) - 6*c*f) + 135*A*a**3*f*x*tan(e/2 + f*x/2)**2/(6*c*f*tan(e/2 + f*x/2)**7 - 6*c*f*tan(e/2 + f*x/2)**6 + 18*c*f*tan(e/2 + f*x/2)**5 - 18*c*f*tan(e/2 + f*x/2)**4 + 18*c*f*tan(e/2 + f*x/2)**3 - 18*c*f*tan(e/2 + f*x/2)**2 + 6*c*f*tan(e/2 + f*x/2) - 6*c*f) - 45*A*a**3*f*x*tan(e/2 + f*x/2)/(6*c*f*tan(e/2 + f*x/2)**7 - 6*c*f*tan(e/2 + f*x/2)**6 + 18*c*f*tan(e/2 + f*x/2)**5 - 18*c*f*tan(e/2 + f*x/2)**4 + 18*c*f*tan(e/2 + f*x/2)**3 - 18*c*f*tan(e/2 + f*x/2)**2 + 6*c*f*tan(e/2 + f*x/2) - 6*c*f) + 45*A*a**3*f*x/(6*c*f*tan(e/2 + f*x/2)**7 - 6*c*f*tan(e/2 + f*x/2)**6 + 18*c*f*tan(e/2 + f*x/2)**5 - 18*c*f*tan(e/2 + f*x/2)**4 + 18*c*f*tan(e/2 + f*x/2)**3 - 18*c*f*tan(e/2 + f*x/2)**2 + 6*c*f*tan(e/2 + f*x/2) - 6*c*f) - 102*A*a**3*tan(e/2 + f*x/2)**6/(6*c*f*tan(e/2 + f*x/2)**7 - 6*c*f*tan(e/2 + f*x/2)**6 + 18*c*f*tan(e/2 + f*x/2)**5 - 18*c*f*tan(e/2 + f*x/2)**4 + 18*c*f*tan(e/2 + f*x/2)**3 - 18*c*f*tan(e/2 + f*x/2)**2 + 6*c*f*tan(e/2 + f*x/2) - 6*c*f) + 54*A*a**3*tan(e/2 + f*x/2)**5/(6*c*f*tan(e/2 + f*x/2)**7 - 6*c*f*tan(e/2 + f*x/2)**6 + 18*c*f*tan(e/2 + f*x/2)**5 - 18*c*f*tan(e/2 + f*x/2)**4 + 18*c*f*tan(e/2 + f*x/2)**3 - 18*c*f*tan(e/2 + f*x/2)**2 + 6*c*f*tan(e/2 + f*x/2) - 6*c*f) - 336*A*a**3*tan(e/2 + f*x/2)**4/(6*c*f*tan(e/2 + f*x/2)**7 - 6*c*f*tan(e/2 + f*x/2)**6 + 18*c*f*tan(e/2 + f*x/2)**5 - 18*c*f*tan(e/2 + f*x/2)**4 + 18*c*f*tan(e/2 + f*x/2)**3 - 18*c*f*tan(e/2 + f*x/2)**2 + 6*c*f*tan(e/2 + f*x/2) - 6*c*f) + 96*A*a**3*tan(e/2 + f*x/2)**3/(6*c*f*tan(e/2 + f*x/2)**7 - 6*c*f*tan(e/2 + f*x/2)**6 + 18*c*f*tan(e/2 + f*x/2)**5 - 18*c*f*tan(e/2 + f*x/2)**4 + 18*c*f*tan(e/2 + f*x/2)**3 - 18*c*f*tan(e/2 + f*x/2)**2 + 6*c*f*tan(e/2 + f*x/2) - 6*c*f) - 378*A*a**3*tan(e/2 + f*x/2)**2/(6*c*f*tan(e/2 + f*x/2)**7 - 6*c*f*tan(e/2 + f*x/2)**6 + 18*c*f*tan(e/2 + f*x/2)**5 - 18*c*f*tan(e/2 + f*x/2)**4 + 18*c*f*tan(e/2 + f*x/2)**3 - 18*c*f*tan(e/2 + f*x/2)**2 + 6*c*f*tan(e/2 + f*x/2) - 6*c*f) + 42*A*a**3*tan(e/2 + f*x/2)/(6*c*f*tan(e/2 + f*x/2)**7 - 6*c*f*tan(e/2 + f*x/2)**6 + 18*c*f*tan(e/2 + f*x/2)**5 - 18*c*f*tan(e/2 + f*x/2)**4 + 18*c*f*tan(e/2 + f*x/2)**3 - 18*c*f*tan(e/2 + f*x/2)**2 + 6*c*f*tan(e/2 + f*x/2) - 6*c*f) - 144*A*a**3/(6*c*f*tan(e/2 + f*x/2)**7 - 6*c*f*tan(e/2 + f*x/2)**6 + 18*c*f*tan(e/2 + f*x/2)**5 - 18*c*f*tan(e/2 + f*x/2)**4 + 18*c*f*tan(e/2 + f*x/2)**3 - 18*c*f*tan(e/2 + f*x/2)**2 + 6*c*f*tan(e/2 + f*x/2) - 6*c*f) - 60*B*a**3*f*x*tan(e/2 + f*x/2)**7/(6*c*f*tan(e/2 + f*x/2)**7 - 6*c*f*tan(e/2 + f*x/2)**6 + 18*c*f*tan(e/2 + f*x/2)**5 - 18*c*f*tan(e/2 + f*x/2)**4 + 18*c*f*tan(e/2 + f*x/2)**3 - 18*c*f*tan(e/2 + f*x/2)**2 + 6*c*f*tan(e/2 + f*x/2) - 6*c*f) + 60*B*a**3*f*x*tan(e/2 + f*x/2)**6/(6*c*f*tan(e/2 + f*x/2)**7 - 6*c*f*tan(e/2 + f*x/2)**6 + 18*c*f*tan(e/2 + f*x/2)**5 - 18*c*f*tan(e/2 + f*x/2)**4 + 18*c*f*tan(e/2 + f*x/2)**3 - 18*c*f*tan(e/2 + f*x/2)**2 + 6*c*f*tan(e/2 + f*x/2) - 6*c*f) - 180*B*a**3*f*x*tan(e/2 + f*x/2)**5/(6*c*f*tan(e/2 + f*x/2)**7 - 6*c*f*tan(e/2 + f*x/2)**6 + 18*c*f*tan(e/2 + f*x/2)**5 - 18*c*f*tan(e/2 + f*x/2)**4 + 18*c*f*tan(e/2 + f*x/2)**3 - 18*c*f*tan(e/2 + f*x/2)**2 + 6*c*f*tan(e/2 + f*x/2) - 6*c*f) + 180*B*a**3*f*x*tan(e/2 + f*x/2)**4/(6*c*f*tan(e/2 + f*x/2)**7 - 6*c*f*tan(e/2 + f*x/2)**6 + 18*c*f*tan(e/2 + f*x/2)**5 - 18*c*f*tan(e/2 + f*x/2)**4 + 18*c*f*tan(e/2 + f*x/2)**3 - 18*c*f*tan(e/2 + f*x/2)**2 + 6*c*f*tan(e/2 + f*x/2) - 6*c*f) - 180*B*a**3*f*x*tan(e/2 + f*x/2)**3/(6*c*f*tan(e/2 + f*x/2)**7 - 6*c*f*tan(e/2 + f*x/2)**6 + 18*c*f*tan(e/2 + f*x/2)**5 - 18*c*f*tan(e/2 + f*x/2)**4 + 18*c*f*tan(e/2 + f*x/2)**3 - 18*c*f*tan(e/2 + f*x/2)**2 + 6*c*f*tan(e/2 + f*x/2) - 6*c*f) + 180*B*a**3*f*x*tan(e/2 + f*x/2)**2/(6*c*f*tan(e/2 + f*x/2)**7 - 6*c*f*tan(e/2 + f*x/2)**6 + 18*c*f*tan(e/2 + f*x/2)**5 - 18*c*f*tan(e/2 + f*x/2)**4 + 18*c*f*tan(e/2 + f*x/2)**3 - 18*c*f*tan(e/2 + f*x/2)**2 + 6*c*f*tan(e/2 + f*x/2) - 6*c*f) - 60*B*a**3*f*x*tan(e/2 + f*x/2)/(6*c*f*tan(e/2 + f*x/2)**7 - 6*c*f*tan(e/2 + f*x/2)**6 + 18*c*f*tan(e/2 + f*x/2)**5 - 18*c*f*tan(e/2 + f*x/2)**4 + 18*c*f*tan(e/2 + f*x/2)**3 - 18*c*f*tan(e/2 + f*x/2)**2 + 6*c*f*tan(e/2 + f*x/2) - 6*c*f) + 60*B*a**3*f*x/(6*c*f*tan(e/2 + f*x/2)**7 - 6*c*f*tan(e/2 + f*x/2)**6 + 18*c*f*tan(e/2 + f*x/2)**5 - 18*c*f*tan(e/2 + f*x/2)**4 + 18*c*f*tan(e/2 + f*x/2)**3 - 18*c*f*tan(e/2 + f*x/2)**2 + 6*c*f*tan(e/2 + f*x/2) - 6*c*f) - 120*B*a**3*tan(e/2 + f*x/2)**6/(6*c*f*tan(e/2 + f*x/2)**7 - 6*c*f*tan(e/2 + f*x/2)**6 + 18*c*f*tan(e/2 + f*x/2)**5 - 18*c*f*tan(e/2 + f*x/2)**4 + 18*c*f*tan(e/2 + f*x/2)**3 - 18*c*f*tan(e/2 + f*x/2)**2 + 6*c*f*tan(e/2 + f*x/2) - 6*c*f) + 108*B*a**3*tan(e/2 + f*x/2)**5/(6*c*f*tan(e/2 + f*x/2)**7 - 6*c*f*tan(e/2 + f*x/2)**6 + 18*c*f*tan(e/2 + f*x/2)**5 - 18*c*f*tan(e/2 + f*x/2)**4 + 18*c*f*tan(e/2 + f*x/2)**3 - 18*c*f*tan(e/2 + f*x/2)**2 + 6*c*f*tan(e/2 + f*x/2) - 6*c*f) - 372*B*a**3*tan(e/2 + f*x/2)**4/(6*c*f*tan(e/2 + f*x/2)**7 - 6*c*f*tan(e/2 + f*x/2)**6 + 18*c*f*tan(e/2 + f*x/2)**5 - 18*c*f*tan(e/2 + f*x/2)**4 + 18*c*f*tan(e/2 + f*x/2)**3 - 18*c*f*tan(e/2 + f*x/2)**2 + 6*c*f*tan(e/2 + f*x/2) - 6*c*f) + 192*B*a**3*tan(e/2 + f*x/2)**3/(6*c*f*tan(e/2 + f*x/2)**7 - 6*c*f*tan(e/2 + f*x/2)**6 + 18*c*f*tan(e/2 + f*x/2)**5 - 18*c*f*tan(e/2 + f*x/2)**4 + 18*c*f*tan(e/2 + f*x/2)**3 - 18*c*f*tan(e/2 + f*x/2)**2 + 6*c*f*tan(e/2 + f*x/2) - 6*c*f) - 456*B*a**3*tan(e/2 + f*x/2)**2/(6*c*f*tan(e/2 + f*x/2)**7 - 6*c*f*tan(e/2 + f*x/2)**6 + 18*c*f*tan(e/2 + f*x/2)**5 - 18*c*f*tan(e/2 + f*x/2)**4 + 18*c*f*tan(e/2 + f*x/2)**3 - 18*c*f*tan(e/2 + f*x/2)**2 + 6*c*f*tan(e/2 + f*x/2) - 6*c*f) + 68*B*a**3*tan(e/2 + f*x/2)/(6*c*f*tan(e/2 + f*x/2)**7 - 6*c*f*tan(e/2 + f*x/2)**6 + 18*c*f*tan(e/2 + f*x/2)**5 - 18*c*f*tan(e/2 + f*x/2)**4 + 18*c*f*tan(e/2 + f*x/2)**3 - 18*c*f*tan(e/2 + f*x/2)**2 + 6*c*f*tan(e/2 + f*x/2) - 6*c*f) - 188*B*a**3/(6*c*f*tan(e/2 + f*x/2)**7 - 6*c*f*tan(e/2 + f*x/2)**6 + 18*c*f*tan(e/2 + f*x/2)**5 - 18*c*f*tan(e/2 + f*x/2)**4 + 18*c*f*tan(e/2 + f*x/2)**3 - 18*c*f*tan(e/2 + f*x/2)**2 + 6*c*f*tan(e/2 + f*x/2) - 6*c*f), Ne(f, 0)), (x*(A + B*sin(e))*(a*sin(e) + a)**3/(-c*sin(e) + c), True))","A",0
45,1,4665,0,29.894145," ","integrate((a+a*sin(f*x+e))**3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**2,x)","\begin{cases} \frac{30 A a^{3} f x \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 42 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c^{2} f} - \frac{90 A a^{3} f x \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 42 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c^{2} f} + \frac{150 A a^{3} f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 42 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c^{2} f} - \frac{210 A a^{3} f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 42 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c^{2} f} + \frac{210 A a^{3} f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 42 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c^{2} f} - \frac{150 A a^{3} f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 42 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c^{2} f} + \frac{90 A a^{3} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 42 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c^{2} f} - \frac{30 A a^{3} f x}{6 c^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 42 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c^{2} f} + \frac{48 A a^{3} \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 42 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c^{2} f} - \frac{204 A a^{3} \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 42 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c^{2} f} + \frac{212 A a^{3} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 42 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c^{2} f} - \frac{432 A a^{3} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 42 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c^{2} f} + \frac{256 A a^{3} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 42 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c^{2} f} - \frac{228 A a^{3} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 42 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c^{2} f} + \frac{92 A a^{3}}{6 c^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 42 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c^{2} f} + \frac{75 B a^{3} f x \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 42 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c^{2} f} - \frac{225 B a^{3} f x \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 42 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c^{2} f} + \frac{375 B a^{3} f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 42 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c^{2} f} - \frac{525 B a^{3} f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 42 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c^{2} f} + \frac{525 B a^{3} f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 42 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c^{2} f} - \frac{375 B a^{3} f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 42 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c^{2} f} + \frac{225 B a^{3} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 42 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c^{2} f} - \frac{75 B a^{3} f x}{6 c^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 42 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c^{2} f} + \frac{150 B a^{3} \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 42 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c^{2} f} - \frac{462 B a^{3} \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 42 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c^{2} f} + \frac{656 B a^{3} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 42 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c^{2} f} - \frac{996 B a^{3} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 42 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c^{2} f} + \frac{718 B a^{3} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 42 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c^{2} f} - \frac{558 B a^{3} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 c^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 42 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c^{2} f} + \frac{236 B a^{3}}{6 c^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 18 c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 42 c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 c^{2} f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right) \left(a \sin{\left(e \right)} + a\right)^{3}}{\left(- c \sin{\left(e \right)} + c\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((30*A*a**3*f*x*tan(e/2 + f*x/2)**7/(6*c**2*f*tan(e/2 + f*x/2)**7 - 18*c**2*f*tan(e/2 + f*x/2)**6 + 30*c**2*f*tan(e/2 + f*x/2)**5 - 42*c**2*f*tan(e/2 + f*x/2)**4 + 42*c**2*f*tan(e/2 + f*x/2)**3 - 30*c**2*f*tan(e/2 + f*x/2)**2 + 18*c**2*f*tan(e/2 + f*x/2) - 6*c**2*f) - 90*A*a**3*f*x*tan(e/2 + f*x/2)**6/(6*c**2*f*tan(e/2 + f*x/2)**7 - 18*c**2*f*tan(e/2 + f*x/2)**6 + 30*c**2*f*tan(e/2 + f*x/2)**5 - 42*c**2*f*tan(e/2 + f*x/2)**4 + 42*c**2*f*tan(e/2 + f*x/2)**3 - 30*c**2*f*tan(e/2 + f*x/2)**2 + 18*c**2*f*tan(e/2 + f*x/2) - 6*c**2*f) + 150*A*a**3*f*x*tan(e/2 + f*x/2)**5/(6*c**2*f*tan(e/2 + f*x/2)**7 - 18*c**2*f*tan(e/2 + f*x/2)**6 + 30*c**2*f*tan(e/2 + f*x/2)**5 - 42*c**2*f*tan(e/2 + f*x/2)**4 + 42*c**2*f*tan(e/2 + f*x/2)**3 - 30*c**2*f*tan(e/2 + f*x/2)**2 + 18*c**2*f*tan(e/2 + f*x/2) - 6*c**2*f) - 210*A*a**3*f*x*tan(e/2 + f*x/2)**4/(6*c**2*f*tan(e/2 + f*x/2)**7 - 18*c**2*f*tan(e/2 + f*x/2)**6 + 30*c**2*f*tan(e/2 + f*x/2)**5 - 42*c**2*f*tan(e/2 + f*x/2)**4 + 42*c**2*f*tan(e/2 + f*x/2)**3 - 30*c**2*f*tan(e/2 + f*x/2)**2 + 18*c**2*f*tan(e/2 + f*x/2) - 6*c**2*f) + 210*A*a**3*f*x*tan(e/2 + f*x/2)**3/(6*c**2*f*tan(e/2 + f*x/2)**7 - 18*c**2*f*tan(e/2 + f*x/2)**6 + 30*c**2*f*tan(e/2 + f*x/2)**5 - 42*c**2*f*tan(e/2 + f*x/2)**4 + 42*c**2*f*tan(e/2 + f*x/2)**3 - 30*c**2*f*tan(e/2 + f*x/2)**2 + 18*c**2*f*tan(e/2 + f*x/2) - 6*c**2*f) - 150*A*a**3*f*x*tan(e/2 + f*x/2)**2/(6*c**2*f*tan(e/2 + f*x/2)**7 - 18*c**2*f*tan(e/2 + f*x/2)**6 + 30*c**2*f*tan(e/2 + f*x/2)**5 - 42*c**2*f*tan(e/2 + f*x/2)**4 + 42*c**2*f*tan(e/2 + f*x/2)**3 - 30*c**2*f*tan(e/2 + f*x/2)**2 + 18*c**2*f*tan(e/2 + f*x/2) - 6*c**2*f) + 90*A*a**3*f*x*tan(e/2 + f*x/2)/(6*c**2*f*tan(e/2 + f*x/2)**7 - 18*c**2*f*tan(e/2 + f*x/2)**6 + 30*c**2*f*tan(e/2 + f*x/2)**5 - 42*c**2*f*tan(e/2 + f*x/2)**4 + 42*c**2*f*tan(e/2 + f*x/2)**3 - 30*c**2*f*tan(e/2 + f*x/2)**2 + 18*c**2*f*tan(e/2 + f*x/2) - 6*c**2*f) - 30*A*a**3*f*x/(6*c**2*f*tan(e/2 + f*x/2)**7 - 18*c**2*f*tan(e/2 + f*x/2)**6 + 30*c**2*f*tan(e/2 + f*x/2)**5 - 42*c**2*f*tan(e/2 + f*x/2)**4 + 42*c**2*f*tan(e/2 + f*x/2)**3 - 30*c**2*f*tan(e/2 + f*x/2)**2 + 18*c**2*f*tan(e/2 + f*x/2) - 6*c**2*f) + 48*A*a**3*tan(e/2 + f*x/2)**6/(6*c**2*f*tan(e/2 + f*x/2)**7 - 18*c**2*f*tan(e/2 + f*x/2)**6 + 30*c**2*f*tan(e/2 + f*x/2)**5 - 42*c**2*f*tan(e/2 + f*x/2)**4 + 42*c**2*f*tan(e/2 + f*x/2)**3 - 30*c**2*f*tan(e/2 + f*x/2)**2 + 18*c**2*f*tan(e/2 + f*x/2) - 6*c**2*f) - 204*A*a**3*tan(e/2 + f*x/2)**5/(6*c**2*f*tan(e/2 + f*x/2)**7 - 18*c**2*f*tan(e/2 + f*x/2)**6 + 30*c**2*f*tan(e/2 + f*x/2)**5 - 42*c**2*f*tan(e/2 + f*x/2)**4 + 42*c**2*f*tan(e/2 + f*x/2)**3 - 30*c**2*f*tan(e/2 + f*x/2)**2 + 18*c**2*f*tan(e/2 + f*x/2) - 6*c**2*f) + 212*A*a**3*tan(e/2 + f*x/2)**4/(6*c**2*f*tan(e/2 + f*x/2)**7 - 18*c**2*f*tan(e/2 + f*x/2)**6 + 30*c**2*f*tan(e/2 + f*x/2)**5 - 42*c**2*f*tan(e/2 + f*x/2)**4 + 42*c**2*f*tan(e/2 + f*x/2)**3 - 30*c**2*f*tan(e/2 + f*x/2)**2 + 18*c**2*f*tan(e/2 + f*x/2) - 6*c**2*f) - 432*A*a**3*tan(e/2 + f*x/2)**3/(6*c**2*f*tan(e/2 + f*x/2)**7 - 18*c**2*f*tan(e/2 + f*x/2)**6 + 30*c**2*f*tan(e/2 + f*x/2)**5 - 42*c**2*f*tan(e/2 + f*x/2)**4 + 42*c**2*f*tan(e/2 + f*x/2)**3 - 30*c**2*f*tan(e/2 + f*x/2)**2 + 18*c**2*f*tan(e/2 + f*x/2) - 6*c**2*f) + 256*A*a**3*tan(e/2 + f*x/2)**2/(6*c**2*f*tan(e/2 + f*x/2)**7 - 18*c**2*f*tan(e/2 + f*x/2)**6 + 30*c**2*f*tan(e/2 + f*x/2)**5 - 42*c**2*f*tan(e/2 + f*x/2)**4 + 42*c**2*f*tan(e/2 + f*x/2)**3 - 30*c**2*f*tan(e/2 + f*x/2)**2 + 18*c**2*f*tan(e/2 + f*x/2) - 6*c**2*f) - 228*A*a**3*tan(e/2 + f*x/2)/(6*c**2*f*tan(e/2 + f*x/2)**7 - 18*c**2*f*tan(e/2 + f*x/2)**6 + 30*c**2*f*tan(e/2 + f*x/2)**5 - 42*c**2*f*tan(e/2 + f*x/2)**4 + 42*c**2*f*tan(e/2 + f*x/2)**3 - 30*c**2*f*tan(e/2 + f*x/2)**2 + 18*c**2*f*tan(e/2 + f*x/2) - 6*c**2*f) + 92*A*a**3/(6*c**2*f*tan(e/2 + f*x/2)**7 - 18*c**2*f*tan(e/2 + f*x/2)**6 + 30*c**2*f*tan(e/2 + f*x/2)**5 - 42*c**2*f*tan(e/2 + f*x/2)**4 + 42*c**2*f*tan(e/2 + f*x/2)**3 - 30*c**2*f*tan(e/2 + f*x/2)**2 + 18*c**2*f*tan(e/2 + f*x/2) - 6*c**2*f) + 75*B*a**3*f*x*tan(e/2 + f*x/2)**7/(6*c**2*f*tan(e/2 + f*x/2)**7 - 18*c**2*f*tan(e/2 + f*x/2)**6 + 30*c**2*f*tan(e/2 + f*x/2)**5 - 42*c**2*f*tan(e/2 + f*x/2)**4 + 42*c**2*f*tan(e/2 + f*x/2)**3 - 30*c**2*f*tan(e/2 + f*x/2)**2 + 18*c**2*f*tan(e/2 + f*x/2) - 6*c**2*f) - 225*B*a**3*f*x*tan(e/2 + f*x/2)**6/(6*c**2*f*tan(e/2 + f*x/2)**7 - 18*c**2*f*tan(e/2 + f*x/2)**6 + 30*c**2*f*tan(e/2 + f*x/2)**5 - 42*c**2*f*tan(e/2 + f*x/2)**4 + 42*c**2*f*tan(e/2 + f*x/2)**3 - 30*c**2*f*tan(e/2 + f*x/2)**2 + 18*c**2*f*tan(e/2 + f*x/2) - 6*c**2*f) + 375*B*a**3*f*x*tan(e/2 + f*x/2)**5/(6*c**2*f*tan(e/2 + f*x/2)**7 - 18*c**2*f*tan(e/2 + f*x/2)**6 + 30*c**2*f*tan(e/2 + f*x/2)**5 - 42*c**2*f*tan(e/2 + f*x/2)**4 + 42*c**2*f*tan(e/2 + f*x/2)**3 - 30*c**2*f*tan(e/2 + f*x/2)**2 + 18*c**2*f*tan(e/2 + f*x/2) - 6*c**2*f) - 525*B*a**3*f*x*tan(e/2 + f*x/2)**4/(6*c**2*f*tan(e/2 + f*x/2)**7 - 18*c**2*f*tan(e/2 + f*x/2)**6 + 30*c**2*f*tan(e/2 + f*x/2)**5 - 42*c**2*f*tan(e/2 + f*x/2)**4 + 42*c**2*f*tan(e/2 + f*x/2)**3 - 30*c**2*f*tan(e/2 + f*x/2)**2 + 18*c**2*f*tan(e/2 + f*x/2) - 6*c**2*f) + 525*B*a**3*f*x*tan(e/2 + f*x/2)**3/(6*c**2*f*tan(e/2 + f*x/2)**7 - 18*c**2*f*tan(e/2 + f*x/2)**6 + 30*c**2*f*tan(e/2 + f*x/2)**5 - 42*c**2*f*tan(e/2 + f*x/2)**4 + 42*c**2*f*tan(e/2 + f*x/2)**3 - 30*c**2*f*tan(e/2 + f*x/2)**2 + 18*c**2*f*tan(e/2 + f*x/2) - 6*c**2*f) - 375*B*a**3*f*x*tan(e/2 + f*x/2)**2/(6*c**2*f*tan(e/2 + f*x/2)**7 - 18*c**2*f*tan(e/2 + f*x/2)**6 + 30*c**2*f*tan(e/2 + f*x/2)**5 - 42*c**2*f*tan(e/2 + f*x/2)**4 + 42*c**2*f*tan(e/2 + f*x/2)**3 - 30*c**2*f*tan(e/2 + f*x/2)**2 + 18*c**2*f*tan(e/2 + f*x/2) - 6*c**2*f) + 225*B*a**3*f*x*tan(e/2 + f*x/2)/(6*c**2*f*tan(e/2 + f*x/2)**7 - 18*c**2*f*tan(e/2 + f*x/2)**6 + 30*c**2*f*tan(e/2 + f*x/2)**5 - 42*c**2*f*tan(e/2 + f*x/2)**4 + 42*c**2*f*tan(e/2 + f*x/2)**3 - 30*c**2*f*tan(e/2 + f*x/2)**2 + 18*c**2*f*tan(e/2 + f*x/2) - 6*c**2*f) - 75*B*a**3*f*x/(6*c**2*f*tan(e/2 + f*x/2)**7 - 18*c**2*f*tan(e/2 + f*x/2)**6 + 30*c**2*f*tan(e/2 + f*x/2)**5 - 42*c**2*f*tan(e/2 + f*x/2)**4 + 42*c**2*f*tan(e/2 + f*x/2)**3 - 30*c**2*f*tan(e/2 + f*x/2)**2 + 18*c**2*f*tan(e/2 + f*x/2) - 6*c**2*f) + 150*B*a**3*tan(e/2 + f*x/2)**6/(6*c**2*f*tan(e/2 + f*x/2)**7 - 18*c**2*f*tan(e/2 + f*x/2)**6 + 30*c**2*f*tan(e/2 + f*x/2)**5 - 42*c**2*f*tan(e/2 + f*x/2)**4 + 42*c**2*f*tan(e/2 + f*x/2)**3 - 30*c**2*f*tan(e/2 + f*x/2)**2 + 18*c**2*f*tan(e/2 + f*x/2) - 6*c**2*f) - 462*B*a**3*tan(e/2 + f*x/2)**5/(6*c**2*f*tan(e/2 + f*x/2)**7 - 18*c**2*f*tan(e/2 + f*x/2)**6 + 30*c**2*f*tan(e/2 + f*x/2)**5 - 42*c**2*f*tan(e/2 + f*x/2)**4 + 42*c**2*f*tan(e/2 + f*x/2)**3 - 30*c**2*f*tan(e/2 + f*x/2)**2 + 18*c**2*f*tan(e/2 + f*x/2) - 6*c**2*f) + 656*B*a**3*tan(e/2 + f*x/2)**4/(6*c**2*f*tan(e/2 + f*x/2)**7 - 18*c**2*f*tan(e/2 + f*x/2)**6 + 30*c**2*f*tan(e/2 + f*x/2)**5 - 42*c**2*f*tan(e/2 + f*x/2)**4 + 42*c**2*f*tan(e/2 + f*x/2)**3 - 30*c**2*f*tan(e/2 + f*x/2)**2 + 18*c**2*f*tan(e/2 + f*x/2) - 6*c**2*f) - 996*B*a**3*tan(e/2 + f*x/2)**3/(6*c**2*f*tan(e/2 + f*x/2)**7 - 18*c**2*f*tan(e/2 + f*x/2)**6 + 30*c**2*f*tan(e/2 + f*x/2)**5 - 42*c**2*f*tan(e/2 + f*x/2)**4 + 42*c**2*f*tan(e/2 + f*x/2)**3 - 30*c**2*f*tan(e/2 + f*x/2)**2 + 18*c**2*f*tan(e/2 + f*x/2) - 6*c**2*f) + 718*B*a**3*tan(e/2 + f*x/2)**2/(6*c**2*f*tan(e/2 + f*x/2)**7 - 18*c**2*f*tan(e/2 + f*x/2)**6 + 30*c**2*f*tan(e/2 + f*x/2)**5 - 42*c**2*f*tan(e/2 + f*x/2)**4 + 42*c**2*f*tan(e/2 + f*x/2)**3 - 30*c**2*f*tan(e/2 + f*x/2)**2 + 18*c**2*f*tan(e/2 + f*x/2) - 6*c**2*f) - 558*B*a**3*tan(e/2 + f*x/2)/(6*c**2*f*tan(e/2 + f*x/2)**7 - 18*c**2*f*tan(e/2 + f*x/2)**6 + 30*c**2*f*tan(e/2 + f*x/2)**5 - 42*c**2*f*tan(e/2 + f*x/2)**4 + 42*c**2*f*tan(e/2 + f*x/2)**3 - 30*c**2*f*tan(e/2 + f*x/2)**2 + 18*c**2*f*tan(e/2 + f*x/2) - 6*c**2*f) + 236*B*a**3/(6*c**2*f*tan(e/2 + f*x/2)**7 - 18*c**2*f*tan(e/2 + f*x/2)**6 + 30*c**2*f*tan(e/2 + f*x/2)**5 - 42*c**2*f*tan(e/2 + f*x/2)**4 + 42*c**2*f*tan(e/2 + f*x/2)**3 - 30*c**2*f*tan(e/2 + f*x/2)**2 + 18*c**2*f*tan(e/2 + f*x/2) - 6*c**2*f), Ne(f, 0)), (x*(A + B*sin(e))*(a*sin(e) + a)**3/(-c*sin(e) + c)**2, True))","A",0
46,1,4665,0,48.976695," ","integrate((a+a*sin(f*x+e))**3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**3,x)","\begin{cases} - \frac{15 A a^{3} f x \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 c^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 225 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 165 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} + \frac{75 A a^{3} f x \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 c^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 225 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 165 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} - \frac{165 A a^{3} f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 c^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 225 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 165 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} + \frac{225 A a^{3} f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 c^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 225 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 165 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} - \frac{225 A a^{3} f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 c^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 225 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 165 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} + \frac{165 A a^{3} f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 c^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 225 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 165 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} - \frac{75 A a^{3} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 c^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 225 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 165 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} + \frac{15 A a^{3} f x}{15 c^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 225 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 165 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} - \frac{60 A a^{3} \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 c^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 225 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 165 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} + \frac{120 A a^{3} \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 c^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 225 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 165 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} - \frac{460 A a^{3} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 c^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 225 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 165 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} + \frac{320 A a^{3} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 c^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 225 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 165 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} - \frac{452 A a^{3} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 c^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 225 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 165 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} + \frac{200 A a^{3} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 c^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 225 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 165 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} - \frac{52 A a^{3}}{15 c^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 225 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 165 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} - \frac{90 B a^{3} f x \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 c^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 225 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 165 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} + \frac{450 B a^{3} f x \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 c^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 225 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 165 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} - \frac{990 B a^{3} f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 c^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 225 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 165 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} + \frac{1350 B a^{3} f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 c^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 225 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 165 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} - \frac{1350 B a^{3} f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 c^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 225 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 165 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} + \frac{990 B a^{3} f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 c^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 225 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 165 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} - \frac{450 B a^{3} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 c^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 225 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 165 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} + \frac{90 B a^{3} f x}{15 c^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 225 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 165 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} - \frac{180 B a^{3} \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 c^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 225 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 165 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} + \frac{870 B a^{3} \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 c^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 225 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 165 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} - \frac{2010 B a^{3} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 c^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 225 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 165 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} + \frac{2220 B a^{3} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 c^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 225 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 165 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} - \frac{2232 B a^{3} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 c^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 225 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 165 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} + \frac{1230 B a^{3} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 c^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 225 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 165 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} - \frac{282 B a^{3}}{15 c^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 225 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 165 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 c^{3} f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right) \left(a \sin{\left(e \right)} + a\right)^{3}}{\left(- c \sin{\left(e \right)} + c\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-15*A*a**3*f*x*tan(e/2 + f*x/2)**7/(15*c**3*f*tan(e/2 + f*x/2)**7 - 75*c**3*f*tan(e/2 + f*x/2)**6 + 165*c**3*f*tan(e/2 + f*x/2)**5 - 225*c**3*f*tan(e/2 + f*x/2)**4 + 225*c**3*f*tan(e/2 + f*x/2)**3 - 165*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) + 75*A*a**3*f*x*tan(e/2 + f*x/2)**6/(15*c**3*f*tan(e/2 + f*x/2)**7 - 75*c**3*f*tan(e/2 + f*x/2)**6 + 165*c**3*f*tan(e/2 + f*x/2)**5 - 225*c**3*f*tan(e/2 + f*x/2)**4 + 225*c**3*f*tan(e/2 + f*x/2)**3 - 165*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) - 165*A*a**3*f*x*tan(e/2 + f*x/2)**5/(15*c**3*f*tan(e/2 + f*x/2)**7 - 75*c**3*f*tan(e/2 + f*x/2)**6 + 165*c**3*f*tan(e/2 + f*x/2)**5 - 225*c**3*f*tan(e/2 + f*x/2)**4 + 225*c**3*f*tan(e/2 + f*x/2)**3 - 165*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) + 225*A*a**3*f*x*tan(e/2 + f*x/2)**4/(15*c**3*f*tan(e/2 + f*x/2)**7 - 75*c**3*f*tan(e/2 + f*x/2)**6 + 165*c**3*f*tan(e/2 + f*x/2)**5 - 225*c**3*f*tan(e/2 + f*x/2)**4 + 225*c**3*f*tan(e/2 + f*x/2)**3 - 165*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) - 225*A*a**3*f*x*tan(e/2 + f*x/2)**3/(15*c**3*f*tan(e/2 + f*x/2)**7 - 75*c**3*f*tan(e/2 + f*x/2)**6 + 165*c**3*f*tan(e/2 + f*x/2)**5 - 225*c**3*f*tan(e/2 + f*x/2)**4 + 225*c**3*f*tan(e/2 + f*x/2)**3 - 165*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) + 165*A*a**3*f*x*tan(e/2 + f*x/2)**2/(15*c**3*f*tan(e/2 + f*x/2)**7 - 75*c**3*f*tan(e/2 + f*x/2)**6 + 165*c**3*f*tan(e/2 + f*x/2)**5 - 225*c**3*f*tan(e/2 + f*x/2)**4 + 225*c**3*f*tan(e/2 + f*x/2)**3 - 165*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) - 75*A*a**3*f*x*tan(e/2 + f*x/2)/(15*c**3*f*tan(e/2 + f*x/2)**7 - 75*c**3*f*tan(e/2 + f*x/2)**6 + 165*c**3*f*tan(e/2 + f*x/2)**5 - 225*c**3*f*tan(e/2 + f*x/2)**4 + 225*c**3*f*tan(e/2 + f*x/2)**3 - 165*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) + 15*A*a**3*f*x/(15*c**3*f*tan(e/2 + f*x/2)**7 - 75*c**3*f*tan(e/2 + f*x/2)**6 + 165*c**3*f*tan(e/2 + f*x/2)**5 - 225*c**3*f*tan(e/2 + f*x/2)**4 + 225*c**3*f*tan(e/2 + f*x/2)**3 - 165*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) - 60*A*a**3*tan(e/2 + f*x/2)**6/(15*c**3*f*tan(e/2 + f*x/2)**7 - 75*c**3*f*tan(e/2 + f*x/2)**6 + 165*c**3*f*tan(e/2 + f*x/2)**5 - 225*c**3*f*tan(e/2 + f*x/2)**4 + 225*c**3*f*tan(e/2 + f*x/2)**3 - 165*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) + 120*A*a**3*tan(e/2 + f*x/2)**5/(15*c**3*f*tan(e/2 + f*x/2)**7 - 75*c**3*f*tan(e/2 + f*x/2)**6 + 165*c**3*f*tan(e/2 + f*x/2)**5 - 225*c**3*f*tan(e/2 + f*x/2)**4 + 225*c**3*f*tan(e/2 + f*x/2)**3 - 165*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) - 460*A*a**3*tan(e/2 + f*x/2)**4/(15*c**3*f*tan(e/2 + f*x/2)**7 - 75*c**3*f*tan(e/2 + f*x/2)**6 + 165*c**3*f*tan(e/2 + f*x/2)**5 - 225*c**3*f*tan(e/2 + f*x/2)**4 + 225*c**3*f*tan(e/2 + f*x/2)**3 - 165*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) + 320*A*a**3*tan(e/2 + f*x/2)**3/(15*c**3*f*tan(e/2 + f*x/2)**7 - 75*c**3*f*tan(e/2 + f*x/2)**6 + 165*c**3*f*tan(e/2 + f*x/2)**5 - 225*c**3*f*tan(e/2 + f*x/2)**4 + 225*c**3*f*tan(e/2 + f*x/2)**3 - 165*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) - 452*A*a**3*tan(e/2 + f*x/2)**2/(15*c**3*f*tan(e/2 + f*x/2)**7 - 75*c**3*f*tan(e/2 + f*x/2)**6 + 165*c**3*f*tan(e/2 + f*x/2)**5 - 225*c**3*f*tan(e/2 + f*x/2)**4 + 225*c**3*f*tan(e/2 + f*x/2)**3 - 165*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) + 200*A*a**3*tan(e/2 + f*x/2)/(15*c**3*f*tan(e/2 + f*x/2)**7 - 75*c**3*f*tan(e/2 + f*x/2)**6 + 165*c**3*f*tan(e/2 + f*x/2)**5 - 225*c**3*f*tan(e/2 + f*x/2)**4 + 225*c**3*f*tan(e/2 + f*x/2)**3 - 165*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) - 52*A*a**3/(15*c**3*f*tan(e/2 + f*x/2)**7 - 75*c**3*f*tan(e/2 + f*x/2)**6 + 165*c**3*f*tan(e/2 + f*x/2)**5 - 225*c**3*f*tan(e/2 + f*x/2)**4 + 225*c**3*f*tan(e/2 + f*x/2)**3 - 165*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) - 90*B*a**3*f*x*tan(e/2 + f*x/2)**7/(15*c**3*f*tan(e/2 + f*x/2)**7 - 75*c**3*f*tan(e/2 + f*x/2)**6 + 165*c**3*f*tan(e/2 + f*x/2)**5 - 225*c**3*f*tan(e/2 + f*x/2)**4 + 225*c**3*f*tan(e/2 + f*x/2)**3 - 165*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) + 450*B*a**3*f*x*tan(e/2 + f*x/2)**6/(15*c**3*f*tan(e/2 + f*x/2)**7 - 75*c**3*f*tan(e/2 + f*x/2)**6 + 165*c**3*f*tan(e/2 + f*x/2)**5 - 225*c**3*f*tan(e/2 + f*x/2)**4 + 225*c**3*f*tan(e/2 + f*x/2)**3 - 165*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) - 990*B*a**3*f*x*tan(e/2 + f*x/2)**5/(15*c**3*f*tan(e/2 + f*x/2)**7 - 75*c**3*f*tan(e/2 + f*x/2)**6 + 165*c**3*f*tan(e/2 + f*x/2)**5 - 225*c**3*f*tan(e/2 + f*x/2)**4 + 225*c**3*f*tan(e/2 + f*x/2)**3 - 165*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) + 1350*B*a**3*f*x*tan(e/2 + f*x/2)**4/(15*c**3*f*tan(e/2 + f*x/2)**7 - 75*c**3*f*tan(e/2 + f*x/2)**6 + 165*c**3*f*tan(e/2 + f*x/2)**5 - 225*c**3*f*tan(e/2 + f*x/2)**4 + 225*c**3*f*tan(e/2 + f*x/2)**3 - 165*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) - 1350*B*a**3*f*x*tan(e/2 + f*x/2)**3/(15*c**3*f*tan(e/2 + f*x/2)**7 - 75*c**3*f*tan(e/2 + f*x/2)**6 + 165*c**3*f*tan(e/2 + f*x/2)**5 - 225*c**3*f*tan(e/2 + f*x/2)**4 + 225*c**3*f*tan(e/2 + f*x/2)**3 - 165*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) + 990*B*a**3*f*x*tan(e/2 + f*x/2)**2/(15*c**3*f*tan(e/2 + f*x/2)**7 - 75*c**3*f*tan(e/2 + f*x/2)**6 + 165*c**3*f*tan(e/2 + f*x/2)**5 - 225*c**3*f*tan(e/2 + f*x/2)**4 + 225*c**3*f*tan(e/2 + f*x/2)**3 - 165*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) - 450*B*a**3*f*x*tan(e/2 + f*x/2)/(15*c**3*f*tan(e/2 + f*x/2)**7 - 75*c**3*f*tan(e/2 + f*x/2)**6 + 165*c**3*f*tan(e/2 + f*x/2)**5 - 225*c**3*f*tan(e/2 + f*x/2)**4 + 225*c**3*f*tan(e/2 + f*x/2)**3 - 165*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) + 90*B*a**3*f*x/(15*c**3*f*tan(e/2 + f*x/2)**7 - 75*c**3*f*tan(e/2 + f*x/2)**6 + 165*c**3*f*tan(e/2 + f*x/2)**5 - 225*c**3*f*tan(e/2 + f*x/2)**4 + 225*c**3*f*tan(e/2 + f*x/2)**3 - 165*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) - 180*B*a**3*tan(e/2 + f*x/2)**6/(15*c**3*f*tan(e/2 + f*x/2)**7 - 75*c**3*f*tan(e/2 + f*x/2)**6 + 165*c**3*f*tan(e/2 + f*x/2)**5 - 225*c**3*f*tan(e/2 + f*x/2)**4 + 225*c**3*f*tan(e/2 + f*x/2)**3 - 165*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) + 870*B*a**3*tan(e/2 + f*x/2)**5/(15*c**3*f*tan(e/2 + f*x/2)**7 - 75*c**3*f*tan(e/2 + f*x/2)**6 + 165*c**3*f*tan(e/2 + f*x/2)**5 - 225*c**3*f*tan(e/2 + f*x/2)**4 + 225*c**3*f*tan(e/2 + f*x/2)**3 - 165*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) - 2010*B*a**3*tan(e/2 + f*x/2)**4/(15*c**3*f*tan(e/2 + f*x/2)**7 - 75*c**3*f*tan(e/2 + f*x/2)**6 + 165*c**3*f*tan(e/2 + f*x/2)**5 - 225*c**3*f*tan(e/2 + f*x/2)**4 + 225*c**3*f*tan(e/2 + f*x/2)**3 - 165*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) + 2220*B*a**3*tan(e/2 + f*x/2)**3/(15*c**3*f*tan(e/2 + f*x/2)**7 - 75*c**3*f*tan(e/2 + f*x/2)**6 + 165*c**3*f*tan(e/2 + f*x/2)**5 - 225*c**3*f*tan(e/2 + f*x/2)**4 + 225*c**3*f*tan(e/2 + f*x/2)**3 - 165*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) - 2232*B*a**3*tan(e/2 + f*x/2)**2/(15*c**3*f*tan(e/2 + f*x/2)**7 - 75*c**3*f*tan(e/2 + f*x/2)**6 + 165*c**3*f*tan(e/2 + f*x/2)**5 - 225*c**3*f*tan(e/2 + f*x/2)**4 + 225*c**3*f*tan(e/2 + f*x/2)**3 - 165*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) + 1230*B*a**3*tan(e/2 + f*x/2)/(15*c**3*f*tan(e/2 + f*x/2)**7 - 75*c**3*f*tan(e/2 + f*x/2)**6 + 165*c**3*f*tan(e/2 + f*x/2)**5 - 225*c**3*f*tan(e/2 + f*x/2)**4 + 225*c**3*f*tan(e/2 + f*x/2)**3 - 165*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f) - 282*B*a**3/(15*c**3*f*tan(e/2 + f*x/2)**7 - 75*c**3*f*tan(e/2 + f*x/2)**6 + 165*c**3*f*tan(e/2 + f*x/2)**5 - 225*c**3*f*tan(e/2 + f*x/2)**4 + 225*c**3*f*tan(e/2 + f*x/2)**3 - 165*c**3*f*tan(e/2 + f*x/2)**2 + 75*c**3*f*tan(e/2 + f*x/2) - 15*c**3*f), Ne(f, 0)), (x*(A + B*sin(e))*(a*sin(e) + a)**3/(-c*sin(e) + c)**3, True))","A",0
47,1,2951,0,76.726452," ","integrate((a+a*sin(f*x+e))**3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**4,x)","\begin{cases} - \frac{210 A a^{3} \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 735 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2205 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3675 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3675 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2205 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 735 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 c^{4} f} - \frac{1050 A a^{3} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 735 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2205 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3675 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3675 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2205 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 735 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 c^{4} f} - \frac{630 A a^{3} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 735 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2205 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3675 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3675 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2205 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 735 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 c^{4} f} - \frac{30 A a^{3}}{105 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 735 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2205 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3675 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3675 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2205 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 735 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 c^{4} f} + \frac{105 B a^{3} f x \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 735 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2205 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3675 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3675 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2205 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 735 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 c^{4} f} - \frac{735 B a^{3} f x \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 735 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2205 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3675 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3675 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2205 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 735 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 c^{4} f} + \frac{2205 B a^{3} f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 735 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2205 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3675 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3675 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2205 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 735 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 c^{4} f} - \frac{3675 B a^{3} f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 735 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2205 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3675 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3675 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2205 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 735 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 c^{4} f} + \frac{3675 B a^{3} f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 735 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2205 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3675 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3675 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2205 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 735 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 c^{4} f} - \frac{2205 B a^{3} f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 735 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2205 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3675 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3675 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2205 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 735 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 c^{4} f} + \frac{735 B a^{3} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 735 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2205 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3675 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3675 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2205 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 735 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 c^{4} f} - \frac{105 B a^{3} f x}{105 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 735 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2205 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3675 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3675 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2205 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 735 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 c^{4} f} + \frac{210 B a^{3} \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 735 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2205 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3675 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3675 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2205 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 735 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 c^{4} f} - \frac{1680 B a^{3} \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 735 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2205 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3675 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3675 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2205 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 735 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 c^{4} f} + \frac{3850 B a^{3} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 735 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2205 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3675 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3675 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2205 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 735 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 c^{4} f} - \frac{7840 B a^{3} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 735 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2205 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3675 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3675 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2205 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 735 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 c^{4} f} + \frac{5334 B a^{3} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 735 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2205 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3675 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3675 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2205 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 735 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 c^{4} f} - \frac{2128 B a^{3} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 735 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2205 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3675 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3675 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2205 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 735 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 c^{4} f} + \frac{334 B a^{3}}{105 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 735 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2205 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3675 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3675 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2205 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 735 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 c^{4} f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right) \left(a \sin{\left(e \right)} + a\right)^{3}}{\left(- c \sin{\left(e \right)} + c\right)^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-210*A*a**3*tan(e/2 + f*x/2)**6/(105*c**4*f*tan(e/2 + f*x/2)**7 - 735*c**4*f*tan(e/2 + f*x/2)**6 + 2205*c**4*f*tan(e/2 + f*x/2)**5 - 3675*c**4*f*tan(e/2 + f*x/2)**4 + 3675*c**4*f*tan(e/2 + f*x/2)**3 - 2205*c**4*f*tan(e/2 + f*x/2)**2 + 735*c**4*f*tan(e/2 + f*x/2) - 105*c**4*f) - 1050*A*a**3*tan(e/2 + f*x/2)**4/(105*c**4*f*tan(e/2 + f*x/2)**7 - 735*c**4*f*tan(e/2 + f*x/2)**6 + 2205*c**4*f*tan(e/2 + f*x/2)**5 - 3675*c**4*f*tan(e/2 + f*x/2)**4 + 3675*c**4*f*tan(e/2 + f*x/2)**3 - 2205*c**4*f*tan(e/2 + f*x/2)**2 + 735*c**4*f*tan(e/2 + f*x/2) - 105*c**4*f) - 630*A*a**3*tan(e/2 + f*x/2)**2/(105*c**4*f*tan(e/2 + f*x/2)**7 - 735*c**4*f*tan(e/2 + f*x/2)**6 + 2205*c**4*f*tan(e/2 + f*x/2)**5 - 3675*c**4*f*tan(e/2 + f*x/2)**4 + 3675*c**4*f*tan(e/2 + f*x/2)**3 - 2205*c**4*f*tan(e/2 + f*x/2)**2 + 735*c**4*f*tan(e/2 + f*x/2) - 105*c**4*f) - 30*A*a**3/(105*c**4*f*tan(e/2 + f*x/2)**7 - 735*c**4*f*tan(e/2 + f*x/2)**6 + 2205*c**4*f*tan(e/2 + f*x/2)**5 - 3675*c**4*f*tan(e/2 + f*x/2)**4 + 3675*c**4*f*tan(e/2 + f*x/2)**3 - 2205*c**4*f*tan(e/2 + f*x/2)**2 + 735*c**4*f*tan(e/2 + f*x/2) - 105*c**4*f) + 105*B*a**3*f*x*tan(e/2 + f*x/2)**7/(105*c**4*f*tan(e/2 + f*x/2)**7 - 735*c**4*f*tan(e/2 + f*x/2)**6 + 2205*c**4*f*tan(e/2 + f*x/2)**5 - 3675*c**4*f*tan(e/2 + f*x/2)**4 + 3675*c**4*f*tan(e/2 + f*x/2)**3 - 2205*c**4*f*tan(e/2 + f*x/2)**2 + 735*c**4*f*tan(e/2 + f*x/2) - 105*c**4*f) - 735*B*a**3*f*x*tan(e/2 + f*x/2)**6/(105*c**4*f*tan(e/2 + f*x/2)**7 - 735*c**4*f*tan(e/2 + f*x/2)**6 + 2205*c**4*f*tan(e/2 + f*x/2)**5 - 3675*c**4*f*tan(e/2 + f*x/2)**4 + 3675*c**4*f*tan(e/2 + f*x/2)**3 - 2205*c**4*f*tan(e/2 + f*x/2)**2 + 735*c**4*f*tan(e/2 + f*x/2) - 105*c**4*f) + 2205*B*a**3*f*x*tan(e/2 + f*x/2)**5/(105*c**4*f*tan(e/2 + f*x/2)**7 - 735*c**4*f*tan(e/2 + f*x/2)**6 + 2205*c**4*f*tan(e/2 + f*x/2)**5 - 3675*c**4*f*tan(e/2 + f*x/2)**4 + 3675*c**4*f*tan(e/2 + f*x/2)**3 - 2205*c**4*f*tan(e/2 + f*x/2)**2 + 735*c**4*f*tan(e/2 + f*x/2) - 105*c**4*f) - 3675*B*a**3*f*x*tan(e/2 + f*x/2)**4/(105*c**4*f*tan(e/2 + f*x/2)**7 - 735*c**4*f*tan(e/2 + f*x/2)**6 + 2205*c**4*f*tan(e/2 + f*x/2)**5 - 3675*c**4*f*tan(e/2 + f*x/2)**4 + 3675*c**4*f*tan(e/2 + f*x/2)**3 - 2205*c**4*f*tan(e/2 + f*x/2)**2 + 735*c**4*f*tan(e/2 + f*x/2) - 105*c**4*f) + 3675*B*a**3*f*x*tan(e/2 + f*x/2)**3/(105*c**4*f*tan(e/2 + f*x/2)**7 - 735*c**4*f*tan(e/2 + f*x/2)**6 + 2205*c**4*f*tan(e/2 + f*x/2)**5 - 3675*c**4*f*tan(e/2 + f*x/2)**4 + 3675*c**4*f*tan(e/2 + f*x/2)**3 - 2205*c**4*f*tan(e/2 + f*x/2)**2 + 735*c**4*f*tan(e/2 + f*x/2) - 105*c**4*f) - 2205*B*a**3*f*x*tan(e/2 + f*x/2)**2/(105*c**4*f*tan(e/2 + f*x/2)**7 - 735*c**4*f*tan(e/2 + f*x/2)**6 + 2205*c**4*f*tan(e/2 + f*x/2)**5 - 3675*c**4*f*tan(e/2 + f*x/2)**4 + 3675*c**4*f*tan(e/2 + f*x/2)**3 - 2205*c**4*f*tan(e/2 + f*x/2)**2 + 735*c**4*f*tan(e/2 + f*x/2) - 105*c**4*f) + 735*B*a**3*f*x*tan(e/2 + f*x/2)/(105*c**4*f*tan(e/2 + f*x/2)**7 - 735*c**4*f*tan(e/2 + f*x/2)**6 + 2205*c**4*f*tan(e/2 + f*x/2)**5 - 3675*c**4*f*tan(e/2 + f*x/2)**4 + 3675*c**4*f*tan(e/2 + f*x/2)**3 - 2205*c**4*f*tan(e/2 + f*x/2)**2 + 735*c**4*f*tan(e/2 + f*x/2) - 105*c**4*f) - 105*B*a**3*f*x/(105*c**4*f*tan(e/2 + f*x/2)**7 - 735*c**4*f*tan(e/2 + f*x/2)**6 + 2205*c**4*f*tan(e/2 + f*x/2)**5 - 3675*c**4*f*tan(e/2 + f*x/2)**4 + 3675*c**4*f*tan(e/2 + f*x/2)**3 - 2205*c**4*f*tan(e/2 + f*x/2)**2 + 735*c**4*f*tan(e/2 + f*x/2) - 105*c**4*f) + 210*B*a**3*tan(e/2 + f*x/2)**6/(105*c**4*f*tan(e/2 + f*x/2)**7 - 735*c**4*f*tan(e/2 + f*x/2)**6 + 2205*c**4*f*tan(e/2 + f*x/2)**5 - 3675*c**4*f*tan(e/2 + f*x/2)**4 + 3675*c**4*f*tan(e/2 + f*x/2)**3 - 2205*c**4*f*tan(e/2 + f*x/2)**2 + 735*c**4*f*tan(e/2 + f*x/2) - 105*c**4*f) - 1680*B*a**3*tan(e/2 + f*x/2)**5/(105*c**4*f*tan(e/2 + f*x/2)**7 - 735*c**4*f*tan(e/2 + f*x/2)**6 + 2205*c**4*f*tan(e/2 + f*x/2)**5 - 3675*c**4*f*tan(e/2 + f*x/2)**4 + 3675*c**4*f*tan(e/2 + f*x/2)**3 - 2205*c**4*f*tan(e/2 + f*x/2)**2 + 735*c**4*f*tan(e/2 + f*x/2) - 105*c**4*f) + 3850*B*a**3*tan(e/2 + f*x/2)**4/(105*c**4*f*tan(e/2 + f*x/2)**7 - 735*c**4*f*tan(e/2 + f*x/2)**6 + 2205*c**4*f*tan(e/2 + f*x/2)**5 - 3675*c**4*f*tan(e/2 + f*x/2)**4 + 3675*c**4*f*tan(e/2 + f*x/2)**3 - 2205*c**4*f*tan(e/2 + f*x/2)**2 + 735*c**4*f*tan(e/2 + f*x/2) - 105*c**4*f) - 7840*B*a**3*tan(e/2 + f*x/2)**3/(105*c**4*f*tan(e/2 + f*x/2)**7 - 735*c**4*f*tan(e/2 + f*x/2)**6 + 2205*c**4*f*tan(e/2 + f*x/2)**5 - 3675*c**4*f*tan(e/2 + f*x/2)**4 + 3675*c**4*f*tan(e/2 + f*x/2)**3 - 2205*c**4*f*tan(e/2 + f*x/2)**2 + 735*c**4*f*tan(e/2 + f*x/2) - 105*c**4*f) + 5334*B*a**3*tan(e/2 + f*x/2)**2/(105*c**4*f*tan(e/2 + f*x/2)**7 - 735*c**4*f*tan(e/2 + f*x/2)**6 + 2205*c**4*f*tan(e/2 + f*x/2)**5 - 3675*c**4*f*tan(e/2 + f*x/2)**4 + 3675*c**4*f*tan(e/2 + f*x/2)**3 - 2205*c**4*f*tan(e/2 + f*x/2)**2 + 735*c**4*f*tan(e/2 + f*x/2) - 105*c**4*f) - 2128*B*a**3*tan(e/2 + f*x/2)/(105*c**4*f*tan(e/2 + f*x/2)**7 - 735*c**4*f*tan(e/2 + f*x/2)**6 + 2205*c**4*f*tan(e/2 + f*x/2)**5 - 3675*c**4*f*tan(e/2 + f*x/2)**4 + 3675*c**4*f*tan(e/2 + f*x/2)**3 - 2205*c**4*f*tan(e/2 + f*x/2)**2 + 735*c**4*f*tan(e/2 + f*x/2) - 105*c**4*f) + 334*B*a**3/(105*c**4*f*tan(e/2 + f*x/2)**7 - 735*c**4*f*tan(e/2 + f*x/2)**6 + 2205*c**4*f*tan(e/2 + f*x/2)**5 - 3675*c**4*f*tan(e/2 + f*x/2)**4 + 3675*c**4*f*tan(e/2 + f*x/2)**3 - 2205*c**4*f*tan(e/2 + f*x/2)**2 + 735*c**4*f*tan(e/2 + f*x/2) - 105*c**4*f), Ne(f, 0)), (x*(A + B*sin(e))*(a*sin(e) + a)**3/(-c*sin(e) + c)**4, True))","A",0
48,1,3262,0,116.395054," ","integrate((a+a*sin(f*x+e))**3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**5,x)","\begin{cases} - \frac{126 A a^{3} \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{63 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 567 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2268 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5292 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 7938 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 7938 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5292 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2268 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 567 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 c^{5} f} + \frac{126 A a^{3} \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{63 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 567 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2268 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5292 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 7938 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 7938 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5292 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2268 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 567 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 c^{5} f} - \frac{966 A a^{3} \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{63 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 567 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2268 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5292 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 7938 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 7938 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5292 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2268 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 567 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 c^{5} f} + \frac{630 A a^{3} \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{63 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 567 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2268 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5292 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 7938 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 7938 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5292 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2268 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 567 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 c^{5} f} - \frac{1386 A a^{3} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{63 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 567 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2268 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5292 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 7938 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 7938 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5292 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2268 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 567 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 c^{5} f} + \frac{378 A a^{3} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{63 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 567 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2268 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5292 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 7938 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 7938 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5292 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2268 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 567 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 c^{5} f} - \frac{450 A a^{3} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{63 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 567 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2268 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5292 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 7938 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 7938 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5292 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2268 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 567 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 c^{5} f} + \frac{18 A a^{3} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{63 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 567 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2268 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5292 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 7938 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 7938 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5292 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2268 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 567 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 c^{5} f} - \frac{16 A a^{3}}{63 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 567 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2268 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5292 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 7938 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 7938 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5292 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2268 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 567 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 c^{5} f} - \frac{126 B a^{3} \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{63 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 567 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2268 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5292 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 7938 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 7938 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5292 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2268 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 567 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 c^{5} f} - \frac{210 B a^{3} \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{63 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 567 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2268 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5292 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 7938 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 7938 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5292 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2268 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 567 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 c^{5} f} - \frac{630 B a^{3} \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{63 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 567 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2268 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5292 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 7938 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 7938 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5292 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2268 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 567 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 c^{5} f} - \frac{378 B a^{3} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{63 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 567 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2268 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5292 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 7938 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 7938 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5292 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2268 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 567 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 c^{5} f} - \frac{378 B a^{3} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{63 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 567 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2268 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5292 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 7938 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 7938 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5292 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2268 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 567 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 c^{5} f} - \frac{54 B a^{3} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{63 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 567 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2268 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5292 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 7938 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 7938 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5292 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2268 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 567 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 c^{5} f} - \frac{18 B a^{3} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{63 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 567 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2268 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5292 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 7938 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 7938 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5292 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2268 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 567 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 c^{5} f} + \frac{2 B a^{3}}{63 c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 567 c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2268 c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5292 c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 7938 c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 7938 c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5292 c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2268 c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 567 c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 c^{5} f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right) \left(a \sin{\left(e \right)} + a\right)^{3}}{\left(- c \sin{\left(e \right)} + c\right)^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-126*A*a**3*tan(e/2 + f*x/2)**8/(63*c**5*f*tan(e/2 + f*x/2)**9 - 567*c**5*f*tan(e/2 + f*x/2)**8 + 2268*c**5*f*tan(e/2 + f*x/2)**7 - 5292*c**5*f*tan(e/2 + f*x/2)**6 + 7938*c**5*f*tan(e/2 + f*x/2)**5 - 7938*c**5*f*tan(e/2 + f*x/2)**4 + 5292*c**5*f*tan(e/2 + f*x/2)**3 - 2268*c**5*f*tan(e/2 + f*x/2)**2 + 567*c**5*f*tan(e/2 + f*x/2) - 63*c**5*f) + 126*A*a**3*tan(e/2 + f*x/2)**7/(63*c**5*f*tan(e/2 + f*x/2)**9 - 567*c**5*f*tan(e/2 + f*x/2)**8 + 2268*c**5*f*tan(e/2 + f*x/2)**7 - 5292*c**5*f*tan(e/2 + f*x/2)**6 + 7938*c**5*f*tan(e/2 + f*x/2)**5 - 7938*c**5*f*tan(e/2 + f*x/2)**4 + 5292*c**5*f*tan(e/2 + f*x/2)**3 - 2268*c**5*f*tan(e/2 + f*x/2)**2 + 567*c**5*f*tan(e/2 + f*x/2) - 63*c**5*f) - 966*A*a**3*tan(e/2 + f*x/2)**6/(63*c**5*f*tan(e/2 + f*x/2)**9 - 567*c**5*f*tan(e/2 + f*x/2)**8 + 2268*c**5*f*tan(e/2 + f*x/2)**7 - 5292*c**5*f*tan(e/2 + f*x/2)**6 + 7938*c**5*f*tan(e/2 + f*x/2)**5 - 7938*c**5*f*tan(e/2 + f*x/2)**4 + 5292*c**5*f*tan(e/2 + f*x/2)**3 - 2268*c**5*f*tan(e/2 + f*x/2)**2 + 567*c**5*f*tan(e/2 + f*x/2) - 63*c**5*f) + 630*A*a**3*tan(e/2 + f*x/2)**5/(63*c**5*f*tan(e/2 + f*x/2)**9 - 567*c**5*f*tan(e/2 + f*x/2)**8 + 2268*c**5*f*tan(e/2 + f*x/2)**7 - 5292*c**5*f*tan(e/2 + f*x/2)**6 + 7938*c**5*f*tan(e/2 + f*x/2)**5 - 7938*c**5*f*tan(e/2 + f*x/2)**4 + 5292*c**5*f*tan(e/2 + f*x/2)**3 - 2268*c**5*f*tan(e/2 + f*x/2)**2 + 567*c**5*f*tan(e/2 + f*x/2) - 63*c**5*f) - 1386*A*a**3*tan(e/2 + f*x/2)**4/(63*c**5*f*tan(e/2 + f*x/2)**9 - 567*c**5*f*tan(e/2 + f*x/2)**8 + 2268*c**5*f*tan(e/2 + f*x/2)**7 - 5292*c**5*f*tan(e/2 + f*x/2)**6 + 7938*c**5*f*tan(e/2 + f*x/2)**5 - 7938*c**5*f*tan(e/2 + f*x/2)**4 + 5292*c**5*f*tan(e/2 + f*x/2)**3 - 2268*c**5*f*tan(e/2 + f*x/2)**2 + 567*c**5*f*tan(e/2 + f*x/2) - 63*c**5*f) + 378*A*a**3*tan(e/2 + f*x/2)**3/(63*c**5*f*tan(e/2 + f*x/2)**9 - 567*c**5*f*tan(e/2 + f*x/2)**8 + 2268*c**5*f*tan(e/2 + f*x/2)**7 - 5292*c**5*f*tan(e/2 + f*x/2)**6 + 7938*c**5*f*tan(e/2 + f*x/2)**5 - 7938*c**5*f*tan(e/2 + f*x/2)**4 + 5292*c**5*f*tan(e/2 + f*x/2)**3 - 2268*c**5*f*tan(e/2 + f*x/2)**2 + 567*c**5*f*tan(e/2 + f*x/2) - 63*c**5*f) - 450*A*a**3*tan(e/2 + f*x/2)**2/(63*c**5*f*tan(e/2 + f*x/2)**9 - 567*c**5*f*tan(e/2 + f*x/2)**8 + 2268*c**5*f*tan(e/2 + f*x/2)**7 - 5292*c**5*f*tan(e/2 + f*x/2)**6 + 7938*c**5*f*tan(e/2 + f*x/2)**5 - 7938*c**5*f*tan(e/2 + f*x/2)**4 + 5292*c**5*f*tan(e/2 + f*x/2)**3 - 2268*c**5*f*tan(e/2 + f*x/2)**2 + 567*c**5*f*tan(e/2 + f*x/2) - 63*c**5*f) + 18*A*a**3*tan(e/2 + f*x/2)/(63*c**5*f*tan(e/2 + f*x/2)**9 - 567*c**5*f*tan(e/2 + f*x/2)**8 + 2268*c**5*f*tan(e/2 + f*x/2)**7 - 5292*c**5*f*tan(e/2 + f*x/2)**6 + 7938*c**5*f*tan(e/2 + f*x/2)**5 - 7938*c**5*f*tan(e/2 + f*x/2)**4 + 5292*c**5*f*tan(e/2 + f*x/2)**3 - 2268*c**5*f*tan(e/2 + f*x/2)**2 + 567*c**5*f*tan(e/2 + f*x/2) - 63*c**5*f) - 16*A*a**3/(63*c**5*f*tan(e/2 + f*x/2)**9 - 567*c**5*f*tan(e/2 + f*x/2)**8 + 2268*c**5*f*tan(e/2 + f*x/2)**7 - 5292*c**5*f*tan(e/2 + f*x/2)**6 + 7938*c**5*f*tan(e/2 + f*x/2)**5 - 7938*c**5*f*tan(e/2 + f*x/2)**4 + 5292*c**5*f*tan(e/2 + f*x/2)**3 - 2268*c**5*f*tan(e/2 + f*x/2)**2 + 567*c**5*f*tan(e/2 + f*x/2) - 63*c**5*f) - 126*B*a**3*tan(e/2 + f*x/2)**7/(63*c**5*f*tan(e/2 + f*x/2)**9 - 567*c**5*f*tan(e/2 + f*x/2)**8 + 2268*c**5*f*tan(e/2 + f*x/2)**7 - 5292*c**5*f*tan(e/2 + f*x/2)**6 + 7938*c**5*f*tan(e/2 + f*x/2)**5 - 7938*c**5*f*tan(e/2 + f*x/2)**4 + 5292*c**5*f*tan(e/2 + f*x/2)**3 - 2268*c**5*f*tan(e/2 + f*x/2)**2 + 567*c**5*f*tan(e/2 + f*x/2) - 63*c**5*f) - 210*B*a**3*tan(e/2 + f*x/2)**6/(63*c**5*f*tan(e/2 + f*x/2)**9 - 567*c**5*f*tan(e/2 + f*x/2)**8 + 2268*c**5*f*tan(e/2 + f*x/2)**7 - 5292*c**5*f*tan(e/2 + f*x/2)**6 + 7938*c**5*f*tan(e/2 + f*x/2)**5 - 7938*c**5*f*tan(e/2 + f*x/2)**4 + 5292*c**5*f*tan(e/2 + f*x/2)**3 - 2268*c**5*f*tan(e/2 + f*x/2)**2 + 567*c**5*f*tan(e/2 + f*x/2) - 63*c**5*f) - 630*B*a**3*tan(e/2 + f*x/2)**5/(63*c**5*f*tan(e/2 + f*x/2)**9 - 567*c**5*f*tan(e/2 + f*x/2)**8 + 2268*c**5*f*tan(e/2 + f*x/2)**7 - 5292*c**5*f*tan(e/2 + f*x/2)**6 + 7938*c**5*f*tan(e/2 + f*x/2)**5 - 7938*c**5*f*tan(e/2 + f*x/2)**4 + 5292*c**5*f*tan(e/2 + f*x/2)**3 - 2268*c**5*f*tan(e/2 + f*x/2)**2 + 567*c**5*f*tan(e/2 + f*x/2) - 63*c**5*f) - 378*B*a**3*tan(e/2 + f*x/2)**4/(63*c**5*f*tan(e/2 + f*x/2)**9 - 567*c**5*f*tan(e/2 + f*x/2)**8 + 2268*c**5*f*tan(e/2 + f*x/2)**7 - 5292*c**5*f*tan(e/2 + f*x/2)**6 + 7938*c**5*f*tan(e/2 + f*x/2)**5 - 7938*c**5*f*tan(e/2 + f*x/2)**4 + 5292*c**5*f*tan(e/2 + f*x/2)**3 - 2268*c**5*f*tan(e/2 + f*x/2)**2 + 567*c**5*f*tan(e/2 + f*x/2) - 63*c**5*f) - 378*B*a**3*tan(e/2 + f*x/2)**3/(63*c**5*f*tan(e/2 + f*x/2)**9 - 567*c**5*f*tan(e/2 + f*x/2)**8 + 2268*c**5*f*tan(e/2 + f*x/2)**7 - 5292*c**5*f*tan(e/2 + f*x/2)**6 + 7938*c**5*f*tan(e/2 + f*x/2)**5 - 7938*c**5*f*tan(e/2 + f*x/2)**4 + 5292*c**5*f*tan(e/2 + f*x/2)**3 - 2268*c**5*f*tan(e/2 + f*x/2)**2 + 567*c**5*f*tan(e/2 + f*x/2) - 63*c**5*f) - 54*B*a**3*tan(e/2 + f*x/2)**2/(63*c**5*f*tan(e/2 + f*x/2)**9 - 567*c**5*f*tan(e/2 + f*x/2)**8 + 2268*c**5*f*tan(e/2 + f*x/2)**7 - 5292*c**5*f*tan(e/2 + f*x/2)**6 + 7938*c**5*f*tan(e/2 + f*x/2)**5 - 7938*c**5*f*tan(e/2 + f*x/2)**4 + 5292*c**5*f*tan(e/2 + f*x/2)**3 - 2268*c**5*f*tan(e/2 + f*x/2)**2 + 567*c**5*f*tan(e/2 + f*x/2) - 63*c**5*f) - 18*B*a**3*tan(e/2 + f*x/2)/(63*c**5*f*tan(e/2 + f*x/2)**9 - 567*c**5*f*tan(e/2 + f*x/2)**8 + 2268*c**5*f*tan(e/2 + f*x/2)**7 - 5292*c**5*f*tan(e/2 + f*x/2)**6 + 7938*c**5*f*tan(e/2 + f*x/2)**5 - 7938*c**5*f*tan(e/2 + f*x/2)**4 + 5292*c**5*f*tan(e/2 + f*x/2)**3 - 2268*c**5*f*tan(e/2 + f*x/2)**2 + 567*c**5*f*tan(e/2 + f*x/2) - 63*c**5*f) + 2*B*a**3/(63*c**5*f*tan(e/2 + f*x/2)**9 - 567*c**5*f*tan(e/2 + f*x/2)**8 + 2268*c**5*f*tan(e/2 + f*x/2)**7 - 5292*c**5*f*tan(e/2 + f*x/2)**6 + 7938*c**5*f*tan(e/2 + f*x/2)**5 - 7938*c**5*f*tan(e/2 + f*x/2)**4 + 5292*c**5*f*tan(e/2 + f*x/2)**3 - 2268*c**5*f*tan(e/2 + f*x/2)**2 + 567*c**5*f*tan(e/2 + f*x/2) - 63*c**5*f), Ne(f, 0)), (x*(A + B*sin(e))*(a*sin(e) + a)**3/(-c*sin(e) + c)**5, True))","A",0
49,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
50,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
51,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
52,1,6690,0,26.866157," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))**4/(a+a*sin(f*x+e)),x)","\begin{cases} - \frac{420 A c^{4} f x \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f} - \frac{420 A c^{4} f x \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f} - \frac{1680 A c^{4} f x \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f} - \frac{1680 A c^{4} f x \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f} - \frac{2520 A c^{4} f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f} - \frac{2520 A c^{4} f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f} - \frac{1680 A c^{4} f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f} - \frac{1680 A c^{4} f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f} - \frac{420 A c^{4} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f} - \frac{420 A c^{4} f x}{24 a f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f} - \frac{888 A c^{4} \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f} - \frac{648 A c^{4} \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f} - \frac{3720 A c^{4} \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f} - \frac{1800 A c^{4} \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f} - \frac{6168 A c^{4} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f} - \frac{1592 A c^{4} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f} - \frac{4664 A c^{4} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f} - \frac{440 A c^{4} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f} - \frac{1328 A c^{4}}{24 a f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f} + \frac{525 B c^{4} f x \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f} + \frac{525 B c^{4} f x \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f} + \frac{2100 B c^{4} f x \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f} + \frac{2100 B c^{4} f x \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f} + \frac{3150 B c^{4} f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f} + \frac{3150 B c^{4} f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f} + \frac{2100 B c^{4} f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f} + \frac{2100 B c^{4} f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f} + \frac{525 B c^{4} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f} + \frac{525 B c^{4} f x}{24 a f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f} + \frac{1050 B c^{4} \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f} + \frac{1002 B c^{4} \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f} + \frac{4122 B c^{4} \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f} + \frac{2970 B c^{4} \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f} + \frac{6918 B c^{4} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f} + \frac{2470 B c^{4} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f} + \frac{5590 B c^{4} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f} + \frac{598 B c^{4} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f} + \frac{1648 B c^{4}}{24 a f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 144 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 96 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right) \left(- c \sin{\left(e \right)} + c\right)^{4}}{a \sin{\left(e \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-420*A*c**4*f*x*tan(e/2 + f*x/2)**9/(24*a*f*tan(e/2 + f*x/2)**9 + 24*a*f*tan(e/2 + f*x/2)**8 + 96*a*f*tan(e/2 + f*x/2)**7 + 96*a*f*tan(e/2 + f*x/2)**6 + 144*a*f*tan(e/2 + f*x/2)**5 + 144*a*f*tan(e/2 + f*x/2)**4 + 96*a*f*tan(e/2 + f*x/2)**3 + 96*a*f*tan(e/2 + f*x/2)**2 + 24*a*f*tan(e/2 + f*x/2) + 24*a*f) - 420*A*c**4*f*x*tan(e/2 + f*x/2)**8/(24*a*f*tan(e/2 + f*x/2)**9 + 24*a*f*tan(e/2 + f*x/2)**8 + 96*a*f*tan(e/2 + f*x/2)**7 + 96*a*f*tan(e/2 + f*x/2)**6 + 144*a*f*tan(e/2 + f*x/2)**5 + 144*a*f*tan(e/2 + f*x/2)**4 + 96*a*f*tan(e/2 + f*x/2)**3 + 96*a*f*tan(e/2 + f*x/2)**2 + 24*a*f*tan(e/2 + f*x/2) + 24*a*f) - 1680*A*c**4*f*x*tan(e/2 + f*x/2)**7/(24*a*f*tan(e/2 + f*x/2)**9 + 24*a*f*tan(e/2 + f*x/2)**8 + 96*a*f*tan(e/2 + f*x/2)**7 + 96*a*f*tan(e/2 + f*x/2)**6 + 144*a*f*tan(e/2 + f*x/2)**5 + 144*a*f*tan(e/2 + f*x/2)**4 + 96*a*f*tan(e/2 + f*x/2)**3 + 96*a*f*tan(e/2 + f*x/2)**2 + 24*a*f*tan(e/2 + f*x/2) + 24*a*f) - 1680*A*c**4*f*x*tan(e/2 + f*x/2)**6/(24*a*f*tan(e/2 + f*x/2)**9 + 24*a*f*tan(e/2 + f*x/2)**8 + 96*a*f*tan(e/2 + f*x/2)**7 + 96*a*f*tan(e/2 + f*x/2)**6 + 144*a*f*tan(e/2 + f*x/2)**5 + 144*a*f*tan(e/2 + f*x/2)**4 + 96*a*f*tan(e/2 + f*x/2)**3 + 96*a*f*tan(e/2 + f*x/2)**2 + 24*a*f*tan(e/2 + f*x/2) + 24*a*f) - 2520*A*c**4*f*x*tan(e/2 + f*x/2)**5/(24*a*f*tan(e/2 + f*x/2)**9 + 24*a*f*tan(e/2 + f*x/2)**8 + 96*a*f*tan(e/2 + f*x/2)**7 + 96*a*f*tan(e/2 + f*x/2)**6 + 144*a*f*tan(e/2 + f*x/2)**5 + 144*a*f*tan(e/2 + f*x/2)**4 + 96*a*f*tan(e/2 + f*x/2)**3 + 96*a*f*tan(e/2 + f*x/2)**2 + 24*a*f*tan(e/2 + f*x/2) + 24*a*f) - 2520*A*c**4*f*x*tan(e/2 + f*x/2)**4/(24*a*f*tan(e/2 + f*x/2)**9 + 24*a*f*tan(e/2 + f*x/2)**8 + 96*a*f*tan(e/2 + f*x/2)**7 + 96*a*f*tan(e/2 + f*x/2)**6 + 144*a*f*tan(e/2 + f*x/2)**5 + 144*a*f*tan(e/2 + f*x/2)**4 + 96*a*f*tan(e/2 + f*x/2)**3 + 96*a*f*tan(e/2 + f*x/2)**2 + 24*a*f*tan(e/2 + f*x/2) + 24*a*f) - 1680*A*c**4*f*x*tan(e/2 + f*x/2)**3/(24*a*f*tan(e/2 + f*x/2)**9 + 24*a*f*tan(e/2 + f*x/2)**8 + 96*a*f*tan(e/2 + f*x/2)**7 + 96*a*f*tan(e/2 + f*x/2)**6 + 144*a*f*tan(e/2 + f*x/2)**5 + 144*a*f*tan(e/2 + f*x/2)**4 + 96*a*f*tan(e/2 + f*x/2)**3 + 96*a*f*tan(e/2 + f*x/2)**2 + 24*a*f*tan(e/2 + f*x/2) + 24*a*f) - 1680*A*c**4*f*x*tan(e/2 + f*x/2)**2/(24*a*f*tan(e/2 + f*x/2)**9 + 24*a*f*tan(e/2 + f*x/2)**8 + 96*a*f*tan(e/2 + f*x/2)**7 + 96*a*f*tan(e/2 + f*x/2)**6 + 144*a*f*tan(e/2 + f*x/2)**5 + 144*a*f*tan(e/2 + f*x/2)**4 + 96*a*f*tan(e/2 + f*x/2)**3 + 96*a*f*tan(e/2 + f*x/2)**2 + 24*a*f*tan(e/2 + f*x/2) + 24*a*f) - 420*A*c**4*f*x*tan(e/2 + f*x/2)/(24*a*f*tan(e/2 + f*x/2)**9 + 24*a*f*tan(e/2 + f*x/2)**8 + 96*a*f*tan(e/2 + f*x/2)**7 + 96*a*f*tan(e/2 + f*x/2)**6 + 144*a*f*tan(e/2 + f*x/2)**5 + 144*a*f*tan(e/2 + f*x/2)**4 + 96*a*f*tan(e/2 + f*x/2)**3 + 96*a*f*tan(e/2 + f*x/2)**2 + 24*a*f*tan(e/2 + f*x/2) + 24*a*f) - 420*A*c**4*f*x/(24*a*f*tan(e/2 + f*x/2)**9 + 24*a*f*tan(e/2 + f*x/2)**8 + 96*a*f*tan(e/2 + f*x/2)**7 + 96*a*f*tan(e/2 + f*x/2)**6 + 144*a*f*tan(e/2 + f*x/2)**5 + 144*a*f*tan(e/2 + f*x/2)**4 + 96*a*f*tan(e/2 + f*x/2)**3 + 96*a*f*tan(e/2 + f*x/2)**2 + 24*a*f*tan(e/2 + f*x/2) + 24*a*f) - 888*A*c**4*tan(e/2 + f*x/2)**8/(24*a*f*tan(e/2 + f*x/2)**9 + 24*a*f*tan(e/2 + f*x/2)**8 + 96*a*f*tan(e/2 + f*x/2)**7 + 96*a*f*tan(e/2 + f*x/2)**6 + 144*a*f*tan(e/2 + f*x/2)**5 + 144*a*f*tan(e/2 + f*x/2)**4 + 96*a*f*tan(e/2 + f*x/2)**3 + 96*a*f*tan(e/2 + f*x/2)**2 + 24*a*f*tan(e/2 + f*x/2) + 24*a*f) - 648*A*c**4*tan(e/2 + f*x/2)**7/(24*a*f*tan(e/2 + f*x/2)**9 + 24*a*f*tan(e/2 + f*x/2)**8 + 96*a*f*tan(e/2 + f*x/2)**7 + 96*a*f*tan(e/2 + f*x/2)**6 + 144*a*f*tan(e/2 + f*x/2)**5 + 144*a*f*tan(e/2 + f*x/2)**4 + 96*a*f*tan(e/2 + f*x/2)**3 + 96*a*f*tan(e/2 + f*x/2)**2 + 24*a*f*tan(e/2 + f*x/2) + 24*a*f) - 3720*A*c**4*tan(e/2 + f*x/2)**6/(24*a*f*tan(e/2 + f*x/2)**9 + 24*a*f*tan(e/2 + f*x/2)**8 + 96*a*f*tan(e/2 + f*x/2)**7 + 96*a*f*tan(e/2 + f*x/2)**6 + 144*a*f*tan(e/2 + f*x/2)**5 + 144*a*f*tan(e/2 + f*x/2)**4 + 96*a*f*tan(e/2 + f*x/2)**3 + 96*a*f*tan(e/2 + f*x/2)**2 + 24*a*f*tan(e/2 + f*x/2) + 24*a*f) - 1800*A*c**4*tan(e/2 + f*x/2)**5/(24*a*f*tan(e/2 + f*x/2)**9 + 24*a*f*tan(e/2 + f*x/2)**8 + 96*a*f*tan(e/2 + f*x/2)**7 + 96*a*f*tan(e/2 + f*x/2)**6 + 144*a*f*tan(e/2 + f*x/2)**5 + 144*a*f*tan(e/2 + f*x/2)**4 + 96*a*f*tan(e/2 + f*x/2)**3 + 96*a*f*tan(e/2 + f*x/2)**2 + 24*a*f*tan(e/2 + f*x/2) + 24*a*f) - 6168*A*c**4*tan(e/2 + f*x/2)**4/(24*a*f*tan(e/2 + f*x/2)**9 + 24*a*f*tan(e/2 + f*x/2)**8 + 96*a*f*tan(e/2 + f*x/2)**7 + 96*a*f*tan(e/2 + f*x/2)**6 + 144*a*f*tan(e/2 + f*x/2)**5 + 144*a*f*tan(e/2 + f*x/2)**4 + 96*a*f*tan(e/2 + f*x/2)**3 + 96*a*f*tan(e/2 + f*x/2)**2 + 24*a*f*tan(e/2 + f*x/2) + 24*a*f) - 1592*A*c**4*tan(e/2 + f*x/2)**3/(24*a*f*tan(e/2 + f*x/2)**9 + 24*a*f*tan(e/2 + f*x/2)**8 + 96*a*f*tan(e/2 + f*x/2)**7 + 96*a*f*tan(e/2 + f*x/2)**6 + 144*a*f*tan(e/2 + f*x/2)**5 + 144*a*f*tan(e/2 + f*x/2)**4 + 96*a*f*tan(e/2 + f*x/2)**3 + 96*a*f*tan(e/2 + f*x/2)**2 + 24*a*f*tan(e/2 + f*x/2) + 24*a*f) - 4664*A*c**4*tan(e/2 + f*x/2)**2/(24*a*f*tan(e/2 + f*x/2)**9 + 24*a*f*tan(e/2 + f*x/2)**8 + 96*a*f*tan(e/2 + f*x/2)**7 + 96*a*f*tan(e/2 + f*x/2)**6 + 144*a*f*tan(e/2 + f*x/2)**5 + 144*a*f*tan(e/2 + f*x/2)**4 + 96*a*f*tan(e/2 + f*x/2)**3 + 96*a*f*tan(e/2 + f*x/2)**2 + 24*a*f*tan(e/2 + f*x/2) + 24*a*f) - 440*A*c**4*tan(e/2 + f*x/2)/(24*a*f*tan(e/2 + f*x/2)**9 + 24*a*f*tan(e/2 + f*x/2)**8 + 96*a*f*tan(e/2 + f*x/2)**7 + 96*a*f*tan(e/2 + f*x/2)**6 + 144*a*f*tan(e/2 + f*x/2)**5 + 144*a*f*tan(e/2 + f*x/2)**4 + 96*a*f*tan(e/2 + f*x/2)**3 + 96*a*f*tan(e/2 + f*x/2)**2 + 24*a*f*tan(e/2 + f*x/2) + 24*a*f) - 1328*A*c**4/(24*a*f*tan(e/2 + f*x/2)**9 + 24*a*f*tan(e/2 + f*x/2)**8 + 96*a*f*tan(e/2 + f*x/2)**7 + 96*a*f*tan(e/2 + f*x/2)**6 + 144*a*f*tan(e/2 + f*x/2)**5 + 144*a*f*tan(e/2 + f*x/2)**4 + 96*a*f*tan(e/2 + f*x/2)**3 + 96*a*f*tan(e/2 + f*x/2)**2 + 24*a*f*tan(e/2 + f*x/2) + 24*a*f) + 525*B*c**4*f*x*tan(e/2 + f*x/2)**9/(24*a*f*tan(e/2 + f*x/2)**9 + 24*a*f*tan(e/2 + f*x/2)**8 + 96*a*f*tan(e/2 + f*x/2)**7 + 96*a*f*tan(e/2 + f*x/2)**6 + 144*a*f*tan(e/2 + f*x/2)**5 + 144*a*f*tan(e/2 + f*x/2)**4 + 96*a*f*tan(e/2 + f*x/2)**3 + 96*a*f*tan(e/2 + f*x/2)**2 + 24*a*f*tan(e/2 + f*x/2) + 24*a*f) + 525*B*c**4*f*x*tan(e/2 + f*x/2)**8/(24*a*f*tan(e/2 + f*x/2)**9 + 24*a*f*tan(e/2 + f*x/2)**8 + 96*a*f*tan(e/2 + f*x/2)**7 + 96*a*f*tan(e/2 + f*x/2)**6 + 144*a*f*tan(e/2 + f*x/2)**5 + 144*a*f*tan(e/2 + f*x/2)**4 + 96*a*f*tan(e/2 + f*x/2)**3 + 96*a*f*tan(e/2 + f*x/2)**2 + 24*a*f*tan(e/2 + f*x/2) + 24*a*f) + 2100*B*c**4*f*x*tan(e/2 + f*x/2)**7/(24*a*f*tan(e/2 + f*x/2)**9 + 24*a*f*tan(e/2 + f*x/2)**8 + 96*a*f*tan(e/2 + f*x/2)**7 + 96*a*f*tan(e/2 + f*x/2)**6 + 144*a*f*tan(e/2 + f*x/2)**5 + 144*a*f*tan(e/2 + f*x/2)**4 + 96*a*f*tan(e/2 + f*x/2)**3 + 96*a*f*tan(e/2 + f*x/2)**2 + 24*a*f*tan(e/2 + f*x/2) + 24*a*f) + 2100*B*c**4*f*x*tan(e/2 + f*x/2)**6/(24*a*f*tan(e/2 + f*x/2)**9 + 24*a*f*tan(e/2 + f*x/2)**8 + 96*a*f*tan(e/2 + f*x/2)**7 + 96*a*f*tan(e/2 + f*x/2)**6 + 144*a*f*tan(e/2 + f*x/2)**5 + 144*a*f*tan(e/2 + f*x/2)**4 + 96*a*f*tan(e/2 + f*x/2)**3 + 96*a*f*tan(e/2 + f*x/2)**2 + 24*a*f*tan(e/2 + f*x/2) + 24*a*f) + 3150*B*c**4*f*x*tan(e/2 + f*x/2)**5/(24*a*f*tan(e/2 + f*x/2)**9 + 24*a*f*tan(e/2 + f*x/2)**8 + 96*a*f*tan(e/2 + f*x/2)**7 + 96*a*f*tan(e/2 + f*x/2)**6 + 144*a*f*tan(e/2 + f*x/2)**5 + 144*a*f*tan(e/2 + f*x/2)**4 + 96*a*f*tan(e/2 + f*x/2)**3 + 96*a*f*tan(e/2 + f*x/2)**2 + 24*a*f*tan(e/2 + f*x/2) + 24*a*f) + 3150*B*c**4*f*x*tan(e/2 + f*x/2)**4/(24*a*f*tan(e/2 + f*x/2)**9 + 24*a*f*tan(e/2 + f*x/2)**8 + 96*a*f*tan(e/2 + f*x/2)**7 + 96*a*f*tan(e/2 + f*x/2)**6 + 144*a*f*tan(e/2 + f*x/2)**5 + 144*a*f*tan(e/2 + f*x/2)**4 + 96*a*f*tan(e/2 + f*x/2)**3 + 96*a*f*tan(e/2 + f*x/2)**2 + 24*a*f*tan(e/2 + f*x/2) + 24*a*f) + 2100*B*c**4*f*x*tan(e/2 + f*x/2)**3/(24*a*f*tan(e/2 + f*x/2)**9 + 24*a*f*tan(e/2 + f*x/2)**8 + 96*a*f*tan(e/2 + f*x/2)**7 + 96*a*f*tan(e/2 + f*x/2)**6 + 144*a*f*tan(e/2 + f*x/2)**5 + 144*a*f*tan(e/2 + f*x/2)**4 + 96*a*f*tan(e/2 + f*x/2)**3 + 96*a*f*tan(e/2 + f*x/2)**2 + 24*a*f*tan(e/2 + f*x/2) + 24*a*f) + 2100*B*c**4*f*x*tan(e/2 + f*x/2)**2/(24*a*f*tan(e/2 + f*x/2)**9 + 24*a*f*tan(e/2 + f*x/2)**8 + 96*a*f*tan(e/2 + f*x/2)**7 + 96*a*f*tan(e/2 + f*x/2)**6 + 144*a*f*tan(e/2 + f*x/2)**5 + 144*a*f*tan(e/2 + f*x/2)**4 + 96*a*f*tan(e/2 + f*x/2)**3 + 96*a*f*tan(e/2 + f*x/2)**2 + 24*a*f*tan(e/2 + f*x/2) + 24*a*f) + 525*B*c**4*f*x*tan(e/2 + f*x/2)/(24*a*f*tan(e/2 + f*x/2)**9 + 24*a*f*tan(e/2 + f*x/2)**8 + 96*a*f*tan(e/2 + f*x/2)**7 + 96*a*f*tan(e/2 + f*x/2)**6 + 144*a*f*tan(e/2 + f*x/2)**5 + 144*a*f*tan(e/2 + f*x/2)**4 + 96*a*f*tan(e/2 + f*x/2)**3 + 96*a*f*tan(e/2 + f*x/2)**2 + 24*a*f*tan(e/2 + f*x/2) + 24*a*f) + 525*B*c**4*f*x/(24*a*f*tan(e/2 + f*x/2)**9 + 24*a*f*tan(e/2 + f*x/2)**8 + 96*a*f*tan(e/2 + f*x/2)**7 + 96*a*f*tan(e/2 + f*x/2)**6 + 144*a*f*tan(e/2 + f*x/2)**5 + 144*a*f*tan(e/2 + f*x/2)**4 + 96*a*f*tan(e/2 + f*x/2)**3 + 96*a*f*tan(e/2 + f*x/2)**2 + 24*a*f*tan(e/2 + f*x/2) + 24*a*f) + 1050*B*c**4*tan(e/2 + f*x/2)**8/(24*a*f*tan(e/2 + f*x/2)**9 + 24*a*f*tan(e/2 + f*x/2)**8 + 96*a*f*tan(e/2 + f*x/2)**7 + 96*a*f*tan(e/2 + f*x/2)**6 + 144*a*f*tan(e/2 + f*x/2)**5 + 144*a*f*tan(e/2 + f*x/2)**4 + 96*a*f*tan(e/2 + f*x/2)**3 + 96*a*f*tan(e/2 + f*x/2)**2 + 24*a*f*tan(e/2 + f*x/2) + 24*a*f) + 1002*B*c**4*tan(e/2 + f*x/2)**7/(24*a*f*tan(e/2 + f*x/2)**9 + 24*a*f*tan(e/2 + f*x/2)**8 + 96*a*f*tan(e/2 + f*x/2)**7 + 96*a*f*tan(e/2 + f*x/2)**6 + 144*a*f*tan(e/2 + f*x/2)**5 + 144*a*f*tan(e/2 + f*x/2)**4 + 96*a*f*tan(e/2 + f*x/2)**3 + 96*a*f*tan(e/2 + f*x/2)**2 + 24*a*f*tan(e/2 + f*x/2) + 24*a*f) + 4122*B*c**4*tan(e/2 + f*x/2)**6/(24*a*f*tan(e/2 + f*x/2)**9 + 24*a*f*tan(e/2 + f*x/2)**8 + 96*a*f*tan(e/2 + f*x/2)**7 + 96*a*f*tan(e/2 + f*x/2)**6 + 144*a*f*tan(e/2 + f*x/2)**5 + 144*a*f*tan(e/2 + f*x/2)**4 + 96*a*f*tan(e/2 + f*x/2)**3 + 96*a*f*tan(e/2 + f*x/2)**2 + 24*a*f*tan(e/2 + f*x/2) + 24*a*f) + 2970*B*c**4*tan(e/2 + f*x/2)**5/(24*a*f*tan(e/2 + f*x/2)**9 + 24*a*f*tan(e/2 + f*x/2)**8 + 96*a*f*tan(e/2 + f*x/2)**7 + 96*a*f*tan(e/2 + f*x/2)**6 + 144*a*f*tan(e/2 + f*x/2)**5 + 144*a*f*tan(e/2 + f*x/2)**4 + 96*a*f*tan(e/2 + f*x/2)**3 + 96*a*f*tan(e/2 + f*x/2)**2 + 24*a*f*tan(e/2 + f*x/2) + 24*a*f) + 6918*B*c**4*tan(e/2 + f*x/2)**4/(24*a*f*tan(e/2 + f*x/2)**9 + 24*a*f*tan(e/2 + f*x/2)**8 + 96*a*f*tan(e/2 + f*x/2)**7 + 96*a*f*tan(e/2 + f*x/2)**6 + 144*a*f*tan(e/2 + f*x/2)**5 + 144*a*f*tan(e/2 + f*x/2)**4 + 96*a*f*tan(e/2 + f*x/2)**3 + 96*a*f*tan(e/2 + f*x/2)**2 + 24*a*f*tan(e/2 + f*x/2) + 24*a*f) + 2470*B*c**4*tan(e/2 + f*x/2)**3/(24*a*f*tan(e/2 + f*x/2)**9 + 24*a*f*tan(e/2 + f*x/2)**8 + 96*a*f*tan(e/2 + f*x/2)**7 + 96*a*f*tan(e/2 + f*x/2)**6 + 144*a*f*tan(e/2 + f*x/2)**5 + 144*a*f*tan(e/2 + f*x/2)**4 + 96*a*f*tan(e/2 + f*x/2)**3 + 96*a*f*tan(e/2 + f*x/2)**2 + 24*a*f*tan(e/2 + f*x/2) + 24*a*f) + 5590*B*c**4*tan(e/2 + f*x/2)**2/(24*a*f*tan(e/2 + f*x/2)**9 + 24*a*f*tan(e/2 + f*x/2)**8 + 96*a*f*tan(e/2 + f*x/2)**7 + 96*a*f*tan(e/2 + f*x/2)**6 + 144*a*f*tan(e/2 + f*x/2)**5 + 144*a*f*tan(e/2 + f*x/2)**4 + 96*a*f*tan(e/2 + f*x/2)**3 + 96*a*f*tan(e/2 + f*x/2)**2 + 24*a*f*tan(e/2 + f*x/2) + 24*a*f) + 598*B*c**4*tan(e/2 + f*x/2)/(24*a*f*tan(e/2 + f*x/2)**9 + 24*a*f*tan(e/2 + f*x/2)**8 + 96*a*f*tan(e/2 + f*x/2)**7 + 96*a*f*tan(e/2 + f*x/2)**6 + 144*a*f*tan(e/2 + f*x/2)**5 + 144*a*f*tan(e/2 + f*x/2)**4 + 96*a*f*tan(e/2 + f*x/2)**3 + 96*a*f*tan(e/2 + f*x/2)**2 + 24*a*f*tan(e/2 + f*x/2) + 24*a*f) + 1648*B*c**4/(24*a*f*tan(e/2 + f*x/2)**9 + 24*a*f*tan(e/2 + f*x/2)**8 + 96*a*f*tan(e/2 + f*x/2)**7 + 96*a*f*tan(e/2 + f*x/2)**6 + 144*a*f*tan(e/2 + f*x/2)**5 + 144*a*f*tan(e/2 + f*x/2)**4 + 96*a*f*tan(e/2 + f*x/2)**3 + 96*a*f*tan(e/2 + f*x/2)**2 + 24*a*f*tan(e/2 + f*x/2) + 24*a*f), Ne(f, 0)), (x*(A + B*sin(e))*(-c*sin(e) + c)**4/(a*sin(e) + a), True))","A",0
53,1,4255,0,16.309708," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))**3/(a+a*sin(f*x+e)),x)","\begin{cases} - \frac{45 A c^{3} f x \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f} - \frac{45 A c^{3} f x \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f} - \frac{135 A c^{3} f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f} - \frac{135 A c^{3} f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f} - \frac{135 A c^{3} f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f} - \frac{135 A c^{3} f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f} - \frac{45 A c^{3} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f} - \frac{45 A c^{3} f x}{6 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f} - \frac{102 A c^{3} \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f} - \frac{54 A c^{3} \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f} - \frac{336 A c^{3} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f} - \frac{96 A c^{3} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f} - \frac{378 A c^{3} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f} - \frac{42 A c^{3} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f} - \frac{144 A c^{3}}{6 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f} + \frac{60 B c^{3} f x \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f} + \frac{60 B c^{3} f x \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f} + \frac{180 B c^{3} f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f} + \frac{180 B c^{3} f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f} + \frac{180 B c^{3} f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f} + \frac{180 B c^{3} f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f} + \frac{60 B c^{3} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f} + \frac{60 B c^{3} f x}{6 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f} + \frac{120 B c^{3} \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f} + \frac{108 B c^{3} \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f} + \frac{372 B c^{3} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f} + \frac{192 B c^{3} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f} + \frac{456 B c^{3} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f} + \frac{68 B c^{3} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f} + \frac{188 B c^{3}}{6 a f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right) \left(- c \sin{\left(e \right)} + c\right)^{3}}{a \sin{\left(e \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-45*A*c**3*f*x*tan(e/2 + f*x/2)**7/(6*a*f*tan(e/2 + f*x/2)**7 + 6*a*f*tan(e/2 + f*x/2)**6 + 18*a*f*tan(e/2 + f*x/2)**5 + 18*a*f*tan(e/2 + f*x/2)**4 + 18*a*f*tan(e/2 + f*x/2)**3 + 18*a*f*tan(e/2 + f*x/2)**2 + 6*a*f*tan(e/2 + f*x/2) + 6*a*f) - 45*A*c**3*f*x*tan(e/2 + f*x/2)**6/(6*a*f*tan(e/2 + f*x/2)**7 + 6*a*f*tan(e/2 + f*x/2)**6 + 18*a*f*tan(e/2 + f*x/2)**5 + 18*a*f*tan(e/2 + f*x/2)**4 + 18*a*f*tan(e/2 + f*x/2)**3 + 18*a*f*tan(e/2 + f*x/2)**2 + 6*a*f*tan(e/2 + f*x/2) + 6*a*f) - 135*A*c**3*f*x*tan(e/2 + f*x/2)**5/(6*a*f*tan(e/2 + f*x/2)**7 + 6*a*f*tan(e/2 + f*x/2)**6 + 18*a*f*tan(e/2 + f*x/2)**5 + 18*a*f*tan(e/2 + f*x/2)**4 + 18*a*f*tan(e/2 + f*x/2)**3 + 18*a*f*tan(e/2 + f*x/2)**2 + 6*a*f*tan(e/2 + f*x/2) + 6*a*f) - 135*A*c**3*f*x*tan(e/2 + f*x/2)**4/(6*a*f*tan(e/2 + f*x/2)**7 + 6*a*f*tan(e/2 + f*x/2)**6 + 18*a*f*tan(e/2 + f*x/2)**5 + 18*a*f*tan(e/2 + f*x/2)**4 + 18*a*f*tan(e/2 + f*x/2)**3 + 18*a*f*tan(e/2 + f*x/2)**2 + 6*a*f*tan(e/2 + f*x/2) + 6*a*f) - 135*A*c**3*f*x*tan(e/2 + f*x/2)**3/(6*a*f*tan(e/2 + f*x/2)**7 + 6*a*f*tan(e/2 + f*x/2)**6 + 18*a*f*tan(e/2 + f*x/2)**5 + 18*a*f*tan(e/2 + f*x/2)**4 + 18*a*f*tan(e/2 + f*x/2)**3 + 18*a*f*tan(e/2 + f*x/2)**2 + 6*a*f*tan(e/2 + f*x/2) + 6*a*f) - 135*A*c**3*f*x*tan(e/2 + f*x/2)**2/(6*a*f*tan(e/2 + f*x/2)**7 + 6*a*f*tan(e/2 + f*x/2)**6 + 18*a*f*tan(e/2 + f*x/2)**5 + 18*a*f*tan(e/2 + f*x/2)**4 + 18*a*f*tan(e/2 + f*x/2)**3 + 18*a*f*tan(e/2 + f*x/2)**2 + 6*a*f*tan(e/2 + f*x/2) + 6*a*f) - 45*A*c**3*f*x*tan(e/2 + f*x/2)/(6*a*f*tan(e/2 + f*x/2)**7 + 6*a*f*tan(e/2 + f*x/2)**6 + 18*a*f*tan(e/2 + f*x/2)**5 + 18*a*f*tan(e/2 + f*x/2)**4 + 18*a*f*tan(e/2 + f*x/2)**3 + 18*a*f*tan(e/2 + f*x/2)**2 + 6*a*f*tan(e/2 + f*x/2) + 6*a*f) - 45*A*c**3*f*x/(6*a*f*tan(e/2 + f*x/2)**7 + 6*a*f*tan(e/2 + f*x/2)**6 + 18*a*f*tan(e/2 + f*x/2)**5 + 18*a*f*tan(e/2 + f*x/2)**4 + 18*a*f*tan(e/2 + f*x/2)**3 + 18*a*f*tan(e/2 + f*x/2)**2 + 6*a*f*tan(e/2 + f*x/2) + 6*a*f) - 102*A*c**3*tan(e/2 + f*x/2)**6/(6*a*f*tan(e/2 + f*x/2)**7 + 6*a*f*tan(e/2 + f*x/2)**6 + 18*a*f*tan(e/2 + f*x/2)**5 + 18*a*f*tan(e/2 + f*x/2)**4 + 18*a*f*tan(e/2 + f*x/2)**3 + 18*a*f*tan(e/2 + f*x/2)**2 + 6*a*f*tan(e/2 + f*x/2) + 6*a*f) - 54*A*c**3*tan(e/2 + f*x/2)**5/(6*a*f*tan(e/2 + f*x/2)**7 + 6*a*f*tan(e/2 + f*x/2)**6 + 18*a*f*tan(e/2 + f*x/2)**5 + 18*a*f*tan(e/2 + f*x/2)**4 + 18*a*f*tan(e/2 + f*x/2)**3 + 18*a*f*tan(e/2 + f*x/2)**2 + 6*a*f*tan(e/2 + f*x/2) + 6*a*f) - 336*A*c**3*tan(e/2 + f*x/2)**4/(6*a*f*tan(e/2 + f*x/2)**7 + 6*a*f*tan(e/2 + f*x/2)**6 + 18*a*f*tan(e/2 + f*x/2)**5 + 18*a*f*tan(e/2 + f*x/2)**4 + 18*a*f*tan(e/2 + f*x/2)**3 + 18*a*f*tan(e/2 + f*x/2)**2 + 6*a*f*tan(e/2 + f*x/2) + 6*a*f) - 96*A*c**3*tan(e/2 + f*x/2)**3/(6*a*f*tan(e/2 + f*x/2)**7 + 6*a*f*tan(e/2 + f*x/2)**6 + 18*a*f*tan(e/2 + f*x/2)**5 + 18*a*f*tan(e/2 + f*x/2)**4 + 18*a*f*tan(e/2 + f*x/2)**3 + 18*a*f*tan(e/2 + f*x/2)**2 + 6*a*f*tan(e/2 + f*x/2) + 6*a*f) - 378*A*c**3*tan(e/2 + f*x/2)**2/(6*a*f*tan(e/2 + f*x/2)**7 + 6*a*f*tan(e/2 + f*x/2)**6 + 18*a*f*tan(e/2 + f*x/2)**5 + 18*a*f*tan(e/2 + f*x/2)**4 + 18*a*f*tan(e/2 + f*x/2)**3 + 18*a*f*tan(e/2 + f*x/2)**2 + 6*a*f*tan(e/2 + f*x/2) + 6*a*f) - 42*A*c**3*tan(e/2 + f*x/2)/(6*a*f*tan(e/2 + f*x/2)**7 + 6*a*f*tan(e/2 + f*x/2)**6 + 18*a*f*tan(e/2 + f*x/2)**5 + 18*a*f*tan(e/2 + f*x/2)**4 + 18*a*f*tan(e/2 + f*x/2)**3 + 18*a*f*tan(e/2 + f*x/2)**2 + 6*a*f*tan(e/2 + f*x/2) + 6*a*f) - 144*A*c**3/(6*a*f*tan(e/2 + f*x/2)**7 + 6*a*f*tan(e/2 + f*x/2)**6 + 18*a*f*tan(e/2 + f*x/2)**5 + 18*a*f*tan(e/2 + f*x/2)**4 + 18*a*f*tan(e/2 + f*x/2)**3 + 18*a*f*tan(e/2 + f*x/2)**2 + 6*a*f*tan(e/2 + f*x/2) + 6*a*f) + 60*B*c**3*f*x*tan(e/2 + f*x/2)**7/(6*a*f*tan(e/2 + f*x/2)**7 + 6*a*f*tan(e/2 + f*x/2)**6 + 18*a*f*tan(e/2 + f*x/2)**5 + 18*a*f*tan(e/2 + f*x/2)**4 + 18*a*f*tan(e/2 + f*x/2)**3 + 18*a*f*tan(e/2 + f*x/2)**2 + 6*a*f*tan(e/2 + f*x/2) + 6*a*f) + 60*B*c**3*f*x*tan(e/2 + f*x/2)**6/(6*a*f*tan(e/2 + f*x/2)**7 + 6*a*f*tan(e/2 + f*x/2)**6 + 18*a*f*tan(e/2 + f*x/2)**5 + 18*a*f*tan(e/2 + f*x/2)**4 + 18*a*f*tan(e/2 + f*x/2)**3 + 18*a*f*tan(e/2 + f*x/2)**2 + 6*a*f*tan(e/2 + f*x/2) + 6*a*f) + 180*B*c**3*f*x*tan(e/2 + f*x/2)**5/(6*a*f*tan(e/2 + f*x/2)**7 + 6*a*f*tan(e/2 + f*x/2)**6 + 18*a*f*tan(e/2 + f*x/2)**5 + 18*a*f*tan(e/2 + f*x/2)**4 + 18*a*f*tan(e/2 + f*x/2)**3 + 18*a*f*tan(e/2 + f*x/2)**2 + 6*a*f*tan(e/2 + f*x/2) + 6*a*f) + 180*B*c**3*f*x*tan(e/2 + f*x/2)**4/(6*a*f*tan(e/2 + f*x/2)**7 + 6*a*f*tan(e/2 + f*x/2)**6 + 18*a*f*tan(e/2 + f*x/2)**5 + 18*a*f*tan(e/2 + f*x/2)**4 + 18*a*f*tan(e/2 + f*x/2)**3 + 18*a*f*tan(e/2 + f*x/2)**2 + 6*a*f*tan(e/2 + f*x/2) + 6*a*f) + 180*B*c**3*f*x*tan(e/2 + f*x/2)**3/(6*a*f*tan(e/2 + f*x/2)**7 + 6*a*f*tan(e/2 + f*x/2)**6 + 18*a*f*tan(e/2 + f*x/2)**5 + 18*a*f*tan(e/2 + f*x/2)**4 + 18*a*f*tan(e/2 + f*x/2)**3 + 18*a*f*tan(e/2 + f*x/2)**2 + 6*a*f*tan(e/2 + f*x/2) + 6*a*f) + 180*B*c**3*f*x*tan(e/2 + f*x/2)**2/(6*a*f*tan(e/2 + f*x/2)**7 + 6*a*f*tan(e/2 + f*x/2)**6 + 18*a*f*tan(e/2 + f*x/2)**5 + 18*a*f*tan(e/2 + f*x/2)**4 + 18*a*f*tan(e/2 + f*x/2)**3 + 18*a*f*tan(e/2 + f*x/2)**2 + 6*a*f*tan(e/2 + f*x/2) + 6*a*f) + 60*B*c**3*f*x*tan(e/2 + f*x/2)/(6*a*f*tan(e/2 + f*x/2)**7 + 6*a*f*tan(e/2 + f*x/2)**6 + 18*a*f*tan(e/2 + f*x/2)**5 + 18*a*f*tan(e/2 + f*x/2)**4 + 18*a*f*tan(e/2 + f*x/2)**3 + 18*a*f*tan(e/2 + f*x/2)**2 + 6*a*f*tan(e/2 + f*x/2) + 6*a*f) + 60*B*c**3*f*x/(6*a*f*tan(e/2 + f*x/2)**7 + 6*a*f*tan(e/2 + f*x/2)**6 + 18*a*f*tan(e/2 + f*x/2)**5 + 18*a*f*tan(e/2 + f*x/2)**4 + 18*a*f*tan(e/2 + f*x/2)**3 + 18*a*f*tan(e/2 + f*x/2)**2 + 6*a*f*tan(e/2 + f*x/2) + 6*a*f) + 120*B*c**3*tan(e/2 + f*x/2)**6/(6*a*f*tan(e/2 + f*x/2)**7 + 6*a*f*tan(e/2 + f*x/2)**6 + 18*a*f*tan(e/2 + f*x/2)**5 + 18*a*f*tan(e/2 + f*x/2)**4 + 18*a*f*tan(e/2 + f*x/2)**3 + 18*a*f*tan(e/2 + f*x/2)**2 + 6*a*f*tan(e/2 + f*x/2) + 6*a*f) + 108*B*c**3*tan(e/2 + f*x/2)**5/(6*a*f*tan(e/2 + f*x/2)**7 + 6*a*f*tan(e/2 + f*x/2)**6 + 18*a*f*tan(e/2 + f*x/2)**5 + 18*a*f*tan(e/2 + f*x/2)**4 + 18*a*f*tan(e/2 + f*x/2)**3 + 18*a*f*tan(e/2 + f*x/2)**2 + 6*a*f*tan(e/2 + f*x/2) + 6*a*f) + 372*B*c**3*tan(e/2 + f*x/2)**4/(6*a*f*tan(e/2 + f*x/2)**7 + 6*a*f*tan(e/2 + f*x/2)**6 + 18*a*f*tan(e/2 + f*x/2)**5 + 18*a*f*tan(e/2 + f*x/2)**4 + 18*a*f*tan(e/2 + f*x/2)**3 + 18*a*f*tan(e/2 + f*x/2)**2 + 6*a*f*tan(e/2 + f*x/2) + 6*a*f) + 192*B*c**3*tan(e/2 + f*x/2)**3/(6*a*f*tan(e/2 + f*x/2)**7 + 6*a*f*tan(e/2 + f*x/2)**6 + 18*a*f*tan(e/2 + f*x/2)**5 + 18*a*f*tan(e/2 + f*x/2)**4 + 18*a*f*tan(e/2 + f*x/2)**3 + 18*a*f*tan(e/2 + f*x/2)**2 + 6*a*f*tan(e/2 + f*x/2) + 6*a*f) + 456*B*c**3*tan(e/2 + f*x/2)**2/(6*a*f*tan(e/2 + f*x/2)**7 + 6*a*f*tan(e/2 + f*x/2)**6 + 18*a*f*tan(e/2 + f*x/2)**5 + 18*a*f*tan(e/2 + f*x/2)**4 + 18*a*f*tan(e/2 + f*x/2)**3 + 18*a*f*tan(e/2 + f*x/2)**2 + 6*a*f*tan(e/2 + f*x/2) + 6*a*f) + 68*B*c**3*tan(e/2 + f*x/2)/(6*a*f*tan(e/2 + f*x/2)**7 + 6*a*f*tan(e/2 + f*x/2)**6 + 18*a*f*tan(e/2 + f*x/2)**5 + 18*a*f*tan(e/2 + f*x/2)**4 + 18*a*f*tan(e/2 + f*x/2)**3 + 18*a*f*tan(e/2 + f*x/2)**2 + 6*a*f*tan(e/2 + f*x/2) + 6*a*f) + 188*B*c**3/(6*a*f*tan(e/2 + f*x/2)**7 + 6*a*f*tan(e/2 + f*x/2)**6 + 18*a*f*tan(e/2 + f*x/2)**5 + 18*a*f*tan(e/2 + f*x/2)**4 + 18*a*f*tan(e/2 + f*x/2)**3 + 18*a*f*tan(e/2 + f*x/2)**2 + 6*a*f*tan(e/2 + f*x/2) + 6*a*f), Ne(f, 0)), (x*(A + B*sin(e))*(-c*sin(e) + c)**3/(a*sin(e) + a), True))","A",0
54,1,2365,0,8.104639," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))**2/(a+a*sin(f*x+e)),x)","\begin{cases} - \frac{6 A c^{2} f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} - \frac{6 A c^{2} f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} - \frac{12 A c^{2} f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} - \frac{12 A c^{2} f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} - \frac{6 A c^{2} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} - \frac{6 A c^{2} f x}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} - \frac{16 A c^{2} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} - \frac{4 A c^{2} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} - \frac{36 A c^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} - \frac{4 A c^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} - \frac{20 A c^{2}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} + \frac{9 B c^{2} f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} + \frac{9 B c^{2} f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} + \frac{18 B c^{2} f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} + \frac{18 B c^{2} f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} + \frac{9 B c^{2} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} + \frac{9 B c^{2} f x}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} + \frac{18 B c^{2} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} + \frac{14 B c^{2} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} + \frac{42 B c^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} + \frac{10 B c^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} + \frac{28 B c^{2}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right) \left(- c \sin{\left(e \right)} + c\right)^{2}}{a \sin{\left(e \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-6*A*c**2*f*x*tan(e/2 + f*x/2)**5/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) - 6*A*c**2*f*x*tan(e/2 + f*x/2)**4/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) - 12*A*c**2*f*x*tan(e/2 + f*x/2)**3/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) - 12*A*c**2*f*x*tan(e/2 + f*x/2)**2/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) - 6*A*c**2*f*x*tan(e/2 + f*x/2)/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) - 6*A*c**2*f*x/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) - 16*A*c**2*tan(e/2 + f*x/2)**4/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) - 4*A*c**2*tan(e/2 + f*x/2)**3/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) - 36*A*c**2*tan(e/2 + f*x/2)**2/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) - 4*A*c**2*tan(e/2 + f*x/2)/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) - 20*A*c**2/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) + 9*B*c**2*f*x*tan(e/2 + f*x/2)**5/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) + 9*B*c**2*f*x*tan(e/2 + f*x/2)**4/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) + 18*B*c**2*f*x*tan(e/2 + f*x/2)**3/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) + 18*B*c**2*f*x*tan(e/2 + f*x/2)**2/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) + 9*B*c**2*f*x*tan(e/2 + f*x/2)/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) + 9*B*c**2*f*x/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) + 18*B*c**2*tan(e/2 + f*x/2)**4/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) + 14*B*c**2*tan(e/2 + f*x/2)**3/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) + 42*B*c**2*tan(e/2 + f*x/2)**2/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) + 10*B*c**2*tan(e/2 + f*x/2)/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) + 28*B*c**2/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f), Ne(f, 0)), (x*(A + B*sin(e))*(-c*sin(e) + c)**2/(a*sin(e) + a), True))","A",0
55,1,828,0,3.944587," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))/(a+a*sin(f*x+e)),x)","\begin{cases} - \frac{A c f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f} - \frac{A c f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f} - \frac{A c f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f} - \frac{A c f x}{a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f} - \frac{4 A c \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f} - \frac{4 A c}{a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f} + \frac{2 B c f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f} + \frac{2 B c f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f} + \frac{2 B c f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f} + \frac{2 B c f x}{a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f} + \frac{4 B c \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f} + \frac{2 B c \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f} + \frac{6 B c}{a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right) \left(- c \sin{\left(e \right)} + c\right)}{a \sin{\left(e \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-A*c*f*x*tan(e/2 + f*x/2)**3/(a*f*tan(e/2 + f*x/2)**3 + a*f*tan(e/2 + f*x/2)**2 + a*f*tan(e/2 + f*x/2) + a*f) - A*c*f*x*tan(e/2 + f*x/2)**2/(a*f*tan(e/2 + f*x/2)**3 + a*f*tan(e/2 + f*x/2)**2 + a*f*tan(e/2 + f*x/2) + a*f) - A*c*f*x*tan(e/2 + f*x/2)/(a*f*tan(e/2 + f*x/2)**3 + a*f*tan(e/2 + f*x/2)**2 + a*f*tan(e/2 + f*x/2) + a*f) - A*c*f*x/(a*f*tan(e/2 + f*x/2)**3 + a*f*tan(e/2 + f*x/2)**2 + a*f*tan(e/2 + f*x/2) + a*f) - 4*A*c*tan(e/2 + f*x/2)**2/(a*f*tan(e/2 + f*x/2)**3 + a*f*tan(e/2 + f*x/2)**2 + a*f*tan(e/2 + f*x/2) + a*f) - 4*A*c/(a*f*tan(e/2 + f*x/2)**3 + a*f*tan(e/2 + f*x/2)**2 + a*f*tan(e/2 + f*x/2) + a*f) + 2*B*c*f*x*tan(e/2 + f*x/2)**3/(a*f*tan(e/2 + f*x/2)**3 + a*f*tan(e/2 + f*x/2)**2 + a*f*tan(e/2 + f*x/2) + a*f) + 2*B*c*f*x*tan(e/2 + f*x/2)**2/(a*f*tan(e/2 + f*x/2)**3 + a*f*tan(e/2 + f*x/2)**2 + a*f*tan(e/2 + f*x/2) + a*f) + 2*B*c*f*x*tan(e/2 + f*x/2)/(a*f*tan(e/2 + f*x/2)**3 + a*f*tan(e/2 + f*x/2)**2 + a*f*tan(e/2 + f*x/2) + a*f) + 2*B*c*f*x/(a*f*tan(e/2 + f*x/2)**3 + a*f*tan(e/2 + f*x/2)**2 + a*f*tan(e/2 + f*x/2) + a*f) + 4*B*c*tan(e/2 + f*x/2)**2/(a*f*tan(e/2 + f*x/2)**3 + a*f*tan(e/2 + f*x/2)**2 + a*f*tan(e/2 + f*x/2) + a*f) + 2*B*c*tan(e/2 + f*x/2)/(a*f*tan(e/2 + f*x/2)**3 + a*f*tan(e/2 + f*x/2)**2 + a*f*tan(e/2 + f*x/2) + a*f) + 6*B*c/(a*f*tan(e/2 + f*x/2)**3 + a*f*tan(e/2 + f*x/2)**2 + a*f*tan(e/2 + f*x/2) + a*f), Ne(f, 0)), (x*(A + B*sin(e))*(-c*sin(e) + c)/(a*sin(e) + a), True))","A",0
56,1,83,0,2.532490," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))/(c-c*sin(f*x+e)),x)","\begin{cases} - \frac{2 A \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - a c f} - \frac{2 B}{a c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - a c f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right)}{\left(a \sin{\left(e \right)} + a\right) \left(- c \sin{\left(e \right)} + c\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*A*tan(e/2 + f*x/2)/(a*c*f*tan(e/2 + f*x/2)**2 - a*c*f) - 2*B/(a*c*f*tan(e/2 + f*x/2)**2 - a*c*f), Ne(f, 0)), (x*(A + B*sin(e))/((a*sin(e) + a)*(-c*sin(e) + c)), True))","A",0
57,1,578,0,7.814515," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))**2,x)","\begin{cases} - \frac{6 A \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 a c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 a c^{2} f} + \frac{6 A \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 a c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 a c^{2} f} - \frac{2 A \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 a c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 a c^{2} f} - \frac{2 A}{3 a c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 a c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 a c^{2} f} - \frac{6 B \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 a c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 a c^{2} f} + \frac{4 B \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 a c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 a c^{2} f} - \frac{2 B}{3 a c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 a c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 a c^{2} f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right)}{\left(a \sin{\left(e \right)} + a\right) \left(- c \sin{\left(e \right)} + c\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-6*A*tan(e/2 + f*x/2)**3/(3*a*c**2*f*tan(e/2 + f*x/2)**4 - 6*a*c**2*f*tan(e/2 + f*x/2)**3 + 6*a*c**2*f*tan(e/2 + f*x/2) - 3*a*c**2*f) + 6*A*tan(e/2 + f*x/2)**2/(3*a*c**2*f*tan(e/2 + f*x/2)**4 - 6*a*c**2*f*tan(e/2 + f*x/2)**3 + 6*a*c**2*f*tan(e/2 + f*x/2) - 3*a*c**2*f) - 2*A*tan(e/2 + f*x/2)/(3*a*c**2*f*tan(e/2 + f*x/2)**4 - 6*a*c**2*f*tan(e/2 + f*x/2)**3 + 6*a*c**2*f*tan(e/2 + f*x/2) - 3*a*c**2*f) - 2*A/(3*a*c**2*f*tan(e/2 + f*x/2)**4 - 6*a*c**2*f*tan(e/2 + f*x/2)**3 + 6*a*c**2*f*tan(e/2 + f*x/2) - 3*a*c**2*f) - 6*B*tan(e/2 + f*x/2)**2/(3*a*c**2*f*tan(e/2 + f*x/2)**4 - 6*a*c**2*f*tan(e/2 + f*x/2)**3 + 6*a*c**2*f*tan(e/2 + f*x/2) - 3*a*c**2*f) + 4*B*tan(e/2 + f*x/2)/(3*a*c**2*f*tan(e/2 + f*x/2)**4 - 6*a*c**2*f*tan(e/2 + f*x/2)**3 + 6*a*c**2*f*tan(e/2 + f*x/2) - 3*a*c**2*f) - 2*B/(3*a*c**2*f*tan(e/2 + f*x/2)**4 - 6*a*c**2*f*tan(e/2 + f*x/2)**3 + 6*a*c**2*f*tan(e/2 + f*x/2) - 3*a*c**2*f), Ne(f, 0)), (x*(A + B*sin(e))/((a*sin(e) + a)*(-c*sin(e) + c)**2), True))","A",0
58,1,1236,0,15.149432," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))**3,x)","\begin{cases} - \frac{30 A \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 60 a c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 a c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a c^{3} f} + \frac{60 A \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 60 a c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 a c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a c^{3} f} - \frac{60 A \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 60 a c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 a c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a c^{3} f} + \frac{18 A \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 60 a c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 a c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a c^{3} f} - \frac{12 A}{15 a c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 60 a c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 a c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a c^{3} f} - \frac{30 B \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 60 a c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 a c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a c^{3} f} + \frac{40 B \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 60 a c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 a c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a c^{3} f} - \frac{40 B \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 60 a c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 a c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a c^{3} f} + \frac{8 B \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 60 a c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 a c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a c^{3} f} - \frac{2 B}{15 a c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 60 a c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 a c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a c^{3} f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right)}{\left(a \sin{\left(e \right)} + a\right) \left(- c \sin{\left(e \right)} + c\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-30*A*tan(e/2 + f*x/2)**5/(15*a*c**3*f*tan(e/2 + f*x/2)**6 - 60*a*c**3*f*tan(e/2 + f*x/2)**5 + 75*a*c**3*f*tan(e/2 + f*x/2)**4 - 75*a*c**3*f*tan(e/2 + f*x/2)**2 + 60*a*c**3*f*tan(e/2 + f*x/2) - 15*a*c**3*f) + 60*A*tan(e/2 + f*x/2)**4/(15*a*c**3*f*tan(e/2 + f*x/2)**6 - 60*a*c**3*f*tan(e/2 + f*x/2)**5 + 75*a*c**3*f*tan(e/2 + f*x/2)**4 - 75*a*c**3*f*tan(e/2 + f*x/2)**2 + 60*a*c**3*f*tan(e/2 + f*x/2) - 15*a*c**3*f) - 60*A*tan(e/2 + f*x/2)**3/(15*a*c**3*f*tan(e/2 + f*x/2)**6 - 60*a*c**3*f*tan(e/2 + f*x/2)**5 + 75*a*c**3*f*tan(e/2 + f*x/2)**4 - 75*a*c**3*f*tan(e/2 + f*x/2)**2 + 60*a*c**3*f*tan(e/2 + f*x/2) - 15*a*c**3*f) + 18*A*tan(e/2 + f*x/2)/(15*a*c**3*f*tan(e/2 + f*x/2)**6 - 60*a*c**3*f*tan(e/2 + f*x/2)**5 + 75*a*c**3*f*tan(e/2 + f*x/2)**4 - 75*a*c**3*f*tan(e/2 + f*x/2)**2 + 60*a*c**3*f*tan(e/2 + f*x/2) - 15*a*c**3*f) - 12*A/(15*a*c**3*f*tan(e/2 + f*x/2)**6 - 60*a*c**3*f*tan(e/2 + f*x/2)**5 + 75*a*c**3*f*tan(e/2 + f*x/2)**4 - 75*a*c**3*f*tan(e/2 + f*x/2)**2 + 60*a*c**3*f*tan(e/2 + f*x/2) - 15*a*c**3*f) - 30*B*tan(e/2 + f*x/2)**4/(15*a*c**3*f*tan(e/2 + f*x/2)**6 - 60*a*c**3*f*tan(e/2 + f*x/2)**5 + 75*a*c**3*f*tan(e/2 + f*x/2)**4 - 75*a*c**3*f*tan(e/2 + f*x/2)**2 + 60*a*c**3*f*tan(e/2 + f*x/2) - 15*a*c**3*f) + 40*B*tan(e/2 + f*x/2)**3/(15*a*c**3*f*tan(e/2 + f*x/2)**6 - 60*a*c**3*f*tan(e/2 + f*x/2)**5 + 75*a*c**3*f*tan(e/2 + f*x/2)**4 - 75*a*c**3*f*tan(e/2 + f*x/2)**2 + 60*a*c**3*f*tan(e/2 + f*x/2) - 15*a*c**3*f) - 40*B*tan(e/2 + f*x/2)**2/(15*a*c**3*f*tan(e/2 + f*x/2)**6 - 60*a*c**3*f*tan(e/2 + f*x/2)**5 + 75*a*c**3*f*tan(e/2 + f*x/2)**4 - 75*a*c**3*f*tan(e/2 + f*x/2)**2 + 60*a*c**3*f*tan(e/2 + f*x/2) - 15*a*c**3*f) + 8*B*tan(e/2 + f*x/2)/(15*a*c**3*f*tan(e/2 + f*x/2)**6 - 60*a*c**3*f*tan(e/2 + f*x/2)**5 + 75*a*c**3*f*tan(e/2 + f*x/2)**4 - 75*a*c**3*f*tan(e/2 + f*x/2)**2 + 60*a*c**3*f*tan(e/2 + f*x/2) - 15*a*c**3*f) - 2*B/(15*a*c**3*f*tan(e/2 + f*x/2)**6 - 60*a*c**3*f*tan(e/2 + f*x/2)**5 + 75*a*c**3*f*tan(e/2 + f*x/2)**4 - 75*a*c**3*f*tan(e/2 + f*x/2)**2 + 60*a*c**3*f*tan(e/2 + f*x/2) - 15*a*c**3*f), Ne(f, 0)), (x*(A + B*sin(e))/((a*sin(e) + a)*(-c*sin(e) + c)**3), True))","A",0
59,1,2468,0,28.582517," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))**4,x)","\begin{cases} - \frac{70 A \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{35 a c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 210 a c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 490 a c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 490 a c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 490 a c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 490 a c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 210 a c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 35 a c^{4} f} + \frac{210 A \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{35 a c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 210 a c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 490 a c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 490 a c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 490 a c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 490 a c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 210 a c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 35 a c^{4} f} - \frac{350 A \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{35 a c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 210 a c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 490 a c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 490 a c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 490 a c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 490 a c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 210 a c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 35 a c^{4} f} + \frac{210 A \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{35 a c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 210 a c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 490 a c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 490 a c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 490 a c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 490 a c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 210 a c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 35 a c^{4} f} + \frac{14 A \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{35 a c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 210 a c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 490 a c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 490 a c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 490 a c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 490 a c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 210 a c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 35 a c^{4} f} - \frac{154 A \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{35 a c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 210 a c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 490 a c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 490 a c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 490 a c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 490 a c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 210 a c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 35 a c^{4} f} + \frac{86 A \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{35 a c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 210 a c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 490 a c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 490 a c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 490 a c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 490 a c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 210 a c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 35 a c^{4} f} - \frac{26 A}{35 a c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 210 a c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 490 a c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 490 a c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 490 a c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 490 a c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 210 a c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 35 a c^{4} f} - \frac{70 B \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{35 a c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 210 a c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 490 a c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 490 a c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 490 a c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 490 a c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 210 a c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 35 a c^{4} f} + \frac{140 B \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{35 a c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 210 a c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 490 a c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 490 a c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 490 a c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 490 a c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 210 a c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 35 a c^{4} f} - \frac{210 B \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{35 a c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 210 a c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 490 a c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 490 a c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 490 a c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 490 a c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 210 a c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 35 a c^{4} f} + \frac{112 B \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{35 a c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 210 a c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 490 a c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 490 a c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 490 a c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 490 a c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 210 a c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 35 a c^{4} f} - \frac{42 B \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{35 a c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 210 a c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 490 a c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 490 a c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 490 a c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 490 a c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 210 a c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 35 a c^{4} f} - \frac{12 B \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{35 a c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 210 a c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 490 a c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 490 a c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 490 a c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 490 a c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 210 a c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 35 a c^{4} f} + \frac{2 B}{35 a c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 210 a c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 490 a c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 490 a c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 490 a c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 490 a c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 210 a c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 35 a c^{4} f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right)}{\left(a \sin{\left(e \right)} + a\right) \left(- c \sin{\left(e \right)} + c\right)^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-70*A*tan(e/2 + f*x/2)**7/(35*a*c**4*f*tan(e/2 + f*x/2)**8 - 210*a*c**4*f*tan(e/2 + f*x/2)**7 + 490*a*c**4*f*tan(e/2 + f*x/2)**6 - 490*a*c**4*f*tan(e/2 + f*x/2)**5 + 490*a*c**4*f*tan(e/2 + f*x/2)**3 - 490*a*c**4*f*tan(e/2 + f*x/2)**2 + 210*a*c**4*f*tan(e/2 + f*x/2) - 35*a*c**4*f) + 210*A*tan(e/2 + f*x/2)**6/(35*a*c**4*f*tan(e/2 + f*x/2)**8 - 210*a*c**4*f*tan(e/2 + f*x/2)**7 + 490*a*c**4*f*tan(e/2 + f*x/2)**6 - 490*a*c**4*f*tan(e/2 + f*x/2)**5 + 490*a*c**4*f*tan(e/2 + f*x/2)**3 - 490*a*c**4*f*tan(e/2 + f*x/2)**2 + 210*a*c**4*f*tan(e/2 + f*x/2) - 35*a*c**4*f) - 350*A*tan(e/2 + f*x/2)**5/(35*a*c**4*f*tan(e/2 + f*x/2)**8 - 210*a*c**4*f*tan(e/2 + f*x/2)**7 + 490*a*c**4*f*tan(e/2 + f*x/2)**6 - 490*a*c**4*f*tan(e/2 + f*x/2)**5 + 490*a*c**4*f*tan(e/2 + f*x/2)**3 - 490*a*c**4*f*tan(e/2 + f*x/2)**2 + 210*a*c**4*f*tan(e/2 + f*x/2) - 35*a*c**4*f) + 210*A*tan(e/2 + f*x/2)**4/(35*a*c**4*f*tan(e/2 + f*x/2)**8 - 210*a*c**4*f*tan(e/2 + f*x/2)**7 + 490*a*c**4*f*tan(e/2 + f*x/2)**6 - 490*a*c**4*f*tan(e/2 + f*x/2)**5 + 490*a*c**4*f*tan(e/2 + f*x/2)**3 - 490*a*c**4*f*tan(e/2 + f*x/2)**2 + 210*a*c**4*f*tan(e/2 + f*x/2) - 35*a*c**4*f) + 14*A*tan(e/2 + f*x/2)**3/(35*a*c**4*f*tan(e/2 + f*x/2)**8 - 210*a*c**4*f*tan(e/2 + f*x/2)**7 + 490*a*c**4*f*tan(e/2 + f*x/2)**6 - 490*a*c**4*f*tan(e/2 + f*x/2)**5 + 490*a*c**4*f*tan(e/2 + f*x/2)**3 - 490*a*c**4*f*tan(e/2 + f*x/2)**2 + 210*a*c**4*f*tan(e/2 + f*x/2) - 35*a*c**4*f) - 154*A*tan(e/2 + f*x/2)**2/(35*a*c**4*f*tan(e/2 + f*x/2)**8 - 210*a*c**4*f*tan(e/2 + f*x/2)**7 + 490*a*c**4*f*tan(e/2 + f*x/2)**6 - 490*a*c**4*f*tan(e/2 + f*x/2)**5 + 490*a*c**4*f*tan(e/2 + f*x/2)**3 - 490*a*c**4*f*tan(e/2 + f*x/2)**2 + 210*a*c**4*f*tan(e/2 + f*x/2) - 35*a*c**4*f) + 86*A*tan(e/2 + f*x/2)/(35*a*c**4*f*tan(e/2 + f*x/2)**8 - 210*a*c**4*f*tan(e/2 + f*x/2)**7 + 490*a*c**4*f*tan(e/2 + f*x/2)**6 - 490*a*c**4*f*tan(e/2 + f*x/2)**5 + 490*a*c**4*f*tan(e/2 + f*x/2)**3 - 490*a*c**4*f*tan(e/2 + f*x/2)**2 + 210*a*c**4*f*tan(e/2 + f*x/2) - 35*a*c**4*f) - 26*A/(35*a*c**4*f*tan(e/2 + f*x/2)**8 - 210*a*c**4*f*tan(e/2 + f*x/2)**7 + 490*a*c**4*f*tan(e/2 + f*x/2)**6 - 490*a*c**4*f*tan(e/2 + f*x/2)**5 + 490*a*c**4*f*tan(e/2 + f*x/2)**3 - 490*a*c**4*f*tan(e/2 + f*x/2)**2 + 210*a*c**4*f*tan(e/2 + f*x/2) - 35*a*c**4*f) - 70*B*tan(e/2 + f*x/2)**6/(35*a*c**4*f*tan(e/2 + f*x/2)**8 - 210*a*c**4*f*tan(e/2 + f*x/2)**7 + 490*a*c**4*f*tan(e/2 + f*x/2)**6 - 490*a*c**4*f*tan(e/2 + f*x/2)**5 + 490*a*c**4*f*tan(e/2 + f*x/2)**3 - 490*a*c**4*f*tan(e/2 + f*x/2)**2 + 210*a*c**4*f*tan(e/2 + f*x/2) - 35*a*c**4*f) + 140*B*tan(e/2 + f*x/2)**5/(35*a*c**4*f*tan(e/2 + f*x/2)**8 - 210*a*c**4*f*tan(e/2 + f*x/2)**7 + 490*a*c**4*f*tan(e/2 + f*x/2)**6 - 490*a*c**4*f*tan(e/2 + f*x/2)**5 + 490*a*c**4*f*tan(e/2 + f*x/2)**3 - 490*a*c**4*f*tan(e/2 + f*x/2)**2 + 210*a*c**4*f*tan(e/2 + f*x/2) - 35*a*c**4*f) - 210*B*tan(e/2 + f*x/2)**4/(35*a*c**4*f*tan(e/2 + f*x/2)**8 - 210*a*c**4*f*tan(e/2 + f*x/2)**7 + 490*a*c**4*f*tan(e/2 + f*x/2)**6 - 490*a*c**4*f*tan(e/2 + f*x/2)**5 + 490*a*c**4*f*tan(e/2 + f*x/2)**3 - 490*a*c**4*f*tan(e/2 + f*x/2)**2 + 210*a*c**4*f*tan(e/2 + f*x/2) - 35*a*c**4*f) + 112*B*tan(e/2 + f*x/2)**3/(35*a*c**4*f*tan(e/2 + f*x/2)**8 - 210*a*c**4*f*tan(e/2 + f*x/2)**7 + 490*a*c**4*f*tan(e/2 + f*x/2)**6 - 490*a*c**4*f*tan(e/2 + f*x/2)**5 + 490*a*c**4*f*tan(e/2 + f*x/2)**3 - 490*a*c**4*f*tan(e/2 + f*x/2)**2 + 210*a*c**4*f*tan(e/2 + f*x/2) - 35*a*c**4*f) - 42*B*tan(e/2 + f*x/2)**2/(35*a*c**4*f*tan(e/2 + f*x/2)**8 - 210*a*c**4*f*tan(e/2 + f*x/2)**7 + 490*a*c**4*f*tan(e/2 + f*x/2)**6 - 490*a*c**4*f*tan(e/2 + f*x/2)**5 + 490*a*c**4*f*tan(e/2 + f*x/2)**3 - 490*a*c**4*f*tan(e/2 + f*x/2)**2 + 210*a*c**4*f*tan(e/2 + f*x/2) - 35*a*c**4*f) - 12*B*tan(e/2 + f*x/2)/(35*a*c**4*f*tan(e/2 + f*x/2)**8 - 210*a*c**4*f*tan(e/2 + f*x/2)**7 + 490*a*c**4*f*tan(e/2 + f*x/2)**6 - 490*a*c**4*f*tan(e/2 + f*x/2)**5 + 490*a*c**4*f*tan(e/2 + f*x/2)**3 - 490*a*c**4*f*tan(e/2 + f*x/2)**2 + 210*a*c**4*f*tan(e/2 + f*x/2) - 35*a*c**4*f) + 2*B/(35*a*c**4*f*tan(e/2 + f*x/2)**8 - 210*a*c**4*f*tan(e/2 + f*x/2)**7 + 490*a*c**4*f*tan(e/2 + f*x/2)**6 - 490*a*c**4*f*tan(e/2 + f*x/2)**5 + 490*a*c**4*f*tan(e/2 + f*x/2)**3 - 490*a*c**4*f*tan(e/2 + f*x/2)**2 + 210*a*c**4*f*tan(e/2 + f*x/2) - 35*a*c**4*f), Ne(f, 0)), (x*(A + B*sin(e))/((a*sin(e) + a)*(-c*sin(e) + c)**4), True))","A",0
60,1,10608,0,68.938216," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))**5/(a+a*sin(f*x+e))**2,x)","\begin{cases} \frac{1260 A c^{5} f x \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} + \frac{3780 A c^{5} f x \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} + \frac{8820 A c^{5} f x \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} + \frac{16380 A c^{5} f x \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} + \frac{22680 A c^{5} f x \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} + \frac{27720 A c^{5} f x \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} + \frac{27720 A c^{5} f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} + \frac{22680 A c^{5} f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} + \frac{16380 A c^{5} f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} + \frac{8820 A c^{5} f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} + \frac{3780 A c^{5} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} + \frac{1260 A c^{5} f x}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} + \frac{2472 A c^{5} \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} + \frac{7752 A c^{5} \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} + \frac{16016 A c^{5} \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} + \frac{31968 A c^{5} \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} + \frac{36752 A c^{5} \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} + \frac{50192 A c^{5} \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} + \frac{39168 A c^{5} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} + \frac{35360 A c^{5} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} + \frac{19912 A c^{5} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} + \frac{9384 A c^{5} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} + \frac{3952 A c^{5}}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} - \frac{2205 B c^{5} f x \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} - \frac{6615 B c^{5} f x \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} - \frac{15435 B c^{5} f x \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} - \frac{28665 B c^{5} f x \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} - \frac{39690 B c^{5} f x \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} - \frac{48510 B c^{5} f x \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} - \frac{48510 B c^{5} f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} - \frac{39690 B c^{5} f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} - \frac{28665 B c^{5} f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} - \frac{15435 B c^{5} f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} - \frac{6615 B c^{5} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} - \frac{2205 B c^{5} f x}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} - \frac{4410 B c^{5} \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} - \frac{13278 B c^{5} \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} - \frac{29096 B c^{5} \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} - \frac{54072 B c^{5} \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} - \frac{67220 B c^{5} \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} - \frac{85196 B c^{5} \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} - \frac{70632 B c^{5} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} - \frac{60968 B c^{5} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} - \frac{35218 B c^{5} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} - \frac{16374 B c^{5} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} - \frac{6928 B c^{5}}{24 a^{2} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 528 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 432 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 312 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24 a^{2} f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right) \left(- c \sin{\left(e \right)} + c\right)^{5}}{\left(a \sin{\left(e \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((1260*A*c**5*f*x*tan(e/2 + f*x/2)**11/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f) + 3780*A*c**5*f*x*tan(e/2 + f*x/2)**10/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f) + 8820*A*c**5*f*x*tan(e/2 + f*x/2)**9/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f) + 16380*A*c**5*f*x*tan(e/2 + f*x/2)**8/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f) + 22680*A*c**5*f*x*tan(e/2 + f*x/2)**7/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f) + 27720*A*c**5*f*x*tan(e/2 + f*x/2)**6/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f) + 27720*A*c**5*f*x*tan(e/2 + f*x/2)**5/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f) + 22680*A*c**5*f*x*tan(e/2 + f*x/2)**4/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f) + 16380*A*c**5*f*x*tan(e/2 + f*x/2)**3/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f) + 8820*A*c**5*f*x*tan(e/2 + f*x/2)**2/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f) + 3780*A*c**5*f*x*tan(e/2 + f*x/2)/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f) + 1260*A*c**5*f*x/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f) + 2472*A*c**5*tan(e/2 + f*x/2)**10/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f) + 7752*A*c**5*tan(e/2 + f*x/2)**9/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f) + 16016*A*c**5*tan(e/2 + f*x/2)**8/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f) + 31968*A*c**5*tan(e/2 + f*x/2)**7/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f) + 36752*A*c**5*tan(e/2 + f*x/2)**6/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f) + 50192*A*c**5*tan(e/2 + f*x/2)**5/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f) + 39168*A*c**5*tan(e/2 + f*x/2)**4/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f) + 35360*A*c**5*tan(e/2 + f*x/2)**3/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f) + 19912*A*c**5*tan(e/2 + f*x/2)**2/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f) + 9384*A*c**5*tan(e/2 + f*x/2)/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f) + 3952*A*c**5/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f) - 2205*B*c**5*f*x*tan(e/2 + f*x/2)**11/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f) - 6615*B*c**5*f*x*tan(e/2 + f*x/2)**10/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f) - 15435*B*c**5*f*x*tan(e/2 + f*x/2)**9/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f) - 28665*B*c**5*f*x*tan(e/2 + f*x/2)**8/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f) - 39690*B*c**5*f*x*tan(e/2 + f*x/2)**7/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f) - 48510*B*c**5*f*x*tan(e/2 + f*x/2)**6/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f) - 48510*B*c**5*f*x*tan(e/2 + f*x/2)**5/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f) - 39690*B*c**5*f*x*tan(e/2 + f*x/2)**4/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f) - 28665*B*c**5*f*x*tan(e/2 + f*x/2)**3/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f) - 15435*B*c**5*f*x*tan(e/2 + f*x/2)**2/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f) - 6615*B*c**5*f*x*tan(e/2 + f*x/2)/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f) - 2205*B*c**5*f*x/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f) - 4410*B*c**5*tan(e/2 + f*x/2)**10/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f) - 13278*B*c**5*tan(e/2 + f*x/2)**9/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f) - 29096*B*c**5*tan(e/2 + f*x/2)**8/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f) - 54072*B*c**5*tan(e/2 + f*x/2)**7/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f) - 67220*B*c**5*tan(e/2 + f*x/2)**6/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f) - 85196*B*c**5*tan(e/2 + f*x/2)**5/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f) - 70632*B*c**5*tan(e/2 + f*x/2)**4/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f) - 60968*B*c**5*tan(e/2 + f*x/2)**3/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f) - 35218*B*c**5*tan(e/2 + f*x/2)**2/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f) - 16374*B*c**5*tan(e/2 + f*x/2)/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f) - 6928*B*c**5/(24*a**2*f*tan(e/2 + f*x/2)**11 + 72*a**2*f*tan(e/2 + f*x/2)**10 + 168*a**2*f*tan(e/2 + f*x/2)**9 + 312*a**2*f*tan(e/2 + f*x/2)**8 + 432*a**2*f*tan(e/2 + f*x/2)**7 + 528*a**2*f*tan(e/2 + f*x/2)**6 + 528*a**2*f*tan(e/2 + f*x/2)**5 + 432*a**2*f*tan(e/2 + f*x/2)**4 + 312*a**2*f*tan(e/2 + f*x/2)**3 + 168*a**2*f*tan(e/2 + f*x/2)**2 + 72*a**2*f*tan(e/2 + f*x/2) + 24*a**2*f), Ne(f, 0)), (x*(A + B*sin(e))*(-c*sin(e) + c)**5/(a*sin(e) + a)**2, True))","A",0
61,1,7337,0,44.147890," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))**4/(a+a*sin(f*x+e))**2,x)","\begin{cases} \frac{105 A c^{4} f x \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} + \frac{315 A c^{4} f x \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} + \frac{630 A c^{4} f x \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} + \frac{1050 A c^{4} f x \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} + \frac{1260 A c^{4} f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} + \frac{1260 A c^{4} f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} + \frac{1050 A c^{4} f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} + \frac{630 A c^{4} f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} + \frac{315 A c^{4} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} + \frac{105 A c^{4} f x}{6 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} + \frac{198 A c^{4} \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} + \frac{666 A c^{4} \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} + \frac{1066 A c^{4} \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} + \frac{2094 A c^{4} \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} + \frac{1842 A c^{4} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} + \frac{2214 A c^{4} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} + \frac{1302 A c^{4} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} + \frac{786 A c^{4} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} + \frac{328 A c^{4}}{6 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} - \frac{210 B c^{4} f x \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} - \frac{630 B c^{4} f x \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} - \frac{1260 B c^{4} f x \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} - \frac{2100 B c^{4} f x \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} - \frac{2520 B c^{4} f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} - \frac{2520 B c^{4} f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} - \frac{2100 B c^{4} f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} - \frac{1260 B c^{4} f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} - \frac{630 B c^{4} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} - \frac{210 B c^{4} f x}{6 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} - \frac{420 B c^{4} \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} - \frac{1272 B c^{4} \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} - \frac{2320 B c^{4} \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} - \frac{3960 B c^{4} \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} - \frac{3960 B c^{4} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} - \frac{4280 B c^{4} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} - \frac{2688 B c^{4} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} - \frac{1560 B c^{4} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} - \frac{660 B c^{4}}{6 a^{2} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 72 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 36 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right) \left(- c \sin{\left(e \right)} + c\right)^{4}}{\left(a \sin{\left(e \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((105*A*c**4*f*x*tan(e/2 + f*x/2)**9/(6*a**2*f*tan(e/2 + f*x/2)**9 + 18*a**2*f*tan(e/2 + f*x/2)**8 + 36*a**2*f*tan(e/2 + f*x/2)**7 + 60*a**2*f*tan(e/2 + f*x/2)**6 + 72*a**2*f*tan(e/2 + f*x/2)**5 + 72*a**2*f*tan(e/2 + f*x/2)**4 + 60*a**2*f*tan(e/2 + f*x/2)**3 + 36*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) + 315*A*c**4*f*x*tan(e/2 + f*x/2)**8/(6*a**2*f*tan(e/2 + f*x/2)**9 + 18*a**2*f*tan(e/2 + f*x/2)**8 + 36*a**2*f*tan(e/2 + f*x/2)**7 + 60*a**2*f*tan(e/2 + f*x/2)**6 + 72*a**2*f*tan(e/2 + f*x/2)**5 + 72*a**2*f*tan(e/2 + f*x/2)**4 + 60*a**2*f*tan(e/2 + f*x/2)**3 + 36*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) + 630*A*c**4*f*x*tan(e/2 + f*x/2)**7/(6*a**2*f*tan(e/2 + f*x/2)**9 + 18*a**2*f*tan(e/2 + f*x/2)**8 + 36*a**2*f*tan(e/2 + f*x/2)**7 + 60*a**2*f*tan(e/2 + f*x/2)**6 + 72*a**2*f*tan(e/2 + f*x/2)**5 + 72*a**2*f*tan(e/2 + f*x/2)**4 + 60*a**2*f*tan(e/2 + f*x/2)**3 + 36*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) + 1050*A*c**4*f*x*tan(e/2 + f*x/2)**6/(6*a**2*f*tan(e/2 + f*x/2)**9 + 18*a**2*f*tan(e/2 + f*x/2)**8 + 36*a**2*f*tan(e/2 + f*x/2)**7 + 60*a**2*f*tan(e/2 + f*x/2)**6 + 72*a**2*f*tan(e/2 + f*x/2)**5 + 72*a**2*f*tan(e/2 + f*x/2)**4 + 60*a**2*f*tan(e/2 + f*x/2)**3 + 36*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) + 1260*A*c**4*f*x*tan(e/2 + f*x/2)**5/(6*a**2*f*tan(e/2 + f*x/2)**9 + 18*a**2*f*tan(e/2 + f*x/2)**8 + 36*a**2*f*tan(e/2 + f*x/2)**7 + 60*a**2*f*tan(e/2 + f*x/2)**6 + 72*a**2*f*tan(e/2 + f*x/2)**5 + 72*a**2*f*tan(e/2 + f*x/2)**4 + 60*a**2*f*tan(e/2 + f*x/2)**3 + 36*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) + 1260*A*c**4*f*x*tan(e/2 + f*x/2)**4/(6*a**2*f*tan(e/2 + f*x/2)**9 + 18*a**2*f*tan(e/2 + f*x/2)**8 + 36*a**2*f*tan(e/2 + f*x/2)**7 + 60*a**2*f*tan(e/2 + f*x/2)**6 + 72*a**2*f*tan(e/2 + f*x/2)**5 + 72*a**2*f*tan(e/2 + f*x/2)**4 + 60*a**2*f*tan(e/2 + f*x/2)**3 + 36*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) + 1050*A*c**4*f*x*tan(e/2 + f*x/2)**3/(6*a**2*f*tan(e/2 + f*x/2)**9 + 18*a**2*f*tan(e/2 + f*x/2)**8 + 36*a**2*f*tan(e/2 + f*x/2)**7 + 60*a**2*f*tan(e/2 + f*x/2)**6 + 72*a**2*f*tan(e/2 + f*x/2)**5 + 72*a**2*f*tan(e/2 + f*x/2)**4 + 60*a**2*f*tan(e/2 + f*x/2)**3 + 36*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) + 630*A*c**4*f*x*tan(e/2 + f*x/2)**2/(6*a**2*f*tan(e/2 + f*x/2)**9 + 18*a**2*f*tan(e/2 + f*x/2)**8 + 36*a**2*f*tan(e/2 + f*x/2)**7 + 60*a**2*f*tan(e/2 + f*x/2)**6 + 72*a**2*f*tan(e/2 + f*x/2)**5 + 72*a**2*f*tan(e/2 + f*x/2)**4 + 60*a**2*f*tan(e/2 + f*x/2)**3 + 36*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) + 315*A*c**4*f*x*tan(e/2 + f*x/2)/(6*a**2*f*tan(e/2 + f*x/2)**9 + 18*a**2*f*tan(e/2 + f*x/2)**8 + 36*a**2*f*tan(e/2 + f*x/2)**7 + 60*a**2*f*tan(e/2 + f*x/2)**6 + 72*a**2*f*tan(e/2 + f*x/2)**5 + 72*a**2*f*tan(e/2 + f*x/2)**4 + 60*a**2*f*tan(e/2 + f*x/2)**3 + 36*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) + 105*A*c**4*f*x/(6*a**2*f*tan(e/2 + f*x/2)**9 + 18*a**2*f*tan(e/2 + f*x/2)**8 + 36*a**2*f*tan(e/2 + f*x/2)**7 + 60*a**2*f*tan(e/2 + f*x/2)**6 + 72*a**2*f*tan(e/2 + f*x/2)**5 + 72*a**2*f*tan(e/2 + f*x/2)**4 + 60*a**2*f*tan(e/2 + f*x/2)**3 + 36*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) + 198*A*c**4*tan(e/2 + f*x/2)**8/(6*a**2*f*tan(e/2 + f*x/2)**9 + 18*a**2*f*tan(e/2 + f*x/2)**8 + 36*a**2*f*tan(e/2 + f*x/2)**7 + 60*a**2*f*tan(e/2 + f*x/2)**6 + 72*a**2*f*tan(e/2 + f*x/2)**5 + 72*a**2*f*tan(e/2 + f*x/2)**4 + 60*a**2*f*tan(e/2 + f*x/2)**3 + 36*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) + 666*A*c**4*tan(e/2 + f*x/2)**7/(6*a**2*f*tan(e/2 + f*x/2)**9 + 18*a**2*f*tan(e/2 + f*x/2)**8 + 36*a**2*f*tan(e/2 + f*x/2)**7 + 60*a**2*f*tan(e/2 + f*x/2)**6 + 72*a**2*f*tan(e/2 + f*x/2)**5 + 72*a**2*f*tan(e/2 + f*x/2)**4 + 60*a**2*f*tan(e/2 + f*x/2)**3 + 36*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) + 1066*A*c**4*tan(e/2 + f*x/2)**6/(6*a**2*f*tan(e/2 + f*x/2)**9 + 18*a**2*f*tan(e/2 + f*x/2)**8 + 36*a**2*f*tan(e/2 + f*x/2)**7 + 60*a**2*f*tan(e/2 + f*x/2)**6 + 72*a**2*f*tan(e/2 + f*x/2)**5 + 72*a**2*f*tan(e/2 + f*x/2)**4 + 60*a**2*f*tan(e/2 + f*x/2)**3 + 36*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) + 2094*A*c**4*tan(e/2 + f*x/2)**5/(6*a**2*f*tan(e/2 + f*x/2)**9 + 18*a**2*f*tan(e/2 + f*x/2)**8 + 36*a**2*f*tan(e/2 + f*x/2)**7 + 60*a**2*f*tan(e/2 + f*x/2)**6 + 72*a**2*f*tan(e/2 + f*x/2)**5 + 72*a**2*f*tan(e/2 + f*x/2)**4 + 60*a**2*f*tan(e/2 + f*x/2)**3 + 36*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) + 1842*A*c**4*tan(e/2 + f*x/2)**4/(6*a**2*f*tan(e/2 + f*x/2)**9 + 18*a**2*f*tan(e/2 + f*x/2)**8 + 36*a**2*f*tan(e/2 + f*x/2)**7 + 60*a**2*f*tan(e/2 + f*x/2)**6 + 72*a**2*f*tan(e/2 + f*x/2)**5 + 72*a**2*f*tan(e/2 + f*x/2)**4 + 60*a**2*f*tan(e/2 + f*x/2)**3 + 36*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) + 2214*A*c**4*tan(e/2 + f*x/2)**3/(6*a**2*f*tan(e/2 + f*x/2)**9 + 18*a**2*f*tan(e/2 + f*x/2)**8 + 36*a**2*f*tan(e/2 + f*x/2)**7 + 60*a**2*f*tan(e/2 + f*x/2)**6 + 72*a**2*f*tan(e/2 + f*x/2)**5 + 72*a**2*f*tan(e/2 + f*x/2)**4 + 60*a**2*f*tan(e/2 + f*x/2)**3 + 36*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) + 1302*A*c**4*tan(e/2 + f*x/2)**2/(6*a**2*f*tan(e/2 + f*x/2)**9 + 18*a**2*f*tan(e/2 + f*x/2)**8 + 36*a**2*f*tan(e/2 + f*x/2)**7 + 60*a**2*f*tan(e/2 + f*x/2)**6 + 72*a**2*f*tan(e/2 + f*x/2)**5 + 72*a**2*f*tan(e/2 + f*x/2)**4 + 60*a**2*f*tan(e/2 + f*x/2)**3 + 36*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) + 786*A*c**4*tan(e/2 + f*x/2)/(6*a**2*f*tan(e/2 + f*x/2)**9 + 18*a**2*f*tan(e/2 + f*x/2)**8 + 36*a**2*f*tan(e/2 + f*x/2)**7 + 60*a**2*f*tan(e/2 + f*x/2)**6 + 72*a**2*f*tan(e/2 + f*x/2)**5 + 72*a**2*f*tan(e/2 + f*x/2)**4 + 60*a**2*f*tan(e/2 + f*x/2)**3 + 36*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) + 328*A*c**4/(6*a**2*f*tan(e/2 + f*x/2)**9 + 18*a**2*f*tan(e/2 + f*x/2)**8 + 36*a**2*f*tan(e/2 + f*x/2)**7 + 60*a**2*f*tan(e/2 + f*x/2)**6 + 72*a**2*f*tan(e/2 + f*x/2)**5 + 72*a**2*f*tan(e/2 + f*x/2)**4 + 60*a**2*f*tan(e/2 + f*x/2)**3 + 36*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) - 210*B*c**4*f*x*tan(e/2 + f*x/2)**9/(6*a**2*f*tan(e/2 + f*x/2)**9 + 18*a**2*f*tan(e/2 + f*x/2)**8 + 36*a**2*f*tan(e/2 + f*x/2)**7 + 60*a**2*f*tan(e/2 + f*x/2)**6 + 72*a**2*f*tan(e/2 + f*x/2)**5 + 72*a**2*f*tan(e/2 + f*x/2)**4 + 60*a**2*f*tan(e/2 + f*x/2)**3 + 36*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) - 630*B*c**4*f*x*tan(e/2 + f*x/2)**8/(6*a**2*f*tan(e/2 + f*x/2)**9 + 18*a**2*f*tan(e/2 + f*x/2)**8 + 36*a**2*f*tan(e/2 + f*x/2)**7 + 60*a**2*f*tan(e/2 + f*x/2)**6 + 72*a**2*f*tan(e/2 + f*x/2)**5 + 72*a**2*f*tan(e/2 + f*x/2)**4 + 60*a**2*f*tan(e/2 + f*x/2)**3 + 36*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) - 1260*B*c**4*f*x*tan(e/2 + f*x/2)**7/(6*a**2*f*tan(e/2 + f*x/2)**9 + 18*a**2*f*tan(e/2 + f*x/2)**8 + 36*a**2*f*tan(e/2 + f*x/2)**7 + 60*a**2*f*tan(e/2 + f*x/2)**6 + 72*a**2*f*tan(e/2 + f*x/2)**5 + 72*a**2*f*tan(e/2 + f*x/2)**4 + 60*a**2*f*tan(e/2 + f*x/2)**3 + 36*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) - 2100*B*c**4*f*x*tan(e/2 + f*x/2)**6/(6*a**2*f*tan(e/2 + f*x/2)**9 + 18*a**2*f*tan(e/2 + f*x/2)**8 + 36*a**2*f*tan(e/2 + f*x/2)**7 + 60*a**2*f*tan(e/2 + f*x/2)**6 + 72*a**2*f*tan(e/2 + f*x/2)**5 + 72*a**2*f*tan(e/2 + f*x/2)**4 + 60*a**2*f*tan(e/2 + f*x/2)**3 + 36*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) - 2520*B*c**4*f*x*tan(e/2 + f*x/2)**5/(6*a**2*f*tan(e/2 + f*x/2)**9 + 18*a**2*f*tan(e/2 + f*x/2)**8 + 36*a**2*f*tan(e/2 + f*x/2)**7 + 60*a**2*f*tan(e/2 + f*x/2)**6 + 72*a**2*f*tan(e/2 + f*x/2)**5 + 72*a**2*f*tan(e/2 + f*x/2)**4 + 60*a**2*f*tan(e/2 + f*x/2)**3 + 36*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) - 2520*B*c**4*f*x*tan(e/2 + f*x/2)**4/(6*a**2*f*tan(e/2 + f*x/2)**9 + 18*a**2*f*tan(e/2 + f*x/2)**8 + 36*a**2*f*tan(e/2 + f*x/2)**7 + 60*a**2*f*tan(e/2 + f*x/2)**6 + 72*a**2*f*tan(e/2 + f*x/2)**5 + 72*a**2*f*tan(e/2 + f*x/2)**4 + 60*a**2*f*tan(e/2 + f*x/2)**3 + 36*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) - 2100*B*c**4*f*x*tan(e/2 + f*x/2)**3/(6*a**2*f*tan(e/2 + f*x/2)**9 + 18*a**2*f*tan(e/2 + f*x/2)**8 + 36*a**2*f*tan(e/2 + f*x/2)**7 + 60*a**2*f*tan(e/2 + f*x/2)**6 + 72*a**2*f*tan(e/2 + f*x/2)**5 + 72*a**2*f*tan(e/2 + f*x/2)**4 + 60*a**2*f*tan(e/2 + f*x/2)**3 + 36*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) - 1260*B*c**4*f*x*tan(e/2 + f*x/2)**2/(6*a**2*f*tan(e/2 + f*x/2)**9 + 18*a**2*f*tan(e/2 + f*x/2)**8 + 36*a**2*f*tan(e/2 + f*x/2)**7 + 60*a**2*f*tan(e/2 + f*x/2)**6 + 72*a**2*f*tan(e/2 + f*x/2)**5 + 72*a**2*f*tan(e/2 + f*x/2)**4 + 60*a**2*f*tan(e/2 + f*x/2)**3 + 36*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) - 630*B*c**4*f*x*tan(e/2 + f*x/2)/(6*a**2*f*tan(e/2 + f*x/2)**9 + 18*a**2*f*tan(e/2 + f*x/2)**8 + 36*a**2*f*tan(e/2 + f*x/2)**7 + 60*a**2*f*tan(e/2 + f*x/2)**6 + 72*a**2*f*tan(e/2 + f*x/2)**5 + 72*a**2*f*tan(e/2 + f*x/2)**4 + 60*a**2*f*tan(e/2 + f*x/2)**3 + 36*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) - 210*B*c**4*f*x/(6*a**2*f*tan(e/2 + f*x/2)**9 + 18*a**2*f*tan(e/2 + f*x/2)**8 + 36*a**2*f*tan(e/2 + f*x/2)**7 + 60*a**2*f*tan(e/2 + f*x/2)**6 + 72*a**2*f*tan(e/2 + f*x/2)**5 + 72*a**2*f*tan(e/2 + f*x/2)**4 + 60*a**2*f*tan(e/2 + f*x/2)**3 + 36*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) - 420*B*c**4*tan(e/2 + f*x/2)**8/(6*a**2*f*tan(e/2 + f*x/2)**9 + 18*a**2*f*tan(e/2 + f*x/2)**8 + 36*a**2*f*tan(e/2 + f*x/2)**7 + 60*a**2*f*tan(e/2 + f*x/2)**6 + 72*a**2*f*tan(e/2 + f*x/2)**5 + 72*a**2*f*tan(e/2 + f*x/2)**4 + 60*a**2*f*tan(e/2 + f*x/2)**3 + 36*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) - 1272*B*c**4*tan(e/2 + f*x/2)**7/(6*a**2*f*tan(e/2 + f*x/2)**9 + 18*a**2*f*tan(e/2 + f*x/2)**8 + 36*a**2*f*tan(e/2 + f*x/2)**7 + 60*a**2*f*tan(e/2 + f*x/2)**6 + 72*a**2*f*tan(e/2 + f*x/2)**5 + 72*a**2*f*tan(e/2 + f*x/2)**4 + 60*a**2*f*tan(e/2 + f*x/2)**3 + 36*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) - 2320*B*c**4*tan(e/2 + f*x/2)**6/(6*a**2*f*tan(e/2 + f*x/2)**9 + 18*a**2*f*tan(e/2 + f*x/2)**8 + 36*a**2*f*tan(e/2 + f*x/2)**7 + 60*a**2*f*tan(e/2 + f*x/2)**6 + 72*a**2*f*tan(e/2 + f*x/2)**5 + 72*a**2*f*tan(e/2 + f*x/2)**4 + 60*a**2*f*tan(e/2 + f*x/2)**3 + 36*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) - 3960*B*c**4*tan(e/2 + f*x/2)**5/(6*a**2*f*tan(e/2 + f*x/2)**9 + 18*a**2*f*tan(e/2 + f*x/2)**8 + 36*a**2*f*tan(e/2 + f*x/2)**7 + 60*a**2*f*tan(e/2 + f*x/2)**6 + 72*a**2*f*tan(e/2 + f*x/2)**5 + 72*a**2*f*tan(e/2 + f*x/2)**4 + 60*a**2*f*tan(e/2 + f*x/2)**3 + 36*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) - 3960*B*c**4*tan(e/2 + f*x/2)**4/(6*a**2*f*tan(e/2 + f*x/2)**9 + 18*a**2*f*tan(e/2 + f*x/2)**8 + 36*a**2*f*tan(e/2 + f*x/2)**7 + 60*a**2*f*tan(e/2 + f*x/2)**6 + 72*a**2*f*tan(e/2 + f*x/2)**5 + 72*a**2*f*tan(e/2 + f*x/2)**4 + 60*a**2*f*tan(e/2 + f*x/2)**3 + 36*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) - 4280*B*c**4*tan(e/2 + f*x/2)**3/(6*a**2*f*tan(e/2 + f*x/2)**9 + 18*a**2*f*tan(e/2 + f*x/2)**8 + 36*a**2*f*tan(e/2 + f*x/2)**7 + 60*a**2*f*tan(e/2 + f*x/2)**6 + 72*a**2*f*tan(e/2 + f*x/2)**5 + 72*a**2*f*tan(e/2 + f*x/2)**4 + 60*a**2*f*tan(e/2 + f*x/2)**3 + 36*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) - 2688*B*c**4*tan(e/2 + f*x/2)**2/(6*a**2*f*tan(e/2 + f*x/2)**9 + 18*a**2*f*tan(e/2 + f*x/2)**8 + 36*a**2*f*tan(e/2 + f*x/2)**7 + 60*a**2*f*tan(e/2 + f*x/2)**6 + 72*a**2*f*tan(e/2 + f*x/2)**5 + 72*a**2*f*tan(e/2 + f*x/2)**4 + 60*a**2*f*tan(e/2 + f*x/2)**3 + 36*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) - 1560*B*c**4*tan(e/2 + f*x/2)/(6*a**2*f*tan(e/2 + f*x/2)**9 + 18*a**2*f*tan(e/2 + f*x/2)**8 + 36*a**2*f*tan(e/2 + f*x/2)**7 + 60*a**2*f*tan(e/2 + f*x/2)**6 + 72*a**2*f*tan(e/2 + f*x/2)**5 + 72*a**2*f*tan(e/2 + f*x/2)**4 + 60*a**2*f*tan(e/2 + f*x/2)**3 + 36*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) - 660*B*c**4/(6*a**2*f*tan(e/2 + f*x/2)**9 + 18*a**2*f*tan(e/2 + f*x/2)**8 + 36*a**2*f*tan(e/2 + f*x/2)**7 + 60*a**2*f*tan(e/2 + f*x/2)**6 + 72*a**2*f*tan(e/2 + f*x/2)**5 + 72*a**2*f*tan(e/2 + f*x/2)**4 + 60*a**2*f*tan(e/2 + f*x/2)**3 + 36*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f), Ne(f, 0)), (x*(A + B*sin(e))*(-c*sin(e) + c)**4/(a*sin(e) + a)**2, True))","A",0
62,1,4665,0,25.784595," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))**3/(a+a*sin(f*x+e))**2,x)","\begin{cases} \frac{30 A c^{3} f x \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} + \frac{90 A c^{3} f x \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} + \frac{150 A c^{3} f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} + \frac{210 A c^{3} f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} + \frac{210 A c^{3} f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} + \frac{150 A c^{3} f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} + \frac{90 A c^{3} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} + \frac{30 A c^{3} f x}{6 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} + \frac{48 A c^{3} \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} + \frac{204 A c^{3} \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} + \frac{212 A c^{3} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} + \frac{432 A c^{3} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} + \frac{256 A c^{3} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} + \frac{228 A c^{3} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} + \frac{92 A c^{3}}{6 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} - \frac{75 B c^{3} f x \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} - \frac{225 B c^{3} f x \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} - \frac{375 B c^{3} f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} - \frac{525 B c^{3} f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} - \frac{525 B c^{3} f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} - \frac{375 B c^{3} f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} - \frac{225 B c^{3} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} - \frac{75 B c^{3} f x}{6 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} - \frac{150 B c^{3} \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} - \frac{462 B c^{3} \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} - \frac{656 B c^{3} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} - \frac{996 B c^{3} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} - \frac{718 B c^{3} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} - \frac{558 B c^{3} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{6 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} - \frac{236 B c^{3}}{6 a^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 42 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 18 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right) \left(- c \sin{\left(e \right)} + c\right)^{3}}{\left(a \sin{\left(e \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((30*A*c**3*f*x*tan(e/2 + f*x/2)**7/(6*a**2*f*tan(e/2 + f*x/2)**7 + 18*a**2*f*tan(e/2 + f*x/2)**6 + 30*a**2*f*tan(e/2 + f*x/2)**5 + 42*a**2*f*tan(e/2 + f*x/2)**4 + 42*a**2*f*tan(e/2 + f*x/2)**3 + 30*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) + 90*A*c**3*f*x*tan(e/2 + f*x/2)**6/(6*a**2*f*tan(e/2 + f*x/2)**7 + 18*a**2*f*tan(e/2 + f*x/2)**6 + 30*a**2*f*tan(e/2 + f*x/2)**5 + 42*a**2*f*tan(e/2 + f*x/2)**4 + 42*a**2*f*tan(e/2 + f*x/2)**3 + 30*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) + 150*A*c**3*f*x*tan(e/2 + f*x/2)**5/(6*a**2*f*tan(e/2 + f*x/2)**7 + 18*a**2*f*tan(e/2 + f*x/2)**6 + 30*a**2*f*tan(e/2 + f*x/2)**5 + 42*a**2*f*tan(e/2 + f*x/2)**4 + 42*a**2*f*tan(e/2 + f*x/2)**3 + 30*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) + 210*A*c**3*f*x*tan(e/2 + f*x/2)**4/(6*a**2*f*tan(e/2 + f*x/2)**7 + 18*a**2*f*tan(e/2 + f*x/2)**6 + 30*a**2*f*tan(e/2 + f*x/2)**5 + 42*a**2*f*tan(e/2 + f*x/2)**4 + 42*a**2*f*tan(e/2 + f*x/2)**3 + 30*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) + 210*A*c**3*f*x*tan(e/2 + f*x/2)**3/(6*a**2*f*tan(e/2 + f*x/2)**7 + 18*a**2*f*tan(e/2 + f*x/2)**6 + 30*a**2*f*tan(e/2 + f*x/2)**5 + 42*a**2*f*tan(e/2 + f*x/2)**4 + 42*a**2*f*tan(e/2 + f*x/2)**3 + 30*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) + 150*A*c**3*f*x*tan(e/2 + f*x/2)**2/(6*a**2*f*tan(e/2 + f*x/2)**7 + 18*a**2*f*tan(e/2 + f*x/2)**6 + 30*a**2*f*tan(e/2 + f*x/2)**5 + 42*a**2*f*tan(e/2 + f*x/2)**4 + 42*a**2*f*tan(e/2 + f*x/2)**3 + 30*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) + 90*A*c**3*f*x*tan(e/2 + f*x/2)/(6*a**2*f*tan(e/2 + f*x/2)**7 + 18*a**2*f*tan(e/2 + f*x/2)**6 + 30*a**2*f*tan(e/2 + f*x/2)**5 + 42*a**2*f*tan(e/2 + f*x/2)**4 + 42*a**2*f*tan(e/2 + f*x/2)**3 + 30*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) + 30*A*c**3*f*x/(6*a**2*f*tan(e/2 + f*x/2)**7 + 18*a**2*f*tan(e/2 + f*x/2)**6 + 30*a**2*f*tan(e/2 + f*x/2)**5 + 42*a**2*f*tan(e/2 + f*x/2)**4 + 42*a**2*f*tan(e/2 + f*x/2)**3 + 30*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) + 48*A*c**3*tan(e/2 + f*x/2)**6/(6*a**2*f*tan(e/2 + f*x/2)**7 + 18*a**2*f*tan(e/2 + f*x/2)**6 + 30*a**2*f*tan(e/2 + f*x/2)**5 + 42*a**2*f*tan(e/2 + f*x/2)**4 + 42*a**2*f*tan(e/2 + f*x/2)**3 + 30*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) + 204*A*c**3*tan(e/2 + f*x/2)**5/(6*a**2*f*tan(e/2 + f*x/2)**7 + 18*a**2*f*tan(e/2 + f*x/2)**6 + 30*a**2*f*tan(e/2 + f*x/2)**5 + 42*a**2*f*tan(e/2 + f*x/2)**4 + 42*a**2*f*tan(e/2 + f*x/2)**3 + 30*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) + 212*A*c**3*tan(e/2 + f*x/2)**4/(6*a**2*f*tan(e/2 + f*x/2)**7 + 18*a**2*f*tan(e/2 + f*x/2)**6 + 30*a**2*f*tan(e/2 + f*x/2)**5 + 42*a**2*f*tan(e/2 + f*x/2)**4 + 42*a**2*f*tan(e/2 + f*x/2)**3 + 30*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) + 432*A*c**3*tan(e/2 + f*x/2)**3/(6*a**2*f*tan(e/2 + f*x/2)**7 + 18*a**2*f*tan(e/2 + f*x/2)**6 + 30*a**2*f*tan(e/2 + f*x/2)**5 + 42*a**2*f*tan(e/2 + f*x/2)**4 + 42*a**2*f*tan(e/2 + f*x/2)**3 + 30*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) + 256*A*c**3*tan(e/2 + f*x/2)**2/(6*a**2*f*tan(e/2 + f*x/2)**7 + 18*a**2*f*tan(e/2 + f*x/2)**6 + 30*a**2*f*tan(e/2 + f*x/2)**5 + 42*a**2*f*tan(e/2 + f*x/2)**4 + 42*a**2*f*tan(e/2 + f*x/2)**3 + 30*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) + 228*A*c**3*tan(e/2 + f*x/2)/(6*a**2*f*tan(e/2 + f*x/2)**7 + 18*a**2*f*tan(e/2 + f*x/2)**6 + 30*a**2*f*tan(e/2 + f*x/2)**5 + 42*a**2*f*tan(e/2 + f*x/2)**4 + 42*a**2*f*tan(e/2 + f*x/2)**3 + 30*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) + 92*A*c**3/(6*a**2*f*tan(e/2 + f*x/2)**7 + 18*a**2*f*tan(e/2 + f*x/2)**6 + 30*a**2*f*tan(e/2 + f*x/2)**5 + 42*a**2*f*tan(e/2 + f*x/2)**4 + 42*a**2*f*tan(e/2 + f*x/2)**3 + 30*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) - 75*B*c**3*f*x*tan(e/2 + f*x/2)**7/(6*a**2*f*tan(e/2 + f*x/2)**7 + 18*a**2*f*tan(e/2 + f*x/2)**6 + 30*a**2*f*tan(e/2 + f*x/2)**5 + 42*a**2*f*tan(e/2 + f*x/2)**4 + 42*a**2*f*tan(e/2 + f*x/2)**3 + 30*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) - 225*B*c**3*f*x*tan(e/2 + f*x/2)**6/(6*a**2*f*tan(e/2 + f*x/2)**7 + 18*a**2*f*tan(e/2 + f*x/2)**6 + 30*a**2*f*tan(e/2 + f*x/2)**5 + 42*a**2*f*tan(e/2 + f*x/2)**4 + 42*a**2*f*tan(e/2 + f*x/2)**3 + 30*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) - 375*B*c**3*f*x*tan(e/2 + f*x/2)**5/(6*a**2*f*tan(e/2 + f*x/2)**7 + 18*a**2*f*tan(e/2 + f*x/2)**6 + 30*a**2*f*tan(e/2 + f*x/2)**5 + 42*a**2*f*tan(e/2 + f*x/2)**4 + 42*a**2*f*tan(e/2 + f*x/2)**3 + 30*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) - 525*B*c**3*f*x*tan(e/2 + f*x/2)**4/(6*a**2*f*tan(e/2 + f*x/2)**7 + 18*a**2*f*tan(e/2 + f*x/2)**6 + 30*a**2*f*tan(e/2 + f*x/2)**5 + 42*a**2*f*tan(e/2 + f*x/2)**4 + 42*a**2*f*tan(e/2 + f*x/2)**3 + 30*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) - 525*B*c**3*f*x*tan(e/2 + f*x/2)**3/(6*a**2*f*tan(e/2 + f*x/2)**7 + 18*a**2*f*tan(e/2 + f*x/2)**6 + 30*a**2*f*tan(e/2 + f*x/2)**5 + 42*a**2*f*tan(e/2 + f*x/2)**4 + 42*a**2*f*tan(e/2 + f*x/2)**3 + 30*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) - 375*B*c**3*f*x*tan(e/2 + f*x/2)**2/(6*a**2*f*tan(e/2 + f*x/2)**7 + 18*a**2*f*tan(e/2 + f*x/2)**6 + 30*a**2*f*tan(e/2 + f*x/2)**5 + 42*a**2*f*tan(e/2 + f*x/2)**4 + 42*a**2*f*tan(e/2 + f*x/2)**3 + 30*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) - 225*B*c**3*f*x*tan(e/2 + f*x/2)/(6*a**2*f*tan(e/2 + f*x/2)**7 + 18*a**2*f*tan(e/2 + f*x/2)**6 + 30*a**2*f*tan(e/2 + f*x/2)**5 + 42*a**2*f*tan(e/2 + f*x/2)**4 + 42*a**2*f*tan(e/2 + f*x/2)**3 + 30*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) - 75*B*c**3*f*x/(6*a**2*f*tan(e/2 + f*x/2)**7 + 18*a**2*f*tan(e/2 + f*x/2)**6 + 30*a**2*f*tan(e/2 + f*x/2)**5 + 42*a**2*f*tan(e/2 + f*x/2)**4 + 42*a**2*f*tan(e/2 + f*x/2)**3 + 30*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) - 150*B*c**3*tan(e/2 + f*x/2)**6/(6*a**2*f*tan(e/2 + f*x/2)**7 + 18*a**2*f*tan(e/2 + f*x/2)**6 + 30*a**2*f*tan(e/2 + f*x/2)**5 + 42*a**2*f*tan(e/2 + f*x/2)**4 + 42*a**2*f*tan(e/2 + f*x/2)**3 + 30*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) - 462*B*c**3*tan(e/2 + f*x/2)**5/(6*a**2*f*tan(e/2 + f*x/2)**7 + 18*a**2*f*tan(e/2 + f*x/2)**6 + 30*a**2*f*tan(e/2 + f*x/2)**5 + 42*a**2*f*tan(e/2 + f*x/2)**4 + 42*a**2*f*tan(e/2 + f*x/2)**3 + 30*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) - 656*B*c**3*tan(e/2 + f*x/2)**4/(6*a**2*f*tan(e/2 + f*x/2)**7 + 18*a**2*f*tan(e/2 + f*x/2)**6 + 30*a**2*f*tan(e/2 + f*x/2)**5 + 42*a**2*f*tan(e/2 + f*x/2)**4 + 42*a**2*f*tan(e/2 + f*x/2)**3 + 30*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) - 996*B*c**3*tan(e/2 + f*x/2)**3/(6*a**2*f*tan(e/2 + f*x/2)**7 + 18*a**2*f*tan(e/2 + f*x/2)**6 + 30*a**2*f*tan(e/2 + f*x/2)**5 + 42*a**2*f*tan(e/2 + f*x/2)**4 + 42*a**2*f*tan(e/2 + f*x/2)**3 + 30*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) - 718*B*c**3*tan(e/2 + f*x/2)**2/(6*a**2*f*tan(e/2 + f*x/2)**7 + 18*a**2*f*tan(e/2 + f*x/2)**6 + 30*a**2*f*tan(e/2 + f*x/2)**5 + 42*a**2*f*tan(e/2 + f*x/2)**4 + 42*a**2*f*tan(e/2 + f*x/2)**3 + 30*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) - 558*B*c**3*tan(e/2 + f*x/2)/(6*a**2*f*tan(e/2 + f*x/2)**7 + 18*a**2*f*tan(e/2 + f*x/2)**6 + 30*a**2*f*tan(e/2 + f*x/2)**5 + 42*a**2*f*tan(e/2 + f*x/2)**4 + 42*a**2*f*tan(e/2 + f*x/2)**3 + 30*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f) - 236*B*c**3/(6*a**2*f*tan(e/2 + f*x/2)**7 + 18*a**2*f*tan(e/2 + f*x/2)**6 + 30*a**2*f*tan(e/2 + f*x/2)**5 + 42*a**2*f*tan(e/2 + f*x/2)**4 + 42*a**2*f*tan(e/2 + f*x/2)**3 + 30*a**2*f*tan(e/2 + f*x/2)**2 + 18*a**2*f*tan(e/2 + f*x/2) + 6*a**2*f), Ne(f, 0)), (x*(A + B*sin(e))*(-c*sin(e) + c)**3/(a*sin(e) + a)**2, True))","A",0
63,1,2474,0,15.056562," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))**2/(a+a*sin(f*x+e))**2,x)","\begin{cases} \frac{3 A c^{2} f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} + \frac{9 A c^{2} f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} + \frac{12 A c^{2} f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} + \frac{12 A c^{2} f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} + \frac{9 A c^{2} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} + \frac{3 A c^{2} f x}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} + \frac{24 A c^{2} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} + \frac{8 A c^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} + \frac{24 A c^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} + \frac{8 A c^{2}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{12 B c^{2} f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{36 B c^{2} f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{48 B c^{2} f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{48 B c^{2} f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{36 B c^{2} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{12 B c^{2} f x}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{24 B c^{2} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{78 B c^{2} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{74 B c^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{90 B c^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{38 B c^{2}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right) \left(- c \sin{\left(e \right)} + c\right)^{2}}{\left(a \sin{\left(e \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*A*c**2*f*x*tan(e/2 + f*x/2)**5/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) + 9*A*c**2*f*x*tan(e/2 + f*x/2)**4/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) + 12*A*c**2*f*x*tan(e/2 + f*x/2)**3/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) + 12*A*c**2*f*x*tan(e/2 + f*x/2)**2/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) + 9*A*c**2*f*x*tan(e/2 + f*x/2)/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) + 3*A*c**2*f*x/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) + 24*A*c**2*tan(e/2 + f*x/2)**3/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) + 8*A*c**2*tan(e/2 + f*x/2)**2/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) + 24*A*c**2*tan(e/2 + f*x/2)/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) + 8*A*c**2/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 12*B*c**2*f*x*tan(e/2 + f*x/2)**5/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 36*B*c**2*f*x*tan(e/2 + f*x/2)**4/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 48*B*c**2*f*x*tan(e/2 + f*x/2)**3/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 48*B*c**2*f*x*tan(e/2 + f*x/2)**2/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 36*B*c**2*f*x*tan(e/2 + f*x/2)/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 12*B*c**2*f*x/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 24*B*c**2*tan(e/2 + f*x/2)**4/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 78*B*c**2*tan(e/2 + f*x/2)**3/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 74*B*c**2*tan(e/2 + f*x/2)**2/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 90*B*c**2*tan(e/2 + f*x/2)/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 38*B*c**2/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f), Ne(f, 0)), (x*(A + B*sin(e))*(-c*sin(e) + c)**2/(a*sin(e) + a)**2, True))","A",0
64,1,702,0,7.385725," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))/(a+a*sin(f*x+e))**2,x)","\begin{cases} - \frac{6 A c \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{2 A c}{3 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{3 B c f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{9 B c f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{9 B c f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{3 B c f x}{3 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{6 B c \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{24 B c \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{10 B c}{3 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right) \left(- c \sin{\left(e \right)} + c\right)}{\left(a \sin{\left(e \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-6*A*c*tan(e/2 + f*x/2)**2/(3*a**2*f*tan(e/2 + f*x/2)**3 + 9*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 2*A*c/(3*a**2*f*tan(e/2 + f*x/2)**3 + 9*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 3*B*c*f*x*tan(e/2 + f*x/2)**3/(3*a**2*f*tan(e/2 + f*x/2)**3 + 9*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 9*B*c*f*x*tan(e/2 + f*x/2)**2/(3*a**2*f*tan(e/2 + f*x/2)**3 + 9*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 9*B*c*f*x*tan(e/2 + f*x/2)/(3*a**2*f*tan(e/2 + f*x/2)**3 + 9*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 3*B*c*f*x/(3*a**2*f*tan(e/2 + f*x/2)**3 + 9*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 6*B*c*tan(e/2 + f*x/2)**2/(3*a**2*f*tan(e/2 + f*x/2)**3 + 9*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 24*B*c*tan(e/2 + f*x/2)/(3*a**2*f*tan(e/2 + f*x/2)**3 + 9*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 10*B*c/(3*a**2*f*tan(e/2 + f*x/2)**3 + 9*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f), Ne(f, 0)), (x*(A + B*sin(e))*(-c*sin(e) + c)/(a*sin(e) + a)**2, True))","A",0
65,1,578,0,7.227843," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))**2/(c-c*sin(f*x+e)),x)","\begin{cases} - \frac{6 A \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 a^{2} c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 a^{2} c f} - \frac{6 A \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 a^{2} c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 a^{2} c f} - \frac{2 A \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 a^{2} c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 a^{2} c f} + \frac{2 A}{3 a^{2} c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 a^{2} c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 a^{2} c f} - \frac{6 B \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 a^{2} c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 a^{2} c f} - \frac{4 B \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 a^{2} c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 a^{2} c f} - \frac{2 B}{3 a^{2} c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6 a^{2} c f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6 a^{2} c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 a^{2} c f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right)}{\left(a \sin{\left(e \right)} + a\right)^{2} \left(- c \sin{\left(e \right)} + c\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-6*A*tan(e/2 + f*x/2)**3/(3*a**2*c*f*tan(e/2 + f*x/2)**4 + 6*a**2*c*f*tan(e/2 + f*x/2)**3 - 6*a**2*c*f*tan(e/2 + f*x/2) - 3*a**2*c*f) - 6*A*tan(e/2 + f*x/2)**2/(3*a**2*c*f*tan(e/2 + f*x/2)**4 + 6*a**2*c*f*tan(e/2 + f*x/2)**3 - 6*a**2*c*f*tan(e/2 + f*x/2) - 3*a**2*c*f) - 2*A*tan(e/2 + f*x/2)/(3*a**2*c*f*tan(e/2 + f*x/2)**4 + 6*a**2*c*f*tan(e/2 + f*x/2)**3 - 6*a**2*c*f*tan(e/2 + f*x/2) - 3*a**2*c*f) + 2*A/(3*a**2*c*f*tan(e/2 + f*x/2)**4 + 6*a**2*c*f*tan(e/2 + f*x/2)**3 - 6*a**2*c*f*tan(e/2 + f*x/2) - 3*a**2*c*f) - 6*B*tan(e/2 + f*x/2)**2/(3*a**2*c*f*tan(e/2 + f*x/2)**4 + 6*a**2*c*f*tan(e/2 + f*x/2)**3 - 6*a**2*c*f*tan(e/2 + f*x/2) - 3*a**2*c*f) - 4*B*tan(e/2 + f*x/2)/(3*a**2*c*f*tan(e/2 + f*x/2)**4 + 6*a**2*c*f*tan(e/2 + f*x/2)**3 - 6*a**2*c*f*tan(e/2 + f*x/2) - 3*a**2*c*f) - 2*B/(3*a**2*c*f*tan(e/2 + f*x/2)**4 + 6*a**2*c*f*tan(e/2 + f*x/2)**3 - 6*a**2*c*f*tan(e/2 + f*x/2) - 3*a**2*c*f), Ne(f, 0)), (x*(A + B*sin(e))/((a*sin(e) + a)**2*(-c*sin(e) + c)), True))","A",0
66,1,469,0,7.631379," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))**2/(c-c*sin(f*x+e))**2,x)","\begin{cases} - \frac{6 A \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 9 a^{2} c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 a^{2} c^{2} f} + \frac{4 A \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 9 a^{2} c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 a^{2} c^{2} f} - \frac{6 A \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 9 a^{2} c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 a^{2} c^{2} f} - \frac{6 B \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 9 a^{2} c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 a^{2} c^{2} f} - \frac{2 B}{3 a^{2} c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 9 a^{2} c^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3 a^{2} c^{2} f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right)}{\left(a \sin{\left(e \right)} + a\right)^{2} \left(- c \sin{\left(e \right)} + c\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-6*A*tan(e/2 + f*x/2)**5/(3*a**2*c**2*f*tan(e/2 + f*x/2)**6 - 9*a**2*c**2*f*tan(e/2 + f*x/2)**4 + 9*a**2*c**2*f*tan(e/2 + f*x/2)**2 - 3*a**2*c**2*f) + 4*A*tan(e/2 + f*x/2)**3/(3*a**2*c**2*f*tan(e/2 + f*x/2)**6 - 9*a**2*c**2*f*tan(e/2 + f*x/2)**4 + 9*a**2*c**2*f*tan(e/2 + f*x/2)**2 - 3*a**2*c**2*f) - 6*A*tan(e/2 + f*x/2)/(3*a**2*c**2*f*tan(e/2 + f*x/2)**6 - 9*a**2*c**2*f*tan(e/2 + f*x/2)**4 + 9*a**2*c**2*f*tan(e/2 + f*x/2)**2 - 3*a**2*c**2*f) - 6*B*tan(e/2 + f*x/2)**4/(3*a**2*c**2*f*tan(e/2 + f*x/2)**6 - 9*a**2*c**2*f*tan(e/2 + f*x/2)**4 + 9*a**2*c**2*f*tan(e/2 + f*x/2)**2 - 3*a**2*c**2*f) - 2*B/(3*a**2*c**2*f*tan(e/2 + f*x/2)**6 - 9*a**2*c**2*f*tan(e/2 + f*x/2)**4 + 9*a**2*c**2*f*tan(e/2 + f*x/2)**2 - 3*a**2*c**2*f), Ne(f, 0)), (x*(A + B*sin(e))/((a*sin(e) + a)**2*(-c*sin(e) + c)**2), True))","A",0
67,1,2674,0,27.731455," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))**2/(c-c*sin(f*x+e))**3,x)","\begin{cases} - \frac{30 A \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{2} c^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{2} c^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{2} c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 90 a^{2} c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 90 a^{2} c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{2} c^{3} f} + \frac{30 A \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{2} c^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{2} c^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{2} c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 90 a^{2} c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 90 a^{2} c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{2} c^{3} f} + \frac{10 A \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{2} c^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{2} c^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{2} c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 90 a^{2} c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 90 a^{2} c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{2} c^{3} f} - \frac{50 A \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{2} c^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{2} c^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{2} c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 90 a^{2} c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 90 a^{2} c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{2} c^{3} f} - \frac{26 A \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{2} c^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{2} c^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{2} c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 90 a^{2} c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 90 a^{2} c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{2} c^{3} f} + \frac{42 A \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{2} c^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{2} c^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{2} c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 90 a^{2} c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 90 a^{2} c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{2} c^{3} f} - \frac{18 A \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{2} c^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{2} c^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{2} c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 90 a^{2} c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 90 a^{2} c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{2} c^{3} f} - \frac{6 A}{15 a^{2} c^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{2} c^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{2} c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 90 a^{2} c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 90 a^{2} c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{2} c^{3} f} - \frac{30 B \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{2} c^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{2} c^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{2} c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 90 a^{2} c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 90 a^{2} c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{2} c^{3} f} + \frac{20 B \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{2} c^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{2} c^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{2} c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 90 a^{2} c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 90 a^{2} c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{2} c^{3} f} - \frac{10 B \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{2} c^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{2} c^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{2} c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 90 a^{2} c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 90 a^{2} c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{2} c^{3} f} - \frac{16 B \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{2} c^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{2} c^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{2} c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 90 a^{2} c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 90 a^{2} c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{2} c^{3} f} - \frac{18 B \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{2} c^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{2} c^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{2} c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 90 a^{2} c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 90 a^{2} c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{2} c^{3} f} + \frac{12 B \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{2} c^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{2} c^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{2} c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 90 a^{2} c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 90 a^{2} c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{2} c^{3} f} - \frac{6 B}{15 a^{2} c^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{2} c^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{2} c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 90 a^{2} c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 90 a^{2} c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{2} c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{2} c^{3} f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right)}{\left(a \sin{\left(e \right)} + a\right)^{2} \left(- c \sin{\left(e \right)} + c\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-30*A*tan(e/2 + f*x/2)**7/(15*a**2*c**3*f*tan(e/2 + f*x/2)**8 - 30*a**2*c**3*f*tan(e/2 + f*x/2)**7 - 30*a**2*c**3*f*tan(e/2 + f*x/2)**6 + 90*a**2*c**3*f*tan(e/2 + f*x/2)**5 - 90*a**2*c**3*f*tan(e/2 + f*x/2)**3 + 30*a**2*c**3*f*tan(e/2 + f*x/2)**2 + 30*a**2*c**3*f*tan(e/2 + f*x/2) - 15*a**2*c**3*f) + 30*A*tan(e/2 + f*x/2)**6/(15*a**2*c**3*f*tan(e/2 + f*x/2)**8 - 30*a**2*c**3*f*tan(e/2 + f*x/2)**7 - 30*a**2*c**3*f*tan(e/2 + f*x/2)**6 + 90*a**2*c**3*f*tan(e/2 + f*x/2)**5 - 90*a**2*c**3*f*tan(e/2 + f*x/2)**3 + 30*a**2*c**3*f*tan(e/2 + f*x/2)**2 + 30*a**2*c**3*f*tan(e/2 + f*x/2) - 15*a**2*c**3*f) + 10*A*tan(e/2 + f*x/2)**5/(15*a**2*c**3*f*tan(e/2 + f*x/2)**8 - 30*a**2*c**3*f*tan(e/2 + f*x/2)**7 - 30*a**2*c**3*f*tan(e/2 + f*x/2)**6 + 90*a**2*c**3*f*tan(e/2 + f*x/2)**5 - 90*a**2*c**3*f*tan(e/2 + f*x/2)**3 + 30*a**2*c**3*f*tan(e/2 + f*x/2)**2 + 30*a**2*c**3*f*tan(e/2 + f*x/2) - 15*a**2*c**3*f) - 50*A*tan(e/2 + f*x/2)**4/(15*a**2*c**3*f*tan(e/2 + f*x/2)**8 - 30*a**2*c**3*f*tan(e/2 + f*x/2)**7 - 30*a**2*c**3*f*tan(e/2 + f*x/2)**6 + 90*a**2*c**3*f*tan(e/2 + f*x/2)**5 - 90*a**2*c**3*f*tan(e/2 + f*x/2)**3 + 30*a**2*c**3*f*tan(e/2 + f*x/2)**2 + 30*a**2*c**3*f*tan(e/2 + f*x/2) - 15*a**2*c**3*f) - 26*A*tan(e/2 + f*x/2)**3/(15*a**2*c**3*f*tan(e/2 + f*x/2)**8 - 30*a**2*c**3*f*tan(e/2 + f*x/2)**7 - 30*a**2*c**3*f*tan(e/2 + f*x/2)**6 + 90*a**2*c**3*f*tan(e/2 + f*x/2)**5 - 90*a**2*c**3*f*tan(e/2 + f*x/2)**3 + 30*a**2*c**3*f*tan(e/2 + f*x/2)**2 + 30*a**2*c**3*f*tan(e/2 + f*x/2) - 15*a**2*c**3*f) + 42*A*tan(e/2 + f*x/2)**2/(15*a**2*c**3*f*tan(e/2 + f*x/2)**8 - 30*a**2*c**3*f*tan(e/2 + f*x/2)**7 - 30*a**2*c**3*f*tan(e/2 + f*x/2)**6 + 90*a**2*c**3*f*tan(e/2 + f*x/2)**5 - 90*a**2*c**3*f*tan(e/2 + f*x/2)**3 + 30*a**2*c**3*f*tan(e/2 + f*x/2)**2 + 30*a**2*c**3*f*tan(e/2 + f*x/2) - 15*a**2*c**3*f) - 18*A*tan(e/2 + f*x/2)/(15*a**2*c**3*f*tan(e/2 + f*x/2)**8 - 30*a**2*c**3*f*tan(e/2 + f*x/2)**7 - 30*a**2*c**3*f*tan(e/2 + f*x/2)**6 + 90*a**2*c**3*f*tan(e/2 + f*x/2)**5 - 90*a**2*c**3*f*tan(e/2 + f*x/2)**3 + 30*a**2*c**3*f*tan(e/2 + f*x/2)**2 + 30*a**2*c**3*f*tan(e/2 + f*x/2) - 15*a**2*c**3*f) - 6*A/(15*a**2*c**3*f*tan(e/2 + f*x/2)**8 - 30*a**2*c**3*f*tan(e/2 + f*x/2)**7 - 30*a**2*c**3*f*tan(e/2 + f*x/2)**6 + 90*a**2*c**3*f*tan(e/2 + f*x/2)**5 - 90*a**2*c**3*f*tan(e/2 + f*x/2)**3 + 30*a**2*c**3*f*tan(e/2 + f*x/2)**2 + 30*a**2*c**3*f*tan(e/2 + f*x/2) - 15*a**2*c**3*f) - 30*B*tan(e/2 + f*x/2)**6/(15*a**2*c**3*f*tan(e/2 + f*x/2)**8 - 30*a**2*c**3*f*tan(e/2 + f*x/2)**7 - 30*a**2*c**3*f*tan(e/2 + f*x/2)**6 + 90*a**2*c**3*f*tan(e/2 + f*x/2)**5 - 90*a**2*c**3*f*tan(e/2 + f*x/2)**3 + 30*a**2*c**3*f*tan(e/2 + f*x/2)**2 + 30*a**2*c**3*f*tan(e/2 + f*x/2) - 15*a**2*c**3*f) + 20*B*tan(e/2 + f*x/2)**5/(15*a**2*c**3*f*tan(e/2 + f*x/2)**8 - 30*a**2*c**3*f*tan(e/2 + f*x/2)**7 - 30*a**2*c**3*f*tan(e/2 + f*x/2)**6 + 90*a**2*c**3*f*tan(e/2 + f*x/2)**5 - 90*a**2*c**3*f*tan(e/2 + f*x/2)**3 + 30*a**2*c**3*f*tan(e/2 + f*x/2)**2 + 30*a**2*c**3*f*tan(e/2 + f*x/2) - 15*a**2*c**3*f) - 10*B*tan(e/2 + f*x/2)**4/(15*a**2*c**3*f*tan(e/2 + f*x/2)**8 - 30*a**2*c**3*f*tan(e/2 + f*x/2)**7 - 30*a**2*c**3*f*tan(e/2 + f*x/2)**6 + 90*a**2*c**3*f*tan(e/2 + f*x/2)**5 - 90*a**2*c**3*f*tan(e/2 + f*x/2)**3 + 30*a**2*c**3*f*tan(e/2 + f*x/2)**2 + 30*a**2*c**3*f*tan(e/2 + f*x/2) - 15*a**2*c**3*f) - 16*B*tan(e/2 + f*x/2)**3/(15*a**2*c**3*f*tan(e/2 + f*x/2)**8 - 30*a**2*c**3*f*tan(e/2 + f*x/2)**7 - 30*a**2*c**3*f*tan(e/2 + f*x/2)**6 + 90*a**2*c**3*f*tan(e/2 + f*x/2)**5 - 90*a**2*c**3*f*tan(e/2 + f*x/2)**3 + 30*a**2*c**3*f*tan(e/2 + f*x/2)**2 + 30*a**2*c**3*f*tan(e/2 + f*x/2) - 15*a**2*c**3*f) - 18*B*tan(e/2 + f*x/2)**2/(15*a**2*c**3*f*tan(e/2 + f*x/2)**8 - 30*a**2*c**3*f*tan(e/2 + f*x/2)**7 - 30*a**2*c**3*f*tan(e/2 + f*x/2)**6 + 90*a**2*c**3*f*tan(e/2 + f*x/2)**5 - 90*a**2*c**3*f*tan(e/2 + f*x/2)**3 + 30*a**2*c**3*f*tan(e/2 + f*x/2)**2 + 30*a**2*c**3*f*tan(e/2 + f*x/2) - 15*a**2*c**3*f) + 12*B*tan(e/2 + f*x/2)/(15*a**2*c**3*f*tan(e/2 + f*x/2)**8 - 30*a**2*c**3*f*tan(e/2 + f*x/2)**7 - 30*a**2*c**3*f*tan(e/2 + f*x/2)**6 + 90*a**2*c**3*f*tan(e/2 + f*x/2)**5 - 90*a**2*c**3*f*tan(e/2 + f*x/2)**3 + 30*a**2*c**3*f*tan(e/2 + f*x/2)**2 + 30*a**2*c**3*f*tan(e/2 + f*x/2) - 15*a**2*c**3*f) - 6*B/(15*a**2*c**3*f*tan(e/2 + f*x/2)**8 - 30*a**2*c**3*f*tan(e/2 + f*x/2)**7 - 30*a**2*c**3*f*tan(e/2 + f*x/2)**6 + 90*a**2*c**3*f*tan(e/2 + f*x/2)**5 - 90*a**2*c**3*f*tan(e/2 + f*x/2)**3 + 30*a**2*c**3*f*tan(e/2 + f*x/2)**2 + 30*a**2*c**3*f*tan(e/2 + f*x/2) - 15*a**2*c**3*f), Ne(f, 0)), (x*(A + B*sin(e))/((a*sin(e) + a)**2*(-c*sin(e) + c)**3), True))","A",0
68,1,4228,0,49.831097," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))**2/(c-c*sin(f*x+e))**4,x)","\begin{cases} - \frac{210 A \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 a^{2} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 420 a^{2} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{2} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 840 a^{2} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1470 a^{2} c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1470 a^{2} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 840 a^{2} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{2} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 420 a^{2} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 a^{2} c^{4} f} + \frac{420 A \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 a^{2} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 420 a^{2} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{2} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 840 a^{2} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1470 a^{2} c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1470 a^{2} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 840 a^{2} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{2} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 420 a^{2} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 a^{2} c^{4} f} - \frac{280 A \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 a^{2} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 420 a^{2} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{2} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 840 a^{2} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1470 a^{2} c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1470 a^{2} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 840 a^{2} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{2} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 420 a^{2} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 a^{2} c^{4} f} - \frac{560 A \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 a^{2} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 420 a^{2} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{2} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 840 a^{2} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1470 a^{2} c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1470 a^{2} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 840 a^{2} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{2} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 420 a^{2} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 a^{2} c^{4} f} + \frac{420 A \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 a^{2} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 420 a^{2} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{2} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 840 a^{2} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1470 a^{2} c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1470 a^{2} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 840 a^{2} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{2} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 420 a^{2} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 a^{2} c^{4} f} + \frac{280 A \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 a^{2} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 420 a^{2} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{2} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 840 a^{2} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1470 a^{2} c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1470 a^{2} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 840 a^{2} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{2} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 420 a^{2} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 a^{2} c^{4} f} - \frac{760 A \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 a^{2} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 420 a^{2} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{2} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 840 a^{2} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1470 a^{2} c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1470 a^{2} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 840 a^{2} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{2} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 420 a^{2} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 a^{2} c^{4} f} + \frac{240 A \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 a^{2} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 420 a^{2} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{2} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 840 a^{2} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1470 a^{2} c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1470 a^{2} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 840 a^{2} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{2} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 420 a^{2} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 a^{2} c^{4} f} + \frac{30 A \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 a^{2} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 420 a^{2} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{2} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 840 a^{2} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1470 a^{2} c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1470 a^{2} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 840 a^{2} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{2} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 420 a^{2} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 a^{2} c^{4} f} - \frac{60 A}{105 a^{2} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 420 a^{2} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{2} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 840 a^{2} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1470 a^{2} c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1470 a^{2} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 840 a^{2} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{2} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 420 a^{2} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 a^{2} c^{4} f} - \frac{210 B \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 a^{2} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 420 a^{2} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{2} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 840 a^{2} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1470 a^{2} c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1470 a^{2} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 840 a^{2} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{2} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 420 a^{2} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 a^{2} c^{4} f} + \frac{280 B \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 a^{2} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 420 a^{2} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{2} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 840 a^{2} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1470 a^{2} c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1470 a^{2} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 840 a^{2} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{2} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 420 a^{2} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 a^{2} c^{4} f} - \frac{280 B \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 a^{2} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 420 a^{2} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{2} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 840 a^{2} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1470 a^{2} c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1470 a^{2} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 840 a^{2} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{2} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 420 a^{2} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 a^{2} c^{4} f} - \frac{168 B \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 a^{2} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 420 a^{2} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{2} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 840 a^{2} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1470 a^{2} c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1470 a^{2} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 840 a^{2} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{2} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 420 a^{2} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 a^{2} c^{4} f} - \frac{28 B \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 a^{2} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 420 a^{2} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{2} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 840 a^{2} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1470 a^{2} c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1470 a^{2} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 840 a^{2} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{2} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 420 a^{2} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 a^{2} c^{4} f} + \frac{136 B \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 a^{2} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 420 a^{2} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{2} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 840 a^{2} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1470 a^{2} c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1470 a^{2} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 840 a^{2} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{2} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 420 a^{2} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 a^{2} c^{4} f} - \frac{264 B \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 a^{2} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 420 a^{2} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{2} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 840 a^{2} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1470 a^{2} c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1470 a^{2} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 840 a^{2} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{2} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 420 a^{2} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 a^{2} c^{4} f} + \frac{72 B \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 a^{2} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 420 a^{2} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{2} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 840 a^{2} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1470 a^{2} c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1470 a^{2} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 840 a^{2} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{2} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 420 a^{2} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 a^{2} c^{4} f} - \frac{18 B}{105 a^{2} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 420 a^{2} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{2} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 840 a^{2} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1470 a^{2} c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1470 a^{2} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 840 a^{2} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{2} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 420 a^{2} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 a^{2} c^{4} f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right)}{\left(a \sin{\left(e \right)} + a\right)^{2} \left(- c \sin{\left(e \right)} + c\right)^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-210*A*tan(e/2 + f*x/2)**9/(105*a**2*c**4*f*tan(e/2 + f*x/2)**10 - 420*a**2*c**4*f*tan(e/2 + f*x/2)**9 + 315*a**2*c**4*f*tan(e/2 + f*x/2)**8 + 840*a**2*c**4*f*tan(e/2 + f*x/2)**7 - 1470*a**2*c**4*f*tan(e/2 + f*x/2)**6 + 1470*a**2*c**4*f*tan(e/2 + f*x/2)**4 - 840*a**2*c**4*f*tan(e/2 + f*x/2)**3 - 315*a**2*c**4*f*tan(e/2 + f*x/2)**2 + 420*a**2*c**4*f*tan(e/2 + f*x/2) - 105*a**2*c**4*f) + 420*A*tan(e/2 + f*x/2)**8/(105*a**2*c**4*f*tan(e/2 + f*x/2)**10 - 420*a**2*c**4*f*tan(e/2 + f*x/2)**9 + 315*a**2*c**4*f*tan(e/2 + f*x/2)**8 + 840*a**2*c**4*f*tan(e/2 + f*x/2)**7 - 1470*a**2*c**4*f*tan(e/2 + f*x/2)**6 + 1470*a**2*c**4*f*tan(e/2 + f*x/2)**4 - 840*a**2*c**4*f*tan(e/2 + f*x/2)**3 - 315*a**2*c**4*f*tan(e/2 + f*x/2)**2 + 420*a**2*c**4*f*tan(e/2 + f*x/2) - 105*a**2*c**4*f) - 280*A*tan(e/2 + f*x/2)**7/(105*a**2*c**4*f*tan(e/2 + f*x/2)**10 - 420*a**2*c**4*f*tan(e/2 + f*x/2)**9 + 315*a**2*c**4*f*tan(e/2 + f*x/2)**8 + 840*a**2*c**4*f*tan(e/2 + f*x/2)**7 - 1470*a**2*c**4*f*tan(e/2 + f*x/2)**6 + 1470*a**2*c**4*f*tan(e/2 + f*x/2)**4 - 840*a**2*c**4*f*tan(e/2 + f*x/2)**3 - 315*a**2*c**4*f*tan(e/2 + f*x/2)**2 + 420*a**2*c**4*f*tan(e/2 + f*x/2) - 105*a**2*c**4*f) - 560*A*tan(e/2 + f*x/2)**6/(105*a**2*c**4*f*tan(e/2 + f*x/2)**10 - 420*a**2*c**4*f*tan(e/2 + f*x/2)**9 + 315*a**2*c**4*f*tan(e/2 + f*x/2)**8 + 840*a**2*c**4*f*tan(e/2 + f*x/2)**7 - 1470*a**2*c**4*f*tan(e/2 + f*x/2)**6 + 1470*a**2*c**4*f*tan(e/2 + f*x/2)**4 - 840*a**2*c**4*f*tan(e/2 + f*x/2)**3 - 315*a**2*c**4*f*tan(e/2 + f*x/2)**2 + 420*a**2*c**4*f*tan(e/2 + f*x/2) - 105*a**2*c**4*f) + 420*A*tan(e/2 + f*x/2)**5/(105*a**2*c**4*f*tan(e/2 + f*x/2)**10 - 420*a**2*c**4*f*tan(e/2 + f*x/2)**9 + 315*a**2*c**4*f*tan(e/2 + f*x/2)**8 + 840*a**2*c**4*f*tan(e/2 + f*x/2)**7 - 1470*a**2*c**4*f*tan(e/2 + f*x/2)**6 + 1470*a**2*c**4*f*tan(e/2 + f*x/2)**4 - 840*a**2*c**4*f*tan(e/2 + f*x/2)**3 - 315*a**2*c**4*f*tan(e/2 + f*x/2)**2 + 420*a**2*c**4*f*tan(e/2 + f*x/2) - 105*a**2*c**4*f) + 280*A*tan(e/2 + f*x/2)**4/(105*a**2*c**4*f*tan(e/2 + f*x/2)**10 - 420*a**2*c**4*f*tan(e/2 + f*x/2)**9 + 315*a**2*c**4*f*tan(e/2 + f*x/2)**8 + 840*a**2*c**4*f*tan(e/2 + f*x/2)**7 - 1470*a**2*c**4*f*tan(e/2 + f*x/2)**6 + 1470*a**2*c**4*f*tan(e/2 + f*x/2)**4 - 840*a**2*c**4*f*tan(e/2 + f*x/2)**3 - 315*a**2*c**4*f*tan(e/2 + f*x/2)**2 + 420*a**2*c**4*f*tan(e/2 + f*x/2) - 105*a**2*c**4*f) - 760*A*tan(e/2 + f*x/2)**3/(105*a**2*c**4*f*tan(e/2 + f*x/2)**10 - 420*a**2*c**4*f*tan(e/2 + f*x/2)**9 + 315*a**2*c**4*f*tan(e/2 + f*x/2)**8 + 840*a**2*c**4*f*tan(e/2 + f*x/2)**7 - 1470*a**2*c**4*f*tan(e/2 + f*x/2)**6 + 1470*a**2*c**4*f*tan(e/2 + f*x/2)**4 - 840*a**2*c**4*f*tan(e/2 + f*x/2)**3 - 315*a**2*c**4*f*tan(e/2 + f*x/2)**2 + 420*a**2*c**4*f*tan(e/2 + f*x/2) - 105*a**2*c**4*f) + 240*A*tan(e/2 + f*x/2)**2/(105*a**2*c**4*f*tan(e/2 + f*x/2)**10 - 420*a**2*c**4*f*tan(e/2 + f*x/2)**9 + 315*a**2*c**4*f*tan(e/2 + f*x/2)**8 + 840*a**2*c**4*f*tan(e/2 + f*x/2)**7 - 1470*a**2*c**4*f*tan(e/2 + f*x/2)**6 + 1470*a**2*c**4*f*tan(e/2 + f*x/2)**4 - 840*a**2*c**4*f*tan(e/2 + f*x/2)**3 - 315*a**2*c**4*f*tan(e/2 + f*x/2)**2 + 420*a**2*c**4*f*tan(e/2 + f*x/2) - 105*a**2*c**4*f) + 30*A*tan(e/2 + f*x/2)/(105*a**2*c**4*f*tan(e/2 + f*x/2)**10 - 420*a**2*c**4*f*tan(e/2 + f*x/2)**9 + 315*a**2*c**4*f*tan(e/2 + f*x/2)**8 + 840*a**2*c**4*f*tan(e/2 + f*x/2)**7 - 1470*a**2*c**4*f*tan(e/2 + f*x/2)**6 + 1470*a**2*c**4*f*tan(e/2 + f*x/2)**4 - 840*a**2*c**4*f*tan(e/2 + f*x/2)**3 - 315*a**2*c**4*f*tan(e/2 + f*x/2)**2 + 420*a**2*c**4*f*tan(e/2 + f*x/2) - 105*a**2*c**4*f) - 60*A/(105*a**2*c**4*f*tan(e/2 + f*x/2)**10 - 420*a**2*c**4*f*tan(e/2 + f*x/2)**9 + 315*a**2*c**4*f*tan(e/2 + f*x/2)**8 + 840*a**2*c**4*f*tan(e/2 + f*x/2)**7 - 1470*a**2*c**4*f*tan(e/2 + f*x/2)**6 + 1470*a**2*c**4*f*tan(e/2 + f*x/2)**4 - 840*a**2*c**4*f*tan(e/2 + f*x/2)**3 - 315*a**2*c**4*f*tan(e/2 + f*x/2)**2 + 420*a**2*c**4*f*tan(e/2 + f*x/2) - 105*a**2*c**4*f) - 210*B*tan(e/2 + f*x/2)**8/(105*a**2*c**4*f*tan(e/2 + f*x/2)**10 - 420*a**2*c**4*f*tan(e/2 + f*x/2)**9 + 315*a**2*c**4*f*tan(e/2 + f*x/2)**8 + 840*a**2*c**4*f*tan(e/2 + f*x/2)**7 - 1470*a**2*c**4*f*tan(e/2 + f*x/2)**6 + 1470*a**2*c**4*f*tan(e/2 + f*x/2)**4 - 840*a**2*c**4*f*tan(e/2 + f*x/2)**3 - 315*a**2*c**4*f*tan(e/2 + f*x/2)**2 + 420*a**2*c**4*f*tan(e/2 + f*x/2) - 105*a**2*c**4*f) + 280*B*tan(e/2 + f*x/2)**7/(105*a**2*c**4*f*tan(e/2 + f*x/2)**10 - 420*a**2*c**4*f*tan(e/2 + f*x/2)**9 + 315*a**2*c**4*f*tan(e/2 + f*x/2)**8 + 840*a**2*c**4*f*tan(e/2 + f*x/2)**7 - 1470*a**2*c**4*f*tan(e/2 + f*x/2)**6 + 1470*a**2*c**4*f*tan(e/2 + f*x/2)**4 - 840*a**2*c**4*f*tan(e/2 + f*x/2)**3 - 315*a**2*c**4*f*tan(e/2 + f*x/2)**2 + 420*a**2*c**4*f*tan(e/2 + f*x/2) - 105*a**2*c**4*f) - 280*B*tan(e/2 + f*x/2)**6/(105*a**2*c**4*f*tan(e/2 + f*x/2)**10 - 420*a**2*c**4*f*tan(e/2 + f*x/2)**9 + 315*a**2*c**4*f*tan(e/2 + f*x/2)**8 + 840*a**2*c**4*f*tan(e/2 + f*x/2)**7 - 1470*a**2*c**4*f*tan(e/2 + f*x/2)**6 + 1470*a**2*c**4*f*tan(e/2 + f*x/2)**4 - 840*a**2*c**4*f*tan(e/2 + f*x/2)**3 - 315*a**2*c**4*f*tan(e/2 + f*x/2)**2 + 420*a**2*c**4*f*tan(e/2 + f*x/2) - 105*a**2*c**4*f) - 168*B*tan(e/2 + f*x/2)**5/(105*a**2*c**4*f*tan(e/2 + f*x/2)**10 - 420*a**2*c**4*f*tan(e/2 + f*x/2)**9 + 315*a**2*c**4*f*tan(e/2 + f*x/2)**8 + 840*a**2*c**4*f*tan(e/2 + f*x/2)**7 - 1470*a**2*c**4*f*tan(e/2 + f*x/2)**6 + 1470*a**2*c**4*f*tan(e/2 + f*x/2)**4 - 840*a**2*c**4*f*tan(e/2 + f*x/2)**3 - 315*a**2*c**4*f*tan(e/2 + f*x/2)**2 + 420*a**2*c**4*f*tan(e/2 + f*x/2) - 105*a**2*c**4*f) - 28*B*tan(e/2 + f*x/2)**4/(105*a**2*c**4*f*tan(e/2 + f*x/2)**10 - 420*a**2*c**4*f*tan(e/2 + f*x/2)**9 + 315*a**2*c**4*f*tan(e/2 + f*x/2)**8 + 840*a**2*c**4*f*tan(e/2 + f*x/2)**7 - 1470*a**2*c**4*f*tan(e/2 + f*x/2)**6 + 1470*a**2*c**4*f*tan(e/2 + f*x/2)**4 - 840*a**2*c**4*f*tan(e/2 + f*x/2)**3 - 315*a**2*c**4*f*tan(e/2 + f*x/2)**2 + 420*a**2*c**4*f*tan(e/2 + f*x/2) - 105*a**2*c**4*f) + 136*B*tan(e/2 + f*x/2)**3/(105*a**2*c**4*f*tan(e/2 + f*x/2)**10 - 420*a**2*c**4*f*tan(e/2 + f*x/2)**9 + 315*a**2*c**4*f*tan(e/2 + f*x/2)**8 + 840*a**2*c**4*f*tan(e/2 + f*x/2)**7 - 1470*a**2*c**4*f*tan(e/2 + f*x/2)**6 + 1470*a**2*c**4*f*tan(e/2 + f*x/2)**4 - 840*a**2*c**4*f*tan(e/2 + f*x/2)**3 - 315*a**2*c**4*f*tan(e/2 + f*x/2)**2 + 420*a**2*c**4*f*tan(e/2 + f*x/2) - 105*a**2*c**4*f) - 264*B*tan(e/2 + f*x/2)**2/(105*a**2*c**4*f*tan(e/2 + f*x/2)**10 - 420*a**2*c**4*f*tan(e/2 + f*x/2)**9 + 315*a**2*c**4*f*tan(e/2 + f*x/2)**8 + 840*a**2*c**4*f*tan(e/2 + f*x/2)**7 - 1470*a**2*c**4*f*tan(e/2 + f*x/2)**6 + 1470*a**2*c**4*f*tan(e/2 + f*x/2)**4 - 840*a**2*c**4*f*tan(e/2 + f*x/2)**3 - 315*a**2*c**4*f*tan(e/2 + f*x/2)**2 + 420*a**2*c**4*f*tan(e/2 + f*x/2) - 105*a**2*c**4*f) + 72*B*tan(e/2 + f*x/2)/(105*a**2*c**4*f*tan(e/2 + f*x/2)**10 - 420*a**2*c**4*f*tan(e/2 + f*x/2)**9 + 315*a**2*c**4*f*tan(e/2 + f*x/2)**8 + 840*a**2*c**4*f*tan(e/2 + f*x/2)**7 - 1470*a**2*c**4*f*tan(e/2 + f*x/2)**6 + 1470*a**2*c**4*f*tan(e/2 + f*x/2)**4 - 840*a**2*c**4*f*tan(e/2 + f*x/2)**3 - 315*a**2*c**4*f*tan(e/2 + f*x/2)**2 + 420*a**2*c**4*f*tan(e/2 + f*x/2) - 105*a**2*c**4*f) - 18*B/(105*a**2*c**4*f*tan(e/2 + f*x/2)**10 - 420*a**2*c**4*f*tan(e/2 + f*x/2)**9 + 315*a**2*c**4*f*tan(e/2 + f*x/2)**8 + 840*a**2*c**4*f*tan(e/2 + f*x/2)**7 - 1470*a**2*c**4*f*tan(e/2 + f*x/2)**6 + 1470*a**2*c**4*f*tan(e/2 + f*x/2)**4 - 840*a**2*c**4*f*tan(e/2 + f*x/2)**3 - 315*a**2*c**4*f*tan(e/2 + f*x/2)**2 + 420*a**2*c**4*f*tan(e/2 + f*x/2) - 105*a**2*c**4*f), Ne(f, 0)), (x*(A + B*sin(e))/((a*sin(e) + a)**2*(-c*sin(e) + c)**4), True))","A",0
69,1,5868,0,90.731547," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))**2/(c-c*sin(f*x+e))**5,x)","\begin{cases} - \frac{126 A \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{63 a^{2} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 378 a^{2} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 756 a^{2} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 126 a^{2} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1701 a^{2} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2268 a^{2} c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2268 a^{2} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1701 a^{2} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 126 a^{2} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 756 a^{2} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 378 a^{2} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 a^{2} c^{5} f} + \frac{378 A \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{63 a^{2} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 378 a^{2} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 756 a^{2} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 126 a^{2} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1701 a^{2} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2268 a^{2} c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2268 a^{2} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1701 a^{2} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 126 a^{2} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 756 a^{2} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 378 a^{2} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 a^{2} c^{5} f} - \frac{546 A \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{63 a^{2} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 378 a^{2} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 756 a^{2} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 126 a^{2} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1701 a^{2} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2268 a^{2} c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2268 a^{2} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1701 a^{2} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 126 a^{2} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 756 a^{2} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 378 a^{2} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 a^{2} c^{5} f} - \frac{126 A \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{63 a^{2} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 378 a^{2} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 756 a^{2} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 126 a^{2} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1701 a^{2} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2268 a^{2} c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2268 a^{2} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1701 a^{2} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 126 a^{2} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 756 a^{2} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 378 a^{2} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 a^{2} c^{5} f} + \frac{756 A \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{63 a^{2} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 378 a^{2} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 756 a^{2} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 126 a^{2} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1701 a^{2} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2268 a^{2} c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2268 a^{2} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1701 a^{2} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 126 a^{2} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 756 a^{2} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 378 a^{2} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 a^{2} c^{5} f} - \frac{588 A \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{63 a^{2} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 378 a^{2} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 756 a^{2} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 126 a^{2} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1701 a^{2} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2268 a^{2} c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2268 a^{2} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1701 a^{2} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 126 a^{2} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 756 a^{2} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 378 a^{2} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 a^{2} c^{5} f} - \frac{612 A \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{63 a^{2} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 378 a^{2} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 756 a^{2} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 126 a^{2} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1701 a^{2} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2268 a^{2} c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2268 a^{2} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1701 a^{2} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 126 a^{2} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 756 a^{2} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 378 a^{2} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 a^{2} c^{5} f} + \frac{900 A \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{63 a^{2} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 378 a^{2} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 756 a^{2} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 126 a^{2} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1701 a^{2} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2268 a^{2} c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2268 a^{2} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1701 a^{2} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 126 a^{2} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 756 a^{2} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 378 a^{2} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 a^{2} c^{5} f} - \frac{470 A \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{63 a^{2} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 378 a^{2} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 756 a^{2} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 126 a^{2} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1701 a^{2} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2268 a^{2} c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2268 a^{2} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1701 a^{2} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 126 a^{2} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 756 a^{2} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 378 a^{2} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 a^{2} c^{5} f} - \frac{78 A \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{63 a^{2} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 378 a^{2} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 756 a^{2} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 126 a^{2} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1701 a^{2} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2268 a^{2} c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2268 a^{2} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1701 a^{2} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 126 a^{2} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 756 a^{2} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 378 a^{2} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 a^{2} c^{5} f} + \frac{102 A \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{63 a^{2} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 378 a^{2} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 756 a^{2} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 126 a^{2} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1701 a^{2} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2268 a^{2} c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2268 a^{2} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1701 a^{2} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 126 a^{2} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 756 a^{2} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 378 a^{2} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 a^{2} c^{5} f} - \frac{38 A}{63 a^{2} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 378 a^{2} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 756 a^{2} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 126 a^{2} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1701 a^{2} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2268 a^{2} c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2268 a^{2} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1701 a^{2} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 126 a^{2} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 756 a^{2} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 378 a^{2} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 a^{2} c^{5} f} - \frac{126 B \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{63 a^{2} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 378 a^{2} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 756 a^{2} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 126 a^{2} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1701 a^{2} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2268 a^{2} c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2268 a^{2} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1701 a^{2} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 126 a^{2} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 756 a^{2} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 378 a^{2} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 a^{2} c^{5} f} + \frac{252 B \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{63 a^{2} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 378 a^{2} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 756 a^{2} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 126 a^{2} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1701 a^{2} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2268 a^{2} c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2268 a^{2} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1701 a^{2} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 126 a^{2} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 756 a^{2} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 378 a^{2} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 a^{2} c^{5} f} - \frac{378 B \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{63 a^{2} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 378 a^{2} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 756 a^{2} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 126 a^{2} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1701 a^{2} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2268 a^{2} c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2268 a^{2} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1701 a^{2} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 126 a^{2} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 756 a^{2} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 378 a^{2} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 a^{2} c^{5} f} + \frac{84 B \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{63 a^{2} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 378 a^{2} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 756 a^{2} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 126 a^{2} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1701 a^{2} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2268 a^{2} c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2268 a^{2} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1701 a^{2} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 126 a^{2} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 756 a^{2} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 378 a^{2} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 a^{2} c^{5} f} - \frac{72 B \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{63 a^{2} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 378 a^{2} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 756 a^{2} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 126 a^{2} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1701 a^{2} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2268 a^{2} c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2268 a^{2} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1701 a^{2} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 126 a^{2} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 756 a^{2} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 378 a^{2} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 a^{2} c^{5} f} - \frac{324 B \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{63 a^{2} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 378 a^{2} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 756 a^{2} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 126 a^{2} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1701 a^{2} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2268 a^{2} c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2268 a^{2} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1701 a^{2} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 126 a^{2} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 756 a^{2} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 378 a^{2} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 a^{2} c^{5} f} + \frac{256 B \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{63 a^{2} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 378 a^{2} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 756 a^{2} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 126 a^{2} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1701 a^{2} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2268 a^{2} c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2268 a^{2} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1701 a^{2} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 126 a^{2} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 756 a^{2} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 378 a^{2} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 a^{2} c^{5} f} - \frac{150 B \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{63 a^{2} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 378 a^{2} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 756 a^{2} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 126 a^{2} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1701 a^{2} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2268 a^{2} c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2268 a^{2} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1701 a^{2} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 126 a^{2} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 756 a^{2} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 378 a^{2} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 a^{2} c^{5} f} + \frac{12 B \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{63 a^{2} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 378 a^{2} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 756 a^{2} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 126 a^{2} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1701 a^{2} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2268 a^{2} c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2268 a^{2} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1701 a^{2} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 126 a^{2} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 756 a^{2} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 378 a^{2} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 a^{2} c^{5} f} - \frac{2 B}{63 a^{2} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 378 a^{2} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 756 a^{2} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 126 a^{2} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1701 a^{2} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2268 a^{2} c^{5} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2268 a^{2} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1701 a^{2} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 126 a^{2} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 756 a^{2} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 378 a^{2} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 a^{2} c^{5} f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right)}{\left(a \sin{\left(e \right)} + a\right)^{2} \left(- c \sin{\left(e \right)} + c\right)^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-126*A*tan(e/2 + f*x/2)**11/(63*a**2*c**5*f*tan(e/2 + f*x/2)**12 - 378*a**2*c**5*f*tan(e/2 + f*x/2)**11 + 756*a**2*c**5*f*tan(e/2 + f*x/2)**10 - 126*a**2*c**5*f*tan(e/2 + f*x/2)**9 - 1701*a**2*c**5*f*tan(e/2 + f*x/2)**8 + 2268*a**2*c**5*f*tan(e/2 + f*x/2)**7 - 2268*a**2*c**5*f*tan(e/2 + f*x/2)**5 + 1701*a**2*c**5*f*tan(e/2 + f*x/2)**4 + 126*a**2*c**5*f*tan(e/2 + f*x/2)**3 - 756*a**2*c**5*f*tan(e/2 + f*x/2)**2 + 378*a**2*c**5*f*tan(e/2 + f*x/2) - 63*a**2*c**5*f) + 378*A*tan(e/2 + f*x/2)**10/(63*a**2*c**5*f*tan(e/2 + f*x/2)**12 - 378*a**2*c**5*f*tan(e/2 + f*x/2)**11 + 756*a**2*c**5*f*tan(e/2 + f*x/2)**10 - 126*a**2*c**5*f*tan(e/2 + f*x/2)**9 - 1701*a**2*c**5*f*tan(e/2 + f*x/2)**8 + 2268*a**2*c**5*f*tan(e/2 + f*x/2)**7 - 2268*a**2*c**5*f*tan(e/2 + f*x/2)**5 + 1701*a**2*c**5*f*tan(e/2 + f*x/2)**4 + 126*a**2*c**5*f*tan(e/2 + f*x/2)**3 - 756*a**2*c**5*f*tan(e/2 + f*x/2)**2 + 378*a**2*c**5*f*tan(e/2 + f*x/2) - 63*a**2*c**5*f) - 546*A*tan(e/2 + f*x/2)**9/(63*a**2*c**5*f*tan(e/2 + f*x/2)**12 - 378*a**2*c**5*f*tan(e/2 + f*x/2)**11 + 756*a**2*c**5*f*tan(e/2 + f*x/2)**10 - 126*a**2*c**5*f*tan(e/2 + f*x/2)**9 - 1701*a**2*c**5*f*tan(e/2 + f*x/2)**8 + 2268*a**2*c**5*f*tan(e/2 + f*x/2)**7 - 2268*a**2*c**5*f*tan(e/2 + f*x/2)**5 + 1701*a**2*c**5*f*tan(e/2 + f*x/2)**4 + 126*a**2*c**5*f*tan(e/2 + f*x/2)**3 - 756*a**2*c**5*f*tan(e/2 + f*x/2)**2 + 378*a**2*c**5*f*tan(e/2 + f*x/2) - 63*a**2*c**5*f) - 126*A*tan(e/2 + f*x/2)**8/(63*a**2*c**5*f*tan(e/2 + f*x/2)**12 - 378*a**2*c**5*f*tan(e/2 + f*x/2)**11 + 756*a**2*c**5*f*tan(e/2 + f*x/2)**10 - 126*a**2*c**5*f*tan(e/2 + f*x/2)**9 - 1701*a**2*c**5*f*tan(e/2 + f*x/2)**8 + 2268*a**2*c**5*f*tan(e/2 + f*x/2)**7 - 2268*a**2*c**5*f*tan(e/2 + f*x/2)**5 + 1701*a**2*c**5*f*tan(e/2 + f*x/2)**4 + 126*a**2*c**5*f*tan(e/2 + f*x/2)**3 - 756*a**2*c**5*f*tan(e/2 + f*x/2)**2 + 378*a**2*c**5*f*tan(e/2 + f*x/2) - 63*a**2*c**5*f) + 756*A*tan(e/2 + f*x/2)**7/(63*a**2*c**5*f*tan(e/2 + f*x/2)**12 - 378*a**2*c**5*f*tan(e/2 + f*x/2)**11 + 756*a**2*c**5*f*tan(e/2 + f*x/2)**10 - 126*a**2*c**5*f*tan(e/2 + f*x/2)**9 - 1701*a**2*c**5*f*tan(e/2 + f*x/2)**8 + 2268*a**2*c**5*f*tan(e/2 + f*x/2)**7 - 2268*a**2*c**5*f*tan(e/2 + f*x/2)**5 + 1701*a**2*c**5*f*tan(e/2 + f*x/2)**4 + 126*a**2*c**5*f*tan(e/2 + f*x/2)**3 - 756*a**2*c**5*f*tan(e/2 + f*x/2)**2 + 378*a**2*c**5*f*tan(e/2 + f*x/2) - 63*a**2*c**5*f) - 588*A*tan(e/2 + f*x/2)**6/(63*a**2*c**5*f*tan(e/2 + f*x/2)**12 - 378*a**2*c**5*f*tan(e/2 + f*x/2)**11 + 756*a**2*c**5*f*tan(e/2 + f*x/2)**10 - 126*a**2*c**5*f*tan(e/2 + f*x/2)**9 - 1701*a**2*c**5*f*tan(e/2 + f*x/2)**8 + 2268*a**2*c**5*f*tan(e/2 + f*x/2)**7 - 2268*a**2*c**5*f*tan(e/2 + f*x/2)**5 + 1701*a**2*c**5*f*tan(e/2 + f*x/2)**4 + 126*a**2*c**5*f*tan(e/2 + f*x/2)**3 - 756*a**2*c**5*f*tan(e/2 + f*x/2)**2 + 378*a**2*c**5*f*tan(e/2 + f*x/2) - 63*a**2*c**5*f) - 612*A*tan(e/2 + f*x/2)**5/(63*a**2*c**5*f*tan(e/2 + f*x/2)**12 - 378*a**2*c**5*f*tan(e/2 + f*x/2)**11 + 756*a**2*c**5*f*tan(e/2 + f*x/2)**10 - 126*a**2*c**5*f*tan(e/2 + f*x/2)**9 - 1701*a**2*c**5*f*tan(e/2 + f*x/2)**8 + 2268*a**2*c**5*f*tan(e/2 + f*x/2)**7 - 2268*a**2*c**5*f*tan(e/2 + f*x/2)**5 + 1701*a**2*c**5*f*tan(e/2 + f*x/2)**4 + 126*a**2*c**5*f*tan(e/2 + f*x/2)**3 - 756*a**2*c**5*f*tan(e/2 + f*x/2)**2 + 378*a**2*c**5*f*tan(e/2 + f*x/2) - 63*a**2*c**5*f) + 900*A*tan(e/2 + f*x/2)**4/(63*a**2*c**5*f*tan(e/2 + f*x/2)**12 - 378*a**2*c**5*f*tan(e/2 + f*x/2)**11 + 756*a**2*c**5*f*tan(e/2 + f*x/2)**10 - 126*a**2*c**5*f*tan(e/2 + f*x/2)**9 - 1701*a**2*c**5*f*tan(e/2 + f*x/2)**8 + 2268*a**2*c**5*f*tan(e/2 + f*x/2)**7 - 2268*a**2*c**5*f*tan(e/2 + f*x/2)**5 + 1701*a**2*c**5*f*tan(e/2 + f*x/2)**4 + 126*a**2*c**5*f*tan(e/2 + f*x/2)**3 - 756*a**2*c**5*f*tan(e/2 + f*x/2)**2 + 378*a**2*c**5*f*tan(e/2 + f*x/2) - 63*a**2*c**5*f) - 470*A*tan(e/2 + f*x/2)**3/(63*a**2*c**5*f*tan(e/2 + f*x/2)**12 - 378*a**2*c**5*f*tan(e/2 + f*x/2)**11 + 756*a**2*c**5*f*tan(e/2 + f*x/2)**10 - 126*a**2*c**5*f*tan(e/2 + f*x/2)**9 - 1701*a**2*c**5*f*tan(e/2 + f*x/2)**8 + 2268*a**2*c**5*f*tan(e/2 + f*x/2)**7 - 2268*a**2*c**5*f*tan(e/2 + f*x/2)**5 + 1701*a**2*c**5*f*tan(e/2 + f*x/2)**4 + 126*a**2*c**5*f*tan(e/2 + f*x/2)**3 - 756*a**2*c**5*f*tan(e/2 + f*x/2)**2 + 378*a**2*c**5*f*tan(e/2 + f*x/2) - 63*a**2*c**5*f) - 78*A*tan(e/2 + f*x/2)**2/(63*a**2*c**5*f*tan(e/2 + f*x/2)**12 - 378*a**2*c**5*f*tan(e/2 + f*x/2)**11 + 756*a**2*c**5*f*tan(e/2 + f*x/2)**10 - 126*a**2*c**5*f*tan(e/2 + f*x/2)**9 - 1701*a**2*c**5*f*tan(e/2 + f*x/2)**8 + 2268*a**2*c**5*f*tan(e/2 + f*x/2)**7 - 2268*a**2*c**5*f*tan(e/2 + f*x/2)**5 + 1701*a**2*c**5*f*tan(e/2 + f*x/2)**4 + 126*a**2*c**5*f*tan(e/2 + f*x/2)**3 - 756*a**2*c**5*f*tan(e/2 + f*x/2)**2 + 378*a**2*c**5*f*tan(e/2 + f*x/2) - 63*a**2*c**5*f) + 102*A*tan(e/2 + f*x/2)/(63*a**2*c**5*f*tan(e/2 + f*x/2)**12 - 378*a**2*c**5*f*tan(e/2 + f*x/2)**11 + 756*a**2*c**5*f*tan(e/2 + f*x/2)**10 - 126*a**2*c**5*f*tan(e/2 + f*x/2)**9 - 1701*a**2*c**5*f*tan(e/2 + f*x/2)**8 + 2268*a**2*c**5*f*tan(e/2 + f*x/2)**7 - 2268*a**2*c**5*f*tan(e/2 + f*x/2)**5 + 1701*a**2*c**5*f*tan(e/2 + f*x/2)**4 + 126*a**2*c**5*f*tan(e/2 + f*x/2)**3 - 756*a**2*c**5*f*tan(e/2 + f*x/2)**2 + 378*a**2*c**5*f*tan(e/2 + f*x/2) - 63*a**2*c**5*f) - 38*A/(63*a**2*c**5*f*tan(e/2 + f*x/2)**12 - 378*a**2*c**5*f*tan(e/2 + f*x/2)**11 + 756*a**2*c**5*f*tan(e/2 + f*x/2)**10 - 126*a**2*c**5*f*tan(e/2 + f*x/2)**9 - 1701*a**2*c**5*f*tan(e/2 + f*x/2)**8 + 2268*a**2*c**5*f*tan(e/2 + f*x/2)**7 - 2268*a**2*c**5*f*tan(e/2 + f*x/2)**5 + 1701*a**2*c**5*f*tan(e/2 + f*x/2)**4 + 126*a**2*c**5*f*tan(e/2 + f*x/2)**3 - 756*a**2*c**5*f*tan(e/2 + f*x/2)**2 + 378*a**2*c**5*f*tan(e/2 + f*x/2) - 63*a**2*c**5*f) - 126*B*tan(e/2 + f*x/2)**10/(63*a**2*c**5*f*tan(e/2 + f*x/2)**12 - 378*a**2*c**5*f*tan(e/2 + f*x/2)**11 + 756*a**2*c**5*f*tan(e/2 + f*x/2)**10 - 126*a**2*c**5*f*tan(e/2 + f*x/2)**9 - 1701*a**2*c**5*f*tan(e/2 + f*x/2)**8 + 2268*a**2*c**5*f*tan(e/2 + f*x/2)**7 - 2268*a**2*c**5*f*tan(e/2 + f*x/2)**5 + 1701*a**2*c**5*f*tan(e/2 + f*x/2)**4 + 126*a**2*c**5*f*tan(e/2 + f*x/2)**3 - 756*a**2*c**5*f*tan(e/2 + f*x/2)**2 + 378*a**2*c**5*f*tan(e/2 + f*x/2) - 63*a**2*c**5*f) + 252*B*tan(e/2 + f*x/2)**9/(63*a**2*c**5*f*tan(e/2 + f*x/2)**12 - 378*a**2*c**5*f*tan(e/2 + f*x/2)**11 + 756*a**2*c**5*f*tan(e/2 + f*x/2)**10 - 126*a**2*c**5*f*tan(e/2 + f*x/2)**9 - 1701*a**2*c**5*f*tan(e/2 + f*x/2)**8 + 2268*a**2*c**5*f*tan(e/2 + f*x/2)**7 - 2268*a**2*c**5*f*tan(e/2 + f*x/2)**5 + 1701*a**2*c**5*f*tan(e/2 + f*x/2)**4 + 126*a**2*c**5*f*tan(e/2 + f*x/2)**3 - 756*a**2*c**5*f*tan(e/2 + f*x/2)**2 + 378*a**2*c**5*f*tan(e/2 + f*x/2) - 63*a**2*c**5*f) - 378*B*tan(e/2 + f*x/2)**8/(63*a**2*c**5*f*tan(e/2 + f*x/2)**12 - 378*a**2*c**5*f*tan(e/2 + f*x/2)**11 + 756*a**2*c**5*f*tan(e/2 + f*x/2)**10 - 126*a**2*c**5*f*tan(e/2 + f*x/2)**9 - 1701*a**2*c**5*f*tan(e/2 + f*x/2)**8 + 2268*a**2*c**5*f*tan(e/2 + f*x/2)**7 - 2268*a**2*c**5*f*tan(e/2 + f*x/2)**5 + 1701*a**2*c**5*f*tan(e/2 + f*x/2)**4 + 126*a**2*c**5*f*tan(e/2 + f*x/2)**3 - 756*a**2*c**5*f*tan(e/2 + f*x/2)**2 + 378*a**2*c**5*f*tan(e/2 + f*x/2) - 63*a**2*c**5*f) + 84*B*tan(e/2 + f*x/2)**6/(63*a**2*c**5*f*tan(e/2 + f*x/2)**12 - 378*a**2*c**5*f*tan(e/2 + f*x/2)**11 + 756*a**2*c**5*f*tan(e/2 + f*x/2)**10 - 126*a**2*c**5*f*tan(e/2 + f*x/2)**9 - 1701*a**2*c**5*f*tan(e/2 + f*x/2)**8 + 2268*a**2*c**5*f*tan(e/2 + f*x/2)**7 - 2268*a**2*c**5*f*tan(e/2 + f*x/2)**5 + 1701*a**2*c**5*f*tan(e/2 + f*x/2)**4 + 126*a**2*c**5*f*tan(e/2 + f*x/2)**3 - 756*a**2*c**5*f*tan(e/2 + f*x/2)**2 + 378*a**2*c**5*f*tan(e/2 + f*x/2) - 63*a**2*c**5*f) - 72*B*tan(e/2 + f*x/2)**5/(63*a**2*c**5*f*tan(e/2 + f*x/2)**12 - 378*a**2*c**5*f*tan(e/2 + f*x/2)**11 + 756*a**2*c**5*f*tan(e/2 + f*x/2)**10 - 126*a**2*c**5*f*tan(e/2 + f*x/2)**9 - 1701*a**2*c**5*f*tan(e/2 + f*x/2)**8 + 2268*a**2*c**5*f*tan(e/2 + f*x/2)**7 - 2268*a**2*c**5*f*tan(e/2 + f*x/2)**5 + 1701*a**2*c**5*f*tan(e/2 + f*x/2)**4 + 126*a**2*c**5*f*tan(e/2 + f*x/2)**3 - 756*a**2*c**5*f*tan(e/2 + f*x/2)**2 + 378*a**2*c**5*f*tan(e/2 + f*x/2) - 63*a**2*c**5*f) - 324*B*tan(e/2 + f*x/2)**4/(63*a**2*c**5*f*tan(e/2 + f*x/2)**12 - 378*a**2*c**5*f*tan(e/2 + f*x/2)**11 + 756*a**2*c**5*f*tan(e/2 + f*x/2)**10 - 126*a**2*c**5*f*tan(e/2 + f*x/2)**9 - 1701*a**2*c**5*f*tan(e/2 + f*x/2)**8 + 2268*a**2*c**5*f*tan(e/2 + f*x/2)**7 - 2268*a**2*c**5*f*tan(e/2 + f*x/2)**5 + 1701*a**2*c**5*f*tan(e/2 + f*x/2)**4 + 126*a**2*c**5*f*tan(e/2 + f*x/2)**3 - 756*a**2*c**5*f*tan(e/2 + f*x/2)**2 + 378*a**2*c**5*f*tan(e/2 + f*x/2) - 63*a**2*c**5*f) + 256*B*tan(e/2 + f*x/2)**3/(63*a**2*c**5*f*tan(e/2 + f*x/2)**12 - 378*a**2*c**5*f*tan(e/2 + f*x/2)**11 + 756*a**2*c**5*f*tan(e/2 + f*x/2)**10 - 126*a**2*c**5*f*tan(e/2 + f*x/2)**9 - 1701*a**2*c**5*f*tan(e/2 + f*x/2)**8 + 2268*a**2*c**5*f*tan(e/2 + f*x/2)**7 - 2268*a**2*c**5*f*tan(e/2 + f*x/2)**5 + 1701*a**2*c**5*f*tan(e/2 + f*x/2)**4 + 126*a**2*c**5*f*tan(e/2 + f*x/2)**3 - 756*a**2*c**5*f*tan(e/2 + f*x/2)**2 + 378*a**2*c**5*f*tan(e/2 + f*x/2) - 63*a**2*c**5*f) - 150*B*tan(e/2 + f*x/2)**2/(63*a**2*c**5*f*tan(e/2 + f*x/2)**12 - 378*a**2*c**5*f*tan(e/2 + f*x/2)**11 + 756*a**2*c**5*f*tan(e/2 + f*x/2)**10 - 126*a**2*c**5*f*tan(e/2 + f*x/2)**9 - 1701*a**2*c**5*f*tan(e/2 + f*x/2)**8 + 2268*a**2*c**5*f*tan(e/2 + f*x/2)**7 - 2268*a**2*c**5*f*tan(e/2 + f*x/2)**5 + 1701*a**2*c**5*f*tan(e/2 + f*x/2)**4 + 126*a**2*c**5*f*tan(e/2 + f*x/2)**3 - 756*a**2*c**5*f*tan(e/2 + f*x/2)**2 + 378*a**2*c**5*f*tan(e/2 + f*x/2) - 63*a**2*c**5*f) + 12*B*tan(e/2 + f*x/2)/(63*a**2*c**5*f*tan(e/2 + f*x/2)**12 - 378*a**2*c**5*f*tan(e/2 + f*x/2)**11 + 756*a**2*c**5*f*tan(e/2 + f*x/2)**10 - 126*a**2*c**5*f*tan(e/2 + f*x/2)**9 - 1701*a**2*c**5*f*tan(e/2 + f*x/2)**8 + 2268*a**2*c**5*f*tan(e/2 + f*x/2)**7 - 2268*a**2*c**5*f*tan(e/2 + f*x/2)**5 + 1701*a**2*c**5*f*tan(e/2 + f*x/2)**4 + 126*a**2*c**5*f*tan(e/2 + f*x/2)**3 - 756*a**2*c**5*f*tan(e/2 + f*x/2)**2 + 378*a**2*c**5*f*tan(e/2 + f*x/2) - 63*a**2*c**5*f) - 2*B/(63*a**2*c**5*f*tan(e/2 + f*x/2)**12 - 378*a**2*c**5*f*tan(e/2 + f*x/2)**11 + 756*a**2*c**5*f*tan(e/2 + f*x/2)**10 - 126*a**2*c**5*f*tan(e/2 + f*x/2)**9 - 1701*a**2*c**5*f*tan(e/2 + f*x/2)**8 + 2268*a**2*c**5*f*tan(e/2 + f*x/2)**7 - 2268*a**2*c**5*f*tan(e/2 + f*x/2)**5 + 1701*a**2*c**5*f*tan(e/2 + f*x/2)**4 + 126*a**2*c**5*f*tan(e/2 + f*x/2)**3 - 756*a**2*c**5*f*tan(e/2 + f*x/2)**2 + 378*a**2*c**5*f*tan(e/2 + f*x/2) - 63*a**2*c**5*f), Ne(f, 0)), (x*(A + B*sin(e))/((a*sin(e) + a)**2*(-c*sin(e) + c)**5), True))","A",0
70,1,10608,0,112.094691," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))**5/(a+a*sin(f*x+e))**3,x)","\begin{cases} - \frac{945 A c^{5} f x \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} - \frac{4725 A c^{5} f x \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} - \frac{12285 A c^{5} f x \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} - \frac{23625 A c^{5} f x \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} - \frac{35910 A c^{5} f x \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} - \frac{43470 A c^{5} f x \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} - \frac{43470 A c^{5} f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} - \frac{35910 A c^{5} f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} - \frac{23625 A c^{5} f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} - \frac{12285 A c^{5} f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} - \frac{4725 A c^{5} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} - \frac{945 A c^{5} f x}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} - \frac{1950 A c^{5} \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} - \frac{9270 A c^{5} \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} - \frac{24780 A c^{5} \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} - \frac{42540 A c^{5} \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} - \frac{66936 A c^{5} \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} - \frac{69960 A c^{5} \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} - \frac{70548 A c^{5} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} - \frac{49620 A c^{5} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} - \frac{29418 A c^{5} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} - \frac{12930 A c^{5} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} - \frac{2976 A c^{5}}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} + \frac{2520 B c^{5} f x \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} + \frac{12600 B c^{5} f x \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} + \frac{32760 B c^{5} f x \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} + \frac{63000 B c^{5} f x \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} + \frac{95760 B c^{5} f x \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} + \frac{115920 B c^{5} f x \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} + \frac{115920 B c^{5} f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} + \frac{95760 B c^{5} f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} + \frac{63000 B c^{5} f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} + \frac{32760 B c^{5} f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} + \frac{12600 B c^{5} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} + \frac{2520 B c^{5} f x}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} + \frac{5040 B c^{5} \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} + \frac{25140 B c^{5} \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} + \frac{64180 B c^{5} \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} + \frac{116360 B c^{5} \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} + \frac{173416 B c^{5} \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} + \frac{190720 B c^{5} \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} + \frac{184448 B c^{5} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} + \frac{133720 B c^{5} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} + \frac{77768 B c^{5} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} + \frac{34540 B c^{5} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} + \frac{7916 B c^{5}}{30 a^{3} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1380 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1140 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 750 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 390 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right) \left(- c \sin{\left(e \right)} + c\right)^{5}}{\left(a \sin{\left(e \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-945*A*c**5*f*x*tan(e/2 + f*x/2)**11/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) - 4725*A*c**5*f*x*tan(e/2 + f*x/2)**10/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) - 12285*A*c**5*f*x*tan(e/2 + f*x/2)**9/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) - 23625*A*c**5*f*x*tan(e/2 + f*x/2)**8/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) - 35910*A*c**5*f*x*tan(e/2 + f*x/2)**7/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) - 43470*A*c**5*f*x*tan(e/2 + f*x/2)**6/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) - 43470*A*c**5*f*x*tan(e/2 + f*x/2)**5/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) - 35910*A*c**5*f*x*tan(e/2 + f*x/2)**4/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) - 23625*A*c**5*f*x*tan(e/2 + f*x/2)**3/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) - 12285*A*c**5*f*x*tan(e/2 + f*x/2)**2/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) - 4725*A*c**5*f*x*tan(e/2 + f*x/2)/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) - 945*A*c**5*f*x/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) - 1950*A*c**5*tan(e/2 + f*x/2)**10/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) - 9270*A*c**5*tan(e/2 + f*x/2)**9/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) - 24780*A*c**5*tan(e/2 + f*x/2)**8/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) - 42540*A*c**5*tan(e/2 + f*x/2)**7/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) - 66936*A*c**5*tan(e/2 + f*x/2)**6/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) - 69960*A*c**5*tan(e/2 + f*x/2)**5/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) - 70548*A*c**5*tan(e/2 + f*x/2)**4/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) - 49620*A*c**5*tan(e/2 + f*x/2)**3/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) - 29418*A*c**5*tan(e/2 + f*x/2)**2/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) - 12930*A*c**5*tan(e/2 + f*x/2)/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) - 2976*A*c**5/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) + 2520*B*c**5*f*x*tan(e/2 + f*x/2)**11/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) + 12600*B*c**5*f*x*tan(e/2 + f*x/2)**10/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) + 32760*B*c**5*f*x*tan(e/2 + f*x/2)**9/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) + 63000*B*c**5*f*x*tan(e/2 + f*x/2)**8/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) + 95760*B*c**5*f*x*tan(e/2 + f*x/2)**7/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) + 115920*B*c**5*f*x*tan(e/2 + f*x/2)**6/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) + 115920*B*c**5*f*x*tan(e/2 + f*x/2)**5/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) + 95760*B*c**5*f*x*tan(e/2 + f*x/2)**4/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) + 63000*B*c**5*f*x*tan(e/2 + f*x/2)**3/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) + 32760*B*c**5*f*x*tan(e/2 + f*x/2)**2/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) + 12600*B*c**5*f*x*tan(e/2 + f*x/2)/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) + 2520*B*c**5*f*x/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) + 5040*B*c**5*tan(e/2 + f*x/2)**10/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) + 25140*B*c**5*tan(e/2 + f*x/2)**9/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) + 64180*B*c**5*tan(e/2 + f*x/2)**8/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) + 116360*B*c**5*tan(e/2 + f*x/2)**7/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) + 173416*B*c**5*tan(e/2 + f*x/2)**6/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) + 190720*B*c**5*tan(e/2 + f*x/2)**5/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) + 184448*B*c**5*tan(e/2 + f*x/2)**4/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) + 133720*B*c**5*tan(e/2 + f*x/2)**3/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) + 77768*B*c**5*tan(e/2 + f*x/2)**2/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) + 34540*B*c**5*tan(e/2 + f*x/2)/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) + 7916*B*c**5/(30*a**3*f*tan(e/2 + f*x/2)**11 + 150*a**3*f*tan(e/2 + f*x/2)**10 + 390*a**3*f*tan(e/2 + f*x/2)**9 + 750*a**3*f*tan(e/2 + f*x/2)**8 + 1140*a**3*f*tan(e/2 + f*x/2)**7 + 1380*a**3*f*tan(e/2 + f*x/2)**6 + 1380*a**3*f*tan(e/2 + f*x/2)**5 + 1140*a**3*f*tan(e/2 + f*x/2)**4 + 750*a**3*f*tan(e/2 + f*x/2)**3 + 390*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f), Ne(f, 0)), (x*(A + B*sin(e))*(-c*sin(e) + c)**5/(a*sin(e) + a)**3, True))","A",0
71,1,7337,0,74.016204," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))**4/(a+a*sin(f*x+e))**3,x)","\begin{cases} - \frac{210 A c^{4} f x \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} - \frac{1050 A c^{4} f x \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} - \frac{2520 A c^{4} f x \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} - \frac{4200 A c^{4} f x \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} - \frac{5460 A c^{4} f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} - \frac{5460 A c^{4} f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} - \frac{4200 A c^{4} f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} - \frac{2520 A c^{4} f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} - \frac{1050 A c^{4} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} - \frac{210 A c^{4} f x}{30 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} - \frac{480 A c^{4} \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} - \frac{1980 A c^{4} \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} - \frac{5420 A c^{4} \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} - \frac{7060 A c^{4} \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} - \frac{10308 A c^{4} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} - \frac{7940 A c^{4} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} - \frac{6036 A c^{4} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} - \frac{2860 A c^{4} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} - \frac{668 A c^{4}}{30 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} + \frac{735 B c^{4} f x \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} + \frac{3675 B c^{4} f x \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} + \frac{8820 B c^{4} f x \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} + \frac{14700 B c^{4} f x \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} + \frac{19110 B c^{4} f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} + \frac{19110 B c^{4} f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} + \frac{14700 B c^{4} f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} + \frac{8820 B c^{4} f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} + \frac{3675 B c^{4} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} + \frac{735 B c^{4} f x}{30 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} + \frac{1470 B c^{4} \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} + \frac{7290 B c^{4} \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} + \frac{17410 B c^{4} \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} + \frac{26210 B c^{4} \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} + \frac{33798 B c^{4} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} + \frac{28750 B c^{4} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} + \frac{20406 B c^{4} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} + \frac{10070 B c^{4} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{30 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} + \frac{2308 B c^{4}}{30 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 780 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 600 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 360 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right) \left(- c \sin{\left(e \right)} + c\right)^{4}}{\left(a \sin{\left(e \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-210*A*c**4*f*x*tan(e/2 + f*x/2)**9/(30*a**3*f*tan(e/2 + f*x/2)**9 + 150*a**3*f*tan(e/2 + f*x/2)**8 + 360*a**3*f*tan(e/2 + f*x/2)**7 + 600*a**3*f*tan(e/2 + f*x/2)**6 + 780*a**3*f*tan(e/2 + f*x/2)**5 + 780*a**3*f*tan(e/2 + f*x/2)**4 + 600*a**3*f*tan(e/2 + f*x/2)**3 + 360*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) - 1050*A*c**4*f*x*tan(e/2 + f*x/2)**8/(30*a**3*f*tan(e/2 + f*x/2)**9 + 150*a**3*f*tan(e/2 + f*x/2)**8 + 360*a**3*f*tan(e/2 + f*x/2)**7 + 600*a**3*f*tan(e/2 + f*x/2)**6 + 780*a**3*f*tan(e/2 + f*x/2)**5 + 780*a**3*f*tan(e/2 + f*x/2)**4 + 600*a**3*f*tan(e/2 + f*x/2)**3 + 360*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) - 2520*A*c**4*f*x*tan(e/2 + f*x/2)**7/(30*a**3*f*tan(e/2 + f*x/2)**9 + 150*a**3*f*tan(e/2 + f*x/2)**8 + 360*a**3*f*tan(e/2 + f*x/2)**7 + 600*a**3*f*tan(e/2 + f*x/2)**6 + 780*a**3*f*tan(e/2 + f*x/2)**5 + 780*a**3*f*tan(e/2 + f*x/2)**4 + 600*a**3*f*tan(e/2 + f*x/2)**3 + 360*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) - 4200*A*c**4*f*x*tan(e/2 + f*x/2)**6/(30*a**3*f*tan(e/2 + f*x/2)**9 + 150*a**3*f*tan(e/2 + f*x/2)**8 + 360*a**3*f*tan(e/2 + f*x/2)**7 + 600*a**3*f*tan(e/2 + f*x/2)**6 + 780*a**3*f*tan(e/2 + f*x/2)**5 + 780*a**3*f*tan(e/2 + f*x/2)**4 + 600*a**3*f*tan(e/2 + f*x/2)**3 + 360*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) - 5460*A*c**4*f*x*tan(e/2 + f*x/2)**5/(30*a**3*f*tan(e/2 + f*x/2)**9 + 150*a**3*f*tan(e/2 + f*x/2)**8 + 360*a**3*f*tan(e/2 + f*x/2)**7 + 600*a**3*f*tan(e/2 + f*x/2)**6 + 780*a**3*f*tan(e/2 + f*x/2)**5 + 780*a**3*f*tan(e/2 + f*x/2)**4 + 600*a**3*f*tan(e/2 + f*x/2)**3 + 360*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) - 5460*A*c**4*f*x*tan(e/2 + f*x/2)**4/(30*a**3*f*tan(e/2 + f*x/2)**9 + 150*a**3*f*tan(e/2 + f*x/2)**8 + 360*a**3*f*tan(e/2 + f*x/2)**7 + 600*a**3*f*tan(e/2 + f*x/2)**6 + 780*a**3*f*tan(e/2 + f*x/2)**5 + 780*a**3*f*tan(e/2 + f*x/2)**4 + 600*a**3*f*tan(e/2 + f*x/2)**3 + 360*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) - 4200*A*c**4*f*x*tan(e/2 + f*x/2)**3/(30*a**3*f*tan(e/2 + f*x/2)**9 + 150*a**3*f*tan(e/2 + f*x/2)**8 + 360*a**3*f*tan(e/2 + f*x/2)**7 + 600*a**3*f*tan(e/2 + f*x/2)**6 + 780*a**3*f*tan(e/2 + f*x/2)**5 + 780*a**3*f*tan(e/2 + f*x/2)**4 + 600*a**3*f*tan(e/2 + f*x/2)**3 + 360*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) - 2520*A*c**4*f*x*tan(e/2 + f*x/2)**2/(30*a**3*f*tan(e/2 + f*x/2)**9 + 150*a**3*f*tan(e/2 + f*x/2)**8 + 360*a**3*f*tan(e/2 + f*x/2)**7 + 600*a**3*f*tan(e/2 + f*x/2)**6 + 780*a**3*f*tan(e/2 + f*x/2)**5 + 780*a**3*f*tan(e/2 + f*x/2)**4 + 600*a**3*f*tan(e/2 + f*x/2)**3 + 360*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) - 1050*A*c**4*f*x*tan(e/2 + f*x/2)/(30*a**3*f*tan(e/2 + f*x/2)**9 + 150*a**3*f*tan(e/2 + f*x/2)**8 + 360*a**3*f*tan(e/2 + f*x/2)**7 + 600*a**3*f*tan(e/2 + f*x/2)**6 + 780*a**3*f*tan(e/2 + f*x/2)**5 + 780*a**3*f*tan(e/2 + f*x/2)**4 + 600*a**3*f*tan(e/2 + f*x/2)**3 + 360*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) - 210*A*c**4*f*x/(30*a**3*f*tan(e/2 + f*x/2)**9 + 150*a**3*f*tan(e/2 + f*x/2)**8 + 360*a**3*f*tan(e/2 + f*x/2)**7 + 600*a**3*f*tan(e/2 + f*x/2)**6 + 780*a**3*f*tan(e/2 + f*x/2)**5 + 780*a**3*f*tan(e/2 + f*x/2)**4 + 600*a**3*f*tan(e/2 + f*x/2)**3 + 360*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) - 480*A*c**4*tan(e/2 + f*x/2)**8/(30*a**3*f*tan(e/2 + f*x/2)**9 + 150*a**3*f*tan(e/2 + f*x/2)**8 + 360*a**3*f*tan(e/2 + f*x/2)**7 + 600*a**3*f*tan(e/2 + f*x/2)**6 + 780*a**3*f*tan(e/2 + f*x/2)**5 + 780*a**3*f*tan(e/2 + f*x/2)**4 + 600*a**3*f*tan(e/2 + f*x/2)**3 + 360*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) - 1980*A*c**4*tan(e/2 + f*x/2)**7/(30*a**3*f*tan(e/2 + f*x/2)**9 + 150*a**3*f*tan(e/2 + f*x/2)**8 + 360*a**3*f*tan(e/2 + f*x/2)**7 + 600*a**3*f*tan(e/2 + f*x/2)**6 + 780*a**3*f*tan(e/2 + f*x/2)**5 + 780*a**3*f*tan(e/2 + f*x/2)**4 + 600*a**3*f*tan(e/2 + f*x/2)**3 + 360*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) - 5420*A*c**4*tan(e/2 + f*x/2)**6/(30*a**3*f*tan(e/2 + f*x/2)**9 + 150*a**3*f*tan(e/2 + f*x/2)**8 + 360*a**3*f*tan(e/2 + f*x/2)**7 + 600*a**3*f*tan(e/2 + f*x/2)**6 + 780*a**3*f*tan(e/2 + f*x/2)**5 + 780*a**3*f*tan(e/2 + f*x/2)**4 + 600*a**3*f*tan(e/2 + f*x/2)**3 + 360*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) - 7060*A*c**4*tan(e/2 + f*x/2)**5/(30*a**3*f*tan(e/2 + f*x/2)**9 + 150*a**3*f*tan(e/2 + f*x/2)**8 + 360*a**3*f*tan(e/2 + f*x/2)**7 + 600*a**3*f*tan(e/2 + f*x/2)**6 + 780*a**3*f*tan(e/2 + f*x/2)**5 + 780*a**3*f*tan(e/2 + f*x/2)**4 + 600*a**3*f*tan(e/2 + f*x/2)**3 + 360*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) - 10308*A*c**4*tan(e/2 + f*x/2)**4/(30*a**3*f*tan(e/2 + f*x/2)**9 + 150*a**3*f*tan(e/2 + f*x/2)**8 + 360*a**3*f*tan(e/2 + f*x/2)**7 + 600*a**3*f*tan(e/2 + f*x/2)**6 + 780*a**3*f*tan(e/2 + f*x/2)**5 + 780*a**3*f*tan(e/2 + f*x/2)**4 + 600*a**3*f*tan(e/2 + f*x/2)**3 + 360*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) - 7940*A*c**4*tan(e/2 + f*x/2)**3/(30*a**3*f*tan(e/2 + f*x/2)**9 + 150*a**3*f*tan(e/2 + f*x/2)**8 + 360*a**3*f*tan(e/2 + f*x/2)**7 + 600*a**3*f*tan(e/2 + f*x/2)**6 + 780*a**3*f*tan(e/2 + f*x/2)**5 + 780*a**3*f*tan(e/2 + f*x/2)**4 + 600*a**3*f*tan(e/2 + f*x/2)**3 + 360*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) - 6036*A*c**4*tan(e/2 + f*x/2)**2/(30*a**3*f*tan(e/2 + f*x/2)**9 + 150*a**3*f*tan(e/2 + f*x/2)**8 + 360*a**3*f*tan(e/2 + f*x/2)**7 + 600*a**3*f*tan(e/2 + f*x/2)**6 + 780*a**3*f*tan(e/2 + f*x/2)**5 + 780*a**3*f*tan(e/2 + f*x/2)**4 + 600*a**3*f*tan(e/2 + f*x/2)**3 + 360*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) - 2860*A*c**4*tan(e/2 + f*x/2)/(30*a**3*f*tan(e/2 + f*x/2)**9 + 150*a**3*f*tan(e/2 + f*x/2)**8 + 360*a**3*f*tan(e/2 + f*x/2)**7 + 600*a**3*f*tan(e/2 + f*x/2)**6 + 780*a**3*f*tan(e/2 + f*x/2)**5 + 780*a**3*f*tan(e/2 + f*x/2)**4 + 600*a**3*f*tan(e/2 + f*x/2)**3 + 360*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) - 668*A*c**4/(30*a**3*f*tan(e/2 + f*x/2)**9 + 150*a**3*f*tan(e/2 + f*x/2)**8 + 360*a**3*f*tan(e/2 + f*x/2)**7 + 600*a**3*f*tan(e/2 + f*x/2)**6 + 780*a**3*f*tan(e/2 + f*x/2)**5 + 780*a**3*f*tan(e/2 + f*x/2)**4 + 600*a**3*f*tan(e/2 + f*x/2)**3 + 360*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) + 735*B*c**4*f*x*tan(e/2 + f*x/2)**9/(30*a**3*f*tan(e/2 + f*x/2)**9 + 150*a**3*f*tan(e/2 + f*x/2)**8 + 360*a**3*f*tan(e/2 + f*x/2)**7 + 600*a**3*f*tan(e/2 + f*x/2)**6 + 780*a**3*f*tan(e/2 + f*x/2)**5 + 780*a**3*f*tan(e/2 + f*x/2)**4 + 600*a**3*f*tan(e/2 + f*x/2)**3 + 360*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) + 3675*B*c**4*f*x*tan(e/2 + f*x/2)**8/(30*a**3*f*tan(e/2 + f*x/2)**9 + 150*a**3*f*tan(e/2 + f*x/2)**8 + 360*a**3*f*tan(e/2 + f*x/2)**7 + 600*a**3*f*tan(e/2 + f*x/2)**6 + 780*a**3*f*tan(e/2 + f*x/2)**5 + 780*a**3*f*tan(e/2 + f*x/2)**4 + 600*a**3*f*tan(e/2 + f*x/2)**3 + 360*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) + 8820*B*c**4*f*x*tan(e/2 + f*x/2)**7/(30*a**3*f*tan(e/2 + f*x/2)**9 + 150*a**3*f*tan(e/2 + f*x/2)**8 + 360*a**3*f*tan(e/2 + f*x/2)**7 + 600*a**3*f*tan(e/2 + f*x/2)**6 + 780*a**3*f*tan(e/2 + f*x/2)**5 + 780*a**3*f*tan(e/2 + f*x/2)**4 + 600*a**3*f*tan(e/2 + f*x/2)**3 + 360*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) + 14700*B*c**4*f*x*tan(e/2 + f*x/2)**6/(30*a**3*f*tan(e/2 + f*x/2)**9 + 150*a**3*f*tan(e/2 + f*x/2)**8 + 360*a**3*f*tan(e/2 + f*x/2)**7 + 600*a**3*f*tan(e/2 + f*x/2)**6 + 780*a**3*f*tan(e/2 + f*x/2)**5 + 780*a**3*f*tan(e/2 + f*x/2)**4 + 600*a**3*f*tan(e/2 + f*x/2)**3 + 360*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) + 19110*B*c**4*f*x*tan(e/2 + f*x/2)**5/(30*a**3*f*tan(e/2 + f*x/2)**9 + 150*a**3*f*tan(e/2 + f*x/2)**8 + 360*a**3*f*tan(e/2 + f*x/2)**7 + 600*a**3*f*tan(e/2 + f*x/2)**6 + 780*a**3*f*tan(e/2 + f*x/2)**5 + 780*a**3*f*tan(e/2 + f*x/2)**4 + 600*a**3*f*tan(e/2 + f*x/2)**3 + 360*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) + 19110*B*c**4*f*x*tan(e/2 + f*x/2)**4/(30*a**3*f*tan(e/2 + f*x/2)**9 + 150*a**3*f*tan(e/2 + f*x/2)**8 + 360*a**3*f*tan(e/2 + f*x/2)**7 + 600*a**3*f*tan(e/2 + f*x/2)**6 + 780*a**3*f*tan(e/2 + f*x/2)**5 + 780*a**3*f*tan(e/2 + f*x/2)**4 + 600*a**3*f*tan(e/2 + f*x/2)**3 + 360*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) + 14700*B*c**4*f*x*tan(e/2 + f*x/2)**3/(30*a**3*f*tan(e/2 + f*x/2)**9 + 150*a**3*f*tan(e/2 + f*x/2)**8 + 360*a**3*f*tan(e/2 + f*x/2)**7 + 600*a**3*f*tan(e/2 + f*x/2)**6 + 780*a**3*f*tan(e/2 + f*x/2)**5 + 780*a**3*f*tan(e/2 + f*x/2)**4 + 600*a**3*f*tan(e/2 + f*x/2)**3 + 360*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) + 8820*B*c**4*f*x*tan(e/2 + f*x/2)**2/(30*a**3*f*tan(e/2 + f*x/2)**9 + 150*a**3*f*tan(e/2 + f*x/2)**8 + 360*a**3*f*tan(e/2 + f*x/2)**7 + 600*a**3*f*tan(e/2 + f*x/2)**6 + 780*a**3*f*tan(e/2 + f*x/2)**5 + 780*a**3*f*tan(e/2 + f*x/2)**4 + 600*a**3*f*tan(e/2 + f*x/2)**3 + 360*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) + 3675*B*c**4*f*x*tan(e/2 + f*x/2)/(30*a**3*f*tan(e/2 + f*x/2)**9 + 150*a**3*f*tan(e/2 + f*x/2)**8 + 360*a**3*f*tan(e/2 + f*x/2)**7 + 600*a**3*f*tan(e/2 + f*x/2)**6 + 780*a**3*f*tan(e/2 + f*x/2)**5 + 780*a**3*f*tan(e/2 + f*x/2)**4 + 600*a**3*f*tan(e/2 + f*x/2)**3 + 360*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) + 735*B*c**4*f*x/(30*a**3*f*tan(e/2 + f*x/2)**9 + 150*a**3*f*tan(e/2 + f*x/2)**8 + 360*a**3*f*tan(e/2 + f*x/2)**7 + 600*a**3*f*tan(e/2 + f*x/2)**6 + 780*a**3*f*tan(e/2 + f*x/2)**5 + 780*a**3*f*tan(e/2 + f*x/2)**4 + 600*a**3*f*tan(e/2 + f*x/2)**3 + 360*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) + 1470*B*c**4*tan(e/2 + f*x/2)**8/(30*a**3*f*tan(e/2 + f*x/2)**9 + 150*a**3*f*tan(e/2 + f*x/2)**8 + 360*a**3*f*tan(e/2 + f*x/2)**7 + 600*a**3*f*tan(e/2 + f*x/2)**6 + 780*a**3*f*tan(e/2 + f*x/2)**5 + 780*a**3*f*tan(e/2 + f*x/2)**4 + 600*a**3*f*tan(e/2 + f*x/2)**3 + 360*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) + 7290*B*c**4*tan(e/2 + f*x/2)**7/(30*a**3*f*tan(e/2 + f*x/2)**9 + 150*a**3*f*tan(e/2 + f*x/2)**8 + 360*a**3*f*tan(e/2 + f*x/2)**7 + 600*a**3*f*tan(e/2 + f*x/2)**6 + 780*a**3*f*tan(e/2 + f*x/2)**5 + 780*a**3*f*tan(e/2 + f*x/2)**4 + 600*a**3*f*tan(e/2 + f*x/2)**3 + 360*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) + 17410*B*c**4*tan(e/2 + f*x/2)**6/(30*a**3*f*tan(e/2 + f*x/2)**9 + 150*a**3*f*tan(e/2 + f*x/2)**8 + 360*a**3*f*tan(e/2 + f*x/2)**7 + 600*a**3*f*tan(e/2 + f*x/2)**6 + 780*a**3*f*tan(e/2 + f*x/2)**5 + 780*a**3*f*tan(e/2 + f*x/2)**4 + 600*a**3*f*tan(e/2 + f*x/2)**3 + 360*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) + 26210*B*c**4*tan(e/2 + f*x/2)**5/(30*a**3*f*tan(e/2 + f*x/2)**9 + 150*a**3*f*tan(e/2 + f*x/2)**8 + 360*a**3*f*tan(e/2 + f*x/2)**7 + 600*a**3*f*tan(e/2 + f*x/2)**6 + 780*a**3*f*tan(e/2 + f*x/2)**5 + 780*a**3*f*tan(e/2 + f*x/2)**4 + 600*a**3*f*tan(e/2 + f*x/2)**3 + 360*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) + 33798*B*c**4*tan(e/2 + f*x/2)**4/(30*a**3*f*tan(e/2 + f*x/2)**9 + 150*a**3*f*tan(e/2 + f*x/2)**8 + 360*a**3*f*tan(e/2 + f*x/2)**7 + 600*a**3*f*tan(e/2 + f*x/2)**6 + 780*a**3*f*tan(e/2 + f*x/2)**5 + 780*a**3*f*tan(e/2 + f*x/2)**4 + 600*a**3*f*tan(e/2 + f*x/2)**3 + 360*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) + 28750*B*c**4*tan(e/2 + f*x/2)**3/(30*a**3*f*tan(e/2 + f*x/2)**9 + 150*a**3*f*tan(e/2 + f*x/2)**8 + 360*a**3*f*tan(e/2 + f*x/2)**7 + 600*a**3*f*tan(e/2 + f*x/2)**6 + 780*a**3*f*tan(e/2 + f*x/2)**5 + 780*a**3*f*tan(e/2 + f*x/2)**4 + 600*a**3*f*tan(e/2 + f*x/2)**3 + 360*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) + 20406*B*c**4*tan(e/2 + f*x/2)**2/(30*a**3*f*tan(e/2 + f*x/2)**9 + 150*a**3*f*tan(e/2 + f*x/2)**8 + 360*a**3*f*tan(e/2 + f*x/2)**7 + 600*a**3*f*tan(e/2 + f*x/2)**6 + 780*a**3*f*tan(e/2 + f*x/2)**5 + 780*a**3*f*tan(e/2 + f*x/2)**4 + 600*a**3*f*tan(e/2 + f*x/2)**3 + 360*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) + 10070*B*c**4*tan(e/2 + f*x/2)/(30*a**3*f*tan(e/2 + f*x/2)**9 + 150*a**3*f*tan(e/2 + f*x/2)**8 + 360*a**3*f*tan(e/2 + f*x/2)**7 + 600*a**3*f*tan(e/2 + f*x/2)**6 + 780*a**3*f*tan(e/2 + f*x/2)**5 + 780*a**3*f*tan(e/2 + f*x/2)**4 + 600*a**3*f*tan(e/2 + f*x/2)**3 + 360*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f) + 2308*B*c**4/(30*a**3*f*tan(e/2 + f*x/2)**9 + 150*a**3*f*tan(e/2 + f*x/2)**8 + 360*a**3*f*tan(e/2 + f*x/2)**7 + 600*a**3*f*tan(e/2 + f*x/2)**6 + 780*a**3*f*tan(e/2 + f*x/2)**5 + 780*a**3*f*tan(e/2 + f*x/2)**4 + 600*a**3*f*tan(e/2 + f*x/2)**3 + 360*a**3*f*tan(e/2 + f*x/2)**2 + 150*a**3*f*tan(e/2 + f*x/2) + 30*a**3*f), Ne(f, 0)), (x*(A + B*sin(e))*(-c*sin(e) + c)**4/(a*sin(e) + a)**3, True))","A",0
72,1,4665,0,46.581919," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))**3/(a+a*sin(f*x+e))**3,x)","\begin{cases} - \frac{15 A c^{3} f x \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{75 A c^{3} f x \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{165 A c^{3} f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{225 A c^{3} f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{225 A c^{3} f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{165 A c^{3} f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{75 A c^{3} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{15 A c^{3} f x}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{60 A c^{3} \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{120 A c^{3} \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{460 A c^{3} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{320 A c^{3} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{452 A c^{3} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{200 A c^{3} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{52 A c^{3}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{90 B c^{3} f x \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{450 B c^{3} f x \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{990 B c^{3} f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{1350 B c^{3} f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{1350 B c^{3} f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{990 B c^{3} f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{450 B c^{3} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{90 B c^{3} f x}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{180 B c^{3} \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{870 B c^{3} \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{2010 B c^{3} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{2220 B c^{3} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{2232 B c^{3} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{1230 B c^{3} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{282 B c^{3}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right) \left(- c \sin{\left(e \right)} + c\right)^{3}}{\left(a \sin{\left(e \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-15*A*c**3*f*x*tan(e/2 + f*x/2)**7/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 75*A*c**3*f*x*tan(e/2 + f*x/2)**6/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 165*A*c**3*f*x*tan(e/2 + f*x/2)**5/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 225*A*c**3*f*x*tan(e/2 + f*x/2)**4/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 225*A*c**3*f*x*tan(e/2 + f*x/2)**3/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 165*A*c**3*f*x*tan(e/2 + f*x/2)**2/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 75*A*c**3*f*x*tan(e/2 + f*x/2)/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 15*A*c**3*f*x/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 60*A*c**3*tan(e/2 + f*x/2)**6/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 120*A*c**3*tan(e/2 + f*x/2)**5/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 460*A*c**3*tan(e/2 + f*x/2)**4/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 320*A*c**3*tan(e/2 + f*x/2)**3/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 452*A*c**3*tan(e/2 + f*x/2)**2/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 200*A*c**3*tan(e/2 + f*x/2)/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 52*A*c**3/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 90*B*c**3*f*x*tan(e/2 + f*x/2)**7/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 450*B*c**3*f*x*tan(e/2 + f*x/2)**6/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 990*B*c**3*f*x*tan(e/2 + f*x/2)**5/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 1350*B*c**3*f*x*tan(e/2 + f*x/2)**4/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 1350*B*c**3*f*x*tan(e/2 + f*x/2)**3/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 990*B*c**3*f*x*tan(e/2 + f*x/2)**2/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 450*B*c**3*f*x*tan(e/2 + f*x/2)/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 90*B*c**3*f*x/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 180*B*c**3*tan(e/2 + f*x/2)**6/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 870*B*c**3*tan(e/2 + f*x/2)**5/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 2010*B*c**3*tan(e/2 + f*x/2)**4/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 2220*B*c**3*tan(e/2 + f*x/2)**3/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 2232*B*c**3*tan(e/2 + f*x/2)**2/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 1230*B*c**3*tan(e/2 + f*x/2)/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 282*B*c**3/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f), Ne(f, 0)), (x*(A + B*sin(e))*(-c*sin(e) + c)**3/(a*sin(e) + a)**3, True))","A",0
73,1,1647,0,26.026251," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))**2/(a+a*sin(f*x+e))**3,x)","\begin{cases} - \frac{30 A c^{2} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{60 A c^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{6 A c^{2}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{15 B c^{2} f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{75 B c^{2} f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{150 B c^{2} f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{150 B c^{2} f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{75 B c^{2} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{15 B c^{2} f x}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{30 B c^{2} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{120 B c^{2} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{340 B c^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{200 B c^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{46 B c^{2}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right) \left(- c \sin{\left(e \right)} + c\right)^{2}}{\left(a \sin{\left(e \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-30*A*c**2*tan(e/2 + f*x/2)**4/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 60*A*c**2*tan(e/2 + f*x/2)**2/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 6*A*c**2/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 15*B*c**2*f*x*tan(e/2 + f*x/2)**5/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 75*B*c**2*f*x*tan(e/2 + f*x/2)**4/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 150*B*c**2*f*x*tan(e/2 + f*x/2)**3/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 150*B*c**2*f*x*tan(e/2 + f*x/2)**2/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 75*B*c**2*f*x*tan(e/2 + f*x/2)/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 15*B*c**2*f*x/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 30*B*c**2*tan(e/2 + f*x/2)**4/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 120*B*c**2*tan(e/2 + f*x/2)**3/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 340*B*c**2*tan(e/2 + f*x/2)**2/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 200*B*c**2*tan(e/2 + f*x/2)/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 46*B*c**2/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f), Ne(f, 0)), (x*(A + B*sin(e))*(-c*sin(e) + c)**2/(a*sin(e) + a)**3, True))","A",0
74,1,1035,0,13.789141," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))/(a+a*sin(f*x+e))**3,x)","\begin{cases} - \frac{30 A c \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{30 A c \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{50 A c \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{10 A c \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{8 A c}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{30 B c \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{10 B c \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{10 B c \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{2 B c}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right) \left(- c \sin{\left(e \right)} + c\right)}{\left(a \sin{\left(e \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-30*A*c*tan(e/2 + f*x/2)**4/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 30*A*c*tan(e/2 + f*x/2)**3/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 50*A*c*tan(e/2 + f*x/2)**2/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 10*A*c*tan(e/2 + f*x/2)/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 8*A*c/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 30*B*c*tan(e/2 + f*x/2)**3/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 10*B*c*tan(e/2 + f*x/2)**2/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 10*B*c*tan(e/2 + f*x/2)/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 2*B*c/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f), Ne(f, 0)), (x*(A + B*sin(e))*(-c*sin(e) + c)/(a*sin(e) + a)**3, True))","A",0
75,1,1236,0,14.444517," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))**3/(c-c*sin(f*x+e)),x)","\begin{cases} - \frac{30 A \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} c f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{3} c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 a^{3} c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 60 a^{3} c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{3} c f} - \frac{60 A \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} c f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{3} c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 a^{3} c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 60 a^{3} c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{3} c f} - \frac{60 A \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} c f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{3} c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 a^{3} c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 60 a^{3} c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{3} c f} + \frac{18 A \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} c f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{3} c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 a^{3} c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 60 a^{3} c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{3} c f} + \frac{12 A}{15 a^{3} c f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{3} c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 a^{3} c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 60 a^{3} c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{3} c f} - \frac{30 B \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} c f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{3} c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 a^{3} c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 60 a^{3} c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{3} c f} - \frac{40 B \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} c f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{3} c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 a^{3} c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 60 a^{3} c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{3} c f} - \frac{40 B \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} c f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{3} c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 a^{3} c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 60 a^{3} c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{3} c f} - \frac{8 B \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} c f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{3} c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 a^{3} c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 60 a^{3} c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{3} c f} - \frac{2 B}{15 a^{3} c f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 60 a^{3} c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 a^{3} c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 60 a^{3} c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{3} c f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right)}{\left(a \sin{\left(e \right)} + a\right)^{3} \left(- c \sin{\left(e \right)} + c\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-30*A*tan(e/2 + f*x/2)**5/(15*a**3*c*f*tan(e/2 + f*x/2)**6 + 60*a**3*c*f*tan(e/2 + f*x/2)**5 + 75*a**3*c*f*tan(e/2 + f*x/2)**4 - 75*a**3*c*f*tan(e/2 + f*x/2)**2 - 60*a**3*c*f*tan(e/2 + f*x/2) - 15*a**3*c*f) - 60*A*tan(e/2 + f*x/2)**4/(15*a**3*c*f*tan(e/2 + f*x/2)**6 + 60*a**3*c*f*tan(e/2 + f*x/2)**5 + 75*a**3*c*f*tan(e/2 + f*x/2)**4 - 75*a**3*c*f*tan(e/2 + f*x/2)**2 - 60*a**3*c*f*tan(e/2 + f*x/2) - 15*a**3*c*f) - 60*A*tan(e/2 + f*x/2)**3/(15*a**3*c*f*tan(e/2 + f*x/2)**6 + 60*a**3*c*f*tan(e/2 + f*x/2)**5 + 75*a**3*c*f*tan(e/2 + f*x/2)**4 - 75*a**3*c*f*tan(e/2 + f*x/2)**2 - 60*a**3*c*f*tan(e/2 + f*x/2) - 15*a**3*c*f) + 18*A*tan(e/2 + f*x/2)/(15*a**3*c*f*tan(e/2 + f*x/2)**6 + 60*a**3*c*f*tan(e/2 + f*x/2)**5 + 75*a**3*c*f*tan(e/2 + f*x/2)**4 - 75*a**3*c*f*tan(e/2 + f*x/2)**2 - 60*a**3*c*f*tan(e/2 + f*x/2) - 15*a**3*c*f) + 12*A/(15*a**3*c*f*tan(e/2 + f*x/2)**6 + 60*a**3*c*f*tan(e/2 + f*x/2)**5 + 75*a**3*c*f*tan(e/2 + f*x/2)**4 - 75*a**3*c*f*tan(e/2 + f*x/2)**2 - 60*a**3*c*f*tan(e/2 + f*x/2) - 15*a**3*c*f) - 30*B*tan(e/2 + f*x/2)**4/(15*a**3*c*f*tan(e/2 + f*x/2)**6 + 60*a**3*c*f*tan(e/2 + f*x/2)**5 + 75*a**3*c*f*tan(e/2 + f*x/2)**4 - 75*a**3*c*f*tan(e/2 + f*x/2)**2 - 60*a**3*c*f*tan(e/2 + f*x/2) - 15*a**3*c*f) - 40*B*tan(e/2 + f*x/2)**3/(15*a**3*c*f*tan(e/2 + f*x/2)**6 + 60*a**3*c*f*tan(e/2 + f*x/2)**5 + 75*a**3*c*f*tan(e/2 + f*x/2)**4 - 75*a**3*c*f*tan(e/2 + f*x/2)**2 - 60*a**3*c*f*tan(e/2 + f*x/2) - 15*a**3*c*f) - 40*B*tan(e/2 + f*x/2)**2/(15*a**3*c*f*tan(e/2 + f*x/2)**6 + 60*a**3*c*f*tan(e/2 + f*x/2)**5 + 75*a**3*c*f*tan(e/2 + f*x/2)**4 - 75*a**3*c*f*tan(e/2 + f*x/2)**2 - 60*a**3*c*f*tan(e/2 + f*x/2) - 15*a**3*c*f) - 8*B*tan(e/2 + f*x/2)/(15*a**3*c*f*tan(e/2 + f*x/2)**6 + 60*a**3*c*f*tan(e/2 + f*x/2)**5 + 75*a**3*c*f*tan(e/2 + f*x/2)**4 - 75*a**3*c*f*tan(e/2 + f*x/2)**2 - 60*a**3*c*f*tan(e/2 + f*x/2) - 15*a**3*c*f) - 2*B/(15*a**3*c*f*tan(e/2 + f*x/2)**6 + 60*a**3*c*f*tan(e/2 + f*x/2)**5 + 75*a**3*c*f*tan(e/2 + f*x/2)**4 - 75*a**3*c*f*tan(e/2 + f*x/2)**2 - 60*a**3*c*f*tan(e/2 + f*x/2) - 15*a**3*c*f), Ne(f, 0)), (x*(A + B*sin(e))/((a*sin(e) + a)**3*(-c*sin(e) + c)), True))","A",0
76,1,2674,0,27.388684," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))**3/(c-c*sin(f*x+e))**2,x)","\begin{cases} - \frac{30 A \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} c^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} c^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{3} c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 90 a^{3} c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 90 a^{3} c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{3} c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{3} c^{2} f} - \frac{30 A \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} c^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} c^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{3} c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 90 a^{3} c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 90 a^{3} c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{3} c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{3} c^{2} f} + \frac{10 A \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} c^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} c^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{3} c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 90 a^{3} c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 90 a^{3} c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{3} c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{3} c^{2} f} + \frac{50 A \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} c^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} c^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{3} c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 90 a^{3} c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 90 a^{3} c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{3} c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{3} c^{2} f} - \frac{26 A \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} c^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} c^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{3} c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 90 a^{3} c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 90 a^{3} c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{3} c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{3} c^{2} f} - \frac{42 A \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} c^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} c^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{3} c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 90 a^{3} c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 90 a^{3} c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{3} c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{3} c^{2} f} - \frac{18 A \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} c^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} c^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{3} c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 90 a^{3} c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 90 a^{3} c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{3} c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{3} c^{2} f} + \frac{6 A}{15 a^{3} c^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} c^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{3} c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 90 a^{3} c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 90 a^{3} c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{3} c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{3} c^{2} f} - \frac{30 B \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} c^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} c^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{3} c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 90 a^{3} c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 90 a^{3} c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{3} c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{3} c^{2} f} - \frac{20 B \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} c^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} c^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{3} c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 90 a^{3} c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 90 a^{3} c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{3} c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{3} c^{2} f} - \frac{10 B \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} c^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} c^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{3} c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 90 a^{3} c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 90 a^{3} c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{3} c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{3} c^{2} f} + \frac{16 B \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} c^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} c^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{3} c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 90 a^{3} c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 90 a^{3} c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{3} c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{3} c^{2} f} - \frac{18 B \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} c^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} c^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{3} c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 90 a^{3} c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 90 a^{3} c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{3} c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{3} c^{2} f} - \frac{12 B \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} c^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} c^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{3} c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 90 a^{3} c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 90 a^{3} c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{3} c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{3} c^{2} f} - \frac{6 B}{15 a^{3} c^{2} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} c^{2} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{3} c^{2} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 90 a^{3} c^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 90 a^{3} c^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 30 a^{3} c^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 30 a^{3} c^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{3} c^{2} f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right)}{\left(a \sin{\left(e \right)} + a\right)^{3} \left(- c \sin{\left(e \right)} + c\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-30*A*tan(e/2 + f*x/2)**7/(15*a**3*c**2*f*tan(e/2 + f*x/2)**8 + 30*a**3*c**2*f*tan(e/2 + f*x/2)**7 - 30*a**3*c**2*f*tan(e/2 + f*x/2)**6 - 90*a**3*c**2*f*tan(e/2 + f*x/2)**5 + 90*a**3*c**2*f*tan(e/2 + f*x/2)**3 + 30*a**3*c**2*f*tan(e/2 + f*x/2)**2 - 30*a**3*c**2*f*tan(e/2 + f*x/2) - 15*a**3*c**2*f) - 30*A*tan(e/2 + f*x/2)**6/(15*a**3*c**2*f*tan(e/2 + f*x/2)**8 + 30*a**3*c**2*f*tan(e/2 + f*x/2)**7 - 30*a**3*c**2*f*tan(e/2 + f*x/2)**6 - 90*a**3*c**2*f*tan(e/2 + f*x/2)**5 + 90*a**3*c**2*f*tan(e/2 + f*x/2)**3 + 30*a**3*c**2*f*tan(e/2 + f*x/2)**2 - 30*a**3*c**2*f*tan(e/2 + f*x/2) - 15*a**3*c**2*f) + 10*A*tan(e/2 + f*x/2)**5/(15*a**3*c**2*f*tan(e/2 + f*x/2)**8 + 30*a**3*c**2*f*tan(e/2 + f*x/2)**7 - 30*a**3*c**2*f*tan(e/2 + f*x/2)**6 - 90*a**3*c**2*f*tan(e/2 + f*x/2)**5 + 90*a**3*c**2*f*tan(e/2 + f*x/2)**3 + 30*a**3*c**2*f*tan(e/2 + f*x/2)**2 - 30*a**3*c**2*f*tan(e/2 + f*x/2) - 15*a**3*c**2*f) + 50*A*tan(e/2 + f*x/2)**4/(15*a**3*c**2*f*tan(e/2 + f*x/2)**8 + 30*a**3*c**2*f*tan(e/2 + f*x/2)**7 - 30*a**3*c**2*f*tan(e/2 + f*x/2)**6 - 90*a**3*c**2*f*tan(e/2 + f*x/2)**5 + 90*a**3*c**2*f*tan(e/2 + f*x/2)**3 + 30*a**3*c**2*f*tan(e/2 + f*x/2)**2 - 30*a**3*c**2*f*tan(e/2 + f*x/2) - 15*a**3*c**2*f) - 26*A*tan(e/2 + f*x/2)**3/(15*a**3*c**2*f*tan(e/2 + f*x/2)**8 + 30*a**3*c**2*f*tan(e/2 + f*x/2)**7 - 30*a**3*c**2*f*tan(e/2 + f*x/2)**6 - 90*a**3*c**2*f*tan(e/2 + f*x/2)**5 + 90*a**3*c**2*f*tan(e/2 + f*x/2)**3 + 30*a**3*c**2*f*tan(e/2 + f*x/2)**2 - 30*a**3*c**2*f*tan(e/2 + f*x/2) - 15*a**3*c**2*f) - 42*A*tan(e/2 + f*x/2)**2/(15*a**3*c**2*f*tan(e/2 + f*x/2)**8 + 30*a**3*c**2*f*tan(e/2 + f*x/2)**7 - 30*a**3*c**2*f*tan(e/2 + f*x/2)**6 - 90*a**3*c**2*f*tan(e/2 + f*x/2)**5 + 90*a**3*c**2*f*tan(e/2 + f*x/2)**3 + 30*a**3*c**2*f*tan(e/2 + f*x/2)**2 - 30*a**3*c**2*f*tan(e/2 + f*x/2) - 15*a**3*c**2*f) - 18*A*tan(e/2 + f*x/2)/(15*a**3*c**2*f*tan(e/2 + f*x/2)**8 + 30*a**3*c**2*f*tan(e/2 + f*x/2)**7 - 30*a**3*c**2*f*tan(e/2 + f*x/2)**6 - 90*a**3*c**2*f*tan(e/2 + f*x/2)**5 + 90*a**3*c**2*f*tan(e/2 + f*x/2)**3 + 30*a**3*c**2*f*tan(e/2 + f*x/2)**2 - 30*a**3*c**2*f*tan(e/2 + f*x/2) - 15*a**3*c**2*f) + 6*A/(15*a**3*c**2*f*tan(e/2 + f*x/2)**8 + 30*a**3*c**2*f*tan(e/2 + f*x/2)**7 - 30*a**3*c**2*f*tan(e/2 + f*x/2)**6 - 90*a**3*c**2*f*tan(e/2 + f*x/2)**5 + 90*a**3*c**2*f*tan(e/2 + f*x/2)**3 + 30*a**3*c**2*f*tan(e/2 + f*x/2)**2 - 30*a**3*c**2*f*tan(e/2 + f*x/2) - 15*a**3*c**2*f) - 30*B*tan(e/2 + f*x/2)**6/(15*a**3*c**2*f*tan(e/2 + f*x/2)**8 + 30*a**3*c**2*f*tan(e/2 + f*x/2)**7 - 30*a**3*c**2*f*tan(e/2 + f*x/2)**6 - 90*a**3*c**2*f*tan(e/2 + f*x/2)**5 + 90*a**3*c**2*f*tan(e/2 + f*x/2)**3 + 30*a**3*c**2*f*tan(e/2 + f*x/2)**2 - 30*a**3*c**2*f*tan(e/2 + f*x/2) - 15*a**3*c**2*f) - 20*B*tan(e/2 + f*x/2)**5/(15*a**3*c**2*f*tan(e/2 + f*x/2)**8 + 30*a**3*c**2*f*tan(e/2 + f*x/2)**7 - 30*a**3*c**2*f*tan(e/2 + f*x/2)**6 - 90*a**3*c**2*f*tan(e/2 + f*x/2)**5 + 90*a**3*c**2*f*tan(e/2 + f*x/2)**3 + 30*a**3*c**2*f*tan(e/2 + f*x/2)**2 - 30*a**3*c**2*f*tan(e/2 + f*x/2) - 15*a**3*c**2*f) - 10*B*tan(e/2 + f*x/2)**4/(15*a**3*c**2*f*tan(e/2 + f*x/2)**8 + 30*a**3*c**2*f*tan(e/2 + f*x/2)**7 - 30*a**3*c**2*f*tan(e/2 + f*x/2)**6 - 90*a**3*c**2*f*tan(e/2 + f*x/2)**5 + 90*a**3*c**2*f*tan(e/2 + f*x/2)**3 + 30*a**3*c**2*f*tan(e/2 + f*x/2)**2 - 30*a**3*c**2*f*tan(e/2 + f*x/2) - 15*a**3*c**2*f) + 16*B*tan(e/2 + f*x/2)**3/(15*a**3*c**2*f*tan(e/2 + f*x/2)**8 + 30*a**3*c**2*f*tan(e/2 + f*x/2)**7 - 30*a**3*c**2*f*tan(e/2 + f*x/2)**6 - 90*a**3*c**2*f*tan(e/2 + f*x/2)**5 + 90*a**3*c**2*f*tan(e/2 + f*x/2)**3 + 30*a**3*c**2*f*tan(e/2 + f*x/2)**2 - 30*a**3*c**2*f*tan(e/2 + f*x/2) - 15*a**3*c**2*f) - 18*B*tan(e/2 + f*x/2)**2/(15*a**3*c**2*f*tan(e/2 + f*x/2)**8 + 30*a**3*c**2*f*tan(e/2 + f*x/2)**7 - 30*a**3*c**2*f*tan(e/2 + f*x/2)**6 - 90*a**3*c**2*f*tan(e/2 + f*x/2)**5 + 90*a**3*c**2*f*tan(e/2 + f*x/2)**3 + 30*a**3*c**2*f*tan(e/2 + f*x/2)**2 - 30*a**3*c**2*f*tan(e/2 + f*x/2) - 15*a**3*c**2*f) - 12*B*tan(e/2 + f*x/2)/(15*a**3*c**2*f*tan(e/2 + f*x/2)**8 + 30*a**3*c**2*f*tan(e/2 + f*x/2)**7 - 30*a**3*c**2*f*tan(e/2 + f*x/2)**6 - 90*a**3*c**2*f*tan(e/2 + f*x/2)**5 + 90*a**3*c**2*f*tan(e/2 + f*x/2)**3 + 30*a**3*c**2*f*tan(e/2 + f*x/2)**2 - 30*a**3*c**2*f*tan(e/2 + f*x/2) - 15*a**3*c**2*f) - 6*B/(15*a**3*c**2*f*tan(e/2 + f*x/2)**8 + 30*a**3*c**2*f*tan(e/2 + f*x/2)**7 - 30*a**3*c**2*f*tan(e/2 + f*x/2)**6 - 90*a**3*c**2*f*tan(e/2 + f*x/2)**5 + 90*a**3*c**2*f*tan(e/2 + f*x/2)**3 + 30*a**3*c**2*f*tan(e/2 + f*x/2)**2 - 30*a**3*c**2*f*tan(e/2 + f*x/2) - 15*a**3*c**2*f), Ne(f, 0)), (x*(A + B*sin(e))/((a*sin(e) + a)**3*(-c*sin(e) + c)**2), True))","A",0
77,1,1098,0,20.934353," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))**3/(c-c*sin(f*x+e))**3,x)","\begin{cases} - \frac{30 A \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} c^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 a^{3} c^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 150 a^{3} c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{3} c^{3} f} + \frac{40 A \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} c^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 a^{3} c^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 150 a^{3} c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{3} c^{3} f} - \frac{116 A \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} c^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 a^{3} c^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 150 a^{3} c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{3} c^{3} f} + \frac{40 A \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} c^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 a^{3} c^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 150 a^{3} c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{3} c^{3} f} - \frac{30 A \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} c^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 a^{3} c^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 150 a^{3} c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{3} c^{3} f} - \frac{30 B \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} c^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 a^{3} c^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 150 a^{3} c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{3} c^{3} f} - \frac{60 B \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} c^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 a^{3} c^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 150 a^{3} c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{3} c^{3} f} - \frac{6 B}{15 a^{3} c^{3} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 75 a^{3} c^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 150 a^{3} c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 15 a^{3} c^{3} f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right)}{\left(a \sin{\left(e \right)} + a\right)^{3} \left(- c \sin{\left(e \right)} + c\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-30*A*tan(e/2 + f*x/2)**9/(15*a**3*c**3*f*tan(e/2 + f*x/2)**10 - 75*a**3*c**3*f*tan(e/2 + f*x/2)**8 + 150*a**3*c**3*f*tan(e/2 + f*x/2)**6 - 150*a**3*c**3*f*tan(e/2 + f*x/2)**4 + 75*a**3*c**3*f*tan(e/2 + f*x/2)**2 - 15*a**3*c**3*f) + 40*A*tan(e/2 + f*x/2)**7/(15*a**3*c**3*f*tan(e/2 + f*x/2)**10 - 75*a**3*c**3*f*tan(e/2 + f*x/2)**8 + 150*a**3*c**3*f*tan(e/2 + f*x/2)**6 - 150*a**3*c**3*f*tan(e/2 + f*x/2)**4 + 75*a**3*c**3*f*tan(e/2 + f*x/2)**2 - 15*a**3*c**3*f) - 116*A*tan(e/2 + f*x/2)**5/(15*a**3*c**3*f*tan(e/2 + f*x/2)**10 - 75*a**3*c**3*f*tan(e/2 + f*x/2)**8 + 150*a**3*c**3*f*tan(e/2 + f*x/2)**6 - 150*a**3*c**3*f*tan(e/2 + f*x/2)**4 + 75*a**3*c**3*f*tan(e/2 + f*x/2)**2 - 15*a**3*c**3*f) + 40*A*tan(e/2 + f*x/2)**3/(15*a**3*c**3*f*tan(e/2 + f*x/2)**10 - 75*a**3*c**3*f*tan(e/2 + f*x/2)**8 + 150*a**3*c**3*f*tan(e/2 + f*x/2)**6 - 150*a**3*c**3*f*tan(e/2 + f*x/2)**4 + 75*a**3*c**3*f*tan(e/2 + f*x/2)**2 - 15*a**3*c**3*f) - 30*A*tan(e/2 + f*x/2)/(15*a**3*c**3*f*tan(e/2 + f*x/2)**10 - 75*a**3*c**3*f*tan(e/2 + f*x/2)**8 + 150*a**3*c**3*f*tan(e/2 + f*x/2)**6 - 150*a**3*c**3*f*tan(e/2 + f*x/2)**4 + 75*a**3*c**3*f*tan(e/2 + f*x/2)**2 - 15*a**3*c**3*f) - 30*B*tan(e/2 + f*x/2)**8/(15*a**3*c**3*f*tan(e/2 + f*x/2)**10 - 75*a**3*c**3*f*tan(e/2 + f*x/2)**8 + 150*a**3*c**3*f*tan(e/2 + f*x/2)**6 - 150*a**3*c**3*f*tan(e/2 + f*x/2)**4 + 75*a**3*c**3*f*tan(e/2 + f*x/2)**2 - 15*a**3*c**3*f) - 60*B*tan(e/2 + f*x/2)**4/(15*a**3*c**3*f*tan(e/2 + f*x/2)**10 - 75*a**3*c**3*f*tan(e/2 + f*x/2)**8 + 150*a**3*c**3*f*tan(e/2 + f*x/2)**6 - 150*a**3*c**3*f*tan(e/2 + f*x/2)**4 + 75*a**3*c**3*f*tan(e/2 + f*x/2)**2 - 15*a**3*c**3*f) - 6*B/(15*a**3*c**3*f*tan(e/2 + f*x/2)**10 - 75*a**3*c**3*f*tan(e/2 + f*x/2)**8 + 150*a**3*c**3*f*tan(e/2 + f*x/2)**6 - 150*a**3*c**3*f*tan(e/2 + f*x/2)**4 + 75*a**3*c**3*f*tan(e/2 + f*x/2)**2 - 15*a**3*c**3*f), Ne(f, 0)), (x*(A + B*sin(e))/((a*sin(e) + a)**3*(-c*sin(e) + c)**3), True))","A",0
78,1,6135,0,92.700595," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))**3/(c-c*sin(f*x+e))**4,x)","\begin{cases} - \frac{210 A \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 a^{3} c^{4} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 210 a^{3} c^{4} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 420 a^{3} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1050 a^{3} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 525 a^{3} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2100 a^{3} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2100 a^{3} c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 525 a^{3} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1050 a^{3} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 420 a^{3} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 210 a^{3} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 a^{3} c^{4} f} + \frac{210 A \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 a^{3} c^{4} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 210 a^{3} c^{4} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 420 a^{3} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1050 a^{3} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 525 a^{3} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2100 a^{3} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2100 a^{3} c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 525 a^{3} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1050 a^{3} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 420 a^{3} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 210 a^{3} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 a^{3} c^{4} f} + \frac{210 A \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 a^{3} c^{4} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 210 a^{3} c^{4} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 420 a^{3} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1050 a^{3} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 525 a^{3} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2100 a^{3} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2100 a^{3} c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 525 a^{3} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1050 a^{3} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 420 a^{3} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 210 a^{3} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 a^{3} c^{4} f} - \frac{630 A \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 a^{3} c^{4} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 210 a^{3} c^{4} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 420 a^{3} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1050 a^{3} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 525 a^{3} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2100 a^{3} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2100 a^{3} c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 525 a^{3} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1050 a^{3} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 420 a^{3} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 210 a^{3} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 a^{3} c^{4} f} - \frac{756 A \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 a^{3} c^{4} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 210 a^{3} c^{4} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 420 a^{3} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1050 a^{3} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 525 a^{3} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2100 a^{3} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2100 a^{3} c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 525 a^{3} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1050 a^{3} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 420 a^{3} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 210 a^{3} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 a^{3} c^{4} f} + \frac{1092 A \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 a^{3} c^{4} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 210 a^{3} c^{4} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 420 a^{3} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1050 a^{3} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 525 a^{3} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2100 a^{3} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2100 a^{3} c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 525 a^{3} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1050 a^{3} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 420 a^{3} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 210 a^{3} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 a^{3} c^{4} f} - \frac{156 A \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 a^{3} c^{4} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 210 a^{3} c^{4} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 420 a^{3} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1050 a^{3} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 525 a^{3} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2100 a^{3} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2100 a^{3} c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 525 a^{3} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1050 a^{3} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 420 a^{3} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 210 a^{3} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 a^{3} c^{4} f} - \frac{780 A \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 a^{3} c^{4} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 210 a^{3} c^{4} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 420 a^{3} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1050 a^{3} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 525 a^{3} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2100 a^{3} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2100 a^{3} c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 525 a^{3} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1050 a^{3} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 420 a^{3} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 210 a^{3} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 a^{3} c^{4} f} - \frac{90 A \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 a^{3} c^{4} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 210 a^{3} c^{4} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 420 a^{3} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1050 a^{3} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 525 a^{3} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2100 a^{3} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2100 a^{3} c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 525 a^{3} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1050 a^{3} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 420 a^{3} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 210 a^{3} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 a^{3} c^{4} f} + \frac{330 A \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 a^{3} c^{4} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 210 a^{3} c^{4} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 420 a^{3} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1050 a^{3} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 525 a^{3} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2100 a^{3} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2100 a^{3} c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 525 a^{3} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1050 a^{3} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 420 a^{3} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 210 a^{3} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 a^{3} c^{4} f} - \frac{150 A \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 a^{3} c^{4} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 210 a^{3} c^{4} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 420 a^{3} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1050 a^{3} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 525 a^{3} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2100 a^{3} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2100 a^{3} c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 525 a^{3} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1050 a^{3} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 420 a^{3} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 210 a^{3} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 a^{3} c^{4} f} - \frac{30 A}{105 a^{3} c^{4} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 210 a^{3} c^{4} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 420 a^{3} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1050 a^{3} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 525 a^{3} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2100 a^{3} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2100 a^{3} c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 525 a^{3} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1050 a^{3} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 420 a^{3} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 210 a^{3} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 a^{3} c^{4} f} - \frac{210 B \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 a^{3} c^{4} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 210 a^{3} c^{4} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 420 a^{3} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1050 a^{3} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 525 a^{3} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2100 a^{3} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2100 a^{3} c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 525 a^{3} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1050 a^{3} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 420 a^{3} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 210 a^{3} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 a^{3} c^{4} f} + \frac{140 B \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 a^{3} c^{4} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 210 a^{3} c^{4} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 420 a^{3} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1050 a^{3} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 525 a^{3} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2100 a^{3} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2100 a^{3} c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 525 a^{3} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1050 a^{3} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 420 a^{3} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 210 a^{3} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 a^{3} c^{4} f} - \frac{70 B \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 a^{3} c^{4} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 210 a^{3} c^{4} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 420 a^{3} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1050 a^{3} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 525 a^{3} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2100 a^{3} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2100 a^{3} c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 525 a^{3} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1050 a^{3} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 420 a^{3} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 210 a^{3} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 a^{3} c^{4} f} - \frac{224 B \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 a^{3} c^{4} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 210 a^{3} c^{4} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 420 a^{3} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1050 a^{3} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 525 a^{3} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2100 a^{3} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2100 a^{3} c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 525 a^{3} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1050 a^{3} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 420 a^{3} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 210 a^{3} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 a^{3} c^{4} f} - \frac{532 B \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 a^{3} c^{4} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 210 a^{3} c^{4} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 420 a^{3} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1050 a^{3} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 525 a^{3} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2100 a^{3} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2100 a^{3} c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 525 a^{3} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1050 a^{3} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 420 a^{3} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 210 a^{3} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 a^{3} c^{4} f} + \frac{376 B \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 a^{3} c^{4} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 210 a^{3} c^{4} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 420 a^{3} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1050 a^{3} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 525 a^{3} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2100 a^{3} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2100 a^{3} c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 525 a^{3} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1050 a^{3} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 420 a^{3} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 210 a^{3} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 a^{3} c^{4} f} - \frac{220 B \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 a^{3} c^{4} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 210 a^{3} c^{4} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 420 a^{3} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1050 a^{3} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 525 a^{3} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2100 a^{3} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2100 a^{3} c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 525 a^{3} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1050 a^{3} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 420 a^{3} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 210 a^{3} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 a^{3} c^{4} f} - \frac{160 B \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 a^{3} c^{4} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 210 a^{3} c^{4} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 420 a^{3} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1050 a^{3} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 525 a^{3} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2100 a^{3} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2100 a^{3} c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 525 a^{3} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1050 a^{3} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 420 a^{3} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 210 a^{3} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 a^{3} c^{4} f} - \frac{90 B \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 a^{3} c^{4} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 210 a^{3} c^{4} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 420 a^{3} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1050 a^{3} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 525 a^{3} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2100 a^{3} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2100 a^{3} c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 525 a^{3} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1050 a^{3} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 420 a^{3} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 210 a^{3} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 a^{3} c^{4} f} + \frac{60 B \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{105 a^{3} c^{4} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 210 a^{3} c^{4} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 420 a^{3} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1050 a^{3} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 525 a^{3} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2100 a^{3} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2100 a^{3} c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 525 a^{3} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1050 a^{3} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 420 a^{3} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 210 a^{3} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 a^{3} c^{4} f} - \frac{30 B}{105 a^{3} c^{4} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 210 a^{3} c^{4} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 420 a^{3} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1050 a^{3} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 525 a^{3} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2100 a^{3} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2100 a^{3} c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 525 a^{3} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1050 a^{3} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 420 a^{3} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 210 a^{3} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 105 a^{3} c^{4} f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right)}{\left(a \sin{\left(e \right)} + a\right)^{3} \left(- c \sin{\left(e \right)} + c\right)^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-210*A*tan(e/2 + f*x/2)**11/(105*a**3*c**4*f*tan(e/2 + f*x/2)**12 - 210*a**3*c**4*f*tan(e/2 + f*x/2)**11 - 420*a**3*c**4*f*tan(e/2 + f*x/2)**10 + 1050*a**3*c**4*f*tan(e/2 + f*x/2)**9 + 525*a**3*c**4*f*tan(e/2 + f*x/2)**8 - 2100*a**3*c**4*f*tan(e/2 + f*x/2)**7 + 2100*a**3*c**4*f*tan(e/2 + f*x/2)**5 - 525*a**3*c**4*f*tan(e/2 + f*x/2)**4 - 1050*a**3*c**4*f*tan(e/2 + f*x/2)**3 + 420*a**3*c**4*f*tan(e/2 + f*x/2)**2 + 210*a**3*c**4*f*tan(e/2 + f*x/2) - 105*a**3*c**4*f) + 210*A*tan(e/2 + f*x/2)**10/(105*a**3*c**4*f*tan(e/2 + f*x/2)**12 - 210*a**3*c**4*f*tan(e/2 + f*x/2)**11 - 420*a**3*c**4*f*tan(e/2 + f*x/2)**10 + 1050*a**3*c**4*f*tan(e/2 + f*x/2)**9 + 525*a**3*c**4*f*tan(e/2 + f*x/2)**8 - 2100*a**3*c**4*f*tan(e/2 + f*x/2)**7 + 2100*a**3*c**4*f*tan(e/2 + f*x/2)**5 - 525*a**3*c**4*f*tan(e/2 + f*x/2)**4 - 1050*a**3*c**4*f*tan(e/2 + f*x/2)**3 + 420*a**3*c**4*f*tan(e/2 + f*x/2)**2 + 210*a**3*c**4*f*tan(e/2 + f*x/2) - 105*a**3*c**4*f) + 210*A*tan(e/2 + f*x/2)**9/(105*a**3*c**4*f*tan(e/2 + f*x/2)**12 - 210*a**3*c**4*f*tan(e/2 + f*x/2)**11 - 420*a**3*c**4*f*tan(e/2 + f*x/2)**10 + 1050*a**3*c**4*f*tan(e/2 + f*x/2)**9 + 525*a**3*c**4*f*tan(e/2 + f*x/2)**8 - 2100*a**3*c**4*f*tan(e/2 + f*x/2)**7 + 2100*a**3*c**4*f*tan(e/2 + f*x/2)**5 - 525*a**3*c**4*f*tan(e/2 + f*x/2)**4 - 1050*a**3*c**4*f*tan(e/2 + f*x/2)**3 + 420*a**3*c**4*f*tan(e/2 + f*x/2)**2 + 210*a**3*c**4*f*tan(e/2 + f*x/2) - 105*a**3*c**4*f) - 630*A*tan(e/2 + f*x/2)**8/(105*a**3*c**4*f*tan(e/2 + f*x/2)**12 - 210*a**3*c**4*f*tan(e/2 + f*x/2)**11 - 420*a**3*c**4*f*tan(e/2 + f*x/2)**10 + 1050*a**3*c**4*f*tan(e/2 + f*x/2)**9 + 525*a**3*c**4*f*tan(e/2 + f*x/2)**8 - 2100*a**3*c**4*f*tan(e/2 + f*x/2)**7 + 2100*a**3*c**4*f*tan(e/2 + f*x/2)**5 - 525*a**3*c**4*f*tan(e/2 + f*x/2)**4 - 1050*a**3*c**4*f*tan(e/2 + f*x/2)**3 + 420*a**3*c**4*f*tan(e/2 + f*x/2)**2 + 210*a**3*c**4*f*tan(e/2 + f*x/2) - 105*a**3*c**4*f) - 756*A*tan(e/2 + f*x/2)**7/(105*a**3*c**4*f*tan(e/2 + f*x/2)**12 - 210*a**3*c**4*f*tan(e/2 + f*x/2)**11 - 420*a**3*c**4*f*tan(e/2 + f*x/2)**10 + 1050*a**3*c**4*f*tan(e/2 + f*x/2)**9 + 525*a**3*c**4*f*tan(e/2 + f*x/2)**8 - 2100*a**3*c**4*f*tan(e/2 + f*x/2)**7 + 2100*a**3*c**4*f*tan(e/2 + f*x/2)**5 - 525*a**3*c**4*f*tan(e/2 + f*x/2)**4 - 1050*a**3*c**4*f*tan(e/2 + f*x/2)**3 + 420*a**3*c**4*f*tan(e/2 + f*x/2)**2 + 210*a**3*c**4*f*tan(e/2 + f*x/2) - 105*a**3*c**4*f) + 1092*A*tan(e/2 + f*x/2)**6/(105*a**3*c**4*f*tan(e/2 + f*x/2)**12 - 210*a**3*c**4*f*tan(e/2 + f*x/2)**11 - 420*a**3*c**4*f*tan(e/2 + f*x/2)**10 + 1050*a**3*c**4*f*tan(e/2 + f*x/2)**9 + 525*a**3*c**4*f*tan(e/2 + f*x/2)**8 - 2100*a**3*c**4*f*tan(e/2 + f*x/2)**7 + 2100*a**3*c**4*f*tan(e/2 + f*x/2)**5 - 525*a**3*c**4*f*tan(e/2 + f*x/2)**4 - 1050*a**3*c**4*f*tan(e/2 + f*x/2)**3 + 420*a**3*c**4*f*tan(e/2 + f*x/2)**2 + 210*a**3*c**4*f*tan(e/2 + f*x/2) - 105*a**3*c**4*f) - 156*A*tan(e/2 + f*x/2)**5/(105*a**3*c**4*f*tan(e/2 + f*x/2)**12 - 210*a**3*c**4*f*tan(e/2 + f*x/2)**11 - 420*a**3*c**4*f*tan(e/2 + f*x/2)**10 + 1050*a**3*c**4*f*tan(e/2 + f*x/2)**9 + 525*a**3*c**4*f*tan(e/2 + f*x/2)**8 - 2100*a**3*c**4*f*tan(e/2 + f*x/2)**7 + 2100*a**3*c**4*f*tan(e/2 + f*x/2)**5 - 525*a**3*c**4*f*tan(e/2 + f*x/2)**4 - 1050*a**3*c**4*f*tan(e/2 + f*x/2)**3 + 420*a**3*c**4*f*tan(e/2 + f*x/2)**2 + 210*a**3*c**4*f*tan(e/2 + f*x/2) - 105*a**3*c**4*f) - 780*A*tan(e/2 + f*x/2)**4/(105*a**3*c**4*f*tan(e/2 + f*x/2)**12 - 210*a**3*c**4*f*tan(e/2 + f*x/2)**11 - 420*a**3*c**4*f*tan(e/2 + f*x/2)**10 + 1050*a**3*c**4*f*tan(e/2 + f*x/2)**9 + 525*a**3*c**4*f*tan(e/2 + f*x/2)**8 - 2100*a**3*c**4*f*tan(e/2 + f*x/2)**7 + 2100*a**3*c**4*f*tan(e/2 + f*x/2)**5 - 525*a**3*c**4*f*tan(e/2 + f*x/2)**4 - 1050*a**3*c**4*f*tan(e/2 + f*x/2)**3 + 420*a**3*c**4*f*tan(e/2 + f*x/2)**2 + 210*a**3*c**4*f*tan(e/2 + f*x/2) - 105*a**3*c**4*f) - 90*A*tan(e/2 + f*x/2)**3/(105*a**3*c**4*f*tan(e/2 + f*x/2)**12 - 210*a**3*c**4*f*tan(e/2 + f*x/2)**11 - 420*a**3*c**4*f*tan(e/2 + f*x/2)**10 + 1050*a**3*c**4*f*tan(e/2 + f*x/2)**9 + 525*a**3*c**4*f*tan(e/2 + f*x/2)**8 - 2100*a**3*c**4*f*tan(e/2 + f*x/2)**7 + 2100*a**3*c**4*f*tan(e/2 + f*x/2)**5 - 525*a**3*c**4*f*tan(e/2 + f*x/2)**4 - 1050*a**3*c**4*f*tan(e/2 + f*x/2)**3 + 420*a**3*c**4*f*tan(e/2 + f*x/2)**2 + 210*a**3*c**4*f*tan(e/2 + f*x/2) - 105*a**3*c**4*f) + 330*A*tan(e/2 + f*x/2)**2/(105*a**3*c**4*f*tan(e/2 + f*x/2)**12 - 210*a**3*c**4*f*tan(e/2 + f*x/2)**11 - 420*a**3*c**4*f*tan(e/2 + f*x/2)**10 + 1050*a**3*c**4*f*tan(e/2 + f*x/2)**9 + 525*a**3*c**4*f*tan(e/2 + f*x/2)**8 - 2100*a**3*c**4*f*tan(e/2 + f*x/2)**7 + 2100*a**3*c**4*f*tan(e/2 + f*x/2)**5 - 525*a**3*c**4*f*tan(e/2 + f*x/2)**4 - 1050*a**3*c**4*f*tan(e/2 + f*x/2)**3 + 420*a**3*c**4*f*tan(e/2 + f*x/2)**2 + 210*a**3*c**4*f*tan(e/2 + f*x/2) - 105*a**3*c**4*f) - 150*A*tan(e/2 + f*x/2)/(105*a**3*c**4*f*tan(e/2 + f*x/2)**12 - 210*a**3*c**4*f*tan(e/2 + f*x/2)**11 - 420*a**3*c**4*f*tan(e/2 + f*x/2)**10 + 1050*a**3*c**4*f*tan(e/2 + f*x/2)**9 + 525*a**3*c**4*f*tan(e/2 + f*x/2)**8 - 2100*a**3*c**4*f*tan(e/2 + f*x/2)**7 + 2100*a**3*c**4*f*tan(e/2 + f*x/2)**5 - 525*a**3*c**4*f*tan(e/2 + f*x/2)**4 - 1050*a**3*c**4*f*tan(e/2 + f*x/2)**3 + 420*a**3*c**4*f*tan(e/2 + f*x/2)**2 + 210*a**3*c**4*f*tan(e/2 + f*x/2) - 105*a**3*c**4*f) - 30*A/(105*a**3*c**4*f*tan(e/2 + f*x/2)**12 - 210*a**3*c**4*f*tan(e/2 + f*x/2)**11 - 420*a**3*c**4*f*tan(e/2 + f*x/2)**10 + 1050*a**3*c**4*f*tan(e/2 + f*x/2)**9 + 525*a**3*c**4*f*tan(e/2 + f*x/2)**8 - 2100*a**3*c**4*f*tan(e/2 + f*x/2)**7 + 2100*a**3*c**4*f*tan(e/2 + f*x/2)**5 - 525*a**3*c**4*f*tan(e/2 + f*x/2)**4 - 1050*a**3*c**4*f*tan(e/2 + f*x/2)**3 + 420*a**3*c**4*f*tan(e/2 + f*x/2)**2 + 210*a**3*c**4*f*tan(e/2 + f*x/2) - 105*a**3*c**4*f) - 210*B*tan(e/2 + f*x/2)**10/(105*a**3*c**4*f*tan(e/2 + f*x/2)**12 - 210*a**3*c**4*f*tan(e/2 + f*x/2)**11 - 420*a**3*c**4*f*tan(e/2 + f*x/2)**10 + 1050*a**3*c**4*f*tan(e/2 + f*x/2)**9 + 525*a**3*c**4*f*tan(e/2 + f*x/2)**8 - 2100*a**3*c**4*f*tan(e/2 + f*x/2)**7 + 2100*a**3*c**4*f*tan(e/2 + f*x/2)**5 - 525*a**3*c**4*f*tan(e/2 + f*x/2)**4 - 1050*a**3*c**4*f*tan(e/2 + f*x/2)**3 + 420*a**3*c**4*f*tan(e/2 + f*x/2)**2 + 210*a**3*c**4*f*tan(e/2 + f*x/2) - 105*a**3*c**4*f) + 140*B*tan(e/2 + f*x/2)**9/(105*a**3*c**4*f*tan(e/2 + f*x/2)**12 - 210*a**3*c**4*f*tan(e/2 + f*x/2)**11 - 420*a**3*c**4*f*tan(e/2 + f*x/2)**10 + 1050*a**3*c**4*f*tan(e/2 + f*x/2)**9 + 525*a**3*c**4*f*tan(e/2 + f*x/2)**8 - 2100*a**3*c**4*f*tan(e/2 + f*x/2)**7 + 2100*a**3*c**4*f*tan(e/2 + f*x/2)**5 - 525*a**3*c**4*f*tan(e/2 + f*x/2)**4 - 1050*a**3*c**4*f*tan(e/2 + f*x/2)**3 + 420*a**3*c**4*f*tan(e/2 + f*x/2)**2 + 210*a**3*c**4*f*tan(e/2 + f*x/2) - 105*a**3*c**4*f) - 70*B*tan(e/2 + f*x/2)**8/(105*a**3*c**4*f*tan(e/2 + f*x/2)**12 - 210*a**3*c**4*f*tan(e/2 + f*x/2)**11 - 420*a**3*c**4*f*tan(e/2 + f*x/2)**10 + 1050*a**3*c**4*f*tan(e/2 + f*x/2)**9 + 525*a**3*c**4*f*tan(e/2 + f*x/2)**8 - 2100*a**3*c**4*f*tan(e/2 + f*x/2)**7 + 2100*a**3*c**4*f*tan(e/2 + f*x/2)**5 - 525*a**3*c**4*f*tan(e/2 + f*x/2)**4 - 1050*a**3*c**4*f*tan(e/2 + f*x/2)**3 + 420*a**3*c**4*f*tan(e/2 + f*x/2)**2 + 210*a**3*c**4*f*tan(e/2 + f*x/2) - 105*a**3*c**4*f) - 224*B*tan(e/2 + f*x/2)**7/(105*a**3*c**4*f*tan(e/2 + f*x/2)**12 - 210*a**3*c**4*f*tan(e/2 + f*x/2)**11 - 420*a**3*c**4*f*tan(e/2 + f*x/2)**10 + 1050*a**3*c**4*f*tan(e/2 + f*x/2)**9 + 525*a**3*c**4*f*tan(e/2 + f*x/2)**8 - 2100*a**3*c**4*f*tan(e/2 + f*x/2)**7 + 2100*a**3*c**4*f*tan(e/2 + f*x/2)**5 - 525*a**3*c**4*f*tan(e/2 + f*x/2)**4 - 1050*a**3*c**4*f*tan(e/2 + f*x/2)**3 + 420*a**3*c**4*f*tan(e/2 + f*x/2)**2 + 210*a**3*c**4*f*tan(e/2 + f*x/2) - 105*a**3*c**4*f) - 532*B*tan(e/2 + f*x/2)**6/(105*a**3*c**4*f*tan(e/2 + f*x/2)**12 - 210*a**3*c**4*f*tan(e/2 + f*x/2)**11 - 420*a**3*c**4*f*tan(e/2 + f*x/2)**10 + 1050*a**3*c**4*f*tan(e/2 + f*x/2)**9 + 525*a**3*c**4*f*tan(e/2 + f*x/2)**8 - 2100*a**3*c**4*f*tan(e/2 + f*x/2)**7 + 2100*a**3*c**4*f*tan(e/2 + f*x/2)**5 - 525*a**3*c**4*f*tan(e/2 + f*x/2)**4 - 1050*a**3*c**4*f*tan(e/2 + f*x/2)**3 + 420*a**3*c**4*f*tan(e/2 + f*x/2)**2 + 210*a**3*c**4*f*tan(e/2 + f*x/2) - 105*a**3*c**4*f) + 376*B*tan(e/2 + f*x/2)**5/(105*a**3*c**4*f*tan(e/2 + f*x/2)**12 - 210*a**3*c**4*f*tan(e/2 + f*x/2)**11 - 420*a**3*c**4*f*tan(e/2 + f*x/2)**10 + 1050*a**3*c**4*f*tan(e/2 + f*x/2)**9 + 525*a**3*c**4*f*tan(e/2 + f*x/2)**8 - 2100*a**3*c**4*f*tan(e/2 + f*x/2)**7 + 2100*a**3*c**4*f*tan(e/2 + f*x/2)**5 - 525*a**3*c**4*f*tan(e/2 + f*x/2)**4 - 1050*a**3*c**4*f*tan(e/2 + f*x/2)**3 + 420*a**3*c**4*f*tan(e/2 + f*x/2)**2 + 210*a**3*c**4*f*tan(e/2 + f*x/2) - 105*a**3*c**4*f) - 220*B*tan(e/2 + f*x/2)**4/(105*a**3*c**4*f*tan(e/2 + f*x/2)**12 - 210*a**3*c**4*f*tan(e/2 + f*x/2)**11 - 420*a**3*c**4*f*tan(e/2 + f*x/2)**10 + 1050*a**3*c**4*f*tan(e/2 + f*x/2)**9 + 525*a**3*c**4*f*tan(e/2 + f*x/2)**8 - 2100*a**3*c**4*f*tan(e/2 + f*x/2)**7 + 2100*a**3*c**4*f*tan(e/2 + f*x/2)**5 - 525*a**3*c**4*f*tan(e/2 + f*x/2)**4 - 1050*a**3*c**4*f*tan(e/2 + f*x/2)**3 + 420*a**3*c**4*f*tan(e/2 + f*x/2)**2 + 210*a**3*c**4*f*tan(e/2 + f*x/2) - 105*a**3*c**4*f) - 160*B*tan(e/2 + f*x/2)**3/(105*a**3*c**4*f*tan(e/2 + f*x/2)**12 - 210*a**3*c**4*f*tan(e/2 + f*x/2)**11 - 420*a**3*c**4*f*tan(e/2 + f*x/2)**10 + 1050*a**3*c**4*f*tan(e/2 + f*x/2)**9 + 525*a**3*c**4*f*tan(e/2 + f*x/2)**8 - 2100*a**3*c**4*f*tan(e/2 + f*x/2)**7 + 2100*a**3*c**4*f*tan(e/2 + f*x/2)**5 - 525*a**3*c**4*f*tan(e/2 + f*x/2)**4 - 1050*a**3*c**4*f*tan(e/2 + f*x/2)**3 + 420*a**3*c**4*f*tan(e/2 + f*x/2)**2 + 210*a**3*c**4*f*tan(e/2 + f*x/2) - 105*a**3*c**4*f) - 90*B*tan(e/2 + f*x/2)**2/(105*a**3*c**4*f*tan(e/2 + f*x/2)**12 - 210*a**3*c**4*f*tan(e/2 + f*x/2)**11 - 420*a**3*c**4*f*tan(e/2 + f*x/2)**10 + 1050*a**3*c**4*f*tan(e/2 + f*x/2)**9 + 525*a**3*c**4*f*tan(e/2 + f*x/2)**8 - 2100*a**3*c**4*f*tan(e/2 + f*x/2)**7 + 2100*a**3*c**4*f*tan(e/2 + f*x/2)**5 - 525*a**3*c**4*f*tan(e/2 + f*x/2)**4 - 1050*a**3*c**4*f*tan(e/2 + f*x/2)**3 + 420*a**3*c**4*f*tan(e/2 + f*x/2)**2 + 210*a**3*c**4*f*tan(e/2 + f*x/2) - 105*a**3*c**4*f) + 60*B*tan(e/2 + f*x/2)/(105*a**3*c**4*f*tan(e/2 + f*x/2)**12 - 210*a**3*c**4*f*tan(e/2 + f*x/2)**11 - 420*a**3*c**4*f*tan(e/2 + f*x/2)**10 + 1050*a**3*c**4*f*tan(e/2 + f*x/2)**9 + 525*a**3*c**4*f*tan(e/2 + f*x/2)**8 - 2100*a**3*c**4*f*tan(e/2 + f*x/2)**7 + 2100*a**3*c**4*f*tan(e/2 + f*x/2)**5 - 525*a**3*c**4*f*tan(e/2 + f*x/2)**4 - 1050*a**3*c**4*f*tan(e/2 + f*x/2)**3 + 420*a**3*c**4*f*tan(e/2 + f*x/2)**2 + 210*a**3*c**4*f*tan(e/2 + f*x/2) - 105*a**3*c**4*f) - 30*B/(105*a**3*c**4*f*tan(e/2 + f*x/2)**12 - 210*a**3*c**4*f*tan(e/2 + f*x/2)**11 - 420*a**3*c**4*f*tan(e/2 + f*x/2)**10 + 1050*a**3*c**4*f*tan(e/2 + f*x/2)**9 + 525*a**3*c**4*f*tan(e/2 + f*x/2)**8 - 2100*a**3*c**4*f*tan(e/2 + f*x/2)**7 + 2100*a**3*c**4*f*tan(e/2 + f*x/2)**5 - 525*a**3*c**4*f*tan(e/2 + f*x/2)**4 - 1050*a**3*c**4*f*tan(e/2 + f*x/2)**3 + 420*a**3*c**4*f*tan(e/2 + f*x/2)**2 + 210*a**3*c**4*f*tan(e/2 + f*x/2) - 105*a**3*c**4*f), Ne(f, 0)), (x*(A + B*sin(e))/((a*sin(e) + a)**3*(-c*sin(e) + c)**4), True))","A",0
79,1,8396,0,155.470623," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))**3/(c-c*sin(f*x+e))**5,x)","\begin{cases} - \frac{630 A \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 a^{3} c^{5} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1260 a^{3} c^{5} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{3} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5040 a^{3} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5985 a^{3} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6300 a^{3} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 14175 a^{3} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 14175 a^{3} c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6300 a^{3} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5985 a^{3} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5040 a^{3} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1260 a^{3} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f} + \frac{1260 A \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 a^{3} c^{5} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1260 a^{3} c^{5} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{3} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5040 a^{3} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5985 a^{3} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6300 a^{3} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 14175 a^{3} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 14175 a^{3} c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6300 a^{3} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5985 a^{3} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5040 a^{3} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1260 a^{3} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f} - \frac{420 A \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 a^{3} c^{5} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1260 a^{3} c^{5} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{3} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5040 a^{3} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5985 a^{3} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6300 a^{3} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 14175 a^{3} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 14175 a^{3} c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6300 a^{3} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5985 a^{3} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5040 a^{3} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1260 a^{3} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f} - \frac{3360 A \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 a^{3} c^{5} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1260 a^{3} c^{5} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{3} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5040 a^{3} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5985 a^{3} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6300 a^{3} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 14175 a^{3} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 14175 a^{3} c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6300 a^{3} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5985 a^{3} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5040 a^{3} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1260 a^{3} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f} + \frac{966 A \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 a^{3} c^{5} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1260 a^{3} c^{5} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{3} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5040 a^{3} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5985 a^{3} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6300 a^{3} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 14175 a^{3} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 14175 a^{3} c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6300 a^{3} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5985 a^{3} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5040 a^{3} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1260 a^{3} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f} + \frac{4956 A \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 a^{3} c^{5} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1260 a^{3} c^{5} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{3} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5040 a^{3} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5985 a^{3} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6300 a^{3} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 14175 a^{3} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 14175 a^{3} c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6300 a^{3} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5985 a^{3} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5040 a^{3} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1260 a^{3} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f} - \frac{7224 A \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 a^{3} c^{5} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1260 a^{3} c^{5} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{3} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5040 a^{3} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5985 a^{3} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6300 a^{3} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 14175 a^{3} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 14175 a^{3} c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6300 a^{3} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5985 a^{3} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5040 a^{3} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1260 a^{3} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f} - \frac{1344 A \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 a^{3} c^{5} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1260 a^{3} c^{5} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{3} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5040 a^{3} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5985 a^{3} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6300 a^{3} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 14175 a^{3} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 14175 a^{3} c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6300 a^{3} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5985 a^{3} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5040 a^{3} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1260 a^{3} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f} + \frac{3766 A \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 a^{3} c^{5} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1260 a^{3} c^{5} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{3} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5040 a^{3} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5985 a^{3} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6300 a^{3} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 14175 a^{3} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 14175 a^{3} c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6300 a^{3} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5985 a^{3} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5040 a^{3} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1260 a^{3} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f} - \frac{700 A \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 a^{3} c^{5} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1260 a^{3} c^{5} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{3} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5040 a^{3} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5985 a^{3} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6300 a^{3} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 14175 a^{3} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 14175 a^{3} c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6300 a^{3} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5985 a^{3} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5040 a^{3} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1260 a^{3} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f} - \frac{2660 A \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 a^{3} c^{5} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1260 a^{3} c^{5} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{3} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5040 a^{3} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5985 a^{3} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6300 a^{3} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 14175 a^{3} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 14175 a^{3} c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6300 a^{3} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5985 a^{3} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5040 a^{3} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1260 a^{3} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f} + \frac{1120 A \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 a^{3} c^{5} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1260 a^{3} c^{5} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{3} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5040 a^{3} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5985 a^{3} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6300 a^{3} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 14175 a^{3} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 14175 a^{3} c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6300 a^{3} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5985 a^{3} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5040 a^{3} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1260 a^{3} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f} - \frac{70 A \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 a^{3} c^{5} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1260 a^{3} c^{5} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{3} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5040 a^{3} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5985 a^{3} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6300 a^{3} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 14175 a^{3} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 14175 a^{3} c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6300 a^{3} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5985 a^{3} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5040 a^{3} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1260 a^{3} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f} - \frac{140 A}{315 a^{3} c^{5} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1260 a^{3} c^{5} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{3} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5040 a^{3} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5985 a^{3} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6300 a^{3} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 14175 a^{3} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 14175 a^{3} c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6300 a^{3} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5985 a^{3} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5040 a^{3} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1260 a^{3} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f} - \frac{630 B \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 a^{3} c^{5} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1260 a^{3} c^{5} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{3} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5040 a^{3} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5985 a^{3} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6300 a^{3} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 14175 a^{3} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 14175 a^{3} c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6300 a^{3} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5985 a^{3} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5040 a^{3} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1260 a^{3} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f} + \frac{840 B \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 a^{3} c^{5} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1260 a^{3} c^{5} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{3} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5040 a^{3} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5985 a^{3} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6300 a^{3} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 14175 a^{3} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 14175 a^{3} c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6300 a^{3} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5985 a^{3} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5040 a^{3} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1260 a^{3} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f} - \frac{840 B \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 a^{3} c^{5} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1260 a^{3} c^{5} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{3} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5040 a^{3} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5985 a^{3} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6300 a^{3} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 14175 a^{3} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 14175 a^{3} c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6300 a^{3} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5985 a^{3} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5040 a^{3} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1260 a^{3} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f} - \frac{1176 B \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 a^{3} c^{5} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1260 a^{3} c^{5} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{3} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5040 a^{3} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5985 a^{3} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6300 a^{3} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 14175 a^{3} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 14175 a^{3} c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6300 a^{3} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5985 a^{3} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5040 a^{3} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1260 a^{3} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f} - \frac{966 B \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 a^{3} c^{5} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1260 a^{3} c^{5} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{3} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5040 a^{3} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5985 a^{3} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6300 a^{3} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 14175 a^{3} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 14175 a^{3} c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6300 a^{3} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5985 a^{3} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5040 a^{3} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1260 a^{3} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f} + \frac{2064 B \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 a^{3} c^{5} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1260 a^{3} c^{5} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{3} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5040 a^{3} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5985 a^{3} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6300 a^{3} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 14175 a^{3} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 14175 a^{3} c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6300 a^{3} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5985 a^{3} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5040 a^{3} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1260 a^{3} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f} - \frac{3216 B \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 a^{3} c^{5} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1260 a^{3} c^{5} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{3} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5040 a^{3} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5985 a^{3} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6300 a^{3} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 14175 a^{3} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 14175 a^{3} c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6300 a^{3} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5985 a^{3} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5040 a^{3} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1260 a^{3} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f} - \frac{176 B \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 a^{3} c^{5} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1260 a^{3} c^{5} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{3} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5040 a^{3} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5985 a^{3} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6300 a^{3} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 14175 a^{3} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 14175 a^{3} c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6300 a^{3} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5985 a^{3} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5040 a^{3} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1260 a^{3} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f} + \frac{110 B \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 a^{3} c^{5} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1260 a^{3} c^{5} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{3} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5040 a^{3} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5985 a^{3} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6300 a^{3} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 14175 a^{3} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 14175 a^{3} c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6300 a^{3} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5985 a^{3} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5040 a^{3} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1260 a^{3} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f} + \frac{40 B \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 a^{3} c^{5} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1260 a^{3} c^{5} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{3} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5040 a^{3} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5985 a^{3} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6300 a^{3} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 14175 a^{3} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 14175 a^{3} c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6300 a^{3} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5985 a^{3} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5040 a^{3} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1260 a^{3} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f} - \frac{680 B \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 a^{3} c^{5} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1260 a^{3} c^{5} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{3} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5040 a^{3} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5985 a^{3} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6300 a^{3} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 14175 a^{3} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 14175 a^{3} c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6300 a^{3} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5985 a^{3} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5040 a^{3} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1260 a^{3} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f} + \frac{200 B \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 a^{3} c^{5} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1260 a^{3} c^{5} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{3} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5040 a^{3} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5985 a^{3} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6300 a^{3} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 14175 a^{3} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 14175 a^{3} c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6300 a^{3} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5985 a^{3} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5040 a^{3} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1260 a^{3} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f} - \frac{50 B}{315 a^{3} c^{5} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1260 a^{3} c^{5} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{3} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5040 a^{3} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5985 a^{3} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 6300 a^{3} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 14175 a^{3} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 14175 a^{3} c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 6300 a^{3} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5985 a^{3} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5040 a^{3} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1260 a^{3} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 315 a^{3} c^{5} f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right)}{\left(a \sin{\left(e \right)} + a\right)^{3} \left(- c \sin{\left(e \right)} + c\right)^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-630*A*tan(e/2 + f*x/2)**13/(315*a**3*c**5*f*tan(e/2 + f*x/2)**14 - 1260*a**3*c**5*f*tan(e/2 + f*x/2)**13 + 315*a**3*c**5*f*tan(e/2 + f*x/2)**12 + 5040*a**3*c**5*f*tan(e/2 + f*x/2)**11 - 5985*a**3*c**5*f*tan(e/2 + f*x/2)**10 - 6300*a**3*c**5*f*tan(e/2 + f*x/2)**9 + 14175*a**3*c**5*f*tan(e/2 + f*x/2)**8 - 14175*a**3*c**5*f*tan(e/2 + f*x/2)**6 + 6300*a**3*c**5*f*tan(e/2 + f*x/2)**5 + 5985*a**3*c**5*f*tan(e/2 + f*x/2)**4 - 5040*a**3*c**5*f*tan(e/2 + f*x/2)**3 - 315*a**3*c**5*f*tan(e/2 + f*x/2)**2 + 1260*a**3*c**5*f*tan(e/2 + f*x/2) - 315*a**3*c**5*f) + 1260*A*tan(e/2 + f*x/2)**12/(315*a**3*c**5*f*tan(e/2 + f*x/2)**14 - 1260*a**3*c**5*f*tan(e/2 + f*x/2)**13 + 315*a**3*c**5*f*tan(e/2 + f*x/2)**12 + 5040*a**3*c**5*f*tan(e/2 + f*x/2)**11 - 5985*a**3*c**5*f*tan(e/2 + f*x/2)**10 - 6300*a**3*c**5*f*tan(e/2 + f*x/2)**9 + 14175*a**3*c**5*f*tan(e/2 + f*x/2)**8 - 14175*a**3*c**5*f*tan(e/2 + f*x/2)**6 + 6300*a**3*c**5*f*tan(e/2 + f*x/2)**5 + 5985*a**3*c**5*f*tan(e/2 + f*x/2)**4 - 5040*a**3*c**5*f*tan(e/2 + f*x/2)**3 - 315*a**3*c**5*f*tan(e/2 + f*x/2)**2 + 1260*a**3*c**5*f*tan(e/2 + f*x/2) - 315*a**3*c**5*f) - 420*A*tan(e/2 + f*x/2)**11/(315*a**3*c**5*f*tan(e/2 + f*x/2)**14 - 1260*a**3*c**5*f*tan(e/2 + f*x/2)**13 + 315*a**3*c**5*f*tan(e/2 + f*x/2)**12 + 5040*a**3*c**5*f*tan(e/2 + f*x/2)**11 - 5985*a**3*c**5*f*tan(e/2 + f*x/2)**10 - 6300*a**3*c**5*f*tan(e/2 + f*x/2)**9 + 14175*a**3*c**5*f*tan(e/2 + f*x/2)**8 - 14175*a**3*c**5*f*tan(e/2 + f*x/2)**6 + 6300*a**3*c**5*f*tan(e/2 + f*x/2)**5 + 5985*a**3*c**5*f*tan(e/2 + f*x/2)**4 - 5040*a**3*c**5*f*tan(e/2 + f*x/2)**3 - 315*a**3*c**5*f*tan(e/2 + f*x/2)**2 + 1260*a**3*c**5*f*tan(e/2 + f*x/2) - 315*a**3*c**5*f) - 3360*A*tan(e/2 + f*x/2)**10/(315*a**3*c**5*f*tan(e/2 + f*x/2)**14 - 1260*a**3*c**5*f*tan(e/2 + f*x/2)**13 + 315*a**3*c**5*f*tan(e/2 + f*x/2)**12 + 5040*a**3*c**5*f*tan(e/2 + f*x/2)**11 - 5985*a**3*c**5*f*tan(e/2 + f*x/2)**10 - 6300*a**3*c**5*f*tan(e/2 + f*x/2)**9 + 14175*a**3*c**5*f*tan(e/2 + f*x/2)**8 - 14175*a**3*c**5*f*tan(e/2 + f*x/2)**6 + 6300*a**3*c**5*f*tan(e/2 + f*x/2)**5 + 5985*a**3*c**5*f*tan(e/2 + f*x/2)**4 - 5040*a**3*c**5*f*tan(e/2 + f*x/2)**3 - 315*a**3*c**5*f*tan(e/2 + f*x/2)**2 + 1260*a**3*c**5*f*tan(e/2 + f*x/2) - 315*a**3*c**5*f) + 966*A*tan(e/2 + f*x/2)**9/(315*a**3*c**5*f*tan(e/2 + f*x/2)**14 - 1260*a**3*c**5*f*tan(e/2 + f*x/2)**13 + 315*a**3*c**5*f*tan(e/2 + f*x/2)**12 + 5040*a**3*c**5*f*tan(e/2 + f*x/2)**11 - 5985*a**3*c**5*f*tan(e/2 + f*x/2)**10 - 6300*a**3*c**5*f*tan(e/2 + f*x/2)**9 + 14175*a**3*c**5*f*tan(e/2 + f*x/2)**8 - 14175*a**3*c**5*f*tan(e/2 + f*x/2)**6 + 6300*a**3*c**5*f*tan(e/2 + f*x/2)**5 + 5985*a**3*c**5*f*tan(e/2 + f*x/2)**4 - 5040*a**3*c**5*f*tan(e/2 + f*x/2)**3 - 315*a**3*c**5*f*tan(e/2 + f*x/2)**2 + 1260*a**3*c**5*f*tan(e/2 + f*x/2) - 315*a**3*c**5*f) + 4956*A*tan(e/2 + f*x/2)**8/(315*a**3*c**5*f*tan(e/2 + f*x/2)**14 - 1260*a**3*c**5*f*tan(e/2 + f*x/2)**13 + 315*a**3*c**5*f*tan(e/2 + f*x/2)**12 + 5040*a**3*c**5*f*tan(e/2 + f*x/2)**11 - 5985*a**3*c**5*f*tan(e/2 + f*x/2)**10 - 6300*a**3*c**5*f*tan(e/2 + f*x/2)**9 + 14175*a**3*c**5*f*tan(e/2 + f*x/2)**8 - 14175*a**3*c**5*f*tan(e/2 + f*x/2)**6 + 6300*a**3*c**5*f*tan(e/2 + f*x/2)**5 + 5985*a**3*c**5*f*tan(e/2 + f*x/2)**4 - 5040*a**3*c**5*f*tan(e/2 + f*x/2)**3 - 315*a**3*c**5*f*tan(e/2 + f*x/2)**2 + 1260*a**3*c**5*f*tan(e/2 + f*x/2) - 315*a**3*c**5*f) - 7224*A*tan(e/2 + f*x/2)**7/(315*a**3*c**5*f*tan(e/2 + f*x/2)**14 - 1260*a**3*c**5*f*tan(e/2 + f*x/2)**13 + 315*a**3*c**5*f*tan(e/2 + f*x/2)**12 + 5040*a**3*c**5*f*tan(e/2 + f*x/2)**11 - 5985*a**3*c**5*f*tan(e/2 + f*x/2)**10 - 6300*a**3*c**5*f*tan(e/2 + f*x/2)**9 + 14175*a**3*c**5*f*tan(e/2 + f*x/2)**8 - 14175*a**3*c**5*f*tan(e/2 + f*x/2)**6 + 6300*a**3*c**5*f*tan(e/2 + f*x/2)**5 + 5985*a**3*c**5*f*tan(e/2 + f*x/2)**4 - 5040*a**3*c**5*f*tan(e/2 + f*x/2)**3 - 315*a**3*c**5*f*tan(e/2 + f*x/2)**2 + 1260*a**3*c**5*f*tan(e/2 + f*x/2) - 315*a**3*c**5*f) - 1344*A*tan(e/2 + f*x/2)**6/(315*a**3*c**5*f*tan(e/2 + f*x/2)**14 - 1260*a**3*c**5*f*tan(e/2 + f*x/2)**13 + 315*a**3*c**5*f*tan(e/2 + f*x/2)**12 + 5040*a**3*c**5*f*tan(e/2 + f*x/2)**11 - 5985*a**3*c**5*f*tan(e/2 + f*x/2)**10 - 6300*a**3*c**5*f*tan(e/2 + f*x/2)**9 + 14175*a**3*c**5*f*tan(e/2 + f*x/2)**8 - 14175*a**3*c**5*f*tan(e/2 + f*x/2)**6 + 6300*a**3*c**5*f*tan(e/2 + f*x/2)**5 + 5985*a**3*c**5*f*tan(e/2 + f*x/2)**4 - 5040*a**3*c**5*f*tan(e/2 + f*x/2)**3 - 315*a**3*c**5*f*tan(e/2 + f*x/2)**2 + 1260*a**3*c**5*f*tan(e/2 + f*x/2) - 315*a**3*c**5*f) + 3766*A*tan(e/2 + f*x/2)**5/(315*a**3*c**5*f*tan(e/2 + f*x/2)**14 - 1260*a**3*c**5*f*tan(e/2 + f*x/2)**13 + 315*a**3*c**5*f*tan(e/2 + f*x/2)**12 + 5040*a**3*c**5*f*tan(e/2 + f*x/2)**11 - 5985*a**3*c**5*f*tan(e/2 + f*x/2)**10 - 6300*a**3*c**5*f*tan(e/2 + f*x/2)**9 + 14175*a**3*c**5*f*tan(e/2 + f*x/2)**8 - 14175*a**3*c**5*f*tan(e/2 + f*x/2)**6 + 6300*a**3*c**5*f*tan(e/2 + f*x/2)**5 + 5985*a**3*c**5*f*tan(e/2 + f*x/2)**4 - 5040*a**3*c**5*f*tan(e/2 + f*x/2)**3 - 315*a**3*c**5*f*tan(e/2 + f*x/2)**2 + 1260*a**3*c**5*f*tan(e/2 + f*x/2) - 315*a**3*c**5*f) - 700*A*tan(e/2 + f*x/2)**4/(315*a**3*c**5*f*tan(e/2 + f*x/2)**14 - 1260*a**3*c**5*f*tan(e/2 + f*x/2)**13 + 315*a**3*c**5*f*tan(e/2 + f*x/2)**12 + 5040*a**3*c**5*f*tan(e/2 + f*x/2)**11 - 5985*a**3*c**5*f*tan(e/2 + f*x/2)**10 - 6300*a**3*c**5*f*tan(e/2 + f*x/2)**9 + 14175*a**3*c**5*f*tan(e/2 + f*x/2)**8 - 14175*a**3*c**5*f*tan(e/2 + f*x/2)**6 + 6300*a**3*c**5*f*tan(e/2 + f*x/2)**5 + 5985*a**3*c**5*f*tan(e/2 + f*x/2)**4 - 5040*a**3*c**5*f*tan(e/2 + f*x/2)**3 - 315*a**3*c**5*f*tan(e/2 + f*x/2)**2 + 1260*a**3*c**5*f*tan(e/2 + f*x/2) - 315*a**3*c**5*f) - 2660*A*tan(e/2 + f*x/2)**3/(315*a**3*c**5*f*tan(e/2 + f*x/2)**14 - 1260*a**3*c**5*f*tan(e/2 + f*x/2)**13 + 315*a**3*c**5*f*tan(e/2 + f*x/2)**12 + 5040*a**3*c**5*f*tan(e/2 + f*x/2)**11 - 5985*a**3*c**5*f*tan(e/2 + f*x/2)**10 - 6300*a**3*c**5*f*tan(e/2 + f*x/2)**9 + 14175*a**3*c**5*f*tan(e/2 + f*x/2)**8 - 14175*a**3*c**5*f*tan(e/2 + f*x/2)**6 + 6300*a**3*c**5*f*tan(e/2 + f*x/2)**5 + 5985*a**3*c**5*f*tan(e/2 + f*x/2)**4 - 5040*a**3*c**5*f*tan(e/2 + f*x/2)**3 - 315*a**3*c**5*f*tan(e/2 + f*x/2)**2 + 1260*a**3*c**5*f*tan(e/2 + f*x/2) - 315*a**3*c**5*f) + 1120*A*tan(e/2 + f*x/2)**2/(315*a**3*c**5*f*tan(e/2 + f*x/2)**14 - 1260*a**3*c**5*f*tan(e/2 + f*x/2)**13 + 315*a**3*c**5*f*tan(e/2 + f*x/2)**12 + 5040*a**3*c**5*f*tan(e/2 + f*x/2)**11 - 5985*a**3*c**5*f*tan(e/2 + f*x/2)**10 - 6300*a**3*c**5*f*tan(e/2 + f*x/2)**9 + 14175*a**3*c**5*f*tan(e/2 + f*x/2)**8 - 14175*a**3*c**5*f*tan(e/2 + f*x/2)**6 + 6300*a**3*c**5*f*tan(e/2 + f*x/2)**5 + 5985*a**3*c**5*f*tan(e/2 + f*x/2)**4 - 5040*a**3*c**5*f*tan(e/2 + f*x/2)**3 - 315*a**3*c**5*f*tan(e/2 + f*x/2)**2 + 1260*a**3*c**5*f*tan(e/2 + f*x/2) - 315*a**3*c**5*f) - 70*A*tan(e/2 + f*x/2)/(315*a**3*c**5*f*tan(e/2 + f*x/2)**14 - 1260*a**3*c**5*f*tan(e/2 + f*x/2)**13 + 315*a**3*c**5*f*tan(e/2 + f*x/2)**12 + 5040*a**3*c**5*f*tan(e/2 + f*x/2)**11 - 5985*a**3*c**5*f*tan(e/2 + f*x/2)**10 - 6300*a**3*c**5*f*tan(e/2 + f*x/2)**9 + 14175*a**3*c**5*f*tan(e/2 + f*x/2)**8 - 14175*a**3*c**5*f*tan(e/2 + f*x/2)**6 + 6300*a**3*c**5*f*tan(e/2 + f*x/2)**5 + 5985*a**3*c**5*f*tan(e/2 + f*x/2)**4 - 5040*a**3*c**5*f*tan(e/2 + f*x/2)**3 - 315*a**3*c**5*f*tan(e/2 + f*x/2)**2 + 1260*a**3*c**5*f*tan(e/2 + f*x/2) - 315*a**3*c**5*f) - 140*A/(315*a**3*c**5*f*tan(e/2 + f*x/2)**14 - 1260*a**3*c**5*f*tan(e/2 + f*x/2)**13 + 315*a**3*c**5*f*tan(e/2 + f*x/2)**12 + 5040*a**3*c**5*f*tan(e/2 + f*x/2)**11 - 5985*a**3*c**5*f*tan(e/2 + f*x/2)**10 - 6300*a**3*c**5*f*tan(e/2 + f*x/2)**9 + 14175*a**3*c**5*f*tan(e/2 + f*x/2)**8 - 14175*a**3*c**5*f*tan(e/2 + f*x/2)**6 + 6300*a**3*c**5*f*tan(e/2 + f*x/2)**5 + 5985*a**3*c**5*f*tan(e/2 + f*x/2)**4 - 5040*a**3*c**5*f*tan(e/2 + f*x/2)**3 - 315*a**3*c**5*f*tan(e/2 + f*x/2)**2 + 1260*a**3*c**5*f*tan(e/2 + f*x/2) - 315*a**3*c**5*f) - 630*B*tan(e/2 + f*x/2)**12/(315*a**3*c**5*f*tan(e/2 + f*x/2)**14 - 1260*a**3*c**5*f*tan(e/2 + f*x/2)**13 + 315*a**3*c**5*f*tan(e/2 + f*x/2)**12 + 5040*a**3*c**5*f*tan(e/2 + f*x/2)**11 - 5985*a**3*c**5*f*tan(e/2 + f*x/2)**10 - 6300*a**3*c**5*f*tan(e/2 + f*x/2)**9 + 14175*a**3*c**5*f*tan(e/2 + f*x/2)**8 - 14175*a**3*c**5*f*tan(e/2 + f*x/2)**6 + 6300*a**3*c**5*f*tan(e/2 + f*x/2)**5 + 5985*a**3*c**5*f*tan(e/2 + f*x/2)**4 - 5040*a**3*c**5*f*tan(e/2 + f*x/2)**3 - 315*a**3*c**5*f*tan(e/2 + f*x/2)**2 + 1260*a**3*c**5*f*tan(e/2 + f*x/2) - 315*a**3*c**5*f) + 840*B*tan(e/2 + f*x/2)**11/(315*a**3*c**5*f*tan(e/2 + f*x/2)**14 - 1260*a**3*c**5*f*tan(e/2 + f*x/2)**13 + 315*a**3*c**5*f*tan(e/2 + f*x/2)**12 + 5040*a**3*c**5*f*tan(e/2 + f*x/2)**11 - 5985*a**3*c**5*f*tan(e/2 + f*x/2)**10 - 6300*a**3*c**5*f*tan(e/2 + f*x/2)**9 + 14175*a**3*c**5*f*tan(e/2 + f*x/2)**8 - 14175*a**3*c**5*f*tan(e/2 + f*x/2)**6 + 6300*a**3*c**5*f*tan(e/2 + f*x/2)**5 + 5985*a**3*c**5*f*tan(e/2 + f*x/2)**4 - 5040*a**3*c**5*f*tan(e/2 + f*x/2)**3 - 315*a**3*c**5*f*tan(e/2 + f*x/2)**2 + 1260*a**3*c**5*f*tan(e/2 + f*x/2) - 315*a**3*c**5*f) - 840*B*tan(e/2 + f*x/2)**10/(315*a**3*c**5*f*tan(e/2 + f*x/2)**14 - 1260*a**3*c**5*f*tan(e/2 + f*x/2)**13 + 315*a**3*c**5*f*tan(e/2 + f*x/2)**12 + 5040*a**3*c**5*f*tan(e/2 + f*x/2)**11 - 5985*a**3*c**5*f*tan(e/2 + f*x/2)**10 - 6300*a**3*c**5*f*tan(e/2 + f*x/2)**9 + 14175*a**3*c**5*f*tan(e/2 + f*x/2)**8 - 14175*a**3*c**5*f*tan(e/2 + f*x/2)**6 + 6300*a**3*c**5*f*tan(e/2 + f*x/2)**5 + 5985*a**3*c**5*f*tan(e/2 + f*x/2)**4 - 5040*a**3*c**5*f*tan(e/2 + f*x/2)**3 - 315*a**3*c**5*f*tan(e/2 + f*x/2)**2 + 1260*a**3*c**5*f*tan(e/2 + f*x/2) - 315*a**3*c**5*f) - 1176*B*tan(e/2 + f*x/2)**9/(315*a**3*c**5*f*tan(e/2 + f*x/2)**14 - 1260*a**3*c**5*f*tan(e/2 + f*x/2)**13 + 315*a**3*c**5*f*tan(e/2 + f*x/2)**12 + 5040*a**3*c**5*f*tan(e/2 + f*x/2)**11 - 5985*a**3*c**5*f*tan(e/2 + f*x/2)**10 - 6300*a**3*c**5*f*tan(e/2 + f*x/2)**9 + 14175*a**3*c**5*f*tan(e/2 + f*x/2)**8 - 14175*a**3*c**5*f*tan(e/2 + f*x/2)**6 + 6300*a**3*c**5*f*tan(e/2 + f*x/2)**5 + 5985*a**3*c**5*f*tan(e/2 + f*x/2)**4 - 5040*a**3*c**5*f*tan(e/2 + f*x/2)**3 - 315*a**3*c**5*f*tan(e/2 + f*x/2)**2 + 1260*a**3*c**5*f*tan(e/2 + f*x/2) - 315*a**3*c**5*f) - 966*B*tan(e/2 + f*x/2)**8/(315*a**3*c**5*f*tan(e/2 + f*x/2)**14 - 1260*a**3*c**5*f*tan(e/2 + f*x/2)**13 + 315*a**3*c**5*f*tan(e/2 + f*x/2)**12 + 5040*a**3*c**5*f*tan(e/2 + f*x/2)**11 - 5985*a**3*c**5*f*tan(e/2 + f*x/2)**10 - 6300*a**3*c**5*f*tan(e/2 + f*x/2)**9 + 14175*a**3*c**5*f*tan(e/2 + f*x/2)**8 - 14175*a**3*c**5*f*tan(e/2 + f*x/2)**6 + 6300*a**3*c**5*f*tan(e/2 + f*x/2)**5 + 5985*a**3*c**5*f*tan(e/2 + f*x/2)**4 - 5040*a**3*c**5*f*tan(e/2 + f*x/2)**3 - 315*a**3*c**5*f*tan(e/2 + f*x/2)**2 + 1260*a**3*c**5*f*tan(e/2 + f*x/2) - 315*a**3*c**5*f) + 2064*B*tan(e/2 + f*x/2)**7/(315*a**3*c**5*f*tan(e/2 + f*x/2)**14 - 1260*a**3*c**5*f*tan(e/2 + f*x/2)**13 + 315*a**3*c**5*f*tan(e/2 + f*x/2)**12 + 5040*a**3*c**5*f*tan(e/2 + f*x/2)**11 - 5985*a**3*c**5*f*tan(e/2 + f*x/2)**10 - 6300*a**3*c**5*f*tan(e/2 + f*x/2)**9 + 14175*a**3*c**5*f*tan(e/2 + f*x/2)**8 - 14175*a**3*c**5*f*tan(e/2 + f*x/2)**6 + 6300*a**3*c**5*f*tan(e/2 + f*x/2)**5 + 5985*a**3*c**5*f*tan(e/2 + f*x/2)**4 - 5040*a**3*c**5*f*tan(e/2 + f*x/2)**3 - 315*a**3*c**5*f*tan(e/2 + f*x/2)**2 + 1260*a**3*c**5*f*tan(e/2 + f*x/2) - 315*a**3*c**5*f) - 3216*B*tan(e/2 + f*x/2)**6/(315*a**3*c**5*f*tan(e/2 + f*x/2)**14 - 1260*a**3*c**5*f*tan(e/2 + f*x/2)**13 + 315*a**3*c**5*f*tan(e/2 + f*x/2)**12 + 5040*a**3*c**5*f*tan(e/2 + f*x/2)**11 - 5985*a**3*c**5*f*tan(e/2 + f*x/2)**10 - 6300*a**3*c**5*f*tan(e/2 + f*x/2)**9 + 14175*a**3*c**5*f*tan(e/2 + f*x/2)**8 - 14175*a**3*c**5*f*tan(e/2 + f*x/2)**6 + 6300*a**3*c**5*f*tan(e/2 + f*x/2)**5 + 5985*a**3*c**5*f*tan(e/2 + f*x/2)**4 - 5040*a**3*c**5*f*tan(e/2 + f*x/2)**3 - 315*a**3*c**5*f*tan(e/2 + f*x/2)**2 + 1260*a**3*c**5*f*tan(e/2 + f*x/2) - 315*a**3*c**5*f) - 176*B*tan(e/2 + f*x/2)**5/(315*a**3*c**5*f*tan(e/2 + f*x/2)**14 - 1260*a**3*c**5*f*tan(e/2 + f*x/2)**13 + 315*a**3*c**5*f*tan(e/2 + f*x/2)**12 + 5040*a**3*c**5*f*tan(e/2 + f*x/2)**11 - 5985*a**3*c**5*f*tan(e/2 + f*x/2)**10 - 6300*a**3*c**5*f*tan(e/2 + f*x/2)**9 + 14175*a**3*c**5*f*tan(e/2 + f*x/2)**8 - 14175*a**3*c**5*f*tan(e/2 + f*x/2)**6 + 6300*a**3*c**5*f*tan(e/2 + f*x/2)**5 + 5985*a**3*c**5*f*tan(e/2 + f*x/2)**4 - 5040*a**3*c**5*f*tan(e/2 + f*x/2)**3 - 315*a**3*c**5*f*tan(e/2 + f*x/2)**2 + 1260*a**3*c**5*f*tan(e/2 + f*x/2) - 315*a**3*c**5*f) + 110*B*tan(e/2 + f*x/2)**4/(315*a**3*c**5*f*tan(e/2 + f*x/2)**14 - 1260*a**3*c**5*f*tan(e/2 + f*x/2)**13 + 315*a**3*c**5*f*tan(e/2 + f*x/2)**12 + 5040*a**3*c**5*f*tan(e/2 + f*x/2)**11 - 5985*a**3*c**5*f*tan(e/2 + f*x/2)**10 - 6300*a**3*c**5*f*tan(e/2 + f*x/2)**9 + 14175*a**3*c**5*f*tan(e/2 + f*x/2)**8 - 14175*a**3*c**5*f*tan(e/2 + f*x/2)**6 + 6300*a**3*c**5*f*tan(e/2 + f*x/2)**5 + 5985*a**3*c**5*f*tan(e/2 + f*x/2)**4 - 5040*a**3*c**5*f*tan(e/2 + f*x/2)**3 - 315*a**3*c**5*f*tan(e/2 + f*x/2)**2 + 1260*a**3*c**5*f*tan(e/2 + f*x/2) - 315*a**3*c**5*f) + 40*B*tan(e/2 + f*x/2)**3/(315*a**3*c**5*f*tan(e/2 + f*x/2)**14 - 1260*a**3*c**5*f*tan(e/2 + f*x/2)**13 + 315*a**3*c**5*f*tan(e/2 + f*x/2)**12 + 5040*a**3*c**5*f*tan(e/2 + f*x/2)**11 - 5985*a**3*c**5*f*tan(e/2 + f*x/2)**10 - 6300*a**3*c**5*f*tan(e/2 + f*x/2)**9 + 14175*a**3*c**5*f*tan(e/2 + f*x/2)**8 - 14175*a**3*c**5*f*tan(e/2 + f*x/2)**6 + 6300*a**3*c**5*f*tan(e/2 + f*x/2)**5 + 5985*a**3*c**5*f*tan(e/2 + f*x/2)**4 - 5040*a**3*c**5*f*tan(e/2 + f*x/2)**3 - 315*a**3*c**5*f*tan(e/2 + f*x/2)**2 + 1260*a**3*c**5*f*tan(e/2 + f*x/2) - 315*a**3*c**5*f) - 680*B*tan(e/2 + f*x/2)**2/(315*a**3*c**5*f*tan(e/2 + f*x/2)**14 - 1260*a**3*c**5*f*tan(e/2 + f*x/2)**13 + 315*a**3*c**5*f*tan(e/2 + f*x/2)**12 + 5040*a**3*c**5*f*tan(e/2 + f*x/2)**11 - 5985*a**3*c**5*f*tan(e/2 + f*x/2)**10 - 6300*a**3*c**5*f*tan(e/2 + f*x/2)**9 + 14175*a**3*c**5*f*tan(e/2 + f*x/2)**8 - 14175*a**3*c**5*f*tan(e/2 + f*x/2)**6 + 6300*a**3*c**5*f*tan(e/2 + f*x/2)**5 + 5985*a**3*c**5*f*tan(e/2 + f*x/2)**4 - 5040*a**3*c**5*f*tan(e/2 + f*x/2)**3 - 315*a**3*c**5*f*tan(e/2 + f*x/2)**2 + 1260*a**3*c**5*f*tan(e/2 + f*x/2) - 315*a**3*c**5*f) + 200*B*tan(e/2 + f*x/2)/(315*a**3*c**5*f*tan(e/2 + f*x/2)**14 - 1260*a**3*c**5*f*tan(e/2 + f*x/2)**13 + 315*a**3*c**5*f*tan(e/2 + f*x/2)**12 + 5040*a**3*c**5*f*tan(e/2 + f*x/2)**11 - 5985*a**3*c**5*f*tan(e/2 + f*x/2)**10 - 6300*a**3*c**5*f*tan(e/2 + f*x/2)**9 + 14175*a**3*c**5*f*tan(e/2 + f*x/2)**8 - 14175*a**3*c**5*f*tan(e/2 + f*x/2)**6 + 6300*a**3*c**5*f*tan(e/2 + f*x/2)**5 + 5985*a**3*c**5*f*tan(e/2 + f*x/2)**4 - 5040*a**3*c**5*f*tan(e/2 + f*x/2)**3 - 315*a**3*c**5*f*tan(e/2 + f*x/2)**2 + 1260*a**3*c**5*f*tan(e/2 + f*x/2) - 315*a**3*c**5*f) - 50*B/(315*a**3*c**5*f*tan(e/2 + f*x/2)**14 - 1260*a**3*c**5*f*tan(e/2 + f*x/2)**13 + 315*a**3*c**5*f*tan(e/2 + f*x/2)**12 + 5040*a**3*c**5*f*tan(e/2 + f*x/2)**11 - 5985*a**3*c**5*f*tan(e/2 + f*x/2)**10 - 6300*a**3*c**5*f*tan(e/2 + f*x/2)**9 + 14175*a**3*c**5*f*tan(e/2 + f*x/2)**8 - 14175*a**3*c**5*f*tan(e/2 + f*x/2)**6 + 6300*a**3*c**5*f*tan(e/2 + f*x/2)**5 + 5985*a**3*c**5*f*tan(e/2 + f*x/2)**4 - 5040*a**3*c**5*f*tan(e/2 + f*x/2)**3 - 315*a**3*c**5*f*tan(e/2 + f*x/2)**2 + 1260*a**3*c**5*f*tan(e/2 + f*x/2) - 315*a**3*c**5*f), Ne(f, 0)), (x*(A + B*sin(e))/((a*sin(e) + a)**3*(-c*sin(e) + c)**5), True))","A",0
80,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))**3/(c-c*sin(f*x+e))**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
81,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
82,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
83,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(3/2),x)","a \left(\int A c \sqrt{- c \sin{\left(e + f x \right)} + c}\, dx + \int \left(- A c \sqrt{- c \sin{\left(e + f x \right)} + c} \sin^{2}{\left(e + f x \right)}\right)\, dx + \int B c \sqrt{- c \sin{\left(e + f x \right)} + c} \sin{\left(e + f x \right)}\, dx + \int \left(- B c \sqrt{- c \sin{\left(e + f x \right)} + c} \sin^{3}{\left(e + f x \right)}\right)\, dx\right)"," ",0,"a*(Integral(A*c*sqrt(-c*sin(e + f*x) + c), x) + Integral(-A*c*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x)**2, x) + Integral(B*c*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x), x) + Integral(-B*c*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x)**3, x))","F",0
84,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(1/2),x)","a \left(\int A \sqrt{- c \sin{\left(e + f x \right)} + c}\, dx + \int A \sqrt{- c \sin{\left(e + f x \right)} + c} \sin{\left(e + f x \right)}\, dx + \int B \sqrt{- c \sin{\left(e + f x \right)} + c} \sin{\left(e + f x \right)}\, dx + \int B \sqrt{- c \sin{\left(e + f x \right)} + c} \sin^{2}{\left(e + f x \right)}\, dx\right)"," ",0,"a*(Integral(A*sqrt(-c*sin(e + f*x) + c), x) + Integral(A*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x), x) + Integral(B*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x), x) + Integral(B*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x)**2, x))","F",0
85,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**(1/2),x)","a \left(\int \frac{A}{\sqrt{- c \sin{\left(e + f x \right)} + c}}\, dx + \int \frac{A \sin{\left(e + f x \right)}}{\sqrt{- c \sin{\left(e + f x \right)} + c}}\, dx + \int \frac{B \sin{\left(e + f x \right)}}{\sqrt{- c \sin{\left(e + f x \right)} + c}}\, dx + \int \frac{B \sin^{2}{\left(e + f x \right)}}{\sqrt{- c \sin{\left(e + f x \right)} + c}}\, dx\right)"," ",0,"a*(Integral(A/sqrt(-c*sin(e + f*x) + c), x) + Integral(A*sin(e + f*x)/sqrt(-c*sin(e + f*x) + c), x) + Integral(B*sin(e + f*x)/sqrt(-c*sin(e + f*x) + c), x) + Integral(B*sin(e + f*x)**2/sqrt(-c*sin(e + f*x) + c), x))","F",0
86,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**(3/2),x)","a \left(\int \frac{A}{- c \sqrt{- c \sin{\left(e + f x \right)} + c} \sin{\left(e + f x \right)} + c \sqrt{- c \sin{\left(e + f x \right)} + c}}\, dx + \int \frac{A \sin{\left(e + f x \right)}}{- c \sqrt{- c \sin{\left(e + f x \right)} + c} \sin{\left(e + f x \right)} + c \sqrt{- c \sin{\left(e + f x \right)} + c}}\, dx + \int \frac{B \sin{\left(e + f x \right)}}{- c \sqrt{- c \sin{\left(e + f x \right)} + c} \sin{\left(e + f x \right)} + c \sqrt{- c \sin{\left(e + f x \right)} + c}}\, dx + \int \frac{B \sin^{2}{\left(e + f x \right)}}{- c \sqrt{- c \sin{\left(e + f x \right)} + c} \sin{\left(e + f x \right)} + c \sqrt{- c \sin{\left(e + f x \right)} + c}}\, dx\right)"," ",0,"a*(Integral(A/(-c*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x) + c*sqrt(-c*sin(e + f*x) + c)), x) + Integral(A*sin(e + f*x)/(-c*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x) + c*sqrt(-c*sin(e + f*x) + c)), x) + Integral(B*sin(e + f*x)/(-c*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x) + c*sqrt(-c*sin(e + f*x) + c)), x) + Integral(B*sin(e + f*x)**2/(-c*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x) + c*sqrt(-c*sin(e + f*x) + c)), x))","F",0
87,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
88,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
89,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**2*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
90,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**2*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
91,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**2*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(3/2),x)","a^{2} \left(\int A c \sqrt{- c \sin{\left(e + f x \right)} + c}\, dx + \int A c \sqrt{- c \sin{\left(e + f x \right)} + c} \sin{\left(e + f x \right)}\, dx + \int \left(- A c \sqrt{- c \sin{\left(e + f x \right)} + c} \sin^{2}{\left(e + f x \right)}\right)\, dx + \int \left(- A c \sqrt{- c \sin{\left(e + f x \right)} + c} \sin^{3}{\left(e + f x \right)}\right)\, dx + \int B c \sqrt{- c \sin{\left(e + f x \right)} + c} \sin{\left(e + f x \right)}\, dx + \int B c \sqrt{- c \sin{\left(e + f x \right)} + c} \sin^{2}{\left(e + f x \right)}\, dx + \int \left(- B c \sqrt{- c \sin{\left(e + f x \right)} + c} \sin^{3}{\left(e + f x \right)}\right)\, dx + \int \left(- B c \sqrt{- c \sin{\left(e + f x \right)} + c} \sin^{4}{\left(e + f x \right)}\right)\, dx\right)"," ",0,"a**2*(Integral(A*c*sqrt(-c*sin(e + f*x) + c), x) + Integral(A*c*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x), x) + Integral(-A*c*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x)**2, x) + Integral(-A*c*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x)**3, x) + Integral(B*c*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x), x) + Integral(B*c*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x)**2, x) + Integral(-B*c*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x)**3, x) + Integral(-B*c*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x)**4, x))","F",0
92,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**2*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(1/2),x)","a^{2} \left(\int A \sqrt{- c \sin{\left(e + f x \right)} + c}\, dx + \int 2 A \sqrt{- c \sin{\left(e + f x \right)} + c} \sin{\left(e + f x \right)}\, dx + \int A \sqrt{- c \sin{\left(e + f x \right)} + c} \sin^{2}{\left(e + f x \right)}\, dx + \int B \sqrt{- c \sin{\left(e + f x \right)} + c} \sin{\left(e + f x \right)}\, dx + \int 2 B \sqrt{- c \sin{\left(e + f x \right)} + c} \sin^{2}{\left(e + f x \right)}\, dx + \int B \sqrt{- c \sin{\left(e + f x \right)} + c} \sin^{3}{\left(e + f x \right)}\, dx\right)"," ",0,"a**2*(Integral(A*sqrt(-c*sin(e + f*x) + c), x) + Integral(2*A*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x), x) + Integral(A*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x)**2, x) + Integral(B*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x), x) + Integral(2*B*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x)**2, x) + Integral(B*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x)**3, x))","F",0
93,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**(1/2),x)","a^{2} \left(\int \frac{A}{\sqrt{- c \sin{\left(e + f x \right)} + c}}\, dx + \int \frac{2 A \sin{\left(e + f x \right)}}{\sqrt{- c \sin{\left(e + f x \right)} + c}}\, dx + \int \frac{A \sin^{2}{\left(e + f x \right)}}{\sqrt{- c \sin{\left(e + f x \right)} + c}}\, dx + \int \frac{B \sin{\left(e + f x \right)}}{\sqrt{- c \sin{\left(e + f x \right)} + c}}\, dx + \int \frac{2 B \sin^{2}{\left(e + f x \right)}}{\sqrt{- c \sin{\left(e + f x \right)} + c}}\, dx + \int \frac{B \sin^{3}{\left(e + f x \right)}}{\sqrt{- c \sin{\left(e + f x \right)} + c}}\, dx\right)"," ",0,"a**2*(Integral(A/sqrt(-c*sin(e + f*x) + c), x) + Integral(2*A*sin(e + f*x)/sqrt(-c*sin(e + f*x) + c), x) + Integral(A*sin(e + f*x)**2/sqrt(-c*sin(e + f*x) + c), x) + Integral(B*sin(e + f*x)/sqrt(-c*sin(e + f*x) + c), x) + Integral(2*B*sin(e + f*x)**2/sqrt(-c*sin(e + f*x) + c), x) + Integral(B*sin(e + f*x)**3/sqrt(-c*sin(e + f*x) + c), x))","F",0
94,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
95,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
96,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
97,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
98,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**3*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
99,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**3*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
100,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**3*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
101,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**3*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(1/2),x)","a^{3} \left(\int A \sqrt{- c \sin{\left(e + f x \right)} + c}\, dx + \int 3 A \sqrt{- c \sin{\left(e + f x \right)} + c} \sin{\left(e + f x \right)}\, dx + \int 3 A \sqrt{- c \sin{\left(e + f x \right)} + c} \sin^{2}{\left(e + f x \right)}\, dx + \int A \sqrt{- c \sin{\left(e + f x \right)} + c} \sin^{3}{\left(e + f x \right)}\, dx + \int B \sqrt{- c \sin{\left(e + f x \right)} + c} \sin{\left(e + f x \right)}\, dx + \int 3 B \sqrt{- c \sin{\left(e + f x \right)} + c} \sin^{2}{\left(e + f x \right)}\, dx + \int 3 B \sqrt{- c \sin{\left(e + f x \right)} + c} \sin^{3}{\left(e + f x \right)}\, dx + \int B \sqrt{- c \sin{\left(e + f x \right)} + c} \sin^{4}{\left(e + f x \right)}\, dx\right)"," ",0,"a**3*(Integral(A*sqrt(-c*sin(e + f*x) + c), x) + Integral(3*A*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x), x) + Integral(3*A*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x)**2, x) + Integral(A*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x)**3, x) + Integral(B*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x), x) + Integral(3*B*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x)**2, x) + Integral(3*B*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x)**3, x) + Integral(B*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x)**4, x))","F",0
102,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**(1/2),x)","a^{3} \left(\int \frac{A}{\sqrt{- c \sin{\left(e + f x \right)} + c}}\, dx + \int \frac{3 A \sin{\left(e + f x \right)}}{\sqrt{- c \sin{\left(e + f x \right)} + c}}\, dx + \int \frac{3 A \sin^{2}{\left(e + f x \right)}}{\sqrt{- c \sin{\left(e + f x \right)} + c}}\, dx + \int \frac{A \sin^{3}{\left(e + f x \right)}}{\sqrt{- c \sin{\left(e + f x \right)} + c}}\, dx + \int \frac{B \sin{\left(e + f x \right)}}{\sqrt{- c \sin{\left(e + f x \right)} + c}}\, dx + \int \frac{3 B \sin^{2}{\left(e + f x \right)}}{\sqrt{- c \sin{\left(e + f x \right)} + c}}\, dx + \int \frac{3 B \sin^{3}{\left(e + f x \right)}}{\sqrt{- c \sin{\left(e + f x \right)} + c}}\, dx + \int \frac{B \sin^{4}{\left(e + f x \right)}}{\sqrt{- c \sin{\left(e + f x \right)} + c}}\, dx\right)"," ",0,"a**3*(Integral(A/sqrt(-c*sin(e + f*x) + c), x) + Integral(3*A*sin(e + f*x)/sqrt(-c*sin(e + f*x) + c), x) + Integral(3*A*sin(e + f*x)**2/sqrt(-c*sin(e + f*x) + c), x) + Integral(A*sin(e + f*x)**3/sqrt(-c*sin(e + f*x) + c), x) + Integral(B*sin(e + f*x)/sqrt(-c*sin(e + f*x) + c), x) + Integral(3*B*sin(e + f*x)**2/sqrt(-c*sin(e + f*x) + c), x) + Integral(3*B*sin(e + f*x)**3/sqrt(-c*sin(e + f*x) + c), x) + Integral(B*sin(e + f*x)**4/sqrt(-c*sin(e + f*x) + c), x))","F",0
103,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
104,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
105,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
106,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
107,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
108,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(7/2)/(a+a*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
109,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(5/2)/(a+a*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
110,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(3/2)/(a+a*sin(f*x+e)),x)","\frac{\int \frac{A c \sqrt{- c \sin{\left(e + f x \right)} + c}}{\sin{\left(e + f x \right)} + 1}\, dx + \int \left(- \frac{A c \sqrt{- c \sin{\left(e + f x \right)} + c} \sin{\left(e + f x \right)}}{\sin{\left(e + f x \right)} + 1}\right)\, dx + \int \frac{B c \sqrt{- c \sin{\left(e + f x \right)} + c} \sin{\left(e + f x \right)}}{\sin{\left(e + f x \right)} + 1}\, dx + \int \left(- \frac{B c \sqrt{- c \sin{\left(e + f x \right)} + c} \sin^{2}{\left(e + f x \right)}}{\sin{\left(e + f x \right)} + 1}\right)\, dx}{a}"," ",0,"(Integral(A*c*sqrt(-c*sin(e + f*x) + c)/(sin(e + f*x) + 1), x) + Integral(-A*c*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x)/(sin(e + f*x) + 1), x) + Integral(B*c*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x)/(sin(e + f*x) + 1), x) + Integral(-B*c*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x)**2/(sin(e + f*x) + 1), x))/a","F",0
111,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(1/2)/(a+a*sin(f*x+e)),x)","\frac{\int \frac{A \sqrt{- c \sin{\left(e + f x \right)} + c}}{\sin{\left(e + f x \right)} + 1}\, dx + \int \frac{B \sqrt{- c \sin{\left(e + f x \right)} + c} \sin{\left(e + f x \right)}}{\sin{\left(e + f x \right)} + 1}\, dx}{a}"," ",0,"(Integral(A*sqrt(-c*sin(e + f*x) + c)/(sin(e + f*x) + 1), x) + Integral(B*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x)/(sin(e + f*x) + 1), x))/a","F",0
112,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))**(1/2),x)","\frac{\int \frac{A}{\sqrt{- c \sin{\left(e + f x \right)} + c} \sin{\left(e + f x \right)} + \sqrt{- c \sin{\left(e + f x \right)} + c}}\, dx + \int \frac{B \sin{\left(e + f x \right)}}{\sqrt{- c \sin{\left(e + f x \right)} + c} \sin{\left(e + f x \right)} + \sqrt{- c \sin{\left(e + f x \right)} + c}}\, dx}{a}"," ",0,"(Integral(A/(sqrt(-c*sin(e + f*x) + c)*sin(e + f*x) + sqrt(-c*sin(e + f*x) + c)), x) + Integral(B*sin(e + f*x)/(sqrt(-c*sin(e + f*x) + c)*sin(e + f*x) + sqrt(-c*sin(e + f*x) + c)), x))/a","F",0
113,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))**(3/2),x)","\frac{\int \frac{A}{- c \sqrt{- c \sin{\left(e + f x \right)} + c} \sin^{2}{\left(e + f x \right)} + c \sqrt{- c \sin{\left(e + f x \right)} + c}}\, dx + \int \frac{B \sin{\left(e + f x \right)}}{- c \sqrt{- c \sin{\left(e + f x \right)} + c} \sin^{2}{\left(e + f x \right)} + c \sqrt{- c \sin{\left(e + f x \right)} + c}}\, dx}{a}"," ",0,"(Integral(A/(-c*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x)**2 + c*sqrt(-c*sin(e + f*x) + c)), x) + Integral(B*sin(e + f*x)/(-c*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x)**2 + c*sqrt(-c*sin(e + f*x) + c)), x))/a","F",0
114,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
115,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(9/2)/(a+a*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
116,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(7/2)/(a+a*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
117,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(5/2)/(a+a*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
118,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(3/2)/(a+a*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
119,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(1/2)/(a+a*sin(f*x+e))**2,x)","\frac{\int \frac{A \sqrt{- c \sin{\left(e + f x \right)} + c}}{\sin^{2}{\left(e + f x \right)} + 2 \sin{\left(e + f x \right)} + 1}\, dx + \int \frac{B \sqrt{- c \sin{\left(e + f x \right)} + c} \sin{\left(e + f x \right)}}{\sin^{2}{\left(e + f x \right)} + 2 \sin{\left(e + f x \right)} + 1}\, dx}{a^{2}}"," ",0,"(Integral(A*sqrt(-c*sin(e + f*x) + c)/(sin(e + f*x)**2 + 2*sin(e + f*x) + 1), x) + Integral(B*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x)/(sin(e + f*x)**2 + 2*sin(e + f*x) + 1), x))/a**2","F",0
120,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))**2/(c-c*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
121,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))**2/(c-c*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
122,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))**2/(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
123,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(9/2)/(a+a*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
124,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(7/2)/(a+a*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
125,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(5/2)/(a+a*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
126,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(3/2)/(a+a*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
127,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(1/2)/(a+a*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
128,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))**3/(c-c*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
129,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))**3/(c-c*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
130,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))**3/(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
131,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(7/2)*(a+a*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
132,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(5/2)*(a+a*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
133,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(3/2)*(a+a*sin(f*x+e))**(1/2),x)","\int \sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)} \left(- c \left(\sin{\left(e + f x \right)} - 1\right)\right)^{\frac{3}{2}} \left(A + B \sin{\left(e + f x \right)}\right)\, dx"," ",0,"Integral(sqrt(a*(sin(e + f*x) + 1))*(-c*(sin(e + f*x) - 1))**(3/2)*(A + B*sin(e + f*x)), x)","F",0
134,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(1/2)*(a+a*sin(f*x+e))**(1/2),x)","\int \sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)} \sqrt{- c \left(\sin{\left(e + f x \right)} - 1\right)} \left(A + B \sin{\left(e + f x \right)}\right)\, dx"," ",0,"Integral(sqrt(a*(sin(e + f*x) + 1))*sqrt(-c*(sin(e + f*x) - 1))*(A + B*sin(e + f*x)), x)","F",0
135,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(a+a*sin(f*x+e))**(1/2)/(c-c*sin(f*x+e))**(1/2),x)","\int \frac{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)} \left(A + B \sin{\left(e + f x \right)}\right)}{\sqrt{- c \left(\sin{\left(e + f x \right)} - 1\right)}}\, dx"," ",0,"Integral(sqrt(a*(sin(e + f*x) + 1))*(A + B*sin(e + f*x))/sqrt(-c*(sin(e + f*x) - 1)), x)","F",0
136,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(a+a*sin(f*x+e))**(1/2)/(c-c*sin(f*x+e))**(3/2),x)","\int \frac{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)} \left(A + B \sin{\left(e + f x \right)}\right)}{\left(- c \left(\sin{\left(e + f x \right)} - 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(a*(sin(e + f*x) + 1))*(A + B*sin(e + f*x))/(-c*(sin(e + f*x) - 1))**(3/2), x)","F",0
137,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(a+a*sin(f*x+e))**(1/2)/(c-c*sin(f*x+e))**(5/2),x)","\int \frac{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)} \left(A + B \sin{\left(e + f x \right)}\right)}{\left(- c \left(\sin{\left(e + f x \right)} - 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt(a*(sin(e + f*x) + 1))*(A + B*sin(e + f*x))/(-c*(sin(e + f*x) - 1))**(5/2), x)","F",0
138,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(a+a*sin(f*x+e))**(1/2)/(c-c*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
139,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(3/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
140,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(3/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
141,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(3/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
142,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(3/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(1/2),x)","\int \left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}} \sqrt{- c \left(\sin{\left(e + f x \right)} - 1\right)} \left(A + B \sin{\left(e + f x \right)}\right)\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**(3/2)*sqrt(-c*(sin(e + f*x) - 1))*(A + B*sin(e + f*x)), x)","F",0
143,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(3/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**(1/2),x)","\int \frac{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}} \left(A + B \sin{\left(e + f x \right)}\right)}{\sqrt{- c \left(\sin{\left(e + f x \right)} - 1\right)}}\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**(3/2)*(A + B*sin(e + f*x))/sqrt(-c*(sin(e + f*x) - 1)), x)","F",0
144,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(3/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**(3/2),x)","\int \frac{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}} \left(A + B \sin{\left(e + f x \right)}\right)}{\left(- c \left(\sin{\left(e + f x \right)} - 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**(3/2)*(A + B*sin(e + f*x))/(-c*(sin(e + f*x) - 1))**(3/2), x)","F",0
145,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(3/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
146,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(3/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
147,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(3/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
148,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(3/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
149,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(5/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
150,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(5/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
151,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(5/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
152,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(5/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
153,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(5/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
154,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(5/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
155,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(5/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
156,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(5/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
157,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(5/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
158,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(5/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
159,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(5/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
160,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(7/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
161,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(7/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
162,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(7/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
163,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(7/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
164,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(7/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
165,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(7/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
166,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(7/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
167,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(7/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
168,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(7/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
169,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(7/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
170,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(7/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
171,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(7/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
172,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(7/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**(15/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
173,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(7/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**(17/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
174,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(5/2)/(a+a*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
175,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(3/2)/(a+a*sin(f*x+e))**(1/2),x)","\int \frac{\left(- c \left(\sin{\left(e + f x \right)} - 1\right)\right)^{\frac{3}{2}} \left(A + B \sin{\left(e + f x \right)}\right)}{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)}}\, dx"," ",0,"Integral((-c*(sin(e + f*x) - 1))**(3/2)*(A + B*sin(e + f*x))/sqrt(a*(sin(e + f*x) + 1)), x)","F",0
176,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(1/2)/(a+a*sin(f*x+e))**(1/2),x)","\int \frac{\sqrt{- c \left(\sin{\left(e + f x \right)} - 1\right)} \left(A + B \sin{\left(e + f x \right)}\right)}{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)}}\, dx"," ",0,"Integral(sqrt(-c*(sin(e + f*x) - 1))*(A + B*sin(e + f*x))/sqrt(a*(sin(e + f*x) + 1)), x)","F",0
177,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(c-c*sin(f*x+e))**(1/2)/(a+a*sin(f*x+e))**(1/2),x)","\int \frac{A + B \sin{\left(e + f x \right)}}{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)} \sqrt{- c \left(\sin{\left(e + f x \right)} - 1\right)}}\, dx"," ",0,"Integral((A + B*sin(e + f*x))/(sqrt(a*(sin(e + f*x) + 1))*sqrt(-c*(sin(e + f*x) - 1))), x)","F",0
178,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(c-c*sin(f*x+e))**(3/2)/(a+a*sin(f*x+e))**(1/2),x)","\int \frac{A + B \sin{\left(e + f x \right)}}{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)} \left(- c \left(\sin{\left(e + f x \right)} - 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*sin(e + f*x))/(sqrt(a*(sin(e + f*x) + 1))*(-c*(sin(e + f*x) - 1))**(3/2)), x)","F",0
179,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(c-c*sin(f*x+e))**(5/2)/(a+a*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
180,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(7/2)/(a+a*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
181,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(5/2)/(a+a*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
182,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(3/2)/(a+a*sin(f*x+e))**(3/2),x)","\int \frac{\left(- c \left(\sin{\left(e + f x \right)} - 1\right)\right)^{\frac{3}{2}} \left(A + B \sin{\left(e + f x \right)}\right)}{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((-c*(sin(e + f*x) - 1))**(3/2)*(A + B*sin(e + f*x))/(a*(sin(e + f*x) + 1))**(3/2), x)","F",0
183,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(1/2)/(a+a*sin(f*x+e))**(3/2),x)","\int \frac{\sqrt{- c \left(\sin{\left(e + f x \right)} - 1\right)} \left(A + B \sin{\left(e + f x \right)}\right)}{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(-c*(sin(e + f*x) - 1))*(A + B*sin(e + f*x))/(a*(sin(e + f*x) + 1))**(3/2), x)","F",0
184,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))**(3/2)/(c-c*sin(f*x+e))**(1/2),x)","\int \frac{A + B \sin{\left(e + f x \right)}}{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}} \sqrt{- c \left(\sin{\left(e + f x \right)} - 1\right)}}\, dx"," ",0,"Integral((A + B*sin(e + f*x))/((a*(sin(e + f*x) + 1))**(3/2)*sqrt(-c*(sin(e + f*x) - 1))), x)","F",0
185,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))**(3/2)/(c-c*sin(f*x+e))**(3/2),x)","\int \frac{A + B \sin{\left(e + f x \right)}}{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}} \left(- c \left(\sin{\left(e + f x \right)} - 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*sin(e + f*x))/((a*(sin(e + f*x) + 1))**(3/2)*(-c*(sin(e + f*x) - 1))**(3/2)), x)","F",0
186,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))**(3/2)/(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
187,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(9/2)/(a+a*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
188,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(7/2)/(a+a*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
189,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(5/2)/(a+a*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
190,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(3/2)/(a+a*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
191,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(1/2)/(a+a*sin(f*x+e))**(5/2),x)","\int \frac{\sqrt{- c \left(\sin{\left(e + f x \right)} - 1\right)} \left(A + B \sin{\left(e + f x \right)}\right)}{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt(-c*(sin(e + f*x) - 1))*(A + B*sin(e + f*x))/(a*(sin(e + f*x) + 1))**(5/2), x)","F",0
192,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))**(5/2)/(c-c*sin(f*x+e))**(1/2),x)","\int \frac{A + B \sin{\left(e + f x \right)}}{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{5}{2}} \sqrt{- c \left(\sin{\left(e + f x \right)} - 1\right)}}\, dx"," ",0,"Integral((A + B*sin(e + f*x))/((a*(sin(e + f*x) + 1))**(5/2)*sqrt(-c*(sin(e + f*x) - 1))), x)","F",0
193,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))**(5/2)/(c-c*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
194,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))**(5/2)/(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
195,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**n,x)","\int \left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{m} \left(- c \left(\sin{\left(e + f x \right)} - 1\right)\right)^{n} \left(A + B \sin{\left(e + f x \right)}\right)\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**m*(-c*(sin(e + f*x) - 1))**n*(A + B*sin(e + f*x)), x)","F",0
196,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
197,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**2,x)","c^{2} \left(\int A \left(a \sin{\left(e + f x \right)} + a\right)^{m}\, dx + \int \left(- 2 A \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}\right)\, dx + \int A \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)}\, dx + \int B \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}\, dx + \int \left(- 2 B \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)}\right)\, dx + \int B \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{3}{\left(e + f x \right)}\, dx\right)"," ",0,"c**2*(Integral(A*(a*sin(e + f*x) + a)**m, x) + Integral(-2*A*(a*sin(e + f*x) + a)**m*sin(e + f*x), x) + Integral(A*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2, x) + Integral(B*(a*sin(e + f*x) + a)**m*sin(e + f*x), x) + Integral(-2*B*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2, x) + Integral(B*(a*sin(e + f*x) + a)**m*sin(e + f*x)**3, x))","F",0
198,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e)),x)","- c \left(\int \left(- A \left(a \sin{\left(e + f x \right)} + a\right)^{m}\right)\, dx + \int A \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}\, dx + \int \left(- B \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}\right)\, dx + \int B \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)}\, dx\right)"," ",0,"-c*(Integral(-A*(a*sin(e + f*x) + a)**m, x) + Integral(A*(a*sin(e + f*x) + a)**m*sin(e + f*x), x) + Integral(-B*(a*sin(e + f*x) + a)**m*sin(e + f*x), x) + Integral(B*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2, x))","F",0
199,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(A+B*sin(f*x+e)),x)","\int \left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{m} \left(A + B \sin{\left(e + f x \right)}\right)\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**m*(A + B*sin(e + f*x)), x)","F",0
200,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(A+B*sin(f*x+e))/(c-c*sin(f*x+e)),x)","- \frac{\int \frac{A \left(a \sin{\left(e + f x \right)} + a\right)^{m}}{\sin{\left(e + f x \right)} - 1}\, dx + \int \frac{B \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}}{\sin{\left(e + f x \right)} - 1}\, dx}{c}"," ",0,"-(Integral(A*(a*sin(e + f*x) + a)**m/(sin(e + f*x) - 1), x) + Integral(B*(a*sin(e + f*x) + a)**m*sin(e + f*x)/(sin(e + f*x) - 1), x))/c","F",0
201,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**2,x)","\frac{\int \frac{A \left(a \sin{\left(e + f x \right)} + a\right)^{m}}{\sin^{2}{\left(e + f x \right)} - 2 \sin{\left(e + f x \right)} + 1}\, dx + \int \frac{B \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}}{\sin^{2}{\left(e + f x \right)} - 2 \sin{\left(e + f x \right)} + 1}\, dx}{c^{2}}"," ",0,"(Integral(A*(a*sin(e + f*x) + a)**m/(sin(e + f*x)**2 - 2*sin(e + f*x) + 1), x) + Integral(B*(a*sin(e + f*x) + a)**m*sin(e + f*x)/(sin(e + f*x)**2 - 2*sin(e + f*x) + 1), x))/c**2","F",0
202,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
203,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**(1/2),x)","\int \frac{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{m} \left(A + B \sin{\left(e + f x \right)}\right)}{\sqrt{- c \left(\sin{\left(e + f x \right)} - 1\right)}}\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**m*(A + B*sin(e + f*x))/sqrt(-c*(sin(e + f*x) - 1)), x)","F",0
204,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c+c*sin(f*x+e))**m/(a-a*sin(f*x+e))**(1/2),x)","\int \frac{\left(c \left(\sin{\left(e + f x \right)} + 1\right)\right)^{m} \left(A + B \sin{\left(e + f x \right)}\right)}{\sqrt{- a \left(\sin{\left(e + f x \right)} - 1\right)}}\, dx"," ",0,"Integral((c*(sin(e + f*x) + 1))**m*(A + B*sin(e + f*x))/sqrt(-a*(sin(e + f*x) - 1)), x)","F",0
205,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
206,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
207,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(1/2),x)","\int \left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{m} \sqrt{- c \left(\sin{\left(e + f x \right)} - 1\right)} \left(A + B \sin{\left(e + f x \right)}\right)\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**m*sqrt(-c*(sin(e + f*x) - 1))*(A + B*sin(e + f*x)), x)","F",0
208,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**(1/2),x)","\int \frac{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{m} \left(A + B \sin{\left(e + f x \right)}\right)}{\sqrt{- c \left(\sin{\left(e + f x \right)} - 1\right)}}\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**m*(A + B*sin(e + f*x))/sqrt(-c*(sin(e + f*x) - 1)), x)","F",0
209,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**(3/2),x)","\int \frac{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{m} \left(A + B \sin{\left(e + f x \right)}\right)}{\left(- c \left(\sin{\left(e + f x \right)} - 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**m*(A + B*sin(e + f*x))/(-c*(sin(e + f*x) - 1))**(3/2), x)","F",0
210,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
211,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(-4-m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
212,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(-3-m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
213,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(-2-m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
214,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(-1-m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
215,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(A+B*sin(f*x+e))/((c-c*sin(f*x+e))**m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
216,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(1-m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
217,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(2-m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
218,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**3*(c-c*sin(f*x+e))**n*(B*(3-n)-B*(4+n)*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
219,-1,0,0,0.000000," ","integrate((a-a*sin(f*x+e))**3*(c+c*sin(f*x+e))**n*(B*(3-n)+B*(4+n)*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
220,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**3*(B*(-3+m)-B*(4+m)*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
221,-1,0,0,0.000000," ","integrate((a-a*sin(f*x+e))**m*(c+c*sin(f*x+e))**3*(B*(-3+m)+B*(4+m)*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
222,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**n*(B*(m-n)-B*(1+m+n)*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
223,-1,0,0,0.000000," ","integrate((a-a*sin(f*x+e))**m*(c+c*sin(f*x+e))**n*(B*(m-n)+B*(1+m+n)*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
224,1,440,0,8.486161," ","integrate(sin(d*x+c)**3*(a+a*sin(d*x+c))**3*(A-A*sin(d*x+c)),x)","\begin{cases} - \frac{5 A a^{3} x \sin^{6}{\left(c + d x \right)}}{8} - \frac{15 A a^{3} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{8} + \frac{3 A a^{3} x \sin^{4}{\left(c + d x \right)}}{4} - \frac{15 A a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 A a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{2} - \frac{5 A a^{3} x \cos^{6}{\left(c + d x \right)}}{8} + \frac{3 A a^{3} x \cos^{4}{\left(c + d x \right)}}{4} + \frac{A a^{3} \sin^{6}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} + \frac{11 A a^{3} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{2 A a^{3} \sin^{4}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{d} + \frac{5 A a^{3} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{5 A a^{3} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 d} + \frac{8 A a^{3} \sin^{2}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{A a^{3} \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} + \frac{5 A a^{3} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{8 d} - \frac{3 A a^{3} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{4 d} + \frac{16 A a^{3} \cos^{7}{\left(c + d x \right)}}{35 d} - \frac{2 A a^{3} \cos^{3}{\left(c + d x \right)}}{3 d} & \text{for}\: d \neq 0 \\x \left(- A \sin{\left(c \right)} + A\right) \left(a \sin{\left(c \right)} + a\right)^{3} \sin^{3}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-5*A*a**3*x*sin(c + d*x)**6/8 - 15*A*a**3*x*sin(c + d*x)**4*cos(c + d*x)**2/8 + 3*A*a**3*x*sin(c + d*x)**4/4 - 15*A*a**3*x*sin(c + d*x)**2*cos(c + d*x)**4/8 + 3*A*a**3*x*sin(c + d*x)**2*cos(c + d*x)**2/2 - 5*A*a**3*x*cos(c + d*x)**6/8 + 3*A*a**3*x*cos(c + d*x)**4/4 + A*a**3*sin(c + d*x)**6*cos(c + d*x)/d + 11*A*a**3*sin(c + d*x)**5*cos(c + d*x)/(8*d) + 2*A*a**3*sin(c + d*x)**4*cos(c + d*x)**3/d + 5*A*a**3*sin(c + d*x)**3*cos(c + d*x)**3/(3*d) - 5*A*a**3*sin(c + d*x)**3*cos(c + d*x)/(4*d) + 8*A*a**3*sin(c + d*x)**2*cos(c + d*x)**5/(5*d) - A*a**3*sin(c + d*x)**2*cos(c + d*x)/d + 5*A*a**3*sin(c + d*x)*cos(c + d*x)**5/(8*d) - 3*A*a**3*sin(c + d*x)*cos(c + d*x)**3/(4*d) + 16*A*a**3*cos(c + d*x)**7/(35*d) - 2*A*a**3*cos(c + d*x)**3/(3*d), Ne(d, 0)), (x*(-A*sin(c) + A)*(a*sin(c) + a)**3*sin(c)**3, True))","A",0
225,1,359,0,5.693138," ","integrate(sin(d*x+c)**2*(a+a*sin(d*x+c))**3*(A-A*sin(d*x+c)),x)","\begin{cases} - \frac{5 A a^{3} x \sin^{6}{\left(c + d x \right)}}{16} - \frac{15 A a^{3} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} - \frac{15 A a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{A a^{3} x \sin^{2}{\left(c + d x \right)}}{2} - \frac{5 A a^{3} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{A a^{3} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{11 A a^{3} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{2 A a^{3} \sin^{4}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} + \frac{5 A a^{3} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{8 A a^{3} \sin^{2}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{2 A a^{3} \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} + \frac{5 A a^{3} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} - \frac{A a^{3} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{16 A a^{3} \cos^{5}{\left(c + d x \right)}}{15 d} - \frac{4 A a^{3} \cos^{3}{\left(c + d x \right)}}{3 d} & \text{for}\: d \neq 0 \\x \left(- A \sin{\left(c \right)} + A\right) \left(a \sin{\left(c \right)} + a\right)^{3} \sin^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-5*A*a**3*x*sin(c + d*x)**6/16 - 15*A*a**3*x*sin(c + d*x)**4*cos(c + d*x)**2/16 - 15*A*a**3*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + A*a**3*x*sin(c + d*x)**2/2 - 5*A*a**3*x*cos(c + d*x)**6/16 + A*a**3*x*cos(c + d*x)**2/2 + 11*A*a**3*sin(c + d*x)**5*cos(c + d*x)/(16*d) + 2*A*a**3*sin(c + d*x)**4*cos(c + d*x)/d + 5*A*a**3*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) + 8*A*a**3*sin(c + d*x)**2*cos(c + d*x)**3/(3*d) - 2*A*a**3*sin(c + d*x)**2*cos(c + d*x)/d + 5*A*a**3*sin(c + d*x)*cos(c + d*x)**5/(16*d) - A*a**3*sin(c + d*x)*cos(c + d*x)/(2*d) + 16*A*a**3*cos(c + d*x)**5/(15*d) - 4*A*a**3*cos(c + d*x)**3/(3*d), Ne(d, 0)), (x*(-A*sin(c) + A)*(a*sin(c) + a)**3*sin(c)**2, True))","A",0
226,1,267,0,3.646525," ","integrate(sin(d*x+c)*(a+a*sin(d*x+c))**3*(A-A*sin(d*x+c)),x)","\begin{cases} - \frac{3 A a^{3} x \sin^{4}{\left(c + d x \right)}}{4} - \frac{3 A a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{2} + A a^{3} x \sin^{2}{\left(c + d x \right)} - \frac{3 A a^{3} x \cos^{4}{\left(c + d x \right)}}{4} + A a^{3} x \cos^{2}{\left(c + d x \right)} + \frac{A a^{3} \sin^{4}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} + \frac{5 A a^{3} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 d} + \frac{4 A a^{3} \sin^{2}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} + \frac{3 A a^{3} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{4 d} - \frac{A a^{3} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} + \frac{8 A a^{3} \cos^{5}{\left(c + d x \right)}}{15 d} - \frac{A a^{3} \cos{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(- A \sin{\left(c \right)} + A\right) \left(a \sin{\left(c \right)} + a\right)^{3} \sin{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*A*a**3*x*sin(c + d*x)**4/4 - 3*A*a**3*x*sin(c + d*x)**2*cos(c + d*x)**2/2 + A*a**3*x*sin(c + d*x)**2 - 3*A*a**3*x*cos(c + d*x)**4/4 + A*a**3*x*cos(c + d*x)**2 + A*a**3*sin(c + d*x)**4*cos(c + d*x)/d + 5*A*a**3*sin(c + d*x)**3*cos(c + d*x)/(4*d) + 4*A*a**3*sin(c + d*x)**2*cos(c + d*x)**3/(3*d) + 3*A*a**3*sin(c + d*x)*cos(c + d*x)**3/(4*d) - A*a**3*sin(c + d*x)*cos(c + d*x)/d + 8*A*a**3*cos(c + d*x)**5/(15*d) - A*a**3*cos(c + d*x)/d, Ne(d, 0)), (x*(-A*sin(c) + A)*(a*sin(c) + a)**3*sin(c), True))","A",0
227,1,196,0,1.372880," ","integrate((a+a*sin(d*x+c))**3*(A-A*sin(d*x+c)),x)","\begin{cases} - \frac{3 A a^{3} x \sin^{4}{\left(c + d x \right)}}{8} - \frac{3 A a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} - \frac{3 A a^{3} x \cos^{4}{\left(c + d x \right)}}{8} + A a^{3} x + \frac{5 A a^{3} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{2 A a^{3} \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} + \frac{3 A a^{3} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{4 A a^{3} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{2 A a^{3} \cos{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(- A \sin{\left(c \right)} + A\right) \left(a \sin{\left(c \right)} + a\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*A*a**3*x*sin(c + d*x)**4/8 - 3*A*a**3*x*sin(c + d*x)**2*cos(c + d*x)**2/4 - 3*A*a**3*x*cos(c + d*x)**4/8 + A*a**3*x + 5*A*a**3*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 2*A*a**3*sin(c + d*x)**2*cos(c + d*x)/d + 3*A*a**3*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 4*A*a**3*cos(c + d*x)**3/(3*d) - 2*A*a**3*cos(c + d*x)/d, Ne(d, 0)), (x*(-A*sin(c) + A)*(a*sin(c) + a)**3, True))","A",0
228,0,0,0,0.000000," ","integrate(csc(d*x+c)*(a+a*sin(d*x+c))**3*(A-A*sin(d*x+c)),x)","- A a^{3} \left(\int \left(- 2 \sin{\left(c + d x \right)} \csc{\left(c + d x \right)}\right)\, dx + \int 2 \sin^{3}{\left(c + d x \right)} \csc{\left(c + d x \right)}\, dx + \int \sin^{4}{\left(c + d x \right)} \csc{\left(c + d x \right)}\, dx + \int \left(- \csc{\left(c + d x \right)}\right)\, dx\right)"," ",0,"-A*a**3*(Integral(-2*sin(c + d*x)*csc(c + d*x), x) + Integral(2*sin(c + d*x)**3*csc(c + d*x), x) + Integral(sin(c + d*x)**4*csc(c + d*x), x) + Integral(-csc(c + d*x), x))","F",0
229,0,0,0,0.000000," ","integrate(csc(d*x+c)**2*(a+a*sin(d*x+c))**3*(A-A*sin(d*x+c)),x)","- A a^{3} \left(\int \left(- 2 \sin{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}\right)\, dx + \int 2 \sin^{3}{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}\, dx + \int \sin^{4}{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}\, dx + \int \left(- \csc^{2}{\left(c + d x \right)}\right)\, dx\right)"," ",0,"-A*a**3*(Integral(-2*sin(c + d*x)*csc(c + d*x)**2, x) + Integral(2*sin(c + d*x)**3*csc(c + d*x)**2, x) + Integral(sin(c + d*x)**4*csc(c + d*x)**2, x) + Integral(-csc(c + d*x)**2, x))","F",0
230,-1,0,0,0.000000," ","integrate(csc(d*x+c)**3*(a+a*sin(d*x+c))**3*(A-A*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
231,-1,0,0,0.000000," ","integrate(csc(d*x+c)**4*(a+a*sin(d*x+c))**3*(A-A*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
232,-1,0,0,0.000000," ","integrate(csc(d*x+c)**5*(a+a*sin(d*x+c))**3*(A-A*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
233,-1,0,0,0.000000," ","integrate(csc(d*x+c)**6*(a+a*sin(d*x+c))**3*(A-A*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
234,-1,0,0,0.000000," ","integrate(csc(d*x+c)**7*(a+a*sin(d*x+c))**3*(A-A*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
235,1,3614,0,78.443694," ","integrate(sin(d*x+c)**4*(A-A*sin(d*x+c))/(a+a*sin(d*x+c))**3,x)","\begin{cases} - \frac{285 A d x \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{30 a^{3} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 360 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 780 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 780 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 360 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d} - \frac{1425 A d x \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{30 a^{3} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 360 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 780 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 780 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 360 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d} - \frac{3420 A d x \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{30 a^{3} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 360 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 780 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 780 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 360 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d} - \frac{5700 A d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{30 a^{3} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 360 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 780 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 780 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 360 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d} - \frac{7410 A d x \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{30 a^{3} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 360 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 780 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 780 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 360 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d} - \frac{7410 A d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{30 a^{3} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 360 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 780 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 780 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 360 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d} - \frac{5700 A d x \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{30 a^{3} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 360 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 780 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 780 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 360 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d} - \frac{3420 A d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{30 a^{3} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 360 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 780 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 780 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 360 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d} - \frac{1425 A d x \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{30 a^{3} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 360 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 780 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 780 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 360 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d} - \frac{285 A d x}{30 a^{3} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 360 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 780 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 780 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 360 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d} - \frac{570 A \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{30 a^{3} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 360 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 780 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 780 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 360 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d} - \frac{2850 A \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{30 a^{3} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 360 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 780 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 780 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 360 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d} - \frac{6650 A \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{30 a^{3} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 360 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 780 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 780 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 360 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d} - \frac{10450 A \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{30 a^{3} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 360 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 780 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 780 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 360 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d} - \frac{12846 A \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{30 a^{3} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 360 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 780 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 780 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 360 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d} - \frac{11270 A \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{30 a^{3} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 360 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 780 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 780 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 360 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d} - \frac{7902 A \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{30 a^{3} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 360 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 780 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 780 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 360 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d} - \frac{3910 A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{30 a^{3} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 360 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 780 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 780 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 360 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d} - \frac{896 A}{30 a^{3} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 360 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 780 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 780 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 360 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \left(- A \sin{\left(c \right)} + A\right) \sin^{4}{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-285*A*d*x*tan(c/2 + d*x/2)**9/(30*a**3*d*tan(c/2 + d*x/2)**9 + 150*a**3*d*tan(c/2 + d*x/2)**8 + 360*a**3*d*tan(c/2 + d*x/2)**7 + 600*a**3*d*tan(c/2 + d*x/2)**6 + 780*a**3*d*tan(c/2 + d*x/2)**5 + 780*a**3*d*tan(c/2 + d*x/2)**4 + 600*a**3*d*tan(c/2 + d*x/2)**3 + 360*a**3*d*tan(c/2 + d*x/2)**2 + 150*a**3*d*tan(c/2 + d*x/2) + 30*a**3*d) - 1425*A*d*x*tan(c/2 + d*x/2)**8/(30*a**3*d*tan(c/2 + d*x/2)**9 + 150*a**3*d*tan(c/2 + d*x/2)**8 + 360*a**3*d*tan(c/2 + d*x/2)**7 + 600*a**3*d*tan(c/2 + d*x/2)**6 + 780*a**3*d*tan(c/2 + d*x/2)**5 + 780*a**3*d*tan(c/2 + d*x/2)**4 + 600*a**3*d*tan(c/2 + d*x/2)**3 + 360*a**3*d*tan(c/2 + d*x/2)**2 + 150*a**3*d*tan(c/2 + d*x/2) + 30*a**3*d) - 3420*A*d*x*tan(c/2 + d*x/2)**7/(30*a**3*d*tan(c/2 + d*x/2)**9 + 150*a**3*d*tan(c/2 + d*x/2)**8 + 360*a**3*d*tan(c/2 + d*x/2)**7 + 600*a**3*d*tan(c/2 + d*x/2)**6 + 780*a**3*d*tan(c/2 + d*x/2)**5 + 780*a**3*d*tan(c/2 + d*x/2)**4 + 600*a**3*d*tan(c/2 + d*x/2)**3 + 360*a**3*d*tan(c/2 + d*x/2)**2 + 150*a**3*d*tan(c/2 + d*x/2) + 30*a**3*d) - 5700*A*d*x*tan(c/2 + d*x/2)**6/(30*a**3*d*tan(c/2 + d*x/2)**9 + 150*a**3*d*tan(c/2 + d*x/2)**8 + 360*a**3*d*tan(c/2 + d*x/2)**7 + 600*a**3*d*tan(c/2 + d*x/2)**6 + 780*a**3*d*tan(c/2 + d*x/2)**5 + 780*a**3*d*tan(c/2 + d*x/2)**4 + 600*a**3*d*tan(c/2 + d*x/2)**3 + 360*a**3*d*tan(c/2 + d*x/2)**2 + 150*a**3*d*tan(c/2 + d*x/2) + 30*a**3*d) - 7410*A*d*x*tan(c/2 + d*x/2)**5/(30*a**3*d*tan(c/2 + d*x/2)**9 + 150*a**3*d*tan(c/2 + d*x/2)**8 + 360*a**3*d*tan(c/2 + d*x/2)**7 + 600*a**3*d*tan(c/2 + d*x/2)**6 + 780*a**3*d*tan(c/2 + d*x/2)**5 + 780*a**3*d*tan(c/2 + d*x/2)**4 + 600*a**3*d*tan(c/2 + d*x/2)**3 + 360*a**3*d*tan(c/2 + d*x/2)**2 + 150*a**3*d*tan(c/2 + d*x/2) + 30*a**3*d) - 7410*A*d*x*tan(c/2 + d*x/2)**4/(30*a**3*d*tan(c/2 + d*x/2)**9 + 150*a**3*d*tan(c/2 + d*x/2)**8 + 360*a**3*d*tan(c/2 + d*x/2)**7 + 600*a**3*d*tan(c/2 + d*x/2)**6 + 780*a**3*d*tan(c/2 + d*x/2)**5 + 780*a**3*d*tan(c/2 + d*x/2)**4 + 600*a**3*d*tan(c/2 + d*x/2)**3 + 360*a**3*d*tan(c/2 + d*x/2)**2 + 150*a**3*d*tan(c/2 + d*x/2) + 30*a**3*d) - 5700*A*d*x*tan(c/2 + d*x/2)**3/(30*a**3*d*tan(c/2 + d*x/2)**9 + 150*a**3*d*tan(c/2 + d*x/2)**8 + 360*a**3*d*tan(c/2 + d*x/2)**7 + 600*a**3*d*tan(c/2 + d*x/2)**6 + 780*a**3*d*tan(c/2 + d*x/2)**5 + 780*a**3*d*tan(c/2 + d*x/2)**4 + 600*a**3*d*tan(c/2 + d*x/2)**3 + 360*a**3*d*tan(c/2 + d*x/2)**2 + 150*a**3*d*tan(c/2 + d*x/2) + 30*a**3*d) - 3420*A*d*x*tan(c/2 + d*x/2)**2/(30*a**3*d*tan(c/2 + d*x/2)**9 + 150*a**3*d*tan(c/2 + d*x/2)**8 + 360*a**3*d*tan(c/2 + d*x/2)**7 + 600*a**3*d*tan(c/2 + d*x/2)**6 + 780*a**3*d*tan(c/2 + d*x/2)**5 + 780*a**3*d*tan(c/2 + d*x/2)**4 + 600*a**3*d*tan(c/2 + d*x/2)**3 + 360*a**3*d*tan(c/2 + d*x/2)**2 + 150*a**3*d*tan(c/2 + d*x/2) + 30*a**3*d) - 1425*A*d*x*tan(c/2 + d*x/2)/(30*a**3*d*tan(c/2 + d*x/2)**9 + 150*a**3*d*tan(c/2 + d*x/2)**8 + 360*a**3*d*tan(c/2 + d*x/2)**7 + 600*a**3*d*tan(c/2 + d*x/2)**6 + 780*a**3*d*tan(c/2 + d*x/2)**5 + 780*a**3*d*tan(c/2 + d*x/2)**4 + 600*a**3*d*tan(c/2 + d*x/2)**3 + 360*a**3*d*tan(c/2 + d*x/2)**2 + 150*a**3*d*tan(c/2 + d*x/2) + 30*a**3*d) - 285*A*d*x/(30*a**3*d*tan(c/2 + d*x/2)**9 + 150*a**3*d*tan(c/2 + d*x/2)**8 + 360*a**3*d*tan(c/2 + d*x/2)**7 + 600*a**3*d*tan(c/2 + d*x/2)**6 + 780*a**3*d*tan(c/2 + d*x/2)**5 + 780*a**3*d*tan(c/2 + d*x/2)**4 + 600*a**3*d*tan(c/2 + d*x/2)**3 + 360*a**3*d*tan(c/2 + d*x/2)**2 + 150*a**3*d*tan(c/2 + d*x/2) + 30*a**3*d) - 570*A*tan(c/2 + d*x/2)**8/(30*a**3*d*tan(c/2 + d*x/2)**9 + 150*a**3*d*tan(c/2 + d*x/2)**8 + 360*a**3*d*tan(c/2 + d*x/2)**7 + 600*a**3*d*tan(c/2 + d*x/2)**6 + 780*a**3*d*tan(c/2 + d*x/2)**5 + 780*a**3*d*tan(c/2 + d*x/2)**4 + 600*a**3*d*tan(c/2 + d*x/2)**3 + 360*a**3*d*tan(c/2 + d*x/2)**2 + 150*a**3*d*tan(c/2 + d*x/2) + 30*a**3*d) - 2850*A*tan(c/2 + d*x/2)**7/(30*a**3*d*tan(c/2 + d*x/2)**9 + 150*a**3*d*tan(c/2 + d*x/2)**8 + 360*a**3*d*tan(c/2 + d*x/2)**7 + 600*a**3*d*tan(c/2 + d*x/2)**6 + 780*a**3*d*tan(c/2 + d*x/2)**5 + 780*a**3*d*tan(c/2 + d*x/2)**4 + 600*a**3*d*tan(c/2 + d*x/2)**3 + 360*a**3*d*tan(c/2 + d*x/2)**2 + 150*a**3*d*tan(c/2 + d*x/2) + 30*a**3*d) - 6650*A*tan(c/2 + d*x/2)**6/(30*a**3*d*tan(c/2 + d*x/2)**9 + 150*a**3*d*tan(c/2 + d*x/2)**8 + 360*a**3*d*tan(c/2 + d*x/2)**7 + 600*a**3*d*tan(c/2 + d*x/2)**6 + 780*a**3*d*tan(c/2 + d*x/2)**5 + 780*a**3*d*tan(c/2 + d*x/2)**4 + 600*a**3*d*tan(c/2 + d*x/2)**3 + 360*a**3*d*tan(c/2 + d*x/2)**2 + 150*a**3*d*tan(c/2 + d*x/2) + 30*a**3*d) - 10450*A*tan(c/2 + d*x/2)**5/(30*a**3*d*tan(c/2 + d*x/2)**9 + 150*a**3*d*tan(c/2 + d*x/2)**8 + 360*a**3*d*tan(c/2 + d*x/2)**7 + 600*a**3*d*tan(c/2 + d*x/2)**6 + 780*a**3*d*tan(c/2 + d*x/2)**5 + 780*a**3*d*tan(c/2 + d*x/2)**4 + 600*a**3*d*tan(c/2 + d*x/2)**3 + 360*a**3*d*tan(c/2 + d*x/2)**2 + 150*a**3*d*tan(c/2 + d*x/2) + 30*a**3*d) - 12846*A*tan(c/2 + d*x/2)**4/(30*a**3*d*tan(c/2 + d*x/2)**9 + 150*a**3*d*tan(c/2 + d*x/2)**8 + 360*a**3*d*tan(c/2 + d*x/2)**7 + 600*a**3*d*tan(c/2 + d*x/2)**6 + 780*a**3*d*tan(c/2 + d*x/2)**5 + 780*a**3*d*tan(c/2 + d*x/2)**4 + 600*a**3*d*tan(c/2 + d*x/2)**3 + 360*a**3*d*tan(c/2 + d*x/2)**2 + 150*a**3*d*tan(c/2 + d*x/2) + 30*a**3*d) - 11270*A*tan(c/2 + d*x/2)**3/(30*a**3*d*tan(c/2 + d*x/2)**9 + 150*a**3*d*tan(c/2 + d*x/2)**8 + 360*a**3*d*tan(c/2 + d*x/2)**7 + 600*a**3*d*tan(c/2 + d*x/2)**6 + 780*a**3*d*tan(c/2 + d*x/2)**5 + 780*a**3*d*tan(c/2 + d*x/2)**4 + 600*a**3*d*tan(c/2 + d*x/2)**3 + 360*a**3*d*tan(c/2 + d*x/2)**2 + 150*a**3*d*tan(c/2 + d*x/2) + 30*a**3*d) - 7902*A*tan(c/2 + d*x/2)**2/(30*a**3*d*tan(c/2 + d*x/2)**9 + 150*a**3*d*tan(c/2 + d*x/2)**8 + 360*a**3*d*tan(c/2 + d*x/2)**7 + 600*a**3*d*tan(c/2 + d*x/2)**6 + 780*a**3*d*tan(c/2 + d*x/2)**5 + 780*a**3*d*tan(c/2 + d*x/2)**4 + 600*a**3*d*tan(c/2 + d*x/2)**3 + 360*a**3*d*tan(c/2 + d*x/2)**2 + 150*a**3*d*tan(c/2 + d*x/2) + 30*a**3*d) - 3910*A*tan(c/2 + d*x/2)/(30*a**3*d*tan(c/2 + d*x/2)**9 + 150*a**3*d*tan(c/2 + d*x/2)**8 + 360*a**3*d*tan(c/2 + d*x/2)**7 + 600*a**3*d*tan(c/2 + d*x/2)**6 + 780*a**3*d*tan(c/2 + d*x/2)**5 + 780*a**3*d*tan(c/2 + d*x/2)**4 + 600*a**3*d*tan(c/2 + d*x/2)**3 + 360*a**3*d*tan(c/2 + d*x/2)**2 + 150*a**3*d*tan(c/2 + d*x/2) + 30*a**3*d) - 896*A/(30*a**3*d*tan(c/2 + d*x/2)**9 + 150*a**3*d*tan(c/2 + d*x/2)**8 + 360*a**3*d*tan(c/2 + d*x/2)**7 + 600*a**3*d*tan(c/2 + d*x/2)**6 + 780*a**3*d*tan(c/2 + d*x/2)**5 + 780*a**3*d*tan(c/2 + d*x/2)**4 + 600*a**3*d*tan(c/2 + d*x/2)**3 + 360*a**3*d*tan(c/2 + d*x/2)**2 + 150*a**3*d*tan(c/2 + d*x/2) + 30*a**3*d), Ne(d, 0)), (x*(-A*sin(c) + A)*sin(c)**4/(a*sin(c) + a)**3, True))","A",0
236,1,2290,0,45.407495," ","integrate(sin(d*x+c)**3*(A-A*sin(d*x+c))/(a+a*sin(d*x+c))**3,x)","\begin{cases} \frac{60 A d x \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{3} d} + \frac{300 A d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{3} d} + \frac{660 A d x \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{3} d} + \frac{900 A d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{3} d} + \frac{900 A d x \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{3} d} + \frac{660 A d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{3} d} + \frac{300 A d x \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{3} d} + \frac{60 A d x}{15 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{3} d} + \frac{120 A \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{3} d} + \frac{600 A \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{3} d} + \frac{1280 A \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{3} d} + \frac{1540 A \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{3} d} + \frac{1468 A \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{3} d} + \frac{820 A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{3} d} + \frac{188 A}{15 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \left(- A \sin{\left(c \right)} + A\right) \sin^{3}{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((60*A*d*x*tan(c/2 + d*x/2)**7/(15*a**3*d*tan(c/2 + d*x/2)**7 + 75*a**3*d*tan(c/2 + d*x/2)**6 + 165*a**3*d*tan(c/2 + d*x/2)**5 + 225*a**3*d*tan(c/2 + d*x/2)**4 + 225*a**3*d*tan(c/2 + d*x/2)**3 + 165*a**3*d*tan(c/2 + d*x/2)**2 + 75*a**3*d*tan(c/2 + d*x/2) + 15*a**3*d) + 300*A*d*x*tan(c/2 + d*x/2)**6/(15*a**3*d*tan(c/2 + d*x/2)**7 + 75*a**3*d*tan(c/2 + d*x/2)**6 + 165*a**3*d*tan(c/2 + d*x/2)**5 + 225*a**3*d*tan(c/2 + d*x/2)**4 + 225*a**3*d*tan(c/2 + d*x/2)**3 + 165*a**3*d*tan(c/2 + d*x/2)**2 + 75*a**3*d*tan(c/2 + d*x/2) + 15*a**3*d) + 660*A*d*x*tan(c/2 + d*x/2)**5/(15*a**3*d*tan(c/2 + d*x/2)**7 + 75*a**3*d*tan(c/2 + d*x/2)**6 + 165*a**3*d*tan(c/2 + d*x/2)**5 + 225*a**3*d*tan(c/2 + d*x/2)**4 + 225*a**3*d*tan(c/2 + d*x/2)**3 + 165*a**3*d*tan(c/2 + d*x/2)**2 + 75*a**3*d*tan(c/2 + d*x/2) + 15*a**3*d) + 900*A*d*x*tan(c/2 + d*x/2)**4/(15*a**3*d*tan(c/2 + d*x/2)**7 + 75*a**3*d*tan(c/2 + d*x/2)**6 + 165*a**3*d*tan(c/2 + d*x/2)**5 + 225*a**3*d*tan(c/2 + d*x/2)**4 + 225*a**3*d*tan(c/2 + d*x/2)**3 + 165*a**3*d*tan(c/2 + d*x/2)**2 + 75*a**3*d*tan(c/2 + d*x/2) + 15*a**3*d) + 900*A*d*x*tan(c/2 + d*x/2)**3/(15*a**3*d*tan(c/2 + d*x/2)**7 + 75*a**3*d*tan(c/2 + d*x/2)**6 + 165*a**3*d*tan(c/2 + d*x/2)**5 + 225*a**3*d*tan(c/2 + d*x/2)**4 + 225*a**3*d*tan(c/2 + d*x/2)**3 + 165*a**3*d*tan(c/2 + d*x/2)**2 + 75*a**3*d*tan(c/2 + d*x/2) + 15*a**3*d) + 660*A*d*x*tan(c/2 + d*x/2)**2/(15*a**3*d*tan(c/2 + d*x/2)**7 + 75*a**3*d*tan(c/2 + d*x/2)**6 + 165*a**3*d*tan(c/2 + d*x/2)**5 + 225*a**3*d*tan(c/2 + d*x/2)**4 + 225*a**3*d*tan(c/2 + d*x/2)**3 + 165*a**3*d*tan(c/2 + d*x/2)**2 + 75*a**3*d*tan(c/2 + d*x/2) + 15*a**3*d) + 300*A*d*x*tan(c/2 + d*x/2)/(15*a**3*d*tan(c/2 + d*x/2)**7 + 75*a**3*d*tan(c/2 + d*x/2)**6 + 165*a**3*d*tan(c/2 + d*x/2)**5 + 225*a**3*d*tan(c/2 + d*x/2)**4 + 225*a**3*d*tan(c/2 + d*x/2)**3 + 165*a**3*d*tan(c/2 + d*x/2)**2 + 75*a**3*d*tan(c/2 + d*x/2) + 15*a**3*d) + 60*A*d*x/(15*a**3*d*tan(c/2 + d*x/2)**7 + 75*a**3*d*tan(c/2 + d*x/2)**6 + 165*a**3*d*tan(c/2 + d*x/2)**5 + 225*a**3*d*tan(c/2 + d*x/2)**4 + 225*a**3*d*tan(c/2 + d*x/2)**3 + 165*a**3*d*tan(c/2 + d*x/2)**2 + 75*a**3*d*tan(c/2 + d*x/2) + 15*a**3*d) + 120*A*tan(c/2 + d*x/2)**6/(15*a**3*d*tan(c/2 + d*x/2)**7 + 75*a**3*d*tan(c/2 + d*x/2)**6 + 165*a**3*d*tan(c/2 + d*x/2)**5 + 225*a**3*d*tan(c/2 + d*x/2)**4 + 225*a**3*d*tan(c/2 + d*x/2)**3 + 165*a**3*d*tan(c/2 + d*x/2)**2 + 75*a**3*d*tan(c/2 + d*x/2) + 15*a**3*d) + 600*A*tan(c/2 + d*x/2)**5/(15*a**3*d*tan(c/2 + d*x/2)**7 + 75*a**3*d*tan(c/2 + d*x/2)**6 + 165*a**3*d*tan(c/2 + d*x/2)**5 + 225*a**3*d*tan(c/2 + d*x/2)**4 + 225*a**3*d*tan(c/2 + d*x/2)**3 + 165*a**3*d*tan(c/2 + d*x/2)**2 + 75*a**3*d*tan(c/2 + d*x/2) + 15*a**3*d) + 1280*A*tan(c/2 + d*x/2)**4/(15*a**3*d*tan(c/2 + d*x/2)**7 + 75*a**3*d*tan(c/2 + d*x/2)**6 + 165*a**3*d*tan(c/2 + d*x/2)**5 + 225*a**3*d*tan(c/2 + d*x/2)**4 + 225*a**3*d*tan(c/2 + d*x/2)**3 + 165*a**3*d*tan(c/2 + d*x/2)**2 + 75*a**3*d*tan(c/2 + d*x/2) + 15*a**3*d) + 1540*A*tan(c/2 + d*x/2)**3/(15*a**3*d*tan(c/2 + d*x/2)**7 + 75*a**3*d*tan(c/2 + d*x/2)**6 + 165*a**3*d*tan(c/2 + d*x/2)**5 + 225*a**3*d*tan(c/2 + d*x/2)**4 + 225*a**3*d*tan(c/2 + d*x/2)**3 + 165*a**3*d*tan(c/2 + d*x/2)**2 + 75*a**3*d*tan(c/2 + d*x/2) + 15*a**3*d) + 1468*A*tan(c/2 + d*x/2)**2/(15*a**3*d*tan(c/2 + d*x/2)**7 + 75*a**3*d*tan(c/2 + d*x/2)**6 + 165*a**3*d*tan(c/2 + d*x/2)**5 + 225*a**3*d*tan(c/2 + d*x/2)**4 + 225*a**3*d*tan(c/2 + d*x/2)**3 + 165*a**3*d*tan(c/2 + d*x/2)**2 + 75*a**3*d*tan(c/2 + d*x/2) + 15*a**3*d) + 820*A*tan(c/2 + d*x/2)/(15*a**3*d*tan(c/2 + d*x/2)**7 + 75*a**3*d*tan(c/2 + d*x/2)**6 + 165*a**3*d*tan(c/2 + d*x/2)**5 + 225*a**3*d*tan(c/2 + d*x/2)**4 + 225*a**3*d*tan(c/2 + d*x/2)**3 + 165*a**3*d*tan(c/2 + d*x/2)**2 + 75*a**3*d*tan(c/2 + d*x/2) + 15*a**3*d) + 188*A/(15*a**3*d*tan(c/2 + d*x/2)**7 + 75*a**3*d*tan(c/2 + d*x/2)**6 + 165*a**3*d*tan(c/2 + d*x/2)**5 + 225*a**3*d*tan(c/2 + d*x/2)**4 + 225*a**3*d*tan(c/2 + d*x/2)**3 + 165*a**3*d*tan(c/2 + d*x/2)**2 + 75*a**3*d*tan(c/2 + d*x/2) + 15*a**3*d), Ne(d, 0)), (x*(-A*sin(c) + A)*sin(c)**3/(a*sin(c) + a)**3, True))","A",0
237,1,1268,0,25.571726," ","integrate(sin(d*x+c)**2*(A-A*sin(d*x+c))/(a+a*sin(d*x+c))**3,x)","\begin{cases} - \frac{5 A d x \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{5 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 25 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 50 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 50 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 25 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5 a^{3} d} - \frac{25 A d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{5 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 25 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 50 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 50 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 25 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5 a^{3} d} - \frac{50 A d x \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{5 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 25 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 50 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 50 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 25 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5 a^{3} d} - \frac{50 A d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{5 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 25 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 50 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 50 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 25 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5 a^{3} d} - \frac{25 A d x \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{5 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 25 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 50 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 50 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 25 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5 a^{3} d} - \frac{5 A d x}{5 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 25 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 50 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 50 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 25 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5 a^{3} d} - \frac{10 A \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{5 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 25 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 50 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 50 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 25 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5 a^{3} d} - \frac{50 A \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{5 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 25 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 50 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 50 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 25 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5 a^{3} d} - \frac{110 A \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{5 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 25 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 50 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 50 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 25 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5 a^{3} d} - \frac{70 A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{5 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 25 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 50 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 50 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 25 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5 a^{3} d} - \frac{16 A}{5 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 25 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 50 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 50 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 25 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5 a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \left(- A \sin{\left(c \right)} + A\right) \sin^{2}{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-5*A*d*x*tan(c/2 + d*x/2)**5/(5*a**3*d*tan(c/2 + d*x/2)**5 + 25*a**3*d*tan(c/2 + d*x/2)**4 + 50*a**3*d*tan(c/2 + d*x/2)**3 + 50*a**3*d*tan(c/2 + d*x/2)**2 + 25*a**3*d*tan(c/2 + d*x/2) + 5*a**3*d) - 25*A*d*x*tan(c/2 + d*x/2)**4/(5*a**3*d*tan(c/2 + d*x/2)**5 + 25*a**3*d*tan(c/2 + d*x/2)**4 + 50*a**3*d*tan(c/2 + d*x/2)**3 + 50*a**3*d*tan(c/2 + d*x/2)**2 + 25*a**3*d*tan(c/2 + d*x/2) + 5*a**3*d) - 50*A*d*x*tan(c/2 + d*x/2)**3/(5*a**3*d*tan(c/2 + d*x/2)**5 + 25*a**3*d*tan(c/2 + d*x/2)**4 + 50*a**3*d*tan(c/2 + d*x/2)**3 + 50*a**3*d*tan(c/2 + d*x/2)**2 + 25*a**3*d*tan(c/2 + d*x/2) + 5*a**3*d) - 50*A*d*x*tan(c/2 + d*x/2)**2/(5*a**3*d*tan(c/2 + d*x/2)**5 + 25*a**3*d*tan(c/2 + d*x/2)**4 + 50*a**3*d*tan(c/2 + d*x/2)**3 + 50*a**3*d*tan(c/2 + d*x/2)**2 + 25*a**3*d*tan(c/2 + d*x/2) + 5*a**3*d) - 25*A*d*x*tan(c/2 + d*x/2)/(5*a**3*d*tan(c/2 + d*x/2)**5 + 25*a**3*d*tan(c/2 + d*x/2)**4 + 50*a**3*d*tan(c/2 + d*x/2)**3 + 50*a**3*d*tan(c/2 + d*x/2)**2 + 25*a**3*d*tan(c/2 + d*x/2) + 5*a**3*d) - 5*A*d*x/(5*a**3*d*tan(c/2 + d*x/2)**5 + 25*a**3*d*tan(c/2 + d*x/2)**4 + 50*a**3*d*tan(c/2 + d*x/2)**3 + 50*a**3*d*tan(c/2 + d*x/2)**2 + 25*a**3*d*tan(c/2 + d*x/2) + 5*a**3*d) - 10*A*tan(c/2 + d*x/2)**4/(5*a**3*d*tan(c/2 + d*x/2)**5 + 25*a**3*d*tan(c/2 + d*x/2)**4 + 50*a**3*d*tan(c/2 + d*x/2)**3 + 50*a**3*d*tan(c/2 + d*x/2)**2 + 25*a**3*d*tan(c/2 + d*x/2) + 5*a**3*d) - 50*A*tan(c/2 + d*x/2)**3/(5*a**3*d*tan(c/2 + d*x/2)**5 + 25*a**3*d*tan(c/2 + d*x/2)**4 + 50*a**3*d*tan(c/2 + d*x/2)**3 + 50*a**3*d*tan(c/2 + d*x/2)**2 + 25*a**3*d*tan(c/2 + d*x/2) + 5*a**3*d) - 110*A*tan(c/2 + d*x/2)**2/(5*a**3*d*tan(c/2 + d*x/2)**5 + 25*a**3*d*tan(c/2 + d*x/2)**4 + 50*a**3*d*tan(c/2 + d*x/2)**3 + 50*a**3*d*tan(c/2 + d*x/2)**2 + 25*a**3*d*tan(c/2 + d*x/2) + 5*a**3*d) - 70*A*tan(c/2 + d*x/2)/(5*a**3*d*tan(c/2 + d*x/2)**5 + 25*a**3*d*tan(c/2 + d*x/2)**4 + 50*a**3*d*tan(c/2 + d*x/2)**3 + 50*a**3*d*tan(c/2 + d*x/2)**2 + 25*a**3*d*tan(c/2 + d*x/2) + 5*a**3*d) - 16*A/(5*a**3*d*tan(c/2 + d*x/2)**5 + 25*a**3*d*tan(c/2 + d*x/2)**4 + 50*a**3*d*tan(c/2 + d*x/2)**3 + 50*a**3*d*tan(c/2 + d*x/2)**2 + 25*a**3*d*tan(c/2 + d*x/2) + 5*a**3*d), Ne(d, 0)), (x*(-A*sin(c) + A)*sin(c)**2/(a*sin(c) + a)**3, True))","A",0
238,1,461,0,14.110373," ","integrate(sin(d*x+c)*(A-A*sin(d*x+c))/(a+a*sin(d*x+c))**3,x)","\begin{cases} - \frac{30 A \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{3} d} + \frac{10 A \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{3} d} - \frac{10 A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{3} d} - \frac{2 A}{15 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \left(- A \sin{\left(c \right)} + A\right) \sin{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-30*A*tan(c/2 + d*x/2)**3/(15*a**3*d*tan(c/2 + d*x/2)**5 + 75*a**3*d*tan(c/2 + d*x/2)**4 + 150*a**3*d*tan(c/2 + d*x/2)**3 + 150*a**3*d*tan(c/2 + d*x/2)**2 + 75*a**3*d*tan(c/2 + d*x/2) + 15*a**3*d) + 10*A*tan(c/2 + d*x/2)**2/(15*a**3*d*tan(c/2 + d*x/2)**5 + 75*a**3*d*tan(c/2 + d*x/2)**4 + 150*a**3*d*tan(c/2 + d*x/2)**3 + 150*a**3*d*tan(c/2 + d*x/2)**2 + 75*a**3*d*tan(c/2 + d*x/2) + 15*a**3*d) - 10*A*tan(c/2 + d*x/2)/(15*a**3*d*tan(c/2 + d*x/2)**5 + 75*a**3*d*tan(c/2 + d*x/2)**4 + 150*a**3*d*tan(c/2 + d*x/2)**3 + 150*a**3*d*tan(c/2 + d*x/2)**2 + 75*a**3*d*tan(c/2 + d*x/2) + 15*a**3*d) - 2*A/(15*a**3*d*tan(c/2 + d*x/2)**5 + 75*a**3*d*tan(c/2 + d*x/2)**4 + 150*a**3*d*tan(c/2 + d*x/2)**3 + 150*a**3*d*tan(c/2 + d*x/2)**2 + 75*a**3*d*tan(c/2 + d*x/2) + 15*a**3*d), Ne(d, 0)), (x*(-A*sin(c) + A)*sin(c)/(a*sin(c) + a)**3, True))","A",0
239,1,573,0,9.113531," ","integrate((A-A*sin(d*x+c))/(a+a*sin(d*x+c))**3,x)","\begin{cases} - \frac{30 A \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{3} d} - \frac{30 A \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{3} d} - \frac{50 A \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{3} d} - \frac{10 A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{3} d} - \frac{8 A}{15 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \left(- A \sin{\left(c \right)} + A\right)}{\left(a \sin{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-30*A*tan(c/2 + d*x/2)**4/(15*a**3*d*tan(c/2 + d*x/2)**5 + 75*a**3*d*tan(c/2 + d*x/2)**4 + 150*a**3*d*tan(c/2 + d*x/2)**3 + 150*a**3*d*tan(c/2 + d*x/2)**2 + 75*a**3*d*tan(c/2 + d*x/2) + 15*a**3*d) - 30*A*tan(c/2 + d*x/2)**3/(15*a**3*d*tan(c/2 + d*x/2)**5 + 75*a**3*d*tan(c/2 + d*x/2)**4 + 150*a**3*d*tan(c/2 + d*x/2)**3 + 150*a**3*d*tan(c/2 + d*x/2)**2 + 75*a**3*d*tan(c/2 + d*x/2) + 15*a**3*d) - 50*A*tan(c/2 + d*x/2)**2/(15*a**3*d*tan(c/2 + d*x/2)**5 + 75*a**3*d*tan(c/2 + d*x/2)**4 + 150*a**3*d*tan(c/2 + d*x/2)**3 + 150*a**3*d*tan(c/2 + d*x/2)**2 + 75*a**3*d*tan(c/2 + d*x/2) + 15*a**3*d) - 10*A*tan(c/2 + d*x/2)/(15*a**3*d*tan(c/2 + d*x/2)**5 + 75*a**3*d*tan(c/2 + d*x/2)**4 + 150*a**3*d*tan(c/2 + d*x/2)**3 + 150*a**3*d*tan(c/2 + d*x/2)**2 + 75*a**3*d*tan(c/2 + d*x/2) + 15*a**3*d) - 8*A/(15*a**3*d*tan(c/2 + d*x/2)**5 + 75*a**3*d*tan(c/2 + d*x/2)**4 + 150*a**3*d*tan(c/2 + d*x/2)**3 + 150*a**3*d*tan(c/2 + d*x/2)**2 + 75*a**3*d*tan(c/2 + d*x/2) + 15*a**3*d), Ne(d, 0)), (x*(-A*sin(c) + A)/(a*sin(c) + a)**3, True))","A",0
240,0,0,0,0.000000," ","integrate(csc(d*x+c)*(A-A*sin(d*x+c))/(a+a*sin(d*x+c))**3,x)","- \frac{A \left(\int \left(- \frac{\csc{\left(c + d x \right)}}{\sin^{3}{\left(c + d x \right)} + 3 \sin^{2}{\left(c + d x \right)} + 3 \sin{\left(c + d x \right)} + 1}\right)\, dx + \int \frac{\sin{\left(c + d x \right)} \csc{\left(c + d x \right)}}{\sin^{3}{\left(c + d x \right)} + 3 \sin^{2}{\left(c + d x \right)} + 3 \sin{\left(c + d x \right)} + 1}\, dx\right)}{a^{3}}"," ",0,"-A*(Integral(-csc(c + d*x)/(sin(c + d*x)**3 + 3*sin(c + d*x)**2 + 3*sin(c + d*x) + 1), x) + Integral(sin(c + d*x)*csc(c + d*x)/(sin(c + d*x)**3 + 3*sin(c + d*x)**2 + 3*sin(c + d*x) + 1), x))/a**3","F",0
241,0,0,0,0.000000," ","integrate(csc(d*x+c)**2*(A-A*sin(d*x+c))/(a+a*sin(d*x+c))**3,x)","- \frac{A \left(\int \left(- \frac{\csc^{2}{\left(c + d x \right)}}{\sin^{3}{\left(c + d x \right)} + 3 \sin^{2}{\left(c + d x \right)} + 3 \sin{\left(c + d x \right)} + 1}\right)\, dx + \int \frac{\sin{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}}{\sin^{3}{\left(c + d x \right)} + 3 \sin^{2}{\left(c + d x \right)} + 3 \sin{\left(c + d x \right)} + 1}\, dx\right)}{a^{3}}"," ",0,"-A*(Integral(-csc(c + d*x)**2/(sin(c + d*x)**3 + 3*sin(c + d*x)**2 + 3*sin(c + d*x) + 1), x) + Integral(sin(c + d*x)*csc(c + d*x)**2/(sin(c + d*x)**3 + 3*sin(c + d*x)**2 + 3*sin(c + d*x) + 1), x))/a**3","F",0
242,0,0,0,0.000000," ","integrate(csc(d*x+c)**3*(A-A*sin(d*x+c))/(a+a*sin(d*x+c))**3,x)","- \frac{A \left(\int \left(- \frac{\csc^{3}{\left(c + d x \right)}}{\sin^{3}{\left(c + d x \right)} + 3 \sin^{2}{\left(c + d x \right)} + 3 \sin{\left(c + d x \right)} + 1}\right)\, dx + \int \frac{\sin{\left(c + d x \right)} \csc^{3}{\left(c + d x \right)}}{\sin^{3}{\left(c + d x \right)} + 3 \sin^{2}{\left(c + d x \right)} + 3 \sin{\left(c + d x \right)} + 1}\, dx\right)}{a^{3}}"," ",0,"-A*(Integral(-csc(c + d*x)**3/(sin(c + d*x)**3 + 3*sin(c + d*x)**2 + 3*sin(c + d*x) + 1), x) + Integral(sin(c + d*x)*csc(c + d*x)**3/(sin(c + d*x)**3 + 3*sin(c + d*x)**2 + 3*sin(c + d*x) + 1), x))/a**3","F",0
243,0,0,0,0.000000," ","integrate(csc(d*x+c)**4*(A-A*sin(d*x+c))/(a+a*sin(d*x+c))**3,x)","- \frac{A \left(\int \left(- \frac{\csc^{4}{\left(c + d x \right)}}{\sin^{3}{\left(c + d x \right)} + 3 \sin^{2}{\left(c + d x \right)} + 3 \sin{\left(c + d x \right)} + 1}\right)\, dx + \int \frac{\sin{\left(c + d x \right)} \csc^{4}{\left(c + d x \right)}}{\sin^{3}{\left(c + d x \right)} + 3 \sin^{2}{\left(c + d x \right)} + 3 \sin{\left(c + d x \right)} + 1}\, dx\right)}{a^{3}}"," ",0,"-A*(Integral(-csc(c + d*x)**4/(sin(c + d*x)**3 + 3*sin(c + d*x)**2 + 3*sin(c + d*x) + 1), x) + Integral(sin(c + d*x)*csc(c + d*x)**4/(sin(c + d*x)**3 + 3*sin(c + d*x)**2 + 3*sin(c + d*x) + 1), x))/a**3","F",0
244,1,996,0,5.370352," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))**3,x)","\begin{cases} A a c^{3} x - \frac{A a c^{3} \cos{\left(e + f x \right)}}{f} + \frac{3 A a c^{2} d x \sin^{2}{\left(e + f x \right)}}{2} + \frac{3 A a c^{2} d x \cos^{2}{\left(e + f x \right)}}{2} - \frac{3 A a c^{2} d \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{3 A a c^{2} d \cos{\left(e + f x \right)}}{f} + \frac{3 A a c d^{2} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{3 A a c d^{2} x \cos^{2}{\left(e + f x \right)}}{2} - \frac{3 A a c d^{2} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{3 A a c d^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{2 A a c d^{2} \cos^{3}{\left(e + f x \right)}}{f} + \frac{3 A a d^{3} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{3 A a d^{3} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{3 A a d^{3} x \cos^{4}{\left(e + f x \right)}}{8} - \frac{5 A a d^{3} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{A a d^{3} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{3 A a d^{3} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{2 A a d^{3} \cos^{3}{\left(e + f x \right)}}{3 f} + \frac{B a c^{3} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{B a c^{3} x \cos^{2}{\left(e + f x \right)}}{2} - \frac{B a c^{3} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{B a c^{3} \cos{\left(e + f x \right)}}{f} + \frac{3 B a c^{2} d x \sin^{2}{\left(e + f x \right)}}{2} + \frac{3 B a c^{2} d x \cos^{2}{\left(e + f x \right)}}{2} - \frac{3 B a c^{2} d \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{3 B a c^{2} d \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{2 B a c^{2} d \cos^{3}{\left(e + f x \right)}}{f} + \frac{9 B a c d^{2} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{9 B a c d^{2} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{9 B a c d^{2} x \cos^{4}{\left(e + f x \right)}}{8} - \frac{15 B a c d^{2} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{3 B a c d^{2} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{9 B a c d^{2} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{2 B a c d^{2} \cos^{3}{\left(e + f x \right)}}{f} + \frac{3 B a d^{3} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{3 B a d^{3} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{3 B a d^{3} x \cos^{4}{\left(e + f x \right)}}{8} - \frac{B a d^{3} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{5 B a d^{3} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{4 B a d^{3} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{3 B a d^{3} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{8 B a d^{3} \cos^{5}{\left(e + f x \right)}}{15 f} & \text{for}\: f \neq 0 \\x \left(A + B \sin{\left(e \right)}\right) \left(c + d \sin{\left(e \right)}\right)^{3} \left(a \sin{\left(e \right)} + a\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a*c**3*x - A*a*c**3*cos(e + f*x)/f + 3*A*a*c**2*d*x*sin(e + f*x)**2/2 + 3*A*a*c**2*d*x*cos(e + f*x)**2/2 - 3*A*a*c**2*d*sin(e + f*x)*cos(e + f*x)/(2*f) - 3*A*a*c**2*d*cos(e + f*x)/f + 3*A*a*c*d**2*x*sin(e + f*x)**2/2 + 3*A*a*c*d**2*x*cos(e + f*x)**2/2 - 3*A*a*c*d**2*sin(e + f*x)**2*cos(e + f*x)/f - 3*A*a*c*d**2*sin(e + f*x)*cos(e + f*x)/(2*f) - 2*A*a*c*d**2*cos(e + f*x)**3/f + 3*A*a*d**3*x*sin(e + f*x)**4/8 + 3*A*a*d**3*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + 3*A*a*d**3*x*cos(e + f*x)**4/8 - 5*A*a*d**3*sin(e + f*x)**3*cos(e + f*x)/(8*f) - A*a*d**3*sin(e + f*x)**2*cos(e + f*x)/f - 3*A*a*d**3*sin(e + f*x)*cos(e + f*x)**3/(8*f) - 2*A*a*d**3*cos(e + f*x)**3/(3*f) + B*a*c**3*x*sin(e + f*x)**2/2 + B*a*c**3*x*cos(e + f*x)**2/2 - B*a*c**3*sin(e + f*x)*cos(e + f*x)/(2*f) - B*a*c**3*cos(e + f*x)/f + 3*B*a*c**2*d*x*sin(e + f*x)**2/2 + 3*B*a*c**2*d*x*cos(e + f*x)**2/2 - 3*B*a*c**2*d*sin(e + f*x)**2*cos(e + f*x)/f - 3*B*a*c**2*d*sin(e + f*x)*cos(e + f*x)/(2*f) - 2*B*a*c**2*d*cos(e + f*x)**3/f + 9*B*a*c*d**2*x*sin(e + f*x)**4/8 + 9*B*a*c*d**2*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + 9*B*a*c*d**2*x*cos(e + f*x)**4/8 - 15*B*a*c*d**2*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 3*B*a*c*d**2*sin(e + f*x)**2*cos(e + f*x)/f - 9*B*a*c*d**2*sin(e + f*x)*cos(e + f*x)**3/(8*f) - 2*B*a*c*d**2*cos(e + f*x)**3/f + 3*B*a*d**3*x*sin(e + f*x)**4/8 + 3*B*a*d**3*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + 3*B*a*d**3*x*cos(e + f*x)**4/8 - B*a*d**3*sin(e + f*x)**4*cos(e + f*x)/f - 5*B*a*d**3*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 4*B*a*d**3*sin(e + f*x)**2*cos(e + f*x)**3/(3*f) - 3*B*a*d**3*sin(e + f*x)*cos(e + f*x)**3/(8*f) - 8*B*a*d**3*cos(e + f*x)**5/(15*f), Ne(f, 0)), (x*(A + B*sin(e))*(c + d*sin(e))**3*(a*sin(e) + a), True))","A",0
245,1,571,0,2.307926," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))**2,x)","\begin{cases} A a c^{2} x - \frac{A a c^{2} \cos{\left(e + f x \right)}}{f} + A a c d x \sin^{2}{\left(e + f x \right)} + A a c d x \cos^{2}{\left(e + f x \right)} - \frac{A a c d \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{2 A a c d \cos{\left(e + f x \right)}}{f} + \frac{A a d^{2} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{A a d^{2} x \cos^{2}{\left(e + f x \right)}}{2} - \frac{A a d^{2} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{A a d^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{2 A a d^{2} \cos^{3}{\left(e + f x \right)}}{3 f} + \frac{B a c^{2} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{B a c^{2} x \cos^{2}{\left(e + f x \right)}}{2} - \frac{B a c^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{B a c^{2} \cos{\left(e + f x \right)}}{f} + B a c d x \sin^{2}{\left(e + f x \right)} + B a c d x \cos^{2}{\left(e + f x \right)} - \frac{2 B a c d \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{B a c d \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{4 B a c d \cos^{3}{\left(e + f x \right)}}{3 f} + \frac{3 B a d^{2} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{3 B a d^{2} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{3 B a d^{2} x \cos^{4}{\left(e + f x \right)}}{8} - \frac{5 B a d^{2} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{B a d^{2} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{3 B a d^{2} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{2 B a d^{2} \cos^{3}{\left(e + f x \right)}}{3 f} & \text{for}\: f \neq 0 \\x \left(A + B \sin{\left(e \right)}\right) \left(c + d \sin{\left(e \right)}\right)^{2} \left(a \sin{\left(e \right)} + a\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a*c**2*x - A*a*c**2*cos(e + f*x)/f + A*a*c*d*x*sin(e + f*x)**2 + A*a*c*d*x*cos(e + f*x)**2 - A*a*c*d*sin(e + f*x)*cos(e + f*x)/f - 2*A*a*c*d*cos(e + f*x)/f + A*a*d**2*x*sin(e + f*x)**2/2 + A*a*d**2*x*cos(e + f*x)**2/2 - A*a*d**2*sin(e + f*x)**2*cos(e + f*x)/f - A*a*d**2*sin(e + f*x)*cos(e + f*x)/(2*f) - 2*A*a*d**2*cos(e + f*x)**3/(3*f) + B*a*c**2*x*sin(e + f*x)**2/2 + B*a*c**2*x*cos(e + f*x)**2/2 - B*a*c**2*sin(e + f*x)*cos(e + f*x)/(2*f) - B*a*c**2*cos(e + f*x)/f + B*a*c*d*x*sin(e + f*x)**2 + B*a*c*d*x*cos(e + f*x)**2 - 2*B*a*c*d*sin(e + f*x)**2*cos(e + f*x)/f - B*a*c*d*sin(e + f*x)*cos(e + f*x)/f - 4*B*a*c*d*cos(e + f*x)**3/(3*f) + 3*B*a*d**2*x*sin(e + f*x)**4/8 + 3*B*a*d**2*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + 3*B*a*d**2*x*cos(e + f*x)**4/8 - 5*B*a*d**2*sin(e + f*x)**3*cos(e + f*x)/(8*f) - B*a*d**2*sin(e + f*x)**2*cos(e + f*x)/f - 3*B*a*d**2*sin(e + f*x)*cos(e + f*x)**3/(8*f) - 2*B*a*d**2*cos(e + f*x)**3/(3*f), Ne(f, 0)), (x*(A + B*sin(e))*(c + d*sin(e))**2*(a*sin(e) + a), True))","A",0
246,1,277,0,1.002337," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c+d*sin(f*x+e)),x)","\begin{cases} A a c x - \frac{A a c \cos{\left(e + f x \right)}}{f} + \frac{A a d x \sin^{2}{\left(e + f x \right)}}{2} + \frac{A a d x \cos^{2}{\left(e + f x \right)}}{2} - \frac{A a d \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{A a d \cos{\left(e + f x \right)}}{f} + \frac{B a c x \sin^{2}{\left(e + f x \right)}}{2} + \frac{B a c x \cos^{2}{\left(e + f x \right)}}{2} - \frac{B a c \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{B a c \cos{\left(e + f x \right)}}{f} + \frac{B a d x \sin^{2}{\left(e + f x \right)}}{2} + \frac{B a d x \cos^{2}{\left(e + f x \right)}}{2} - \frac{B a d \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{B a d \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{2 B a d \cos^{3}{\left(e + f x \right)}}{3 f} & \text{for}\: f \neq 0 \\x \left(A + B \sin{\left(e \right)}\right) \left(c + d \sin{\left(e \right)}\right) \left(a \sin{\left(e \right)} + a\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a*c*x - A*a*c*cos(e + f*x)/f + A*a*d*x*sin(e + f*x)**2/2 + A*a*d*x*cos(e + f*x)**2/2 - A*a*d*sin(e + f*x)*cos(e + f*x)/(2*f) - A*a*d*cos(e + f*x)/f + B*a*c*x*sin(e + f*x)**2/2 + B*a*c*x*cos(e + f*x)**2/2 - B*a*c*sin(e + f*x)*cos(e + f*x)/(2*f) - B*a*c*cos(e + f*x)/f + B*a*d*x*sin(e + f*x)**2/2 + B*a*d*x*cos(e + f*x)**2/2 - B*a*d*sin(e + f*x)**2*cos(e + f*x)/f - B*a*d*sin(e + f*x)*cos(e + f*x)/(2*f) - 2*B*a*d*cos(e + f*x)**3/(3*f), Ne(f, 0)), (x*(A + B*sin(e))*(c + d*sin(e))*(a*sin(e) + a), True))","A",0
247,1,94,0,0.350661," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e)),x)","\begin{cases} A a x - \frac{A a \cos{\left(e + f x \right)}}{f} + \frac{B a x \sin^{2}{\left(e + f x \right)}}{2} + \frac{B a x \cos^{2}{\left(e + f x \right)}}{2} - \frac{B a \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{B a \cos{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \left(A + B \sin{\left(e \right)}\right) \left(a \sin{\left(e \right)} + a\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a*x - A*a*cos(e + f*x)/f + B*a*x*sin(e + f*x)**2/2 + B*a*x*cos(e + f*x)**2/2 - B*a*sin(e + f*x)*cos(e + f*x)/(2*f) - B*a*cos(e + f*x)/f, Ne(f, 0)), (x*(A + B*sin(e))*(a*sin(e) + a), True))","A",0
248,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c+d*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
249,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
250,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
251,1,1865,0,11.952402," ","integrate((a+a*sin(f*x+e))**2*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))**3,x)","\begin{cases} \frac{A a^{2} c^{3} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{A a^{2} c^{3} x \cos^{2}{\left(e + f x \right)}}{2} + A a^{2} c^{3} x - \frac{A a^{2} c^{3} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{2 A a^{2} c^{3} \cos{\left(e + f x \right)}}{f} + 3 A a^{2} c^{2} d x \sin^{2}{\left(e + f x \right)} + 3 A a^{2} c^{2} d x \cos^{2}{\left(e + f x \right)} - \frac{3 A a^{2} c^{2} d \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{3 A a^{2} c^{2} d \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{2 A a^{2} c^{2} d \cos^{3}{\left(e + f x \right)}}{f} - \frac{3 A a^{2} c^{2} d \cos{\left(e + f x \right)}}{f} + \frac{9 A a^{2} c d^{2} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{9 A a^{2} c d^{2} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{3 A a^{2} c d^{2} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{9 A a^{2} c d^{2} x \cos^{4}{\left(e + f x \right)}}{8} + \frac{3 A a^{2} c d^{2} x \cos^{2}{\left(e + f x \right)}}{2} - \frac{15 A a^{2} c d^{2} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{6 A a^{2} c d^{2} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{9 A a^{2} c d^{2} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{3 A a^{2} c d^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{4 A a^{2} c d^{2} \cos^{3}{\left(e + f x \right)}}{f} + \frac{3 A a^{2} d^{3} x \sin^{4}{\left(e + f x \right)}}{4} + \frac{3 A a^{2} d^{3} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{2} + \frac{3 A a^{2} d^{3} x \cos^{4}{\left(e + f x \right)}}{4} - \frac{A a^{2} d^{3} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{5 A a^{2} d^{3} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{4 f} - \frac{4 A a^{2} d^{3} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{A a^{2} d^{3} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{3 A a^{2} d^{3} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{4 f} - \frac{8 A a^{2} d^{3} \cos^{5}{\left(e + f x \right)}}{15 f} - \frac{2 A a^{2} d^{3} \cos^{3}{\left(e + f x \right)}}{3 f} + B a^{2} c^{3} x \sin^{2}{\left(e + f x \right)} + B a^{2} c^{3} x \cos^{2}{\left(e + f x \right)} - \frac{B a^{2} c^{3} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{B a^{2} c^{3} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{2 B a^{2} c^{3} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{B a^{2} c^{3} \cos{\left(e + f x \right)}}{f} + \frac{9 B a^{2} c^{2} d x \sin^{4}{\left(e + f x \right)}}{8} + \frac{9 B a^{2} c^{2} d x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{3 B a^{2} c^{2} d x \sin^{2}{\left(e + f x \right)}}{2} + \frac{9 B a^{2} c^{2} d x \cos^{4}{\left(e + f x \right)}}{8} + \frac{3 B a^{2} c^{2} d x \cos^{2}{\left(e + f x \right)}}{2} - \frac{15 B a^{2} c^{2} d \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{6 B a^{2} c^{2} d \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{9 B a^{2} c^{2} d \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{3 B a^{2} c^{2} d \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{4 B a^{2} c^{2} d \cos^{3}{\left(e + f x \right)}}{f} + \frac{9 B a^{2} c d^{2} x \sin^{4}{\left(e + f x \right)}}{4} + \frac{9 B a^{2} c d^{2} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{2} + \frac{9 B a^{2} c d^{2} x \cos^{4}{\left(e + f x \right)}}{4} - \frac{3 B a^{2} c d^{2} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{15 B a^{2} c d^{2} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{4 f} - \frac{4 B a^{2} c d^{2} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{f} - \frac{3 B a^{2} c d^{2} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{9 B a^{2} c d^{2} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{4 f} - \frac{8 B a^{2} c d^{2} \cos^{5}{\left(e + f x \right)}}{5 f} - \frac{2 B a^{2} c d^{2} \cos^{3}{\left(e + f x \right)}}{f} + \frac{5 B a^{2} d^{3} x \sin^{6}{\left(e + f x \right)}}{16} + \frac{15 B a^{2} d^{3} x \sin^{4}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{16} + \frac{3 B a^{2} d^{3} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{15 B a^{2} d^{3} x \sin^{2}{\left(e + f x \right)} \cos^{4}{\left(e + f x \right)}}{16} + \frac{3 B a^{2} d^{3} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{5 B a^{2} d^{3} x \cos^{6}{\left(e + f x \right)}}{16} + \frac{3 B a^{2} d^{3} x \cos^{4}{\left(e + f x \right)}}{8} - \frac{11 B a^{2} d^{3} \sin^{5}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{16 f} - \frac{2 B a^{2} d^{3} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{5 B a^{2} d^{3} \sin^{3}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{6 f} - \frac{5 B a^{2} d^{3} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{8 B a^{2} d^{3} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{5 B a^{2} d^{3} \sin{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{16 f} - \frac{3 B a^{2} d^{3} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{16 B a^{2} d^{3} \cos^{5}{\left(e + f x \right)}}{15 f} & \text{for}\: f \neq 0 \\x \left(A + B \sin{\left(e \right)}\right) \left(c + d \sin{\left(e \right)}\right)^{3} \left(a \sin{\left(e \right)} + a\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a**2*c**3*x*sin(e + f*x)**2/2 + A*a**2*c**3*x*cos(e + f*x)**2/2 + A*a**2*c**3*x - A*a**2*c**3*sin(e + f*x)*cos(e + f*x)/(2*f) - 2*A*a**2*c**3*cos(e + f*x)/f + 3*A*a**2*c**2*d*x*sin(e + f*x)**2 + 3*A*a**2*c**2*d*x*cos(e + f*x)**2 - 3*A*a**2*c**2*d*sin(e + f*x)**2*cos(e + f*x)/f - 3*A*a**2*c**2*d*sin(e + f*x)*cos(e + f*x)/f - 2*A*a**2*c**2*d*cos(e + f*x)**3/f - 3*A*a**2*c**2*d*cos(e + f*x)/f + 9*A*a**2*c*d**2*x*sin(e + f*x)**4/8 + 9*A*a**2*c*d**2*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + 3*A*a**2*c*d**2*x*sin(e + f*x)**2/2 + 9*A*a**2*c*d**2*x*cos(e + f*x)**4/8 + 3*A*a**2*c*d**2*x*cos(e + f*x)**2/2 - 15*A*a**2*c*d**2*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 6*A*a**2*c*d**2*sin(e + f*x)**2*cos(e + f*x)/f - 9*A*a**2*c*d**2*sin(e + f*x)*cos(e + f*x)**3/(8*f) - 3*A*a**2*c*d**2*sin(e + f*x)*cos(e + f*x)/(2*f) - 4*A*a**2*c*d**2*cos(e + f*x)**3/f + 3*A*a**2*d**3*x*sin(e + f*x)**4/4 + 3*A*a**2*d**3*x*sin(e + f*x)**2*cos(e + f*x)**2/2 + 3*A*a**2*d**3*x*cos(e + f*x)**4/4 - A*a**2*d**3*sin(e + f*x)**4*cos(e + f*x)/f - 5*A*a**2*d**3*sin(e + f*x)**3*cos(e + f*x)/(4*f) - 4*A*a**2*d**3*sin(e + f*x)**2*cos(e + f*x)**3/(3*f) - A*a**2*d**3*sin(e + f*x)**2*cos(e + f*x)/f - 3*A*a**2*d**3*sin(e + f*x)*cos(e + f*x)**3/(4*f) - 8*A*a**2*d**3*cos(e + f*x)**5/(15*f) - 2*A*a**2*d**3*cos(e + f*x)**3/(3*f) + B*a**2*c**3*x*sin(e + f*x)**2 + B*a**2*c**3*x*cos(e + f*x)**2 - B*a**2*c**3*sin(e + f*x)**2*cos(e + f*x)/f - B*a**2*c**3*sin(e + f*x)*cos(e + f*x)/f - 2*B*a**2*c**3*cos(e + f*x)**3/(3*f) - B*a**2*c**3*cos(e + f*x)/f + 9*B*a**2*c**2*d*x*sin(e + f*x)**4/8 + 9*B*a**2*c**2*d*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + 3*B*a**2*c**2*d*x*sin(e + f*x)**2/2 + 9*B*a**2*c**2*d*x*cos(e + f*x)**4/8 + 3*B*a**2*c**2*d*x*cos(e + f*x)**2/2 - 15*B*a**2*c**2*d*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 6*B*a**2*c**2*d*sin(e + f*x)**2*cos(e + f*x)/f - 9*B*a**2*c**2*d*sin(e + f*x)*cos(e + f*x)**3/(8*f) - 3*B*a**2*c**2*d*sin(e + f*x)*cos(e + f*x)/(2*f) - 4*B*a**2*c**2*d*cos(e + f*x)**3/f + 9*B*a**2*c*d**2*x*sin(e + f*x)**4/4 + 9*B*a**2*c*d**2*x*sin(e + f*x)**2*cos(e + f*x)**2/2 + 9*B*a**2*c*d**2*x*cos(e + f*x)**4/4 - 3*B*a**2*c*d**2*sin(e + f*x)**4*cos(e + f*x)/f - 15*B*a**2*c*d**2*sin(e + f*x)**3*cos(e + f*x)/(4*f) - 4*B*a**2*c*d**2*sin(e + f*x)**2*cos(e + f*x)**3/f - 3*B*a**2*c*d**2*sin(e + f*x)**2*cos(e + f*x)/f - 9*B*a**2*c*d**2*sin(e + f*x)*cos(e + f*x)**3/(4*f) - 8*B*a**2*c*d**2*cos(e + f*x)**5/(5*f) - 2*B*a**2*c*d**2*cos(e + f*x)**3/f + 5*B*a**2*d**3*x*sin(e + f*x)**6/16 + 15*B*a**2*d**3*x*sin(e + f*x)**4*cos(e + f*x)**2/16 + 3*B*a**2*d**3*x*sin(e + f*x)**4/8 + 15*B*a**2*d**3*x*sin(e + f*x)**2*cos(e + f*x)**4/16 + 3*B*a**2*d**3*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + 5*B*a**2*d**3*x*cos(e + f*x)**6/16 + 3*B*a**2*d**3*x*cos(e + f*x)**4/8 - 11*B*a**2*d**3*sin(e + f*x)**5*cos(e + f*x)/(16*f) - 2*B*a**2*d**3*sin(e + f*x)**4*cos(e + f*x)/f - 5*B*a**2*d**3*sin(e + f*x)**3*cos(e + f*x)**3/(6*f) - 5*B*a**2*d**3*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 8*B*a**2*d**3*sin(e + f*x)**2*cos(e + f*x)**3/(3*f) - 5*B*a**2*d**3*sin(e + f*x)*cos(e + f*x)**5/(16*f) - 3*B*a**2*d**3*sin(e + f*x)*cos(e + f*x)**3/(8*f) - 16*B*a**2*d**3*cos(e + f*x)**5/(15*f), Ne(f, 0)), (x*(A + B*sin(e))*(c + d*sin(e))**3*(a*sin(e) + a)**2, True))","A",0
252,1,1129,0,6.001548," ","integrate((a+a*sin(f*x+e))**2*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))**2,x)","\begin{cases} \frac{A a^{2} c^{2} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{A a^{2} c^{2} x \cos^{2}{\left(e + f x \right)}}{2} + A a^{2} c^{2} x - \frac{A a^{2} c^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{2 A a^{2} c^{2} \cos{\left(e + f x \right)}}{f} + 2 A a^{2} c d x \sin^{2}{\left(e + f x \right)} + 2 A a^{2} c d x \cos^{2}{\left(e + f x \right)} - \frac{2 A a^{2} c d \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{2 A a^{2} c d \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{4 A a^{2} c d \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{2 A a^{2} c d \cos{\left(e + f x \right)}}{f} + \frac{3 A a^{2} d^{2} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{3 A a^{2} d^{2} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{A a^{2} d^{2} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{3 A a^{2} d^{2} x \cos^{4}{\left(e + f x \right)}}{8} + \frac{A a^{2} d^{2} x \cos^{2}{\left(e + f x \right)}}{2} - \frac{5 A a^{2} d^{2} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{2 A a^{2} d^{2} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{3 A a^{2} d^{2} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{A a^{2} d^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{4 A a^{2} d^{2} \cos^{3}{\left(e + f x \right)}}{3 f} + B a^{2} c^{2} x \sin^{2}{\left(e + f x \right)} + B a^{2} c^{2} x \cos^{2}{\left(e + f x \right)} - \frac{B a^{2} c^{2} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{B a^{2} c^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{2 B a^{2} c^{2} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{B a^{2} c^{2} \cos{\left(e + f x \right)}}{f} + \frac{3 B a^{2} c d x \sin^{4}{\left(e + f x \right)}}{4} + \frac{3 B a^{2} c d x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{2} + B a^{2} c d x \sin^{2}{\left(e + f x \right)} + \frac{3 B a^{2} c d x \cos^{4}{\left(e + f x \right)}}{4} + B a^{2} c d x \cos^{2}{\left(e + f x \right)} - \frac{5 B a^{2} c d \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{4 f} - \frac{4 B a^{2} c d \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{3 B a^{2} c d \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{4 f} - \frac{B a^{2} c d \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{8 B a^{2} c d \cos^{3}{\left(e + f x \right)}}{3 f} + \frac{3 B a^{2} d^{2} x \sin^{4}{\left(e + f x \right)}}{4} + \frac{3 B a^{2} d^{2} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{2} + \frac{3 B a^{2} d^{2} x \cos^{4}{\left(e + f x \right)}}{4} - \frac{B a^{2} d^{2} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{5 B a^{2} d^{2} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{4 f} - \frac{4 B a^{2} d^{2} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{B a^{2} d^{2} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{3 B a^{2} d^{2} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{4 f} - \frac{8 B a^{2} d^{2} \cos^{5}{\left(e + f x \right)}}{15 f} - \frac{2 B a^{2} d^{2} \cos^{3}{\left(e + f x \right)}}{3 f} & \text{for}\: f \neq 0 \\x \left(A + B \sin{\left(e \right)}\right) \left(c + d \sin{\left(e \right)}\right)^{2} \left(a \sin{\left(e \right)} + a\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a**2*c**2*x*sin(e + f*x)**2/2 + A*a**2*c**2*x*cos(e + f*x)**2/2 + A*a**2*c**2*x - A*a**2*c**2*sin(e + f*x)*cos(e + f*x)/(2*f) - 2*A*a**2*c**2*cos(e + f*x)/f + 2*A*a**2*c*d*x*sin(e + f*x)**2 + 2*A*a**2*c*d*x*cos(e + f*x)**2 - 2*A*a**2*c*d*sin(e + f*x)**2*cos(e + f*x)/f - 2*A*a**2*c*d*sin(e + f*x)*cos(e + f*x)/f - 4*A*a**2*c*d*cos(e + f*x)**3/(3*f) - 2*A*a**2*c*d*cos(e + f*x)/f + 3*A*a**2*d**2*x*sin(e + f*x)**4/8 + 3*A*a**2*d**2*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + A*a**2*d**2*x*sin(e + f*x)**2/2 + 3*A*a**2*d**2*x*cos(e + f*x)**4/8 + A*a**2*d**2*x*cos(e + f*x)**2/2 - 5*A*a**2*d**2*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 2*A*a**2*d**2*sin(e + f*x)**2*cos(e + f*x)/f - 3*A*a**2*d**2*sin(e + f*x)*cos(e + f*x)**3/(8*f) - A*a**2*d**2*sin(e + f*x)*cos(e + f*x)/(2*f) - 4*A*a**2*d**2*cos(e + f*x)**3/(3*f) + B*a**2*c**2*x*sin(e + f*x)**2 + B*a**2*c**2*x*cos(e + f*x)**2 - B*a**2*c**2*sin(e + f*x)**2*cos(e + f*x)/f - B*a**2*c**2*sin(e + f*x)*cos(e + f*x)/f - 2*B*a**2*c**2*cos(e + f*x)**3/(3*f) - B*a**2*c**2*cos(e + f*x)/f + 3*B*a**2*c*d*x*sin(e + f*x)**4/4 + 3*B*a**2*c*d*x*sin(e + f*x)**2*cos(e + f*x)**2/2 + B*a**2*c*d*x*sin(e + f*x)**2 + 3*B*a**2*c*d*x*cos(e + f*x)**4/4 + B*a**2*c*d*x*cos(e + f*x)**2 - 5*B*a**2*c*d*sin(e + f*x)**3*cos(e + f*x)/(4*f) - 4*B*a**2*c*d*sin(e + f*x)**2*cos(e + f*x)/f - 3*B*a**2*c*d*sin(e + f*x)*cos(e + f*x)**3/(4*f) - B*a**2*c*d*sin(e + f*x)*cos(e + f*x)/f - 8*B*a**2*c*d*cos(e + f*x)**3/(3*f) + 3*B*a**2*d**2*x*sin(e + f*x)**4/4 + 3*B*a**2*d**2*x*sin(e + f*x)**2*cos(e + f*x)**2/2 + 3*B*a**2*d**2*x*cos(e + f*x)**4/4 - B*a**2*d**2*sin(e + f*x)**4*cos(e + f*x)/f - 5*B*a**2*d**2*sin(e + f*x)**3*cos(e + f*x)/(4*f) - 4*B*a**2*d**2*sin(e + f*x)**2*cos(e + f*x)**3/(3*f) - B*a**2*d**2*sin(e + f*x)**2*cos(e + f*x)/f - 3*B*a**2*d**2*sin(e + f*x)*cos(e + f*x)**3/(4*f) - 8*B*a**2*d**2*cos(e + f*x)**5/(15*f) - 2*B*a**2*d**2*cos(e + f*x)**3/(3*f), Ne(f, 0)), (x*(A + B*sin(e))*(c + d*sin(e))**2*(a*sin(e) + a)**2, True))","A",0
253,1,571,0,2.759712," ","integrate((a+a*sin(f*x+e))**2*(A+B*sin(f*x+e))*(c+d*sin(f*x+e)),x)","\begin{cases} \frac{A a^{2} c x \sin^{2}{\left(e + f x \right)}}{2} + \frac{A a^{2} c x \cos^{2}{\left(e + f x \right)}}{2} + A a^{2} c x - \frac{A a^{2} c \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{2 A a^{2} c \cos{\left(e + f x \right)}}{f} + A a^{2} d x \sin^{2}{\left(e + f x \right)} + A a^{2} d x \cos^{2}{\left(e + f x \right)} - \frac{A a^{2} d \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{A a^{2} d \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{2 A a^{2} d \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{A a^{2} d \cos{\left(e + f x \right)}}{f} + B a^{2} c x \sin^{2}{\left(e + f x \right)} + B a^{2} c x \cos^{2}{\left(e + f x \right)} - \frac{B a^{2} c \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{B a^{2} c \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{2 B a^{2} c \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{B a^{2} c \cos{\left(e + f x \right)}}{f} + \frac{3 B a^{2} d x \sin^{4}{\left(e + f x \right)}}{8} + \frac{3 B a^{2} d x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{B a^{2} d x \sin^{2}{\left(e + f x \right)}}{2} + \frac{3 B a^{2} d x \cos^{4}{\left(e + f x \right)}}{8} + \frac{B a^{2} d x \cos^{2}{\left(e + f x \right)}}{2} - \frac{5 B a^{2} d \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{2 B a^{2} d \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{3 B a^{2} d \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{B a^{2} d \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{4 B a^{2} d \cos^{3}{\left(e + f x \right)}}{3 f} & \text{for}\: f \neq 0 \\x \left(A + B \sin{\left(e \right)}\right) \left(c + d \sin{\left(e \right)}\right) \left(a \sin{\left(e \right)} + a\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a**2*c*x*sin(e + f*x)**2/2 + A*a**2*c*x*cos(e + f*x)**2/2 + A*a**2*c*x - A*a**2*c*sin(e + f*x)*cos(e + f*x)/(2*f) - 2*A*a**2*c*cos(e + f*x)/f + A*a**2*d*x*sin(e + f*x)**2 + A*a**2*d*x*cos(e + f*x)**2 - A*a**2*d*sin(e + f*x)**2*cos(e + f*x)/f - A*a**2*d*sin(e + f*x)*cos(e + f*x)/f - 2*A*a**2*d*cos(e + f*x)**3/(3*f) - A*a**2*d*cos(e + f*x)/f + B*a**2*c*x*sin(e + f*x)**2 + B*a**2*c*x*cos(e + f*x)**2 - B*a**2*c*sin(e + f*x)**2*cos(e + f*x)/f - B*a**2*c*sin(e + f*x)*cos(e + f*x)/f - 2*B*a**2*c*cos(e + f*x)**3/(3*f) - B*a**2*c*cos(e + f*x)/f + 3*B*a**2*d*x*sin(e + f*x)**4/8 + 3*B*a**2*d*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + B*a**2*d*x*sin(e + f*x)**2/2 + 3*B*a**2*d*x*cos(e + f*x)**4/8 + B*a**2*d*x*cos(e + f*x)**2/2 - 5*B*a**2*d*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 2*B*a**2*d*sin(e + f*x)**2*cos(e + f*x)/f - 3*B*a**2*d*sin(e + f*x)*cos(e + f*x)**3/(8*f) - B*a**2*d*sin(e + f*x)*cos(e + f*x)/(2*f) - 4*B*a**2*d*cos(e + f*x)**3/(3*f), Ne(f, 0)), (x*(A + B*sin(e))*(c + d*sin(e))*(a*sin(e) + a)**2, True))","A",0
254,1,199,0,0.948939," ","integrate((a+a*sin(f*x+e))**2*(A+B*sin(f*x+e)),x)","\begin{cases} \frac{A a^{2} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{A a^{2} x \cos^{2}{\left(e + f x \right)}}{2} + A a^{2} x - \frac{A a^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{2 A a^{2} \cos{\left(e + f x \right)}}{f} + B a^{2} x \sin^{2}{\left(e + f x \right)} + B a^{2} x \cos^{2}{\left(e + f x \right)} - \frac{B a^{2} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{B a^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{2 B a^{2} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{B a^{2} \cos{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \left(A + B \sin{\left(e \right)}\right) \left(a \sin{\left(e \right)} + a\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a**2*x*sin(e + f*x)**2/2 + A*a**2*x*cos(e + f*x)**2/2 + A*a**2*x - A*a**2*sin(e + f*x)*cos(e + f*x)/(2*f) - 2*A*a**2*cos(e + f*x)/f + B*a**2*x*sin(e + f*x)**2 + B*a**2*x*cos(e + f*x)**2 - B*a**2*sin(e + f*x)**2*cos(e + f*x)/f - B*a**2*sin(e + f*x)*cos(e + f*x)/f - 2*B*a**2*cos(e + f*x)**3/(3*f) - B*a**2*cos(e + f*x)/f, Ne(f, 0)), (x*(A + B*sin(e))*(a*sin(e) + a)**2, True))","A",0
255,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**2*(A+B*sin(f*x+e))/(c+d*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
256,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**2*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
257,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**2*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
258,1,2878,0,22.093406," ","integrate((a+a*sin(f*x+e))**3*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))**3,x)","\begin{cases} \frac{3 A a^{3} c^{3} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{3 A a^{3} c^{3} x \cos^{2}{\left(e + f x \right)}}{2} + A a^{3} c^{3} x - \frac{A a^{3} c^{3} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{3 A a^{3} c^{3} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{2 A a^{3} c^{3} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{3 A a^{3} c^{3} \cos{\left(e + f x \right)}}{f} + \frac{9 A a^{3} c^{2} d x \sin^{4}{\left(e + f x \right)}}{8} + \frac{9 A a^{3} c^{2} d x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{9 A a^{3} c^{2} d x \sin^{2}{\left(e + f x \right)}}{2} + \frac{9 A a^{3} c^{2} d x \cos^{4}{\left(e + f x \right)}}{8} + \frac{9 A a^{3} c^{2} d x \cos^{2}{\left(e + f x \right)}}{2} - \frac{15 A a^{3} c^{2} d \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{9 A a^{3} c^{2} d \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{9 A a^{3} c^{2} d \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{9 A a^{3} c^{2} d \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{6 A a^{3} c^{2} d \cos^{3}{\left(e + f x \right)}}{f} - \frac{3 A a^{3} c^{2} d \cos{\left(e + f x \right)}}{f} + \frac{27 A a^{3} c d^{2} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{27 A a^{3} c d^{2} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{3 A a^{3} c d^{2} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{27 A a^{3} c d^{2} x \cos^{4}{\left(e + f x \right)}}{8} + \frac{3 A a^{3} c d^{2} x \cos^{2}{\left(e + f x \right)}}{2} - \frac{3 A a^{3} c d^{2} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{45 A a^{3} c d^{2} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{4 A a^{3} c d^{2} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{f} - \frac{9 A a^{3} c d^{2} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{27 A a^{3} c d^{2} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{3 A a^{3} c d^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{8 A a^{3} c d^{2} \cos^{5}{\left(e + f x \right)}}{5 f} - \frac{6 A a^{3} c d^{2} \cos^{3}{\left(e + f x \right)}}{f} + \frac{5 A a^{3} d^{3} x \sin^{6}{\left(e + f x \right)}}{16} + \frac{15 A a^{3} d^{3} x \sin^{4}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{16} + \frac{9 A a^{3} d^{3} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{15 A a^{3} d^{3} x \sin^{2}{\left(e + f x \right)} \cos^{4}{\left(e + f x \right)}}{16} + \frac{9 A a^{3} d^{3} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{5 A a^{3} d^{3} x \cos^{6}{\left(e + f x \right)}}{16} + \frac{9 A a^{3} d^{3} x \cos^{4}{\left(e + f x \right)}}{8} - \frac{11 A a^{3} d^{3} \sin^{5}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{16 f} - \frac{3 A a^{3} d^{3} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{5 A a^{3} d^{3} \sin^{3}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{6 f} - \frac{15 A a^{3} d^{3} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{4 A a^{3} d^{3} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{f} - \frac{A a^{3} d^{3} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{5 A a^{3} d^{3} \sin{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{16 f} - \frac{9 A a^{3} d^{3} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{8 A a^{3} d^{3} \cos^{5}{\left(e + f x \right)}}{5 f} - \frac{2 A a^{3} d^{3} \cos^{3}{\left(e + f x \right)}}{3 f} + \frac{3 B a^{3} c^{3} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{3 B a^{3} c^{3} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{3 B a^{3} c^{3} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{3 B a^{3} c^{3} x \cos^{4}{\left(e + f x \right)}}{8} + \frac{3 B a^{3} c^{3} x \cos^{2}{\left(e + f x \right)}}{2} - \frac{5 B a^{3} c^{3} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{3 B a^{3} c^{3} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{3 B a^{3} c^{3} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{3 B a^{3} c^{3} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{2 B a^{3} c^{3} \cos^{3}{\left(e + f x \right)}}{f} - \frac{B a^{3} c^{3} \cos{\left(e + f x \right)}}{f} + \frac{27 B a^{3} c^{2} d x \sin^{4}{\left(e + f x \right)}}{8} + \frac{27 B a^{3} c^{2} d x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{3 B a^{3} c^{2} d x \sin^{2}{\left(e + f x \right)}}{2} + \frac{27 B a^{3} c^{2} d x \cos^{4}{\left(e + f x \right)}}{8} + \frac{3 B a^{3} c^{2} d x \cos^{2}{\left(e + f x \right)}}{2} - \frac{3 B a^{3} c^{2} d \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{45 B a^{3} c^{2} d \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{4 B a^{3} c^{2} d \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{f} - \frac{9 B a^{3} c^{2} d \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{27 B a^{3} c^{2} d \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{3 B a^{3} c^{2} d \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{8 B a^{3} c^{2} d \cos^{5}{\left(e + f x \right)}}{5 f} - \frac{6 B a^{3} c^{2} d \cos^{3}{\left(e + f x \right)}}{f} + \frac{15 B a^{3} c d^{2} x \sin^{6}{\left(e + f x \right)}}{16} + \frac{45 B a^{3} c d^{2} x \sin^{4}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{16} + \frac{27 B a^{3} c d^{2} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{45 B a^{3} c d^{2} x \sin^{2}{\left(e + f x \right)} \cos^{4}{\left(e + f x \right)}}{16} + \frac{27 B a^{3} c d^{2} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{15 B a^{3} c d^{2} x \cos^{6}{\left(e + f x \right)}}{16} + \frac{27 B a^{3} c d^{2} x \cos^{4}{\left(e + f x \right)}}{8} - \frac{33 B a^{3} c d^{2} \sin^{5}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{16 f} - \frac{9 B a^{3} c d^{2} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{5 B a^{3} c d^{2} \sin^{3}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{2 f} - \frac{45 B a^{3} c d^{2} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{12 B a^{3} c d^{2} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{f} - \frac{3 B a^{3} c d^{2} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{15 B a^{3} c d^{2} \sin{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{16 f} - \frac{27 B a^{3} c d^{2} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{24 B a^{3} c d^{2} \cos^{5}{\left(e + f x \right)}}{5 f} - \frac{2 B a^{3} c d^{2} \cos^{3}{\left(e + f x \right)}}{f} + \frac{15 B a^{3} d^{3} x \sin^{6}{\left(e + f x \right)}}{16} + \frac{45 B a^{3} d^{3} x \sin^{4}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{16} + \frac{3 B a^{3} d^{3} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{45 B a^{3} d^{3} x \sin^{2}{\left(e + f x \right)} \cos^{4}{\left(e + f x \right)}}{16} + \frac{3 B a^{3} d^{3} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{15 B a^{3} d^{3} x \cos^{6}{\left(e + f x \right)}}{16} + \frac{3 B a^{3} d^{3} x \cos^{4}{\left(e + f x \right)}}{8} - \frac{B a^{3} d^{3} \sin^{6}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{33 B a^{3} d^{3} \sin^{5}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{16 f} - \frac{2 B a^{3} d^{3} \sin^{4}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{f} - \frac{3 B a^{3} d^{3} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{5 B a^{3} d^{3} \sin^{3}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{2 f} - \frac{5 B a^{3} d^{3} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{8 B a^{3} d^{3} \sin^{2}{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{5 f} - \frac{4 B a^{3} d^{3} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{f} - \frac{15 B a^{3} d^{3} \sin{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{16 f} - \frac{3 B a^{3} d^{3} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{16 B a^{3} d^{3} \cos^{7}{\left(e + f x \right)}}{35 f} - \frac{8 B a^{3} d^{3} \cos^{5}{\left(e + f x \right)}}{5 f} & \text{for}\: f \neq 0 \\x \left(A + B \sin{\left(e \right)}\right) \left(c + d \sin{\left(e \right)}\right)^{3} \left(a \sin{\left(e \right)} + a\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*A*a**3*c**3*x*sin(e + f*x)**2/2 + 3*A*a**3*c**3*x*cos(e + f*x)**2/2 + A*a**3*c**3*x - A*a**3*c**3*sin(e + f*x)**2*cos(e + f*x)/f - 3*A*a**3*c**3*sin(e + f*x)*cos(e + f*x)/(2*f) - 2*A*a**3*c**3*cos(e + f*x)**3/(3*f) - 3*A*a**3*c**3*cos(e + f*x)/f + 9*A*a**3*c**2*d*x*sin(e + f*x)**4/8 + 9*A*a**3*c**2*d*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + 9*A*a**3*c**2*d*x*sin(e + f*x)**2/2 + 9*A*a**3*c**2*d*x*cos(e + f*x)**4/8 + 9*A*a**3*c**2*d*x*cos(e + f*x)**2/2 - 15*A*a**3*c**2*d*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 9*A*a**3*c**2*d*sin(e + f*x)**2*cos(e + f*x)/f - 9*A*a**3*c**2*d*sin(e + f*x)*cos(e + f*x)**3/(8*f) - 9*A*a**3*c**2*d*sin(e + f*x)*cos(e + f*x)/(2*f) - 6*A*a**3*c**2*d*cos(e + f*x)**3/f - 3*A*a**3*c**2*d*cos(e + f*x)/f + 27*A*a**3*c*d**2*x*sin(e + f*x)**4/8 + 27*A*a**3*c*d**2*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + 3*A*a**3*c*d**2*x*sin(e + f*x)**2/2 + 27*A*a**3*c*d**2*x*cos(e + f*x)**4/8 + 3*A*a**3*c*d**2*x*cos(e + f*x)**2/2 - 3*A*a**3*c*d**2*sin(e + f*x)**4*cos(e + f*x)/f - 45*A*a**3*c*d**2*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 4*A*a**3*c*d**2*sin(e + f*x)**2*cos(e + f*x)**3/f - 9*A*a**3*c*d**2*sin(e + f*x)**2*cos(e + f*x)/f - 27*A*a**3*c*d**2*sin(e + f*x)*cos(e + f*x)**3/(8*f) - 3*A*a**3*c*d**2*sin(e + f*x)*cos(e + f*x)/(2*f) - 8*A*a**3*c*d**2*cos(e + f*x)**5/(5*f) - 6*A*a**3*c*d**2*cos(e + f*x)**3/f + 5*A*a**3*d**3*x*sin(e + f*x)**6/16 + 15*A*a**3*d**3*x*sin(e + f*x)**4*cos(e + f*x)**2/16 + 9*A*a**3*d**3*x*sin(e + f*x)**4/8 + 15*A*a**3*d**3*x*sin(e + f*x)**2*cos(e + f*x)**4/16 + 9*A*a**3*d**3*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + 5*A*a**3*d**3*x*cos(e + f*x)**6/16 + 9*A*a**3*d**3*x*cos(e + f*x)**4/8 - 11*A*a**3*d**3*sin(e + f*x)**5*cos(e + f*x)/(16*f) - 3*A*a**3*d**3*sin(e + f*x)**4*cos(e + f*x)/f - 5*A*a**3*d**3*sin(e + f*x)**3*cos(e + f*x)**3/(6*f) - 15*A*a**3*d**3*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 4*A*a**3*d**3*sin(e + f*x)**2*cos(e + f*x)**3/f - A*a**3*d**3*sin(e + f*x)**2*cos(e + f*x)/f - 5*A*a**3*d**3*sin(e + f*x)*cos(e + f*x)**5/(16*f) - 9*A*a**3*d**3*sin(e + f*x)*cos(e + f*x)**3/(8*f) - 8*A*a**3*d**3*cos(e + f*x)**5/(5*f) - 2*A*a**3*d**3*cos(e + f*x)**3/(3*f) + 3*B*a**3*c**3*x*sin(e + f*x)**4/8 + 3*B*a**3*c**3*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + 3*B*a**3*c**3*x*sin(e + f*x)**2/2 + 3*B*a**3*c**3*x*cos(e + f*x)**4/8 + 3*B*a**3*c**3*x*cos(e + f*x)**2/2 - 5*B*a**3*c**3*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 3*B*a**3*c**3*sin(e + f*x)**2*cos(e + f*x)/f - 3*B*a**3*c**3*sin(e + f*x)*cos(e + f*x)**3/(8*f) - 3*B*a**3*c**3*sin(e + f*x)*cos(e + f*x)/(2*f) - 2*B*a**3*c**3*cos(e + f*x)**3/f - B*a**3*c**3*cos(e + f*x)/f + 27*B*a**3*c**2*d*x*sin(e + f*x)**4/8 + 27*B*a**3*c**2*d*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + 3*B*a**3*c**2*d*x*sin(e + f*x)**2/2 + 27*B*a**3*c**2*d*x*cos(e + f*x)**4/8 + 3*B*a**3*c**2*d*x*cos(e + f*x)**2/2 - 3*B*a**3*c**2*d*sin(e + f*x)**4*cos(e + f*x)/f - 45*B*a**3*c**2*d*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 4*B*a**3*c**2*d*sin(e + f*x)**2*cos(e + f*x)**3/f - 9*B*a**3*c**2*d*sin(e + f*x)**2*cos(e + f*x)/f - 27*B*a**3*c**2*d*sin(e + f*x)*cos(e + f*x)**3/(8*f) - 3*B*a**3*c**2*d*sin(e + f*x)*cos(e + f*x)/(2*f) - 8*B*a**3*c**2*d*cos(e + f*x)**5/(5*f) - 6*B*a**3*c**2*d*cos(e + f*x)**3/f + 15*B*a**3*c*d**2*x*sin(e + f*x)**6/16 + 45*B*a**3*c*d**2*x*sin(e + f*x)**4*cos(e + f*x)**2/16 + 27*B*a**3*c*d**2*x*sin(e + f*x)**4/8 + 45*B*a**3*c*d**2*x*sin(e + f*x)**2*cos(e + f*x)**4/16 + 27*B*a**3*c*d**2*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + 15*B*a**3*c*d**2*x*cos(e + f*x)**6/16 + 27*B*a**3*c*d**2*x*cos(e + f*x)**4/8 - 33*B*a**3*c*d**2*sin(e + f*x)**5*cos(e + f*x)/(16*f) - 9*B*a**3*c*d**2*sin(e + f*x)**4*cos(e + f*x)/f - 5*B*a**3*c*d**2*sin(e + f*x)**3*cos(e + f*x)**3/(2*f) - 45*B*a**3*c*d**2*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 12*B*a**3*c*d**2*sin(e + f*x)**2*cos(e + f*x)**3/f - 3*B*a**3*c*d**2*sin(e + f*x)**2*cos(e + f*x)/f - 15*B*a**3*c*d**2*sin(e + f*x)*cos(e + f*x)**5/(16*f) - 27*B*a**3*c*d**2*sin(e + f*x)*cos(e + f*x)**3/(8*f) - 24*B*a**3*c*d**2*cos(e + f*x)**5/(5*f) - 2*B*a**3*c*d**2*cos(e + f*x)**3/f + 15*B*a**3*d**3*x*sin(e + f*x)**6/16 + 45*B*a**3*d**3*x*sin(e + f*x)**4*cos(e + f*x)**2/16 + 3*B*a**3*d**3*x*sin(e + f*x)**4/8 + 45*B*a**3*d**3*x*sin(e + f*x)**2*cos(e + f*x)**4/16 + 3*B*a**3*d**3*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + 15*B*a**3*d**3*x*cos(e + f*x)**6/16 + 3*B*a**3*d**3*x*cos(e + f*x)**4/8 - B*a**3*d**3*sin(e + f*x)**6*cos(e + f*x)/f - 33*B*a**3*d**3*sin(e + f*x)**5*cos(e + f*x)/(16*f) - 2*B*a**3*d**3*sin(e + f*x)**4*cos(e + f*x)**3/f - 3*B*a**3*d**3*sin(e + f*x)**4*cos(e + f*x)/f - 5*B*a**3*d**3*sin(e + f*x)**3*cos(e + f*x)**3/(2*f) - 5*B*a**3*d**3*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 8*B*a**3*d**3*sin(e + f*x)**2*cos(e + f*x)**5/(5*f) - 4*B*a**3*d**3*sin(e + f*x)**2*cos(e + f*x)**3/f - 15*B*a**3*d**3*sin(e + f*x)*cos(e + f*x)**5/(16*f) - 3*B*a**3*d**3*sin(e + f*x)*cos(e + f*x)**3/(8*f) - 16*B*a**3*d**3*cos(e + f*x)**7/(35*f) - 8*B*a**3*d**3*cos(e + f*x)**5/(5*f), Ne(f, 0)), (x*(A + B*sin(e))*(c + d*sin(e))**3*(a*sin(e) + a)**3, True))","A",0
259,1,1804,0,10.853965," ","integrate((a+a*sin(f*x+e))**3*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))**2,x)","\begin{cases} \frac{3 A a^{3} c^{2} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{3 A a^{3} c^{2} x \cos^{2}{\left(e + f x \right)}}{2} + A a^{3} c^{2} x - \frac{A a^{3} c^{2} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{3 A a^{3} c^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{2 A a^{3} c^{2} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{3 A a^{3} c^{2} \cos{\left(e + f x \right)}}{f} + \frac{3 A a^{3} c d x \sin^{4}{\left(e + f x \right)}}{4} + \frac{3 A a^{3} c d x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{2} + 3 A a^{3} c d x \sin^{2}{\left(e + f x \right)} + \frac{3 A a^{3} c d x \cos^{4}{\left(e + f x \right)}}{4} + 3 A a^{3} c d x \cos^{2}{\left(e + f x \right)} - \frac{5 A a^{3} c d \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{4 f} - \frac{6 A a^{3} c d \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{3 A a^{3} c d \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{4 f} - \frac{3 A a^{3} c d \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{4 A a^{3} c d \cos^{3}{\left(e + f x \right)}}{f} - \frac{2 A a^{3} c d \cos{\left(e + f x \right)}}{f} + \frac{9 A a^{3} d^{2} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{9 A a^{3} d^{2} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{A a^{3} d^{2} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{9 A a^{3} d^{2} x \cos^{4}{\left(e + f x \right)}}{8} + \frac{A a^{3} d^{2} x \cos^{2}{\left(e + f x \right)}}{2} - \frac{A a^{3} d^{2} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{15 A a^{3} d^{2} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{4 A a^{3} d^{2} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{3 A a^{3} d^{2} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{9 A a^{3} d^{2} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{A a^{3} d^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{8 A a^{3} d^{2} \cos^{5}{\left(e + f x \right)}}{15 f} - \frac{2 A a^{3} d^{2} \cos^{3}{\left(e + f x \right)}}{f} + \frac{3 B a^{3} c^{2} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{3 B a^{3} c^{2} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{3 B a^{3} c^{2} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{3 B a^{3} c^{2} x \cos^{4}{\left(e + f x \right)}}{8} + \frac{3 B a^{3} c^{2} x \cos^{2}{\left(e + f x \right)}}{2} - \frac{5 B a^{3} c^{2} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{3 B a^{3} c^{2} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{3 B a^{3} c^{2} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{3 B a^{3} c^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{2 B a^{3} c^{2} \cos^{3}{\left(e + f x \right)}}{f} - \frac{B a^{3} c^{2} \cos{\left(e + f x \right)}}{f} + \frac{9 B a^{3} c d x \sin^{4}{\left(e + f x \right)}}{4} + \frac{9 B a^{3} c d x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{2} + B a^{3} c d x \sin^{2}{\left(e + f x \right)} + \frac{9 B a^{3} c d x \cos^{4}{\left(e + f x \right)}}{4} + B a^{3} c d x \cos^{2}{\left(e + f x \right)} - \frac{2 B a^{3} c d \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{15 B a^{3} c d \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{4 f} - \frac{8 B a^{3} c d \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{6 B a^{3} c d \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{9 B a^{3} c d \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{4 f} - \frac{B a^{3} c d \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{16 B a^{3} c d \cos^{5}{\left(e + f x \right)}}{15 f} - \frac{4 B a^{3} c d \cos^{3}{\left(e + f x \right)}}{f} + \frac{5 B a^{3} d^{2} x \sin^{6}{\left(e + f x \right)}}{16} + \frac{15 B a^{3} d^{2} x \sin^{4}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{16} + \frac{9 B a^{3} d^{2} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{15 B a^{3} d^{2} x \sin^{2}{\left(e + f x \right)} \cos^{4}{\left(e + f x \right)}}{16} + \frac{9 B a^{3} d^{2} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{5 B a^{3} d^{2} x \cos^{6}{\left(e + f x \right)}}{16} + \frac{9 B a^{3} d^{2} x \cos^{4}{\left(e + f x \right)}}{8} - \frac{11 B a^{3} d^{2} \sin^{5}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{16 f} - \frac{3 B a^{3} d^{2} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{5 B a^{3} d^{2} \sin^{3}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{6 f} - \frac{15 B a^{3} d^{2} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{4 B a^{3} d^{2} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{f} - \frac{B a^{3} d^{2} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{5 B a^{3} d^{2} \sin{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{16 f} - \frac{9 B a^{3} d^{2} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{8 B a^{3} d^{2} \cos^{5}{\left(e + f x \right)}}{5 f} - \frac{2 B a^{3} d^{2} \cos^{3}{\left(e + f x \right)}}{3 f} & \text{for}\: f \neq 0 \\x \left(A + B \sin{\left(e \right)}\right) \left(c + d \sin{\left(e \right)}\right)^{2} \left(a \sin{\left(e \right)} + a\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*A*a**3*c**2*x*sin(e + f*x)**2/2 + 3*A*a**3*c**2*x*cos(e + f*x)**2/2 + A*a**3*c**2*x - A*a**3*c**2*sin(e + f*x)**2*cos(e + f*x)/f - 3*A*a**3*c**2*sin(e + f*x)*cos(e + f*x)/(2*f) - 2*A*a**3*c**2*cos(e + f*x)**3/(3*f) - 3*A*a**3*c**2*cos(e + f*x)/f + 3*A*a**3*c*d*x*sin(e + f*x)**4/4 + 3*A*a**3*c*d*x*sin(e + f*x)**2*cos(e + f*x)**2/2 + 3*A*a**3*c*d*x*sin(e + f*x)**2 + 3*A*a**3*c*d*x*cos(e + f*x)**4/4 + 3*A*a**3*c*d*x*cos(e + f*x)**2 - 5*A*a**3*c*d*sin(e + f*x)**3*cos(e + f*x)/(4*f) - 6*A*a**3*c*d*sin(e + f*x)**2*cos(e + f*x)/f - 3*A*a**3*c*d*sin(e + f*x)*cos(e + f*x)**3/(4*f) - 3*A*a**3*c*d*sin(e + f*x)*cos(e + f*x)/f - 4*A*a**3*c*d*cos(e + f*x)**3/f - 2*A*a**3*c*d*cos(e + f*x)/f + 9*A*a**3*d**2*x*sin(e + f*x)**4/8 + 9*A*a**3*d**2*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + A*a**3*d**2*x*sin(e + f*x)**2/2 + 9*A*a**3*d**2*x*cos(e + f*x)**4/8 + A*a**3*d**2*x*cos(e + f*x)**2/2 - A*a**3*d**2*sin(e + f*x)**4*cos(e + f*x)/f - 15*A*a**3*d**2*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 4*A*a**3*d**2*sin(e + f*x)**2*cos(e + f*x)**3/(3*f) - 3*A*a**3*d**2*sin(e + f*x)**2*cos(e + f*x)/f - 9*A*a**3*d**2*sin(e + f*x)*cos(e + f*x)**3/(8*f) - A*a**3*d**2*sin(e + f*x)*cos(e + f*x)/(2*f) - 8*A*a**3*d**2*cos(e + f*x)**5/(15*f) - 2*A*a**3*d**2*cos(e + f*x)**3/f + 3*B*a**3*c**2*x*sin(e + f*x)**4/8 + 3*B*a**3*c**2*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + 3*B*a**3*c**2*x*sin(e + f*x)**2/2 + 3*B*a**3*c**2*x*cos(e + f*x)**4/8 + 3*B*a**3*c**2*x*cos(e + f*x)**2/2 - 5*B*a**3*c**2*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 3*B*a**3*c**2*sin(e + f*x)**2*cos(e + f*x)/f - 3*B*a**3*c**2*sin(e + f*x)*cos(e + f*x)**3/(8*f) - 3*B*a**3*c**2*sin(e + f*x)*cos(e + f*x)/(2*f) - 2*B*a**3*c**2*cos(e + f*x)**3/f - B*a**3*c**2*cos(e + f*x)/f + 9*B*a**3*c*d*x*sin(e + f*x)**4/4 + 9*B*a**3*c*d*x*sin(e + f*x)**2*cos(e + f*x)**2/2 + B*a**3*c*d*x*sin(e + f*x)**2 + 9*B*a**3*c*d*x*cos(e + f*x)**4/4 + B*a**3*c*d*x*cos(e + f*x)**2 - 2*B*a**3*c*d*sin(e + f*x)**4*cos(e + f*x)/f - 15*B*a**3*c*d*sin(e + f*x)**3*cos(e + f*x)/(4*f) - 8*B*a**3*c*d*sin(e + f*x)**2*cos(e + f*x)**3/(3*f) - 6*B*a**3*c*d*sin(e + f*x)**2*cos(e + f*x)/f - 9*B*a**3*c*d*sin(e + f*x)*cos(e + f*x)**3/(4*f) - B*a**3*c*d*sin(e + f*x)*cos(e + f*x)/f - 16*B*a**3*c*d*cos(e + f*x)**5/(15*f) - 4*B*a**3*c*d*cos(e + f*x)**3/f + 5*B*a**3*d**2*x*sin(e + f*x)**6/16 + 15*B*a**3*d**2*x*sin(e + f*x)**4*cos(e + f*x)**2/16 + 9*B*a**3*d**2*x*sin(e + f*x)**4/8 + 15*B*a**3*d**2*x*sin(e + f*x)**2*cos(e + f*x)**4/16 + 9*B*a**3*d**2*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + 5*B*a**3*d**2*x*cos(e + f*x)**6/16 + 9*B*a**3*d**2*x*cos(e + f*x)**4/8 - 11*B*a**3*d**2*sin(e + f*x)**5*cos(e + f*x)/(16*f) - 3*B*a**3*d**2*sin(e + f*x)**4*cos(e + f*x)/f - 5*B*a**3*d**2*sin(e + f*x)**3*cos(e + f*x)**3/(6*f) - 15*B*a**3*d**2*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 4*B*a**3*d**2*sin(e + f*x)**2*cos(e + f*x)**3/f - B*a**3*d**2*sin(e + f*x)**2*cos(e + f*x)/f - 5*B*a**3*d**2*sin(e + f*x)*cos(e + f*x)**5/(16*f) - 9*B*a**3*d**2*sin(e + f*x)*cos(e + f*x)**3/(8*f) - 8*B*a**3*d**2*cos(e + f*x)**5/(5*f) - 2*B*a**3*d**2*cos(e + f*x)**3/(3*f), Ne(f, 0)), (x*(A + B*sin(e))*(c + d*sin(e))**2*(a*sin(e) + a)**3, True))","A",0
260,1,960,0,5.283373," ","integrate((a+a*sin(f*x+e))**3*(A+B*sin(f*x+e))*(c+d*sin(f*x+e)),x)","\begin{cases} \frac{3 A a^{3} c x \sin^{2}{\left(e + f x \right)}}{2} + \frac{3 A a^{3} c x \cos^{2}{\left(e + f x \right)}}{2} + A a^{3} c x - \frac{A a^{3} c \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{3 A a^{3} c \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{2 A a^{3} c \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{3 A a^{3} c \cos{\left(e + f x \right)}}{f} + \frac{3 A a^{3} d x \sin^{4}{\left(e + f x \right)}}{8} + \frac{3 A a^{3} d x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{3 A a^{3} d x \sin^{2}{\left(e + f x \right)}}{2} + \frac{3 A a^{3} d x \cos^{4}{\left(e + f x \right)}}{8} + \frac{3 A a^{3} d x \cos^{2}{\left(e + f x \right)}}{2} - \frac{5 A a^{3} d \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{3 A a^{3} d \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{3 A a^{3} d \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{3 A a^{3} d \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{2 A a^{3} d \cos^{3}{\left(e + f x \right)}}{f} - \frac{A a^{3} d \cos{\left(e + f x \right)}}{f} + \frac{3 B a^{3} c x \sin^{4}{\left(e + f x \right)}}{8} + \frac{3 B a^{3} c x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{3 B a^{3} c x \sin^{2}{\left(e + f x \right)}}{2} + \frac{3 B a^{3} c x \cos^{4}{\left(e + f x \right)}}{8} + \frac{3 B a^{3} c x \cos^{2}{\left(e + f x \right)}}{2} - \frac{5 B a^{3} c \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{3 B a^{3} c \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{3 B a^{3} c \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{3 B a^{3} c \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{2 B a^{3} c \cos^{3}{\left(e + f x \right)}}{f} - \frac{B a^{3} c \cos{\left(e + f x \right)}}{f} + \frac{9 B a^{3} d x \sin^{4}{\left(e + f x \right)}}{8} + \frac{9 B a^{3} d x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{B a^{3} d x \sin^{2}{\left(e + f x \right)}}{2} + \frac{9 B a^{3} d x \cos^{4}{\left(e + f x \right)}}{8} + \frac{B a^{3} d x \cos^{2}{\left(e + f x \right)}}{2} - \frac{B a^{3} d \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{15 B a^{3} d \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{4 B a^{3} d \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{3 B a^{3} d \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{9 B a^{3} d \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{B a^{3} d \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{8 B a^{3} d \cos^{5}{\left(e + f x \right)}}{15 f} - \frac{2 B a^{3} d \cos^{3}{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \left(A + B \sin{\left(e \right)}\right) \left(c + d \sin{\left(e \right)}\right) \left(a \sin{\left(e \right)} + a\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*A*a**3*c*x*sin(e + f*x)**2/2 + 3*A*a**3*c*x*cos(e + f*x)**2/2 + A*a**3*c*x - A*a**3*c*sin(e + f*x)**2*cos(e + f*x)/f - 3*A*a**3*c*sin(e + f*x)*cos(e + f*x)/(2*f) - 2*A*a**3*c*cos(e + f*x)**3/(3*f) - 3*A*a**3*c*cos(e + f*x)/f + 3*A*a**3*d*x*sin(e + f*x)**4/8 + 3*A*a**3*d*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + 3*A*a**3*d*x*sin(e + f*x)**2/2 + 3*A*a**3*d*x*cos(e + f*x)**4/8 + 3*A*a**3*d*x*cos(e + f*x)**2/2 - 5*A*a**3*d*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 3*A*a**3*d*sin(e + f*x)**2*cos(e + f*x)/f - 3*A*a**3*d*sin(e + f*x)*cos(e + f*x)**3/(8*f) - 3*A*a**3*d*sin(e + f*x)*cos(e + f*x)/(2*f) - 2*A*a**3*d*cos(e + f*x)**3/f - A*a**3*d*cos(e + f*x)/f + 3*B*a**3*c*x*sin(e + f*x)**4/8 + 3*B*a**3*c*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + 3*B*a**3*c*x*sin(e + f*x)**2/2 + 3*B*a**3*c*x*cos(e + f*x)**4/8 + 3*B*a**3*c*x*cos(e + f*x)**2/2 - 5*B*a**3*c*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 3*B*a**3*c*sin(e + f*x)**2*cos(e + f*x)/f - 3*B*a**3*c*sin(e + f*x)*cos(e + f*x)**3/(8*f) - 3*B*a**3*c*sin(e + f*x)*cos(e + f*x)/(2*f) - 2*B*a**3*c*cos(e + f*x)**3/f - B*a**3*c*cos(e + f*x)/f + 9*B*a**3*d*x*sin(e + f*x)**4/8 + 9*B*a**3*d*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + B*a**3*d*x*sin(e + f*x)**2/2 + 9*B*a**3*d*x*cos(e + f*x)**4/8 + B*a**3*d*x*cos(e + f*x)**2/2 - B*a**3*d*sin(e + f*x)**4*cos(e + f*x)/f - 15*B*a**3*d*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 4*B*a**3*d*sin(e + f*x)**2*cos(e + f*x)**3/(3*f) - 3*B*a**3*d*sin(e + f*x)**2*cos(e + f*x)/f - 9*B*a**3*d*sin(e + f*x)*cos(e + f*x)**3/(8*f) - B*a**3*d*sin(e + f*x)*cos(e + f*x)/(2*f) - 8*B*a**3*d*cos(e + f*x)**5/(15*f) - 2*B*a**3*d*cos(e + f*x)**3/f, Ne(f, 0)), (x*(A + B*sin(e))*(c + d*sin(e))*(a*sin(e) + a)**3, True))","A",0
261,1,371,0,2.084537," ","integrate((a+a*sin(f*x+e))**3*(A+B*sin(f*x+e)),x)","\begin{cases} \frac{3 A a^{3} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{3 A a^{3} x \cos^{2}{\left(e + f x \right)}}{2} + A a^{3} x - \frac{A a^{3} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{3 A a^{3} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{2 A a^{3} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{3 A a^{3} \cos{\left(e + f x \right)}}{f} + \frac{3 B a^{3} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{3 B a^{3} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{3 B a^{3} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{3 B a^{3} x \cos^{4}{\left(e + f x \right)}}{8} + \frac{3 B a^{3} x \cos^{2}{\left(e + f x \right)}}{2} - \frac{5 B a^{3} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{3 B a^{3} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{3 B a^{3} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{3 B a^{3} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{2 B a^{3} \cos^{3}{\left(e + f x \right)}}{f} - \frac{B a^{3} \cos{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \left(A + B \sin{\left(e \right)}\right) \left(a \sin{\left(e \right)} + a\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*A*a**3*x*sin(e + f*x)**2/2 + 3*A*a**3*x*cos(e + f*x)**2/2 + A*a**3*x - A*a**3*sin(e + f*x)**2*cos(e + f*x)/f - 3*A*a**3*sin(e + f*x)*cos(e + f*x)/(2*f) - 2*A*a**3*cos(e + f*x)**3/(3*f) - 3*A*a**3*cos(e + f*x)/f + 3*B*a**3*x*sin(e + f*x)**4/8 + 3*B*a**3*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + 3*B*a**3*x*sin(e + f*x)**2/2 + 3*B*a**3*x*cos(e + f*x)**4/8 + 3*B*a**3*x*cos(e + f*x)**2/2 - 5*B*a**3*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 3*B*a**3*sin(e + f*x)**2*cos(e + f*x)/f - 3*B*a**3*sin(e + f*x)*cos(e + f*x)**3/(8*f) - 3*B*a**3*sin(e + f*x)*cos(e + f*x)/(2*f) - 2*B*a**3*cos(e + f*x)**3/f - B*a**3*cos(e + f*x)/f, Ne(f, 0)), (x*(A + B*sin(e))*(a*sin(e) + a)**3, True))","A",0
262,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**3*(A+B*sin(f*x+e))/(c+d*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
263,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**3*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
264,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**3*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
265,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))**3/(a+a*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
266,1,5763,0,9.444697," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))**2/(a+a*sin(f*x+e)),x)","\begin{cases} - \frac{4 A c^{2} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} - \frac{8 A c^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} - \frac{4 A c^{2}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} + \frac{4 A c d f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} + \frac{4 A c d f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} + \frac{8 A c d f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} + \frac{8 A c d f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} + \frac{4 A c d f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} + \frac{4 A c d f x}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} + \frac{8 A c d \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} + \frac{16 A c d \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} + \frac{8 A c d}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} - \frac{2 A d^{2} f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} - \frac{2 A d^{2} f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} - \frac{4 A d^{2} f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} - \frac{4 A d^{2} f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} - \frac{2 A d^{2} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} - \frac{2 A d^{2} f x}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} - \frac{4 A d^{2} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} - \frac{4 A d^{2} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} - \frac{12 A d^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} - \frac{4 A d^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} - \frac{8 A d^{2}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} + \frac{2 B c^{2} f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} + \frac{2 B c^{2} f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} + \frac{4 B c^{2} f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} + \frac{4 B c^{2} f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} + \frac{2 B c^{2} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} + \frac{2 B c^{2} f x}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} + \frac{4 B c^{2} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} + \frac{8 B c^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} + \frac{4 B c^{2}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} - \frac{4 B c d f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} - \frac{4 B c d f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} - \frac{8 B c d f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} - \frac{8 B c d f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} - \frac{4 B c d f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} - \frac{4 B c d f x}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} - \frac{8 B c d \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} - \frac{8 B c d \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} - \frac{24 B c d \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} - \frac{8 B c d \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} - \frac{16 B c d}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} + \frac{3 B d^{2} f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} + \frac{3 B d^{2} f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} + \frac{6 B d^{2} f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} + \frac{6 B d^{2} f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} + \frac{3 B d^{2} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} + \frac{3 B d^{2} f x}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} + \frac{6 B d^{2} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} + \frac{6 B d^{2} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} + \frac{10 B d^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} + \frac{2 B d^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} + \frac{8 B d^{2}}{2 a f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right) \left(c + d \sin{\left(e \right)}\right)^{2}}{a \sin{\left(e \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-4*A*c**2*tan(e/2 + f*x/2)**4/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) - 8*A*c**2*tan(e/2 + f*x/2)**2/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) - 4*A*c**2/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) + 4*A*c*d*f*x*tan(e/2 + f*x/2)**5/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) + 4*A*c*d*f*x*tan(e/2 + f*x/2)**4/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) + 8*A*c*d*f*x*tan(e/2 + f*x/2)**3/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) + 8*A*c*d*f*x*tan(e/2 + f*x/2)**2/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) + 4*A*c*d*f*x*tan(e/2 + f*x/2)/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) + 4*A*c*d*f*x/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) + 8*A*c*d*tan(e/2 + f*x/2)**4/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) + 16*A*c*d*tan(e/2 + f*x/2)**2/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) + 8*A*c*d/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) - 2*A*d**2*f*x*tan(e/2 + f*x/2)**5/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) - 2*A*d**2*f*x*tan(e/2 + f*x/2)**4/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) - 4*A*d**2*f*x*tan(e/2 + f*x/2)**3/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) - 4*A*d**2*f*x*tan(e/2 + f*x/2)**2/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) - 2*A*d**2*f*x*tan(e/2 + f*x/2)/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) - 2*A*d**2*f*x/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) - 4*A*d**2*tan(e/2 + f*x/2)**4/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) - 4*A*d**2*tan(e/2 + f*x/2)**3/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) - 12*A*d**2*tan(e/2 + f*x/2)**2/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) - 4*A*d**2*tan(e/2 + f*x/2)/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) - 8*A*d**2/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) + 2*B*c**2*f*x*tan(e/2 + f*x/2)**5/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) + 2*B*c**2*f*x*tan(e/2 + f*x/2)**4/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) + 4*B*c**2*f*x*tan(e/2 + f*x/2)**3/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) + 4*B*c**2*f*x*tan(e/2 + f*x/2)**2/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) + 2*B*c**2*f*x*tan(e/2 + f*x/2)/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) + 2*B*c**2*f*x/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) + 4*B*c**2*tan(e/2 + f*x/2)**4/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) + 8*B*c**2*tan(e/2 + f*x/2)**2/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) + 4*B*c**2/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) - 4*B*c*d*f*x*tan(e/2 + f*x/2)**5/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) - 4*B*c*d*f*x*tan(e/2 + f*x/2)**4/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) - 8*B*c*d*f*x*tan(e/2 + f*x/2)**3/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) - 8*B*c*d*f*x*tan(e/2 + f*x/2)**2/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) - 4*B*c*d*f*x*tan(e/2 + f*x/2)/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) - 4*B*c*d*f*x/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) - 8*B*c*d*tan(e/2 + f*x/2)**4/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) - 8*B*c*d*tan(e/2 + f*x/2)**3/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) - 24*B*c*d*tan(e/2 + f*x/2)**2/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) - 8*B*c*d*tan(e/2 + f*x/2)/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) - 16*B*c*d/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) + 3*B*d**2*f*x*tan(e/2 + f*x/2)**5/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) + 3*B*d**2*f*x*tan(e/2 + f*x/2)**4/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) + 6*B*d**2*f*x*tan(e/2 + f*x/2)**3/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) + 6*B*d**2*f*x*tan(e/2 + f*x/2)**2/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) + 3*B*d**2*f*x*tan(e/2 + f*x/2)/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) + 3*B*d**2*f*x/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) + 6*B*d**2*tan(e/2 + f*x/2)**4/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) + 6*B*d**2*tan(e/2 + f*x/2)**3/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) + 10*B*d**2*tan(e/2 + f*x/2)**2/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) + 2*B*d**2*tan(e/2 + f*x/2)/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f) + 8*B*d**2/(2*a*f*tan(e/2 + f*x/2)**5 + 2*a*f*tan(e/2 + f*x/2)**4 + 4*a*f*tan(e/2 + f*x/2)**3 + 4*a*f*tan(e/2 + f*x/2)**2 + 2*a*f*tan(e/2 + f*x/2) + 2*a*f), Ne(f, 0)), (x*(A + B*sin(e))*(c + d*sin(e))**2/(a*sin(e) + a), True))","A",0
267,1,1307,0,4.181243," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))/(a+a*sin(f*x+e)),x)","\begin{cases} - \frac{2 A c \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f} - \frac{2 A c}{a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f} + \frac{A d f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f} + \frac{A d f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f} + \frac{A d f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f} + \frac{A d f x}{a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f} + \frac{2 A d \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f} + \frac{2 A d}{a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f} + \frac{B c f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f} + \frac{B c f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f} + \frac{B c f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f} + \frac{B c f x}{a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f} + \frac{2 B c \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f} + \frac{2 B c}{a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f} - \frac{B d f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f} - \frac{B d f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f} - \frac{B d f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f} - \frac{B d f x}{a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f} - \frac{2 B d \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f} - \frac{2 B d \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f} - \frac{4 B d}{a f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right) \left(c + d \sin{\left(e \right)}\right)}{a \sin{\left(e \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*A*c*tan(e/2 + f*x/2)**2/(a*f*tan(e/2 + f*x/2)**3 + a*f*tan(e/2 + f*x/2)**2 + a*f*tan(e/2 + f*x/2) + a*f) - 2*A*c/(a*f*tan(e/2 + f*x/2)**3 + a*f*tan(e/2 + f*x/2)**2 + a*f*tan(e/2 + f*x/2) + a*f) + A*d*f*x*tan(e/2 + f*x/2)**3/(a*f*tan(e/2 + f*x/2)**3 + a*f*tan(e/2 + f*x/2)**2 + a*f*tan(e/2 + f*x/2) + a*f) + A*d*f*x*tan(e/2 + f*x/2)**2/(a*f*tan(e/2 + f*x/2)**3 + a*f*tan(e/2 + f*x/2)**2 + a*f*tan(e/2 + f*x/2) + a*f) + A*d*f*x*tan(e/2 + f*x/2)/(a*f*tan(e/2 + f*x/2)**3 + a*f*tan(e/2 + f*x/2)**2 + a*f*tan(e/2 + f*x/2) + a*f) + A*d*f*x/(a*f*tan(e/2 + f*x/2)**3 + a*f*tan(e/2 + f*x/2)**2 + a*f*tan(e/2 + f*x/2) + a*f) + 2*A*d*tan(e/2 + f*x/2)**2/(a*f*tan(e/2 + f*x/2)**3 + a*f*tan(e/2 + f*x/2)**2 + a*f*tan(e/2 + f*x/2) + a*f) + 2*A*d/(a*f*tan(e/2 + f*x/2)**3 + a*f*tan(e/2 + f*x/2)**2 + a*f*tan(e/2 + f*x/2) + a*f) + B*c*f*x*tan(e/2 + f*x/2)**3/(a*f*tan(e/2 + f*x/2)**3 + a*f*tan(e/2 + f*x/2)**2 + a*f*tan(e/2 + f*x/2) + a*f) + B*c*f*x*tan(e/2 + f*x/2)**2/(a*f*tan(e/2 + f*x/2)**3 + a*f*tan(e/2 + f*x/2)**2 + a*f*tan(e/2 + f*x/2) + a*f) + B*c*f*x*tan(e/2 + f*x/2)/(a*f*tan(e/2 + f*x/2)**3 + a*f*tan(e/2 + f*x/2)**2 + a*f*tan(e/2 + f*x/2) + a*f) + B*c*f*x/(a*f*tan(e/2 + f*x/2)**3 + a*f*tan(e/2 + f*x/2)**2 + a*f*tan(e/2 + f*x/2) + a*f) + 2*B*c*tan(e/2 + f*x/2)**2/(a*f*tan(e/2 + f*x/2)**3 + a*f*tan(e/2 + f*x/2)**2 + a*f*tan(e/2 + f*x/2) + a*f) + 2*B*c/(a*f*tan(e/2 + f*x/2)**3 + a*f*tan(e/2 + f*x/2)**2 + a*f*tan(e/2 + f*x/2) + a*f) - B*d*f*x*tan(e/2 + f*x/2)**3/(a*f*tan(e/2 + f*x/2)**3 + a*f*tan(e/2 + f*x/2)**2 + a*f*tan(e/2 + f*x/2) + a*f) - B*d*f*x*tan(e/2 + f*x/2)**2/(a*f*tan(e/2 + f*x/2)**3 + a*f*tan(e/2 + f*x/2)**2 + a*f*tan(e/2 + f*x/2) + a*f) - B*d*f*x*tan(e/2 + f*x/2)/(a*f*tan(e/2 + f*x/2)**3 + a*f*tan(e/2 + f*x/2)**2 + a*f*tan(e/2 + f*x/2) + a*f) - B*d*f*x/(a*f*tan(e/2 + f*x/2)**3 + a*f*tan(e/2 + f*x/2)**2 + a*f*tan(e/2 + f*x/2) + a*f) - 2*B*d*tan(e/2 + f*x/2)**2/(a*f*tan(e/2 + f*x/2)**3 + a*f*tan(e/2 + f*x/2)**2 + a*f*tan(e/2 + f*x/2) + a*f) - 2*B*d*tan(e/2 + f*x/2)/(a*f*tan(e/2 + f*x/2)**3 + a*f*tan(e/2 + f*x/2)**2 + a*f*tan(e/2 + f*x/2) + a*f) - 4*B*d/(a*f*tan(e/2 + f*x/2)**3 + a*f*tan(e/2 + f*x/2)**2 + a*f*tan(e/2 + f*x/2) + a*f), Ne(f, 0)), (x*(A + B*sin(e))*(c + d*sin(e))/(a*sin(e) + a), True))","A",0
268,1,109,0,1.832420," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e)),x)","\begin{cases} - \frac{2 A}{a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f} + \frac{B f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f} + \frac{B f x}{a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f} + \frac{2 B}{a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right)}{a \sin{\left(e \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*A/(a*f*tan(e/2 + f*x/2) + a*f) + B*f*x*tan(e/2 + f*x/2)/(a*f*tan(e/2 + f*x/2) + a*f) + B*f*x/(a*f*tan(e/2 + f*x/2) + a*f) + 2*B/(a*f*tan(e/2 + f*x/2) + a*f), Ne(f, 0)), (x*(A + B*sin(e))/(a*sin(e) + a), True))","A",0
269,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))/(c+d*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
270,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))/(c+d*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
271,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))/(c+d*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
272,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))**3/(a+a*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
273,1,5358,0,17.794590," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))**2/(a+a*sin(f*x+e))**2,x)","\begin{cases} - \frac{6 A c^{2} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{6 A c^{2} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{10 A c^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{6 A c^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{4 A c^{2}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{12 A c d \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{4 A c d \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{12 A c d \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{4 A c d}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} + \frac{3 A d^{2} f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} + \frac{9 A d^{2} f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} + \frac{12 A d^{2} f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} + \frac{12 A d^{2} f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} + \frac{9 A d^{2} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} + \frac{3 A d^{2} f x}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} + \frac{6 A d^{2} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} + \frac{18 A d^{2} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} + \frac{14 A d^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} + \frac{18 A d^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} + \frac{8 A d^{2}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{6 B c^{2} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{2 B c^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{6 B c^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{2 B c^{2}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} + \frac{6 B c d f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} + \frac{18 B c d f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} + \frac{24 B c d f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} + \frac{24 B c d f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} + \frac{18 B c d f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} + \frac{6 B c d f x}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} + \frac{12 B c d \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} + \frac{36 B c d \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} + \frac{28 B c d \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} + \frac{36 B c d \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} + \frac{16 B c d}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{6 B d^{2} f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{18 B d^{2} f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{24 B d^{2} f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{24 B d^{2} f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{18 B d^{2} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{6 B d^{2} f x}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{12 B d^{2} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{36 B d^{2} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{44 B d^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{48 B d^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{20 B d^{2}}{3 a^{2} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right) \left(c + d \sin{\left(e \right)}\right)^{2}}{\left(a \sin{\left(e \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-6*A*c**2*tan(e/2 + f*x/2)**4/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 6*A*c**2*tan(e/2 + f*x/2)**3/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 10*A*c**2*tan(e/2 + f*x/2)**2/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 6*A*c**2*tan(e/2 + f*x/2)/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 4*A*c**2/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 12*A*c*d*tan(e/2 + f*x/2)**3/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 4*A*c*d*tan(e/2 + f*x/2)**2/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 12*A*c*d*tan(e/2 + f*x/2)/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 4*A*c*d/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) + 3*A*d**2*f*x*tan(e/2 + f*x/2)**5/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) + 9*A*d**2*f*x*tan(e/2 + f*x/2)**4/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) + 12*A*d**2*f*x*tan(e/2 + f*x/2)**3/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) + 12*A*d**2*f*x*tan(e/2 + f*x/2)**2/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) + 9*A*d**2*f*x*tan(e/2 + f*x/2)/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) + 3*A*d**2*f*x/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) + 6*A*d**2*tan(e/2 + f*x/2)**4/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) + 18*A*d**2*tan(e/2 + f*x/2)**3/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) + 14*A*d**2*tan(e/2 + f*x/2)**2/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) + 18*A*d**2*tan(e/2 + f*x/2)/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) + 8*A*d**2/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 6*B*c**2*tan(e/2 + f*x/2)**3/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 2*B*c**2*tan(e/2 + f*x/2)**2/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 6*B*c**2*tan(e/2 + f*x/2)/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 2*B*c**2/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) + 6*B*c*d*f*x*tan(e/2 + f*x/2)**5/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) + 18*B*c*d*f*x*tan(e/2 + f*x/2)**4/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) + 24*B*c*d*f*x*tan(e/2 + f*x/2)**3/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) + 24*B*c*d*f*x*tan(e/2 + f*x/2)**2/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) + 18*B*c*d*f*x*tan(e/2 + f*x/2)/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) + 6*B*c*d*f*x/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) + 12*B*c*d*tan(e/2 + f*x/2)**4/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) + 36*B*c*d*tan(e/2 + f*x/2)**3/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) + 28*B*c*d*tan(e/2 + f*x/2)**2/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) + 36*B*c*d*tan(e/2 + f*x/2)/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) + 16*B*c*d/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 6*B*d**2*f*x*tan(e/2 + f*x/2)**5/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 18*B*d**2*f*x*tan(e/2 + f*x/2)**4/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 24*B*d**2*f*x*tan(e/2 + f*x/2)**3/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 24*B*d**2*f*x*tan(e/2 + f*x/2)**2/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 18*B*d**2*f*x*tan(e/2 + f*x/2)/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 6*B*d**2*f*x/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 12*B*d**2*tan(e/2 + f*x/2)**4/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 36*B*d**2*tan(e/2 + f*x/2)**3/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 44*B*d**2*tan(e/2 + f*x/2)**2/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 48*B*d**2*tan(e/2 + f*x/2)/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 20*B*d**2/(3*a**2*f*tan(e/2 + f*x/2)**5 + 9*a**2*f*tan(e/2 + f*x/2)**4 + 12*a**2*f*tan(e/2 + f*x/2)**3 + 12*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f), Ne(f, 0)), (x*(A + B*sin(e))*(c + d*sin(e))**2/(a*sin(e) + a)**2, True))","A",0
274,1,1062,0,8.342678," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))/(a+a*sin(f*x+e))**2,x)","\begin{cases} - \frac{6 A c \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{6 A c \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{4 A c}{3 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{6 A d \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{2 A d}{3 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{6 B c \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{2 B c}{3 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} + \frac{3 B d f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} + \frac{9 B d f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} + \frac{9 B d f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} + \frac{3 B d f x}{3 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} + \frac{6 B d \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} + \frac{18 B d \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} + \frac{8 B d}{3 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right) \left(c + d \sin{\left(e \right)}\right)}{\left(a \sin{\left(e \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-6*A*c*tan(e/2 + f*x/2)**2/(3*a**2*f*tan(e/2 + f*x/2)**3 + 9*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 6*A*c*tan(e/2 + f*x/2)/(3*a**2*f*tan(e/2 + f*x/2)**3 + 9*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 4*A*c/(3*a**2*f*tan(e/2 + f*x/2)**3 + 9*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 6*A*d*tan(e/2 + f*x/2)/(3*a**2*f*tan(e/2 + f*x/2)**3 + 9*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 2*A*d/(3*a**2*f*tan(e/2 + f*x/2)**3 + 9*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 6*B*c*tan(e/2 + f*x/2)/(3*a**2*f*tan(e/2 + f*x/2)**3 + 9*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 2*B*c/(3*a**2*f*tan(e/2 + f*x/2)**3 + 9*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) + 3*B*d*f*x*tan(e/2 + f*x/2)**3/(3*a**2*f*tan(e/2 + f*x/2)**3 + 9*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) + 9*B*d*f*x*tan(e/2 + f*x/2)**2/(3*a**2*f*tan(e/2 + f*x/2)**3 + 9*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) + 9*B*d*f*x*tan(e/2 + f*x/2)/(3*a**2*f*tan(e/2 + f*x/2)**3 + 9*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) + 3*B*d*f*x/(3*a**2*f*tan(e/2 + f*x/2)**3 + 9*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) + 6*B*d*tan(e/2 + f*x/2)**2/(3*a**2*f*tan(e/2 + f*x/2)**3 + 9*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) + 18*B*d*tan(e/2 + f*x/2)/(3*a**2*f*tan(e/2 + f*x/2)**3 + 9*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) + 8*B*d/(3*a**2*f*tan(e/2 + f*x/2)**3 + 9*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f), Ne(f, 0)), (x*(A + B*sin(e))*(c + d*sin(e))/(a*sin(e) + a)**2, True))","A",0
275,1,372,0,4.584593," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))**2,x)","\begin{cases} - \frac{6 A \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{6 A \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{4 A}{3 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{6 B \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} - \frac{2 B}{3 a^{2} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a^{2} f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right)}{\left(a \sin{\left(e \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-6*A*tan(e/2 + f*x/2)**2/(3*a**2*f*tan(e/2 + f*x/2)**3 + 9*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 6*A*tan(e/2 + f*x/2)/(3*a**2*f*tan(e/2 + f*x/2)**3 + 9*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 4*A/(3*a**2*f*tan(e/2 + f*x/2)**3 + 9*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 6*B*tan(e/2 + f*x/2)/(3*a**2*f*tan(e/2 + f*x/2)**3 + 9*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f) - 2*B/(3*a**2*f*tan(e/2 + f*x/2)**3 + 9*a**2*f*tan(e/2 + f*x/2)**2 + 9*a**2*f*tan(e/2 + f*x/2) + 3*a**2*f), Ne(f, 0)), (x*(A + B*sin(e))/(a*sin(e) + a)**2, True))","A",0
276,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))**2/(c+d*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
277,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))**2/(c+d*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
278,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))**2/(c+d*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
279,1,11456,0,56.434736," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))**3/(a+a*sin(f*x+e))**3,x)","\begin{cases} - \frac{30 A c^{3} \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{60 A c^{3} \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{110 A c^{3} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{100 A c^{3} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{94 A c^{3} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{40 A c^{3} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{14 A c^{3}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{90 A c^{2} d \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{90 A c^{2} d \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{180 A c^{2} d \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{108 A c^{2} d \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{90 A c^{2} d \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{18 A c^{2} d}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{120 A c d^{2} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{60 A c d^{2} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{132 A c d^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{60 A c d^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{12 A c d^{2}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{15 A d^{3} f x \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{75 A d^{3} f x \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{165 A d^{3} f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{225 A d^{3} f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{225 A d^{3} f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{165 A d^{3} f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{75 A d^{3} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{15 A d^{3} f x}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{30 A d^{3} \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{150 A d^{3} \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{320 A d^{3} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{340 A d^{3} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{334 A d^{3} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{190 A d^{3} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{44 A d^{3}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{30 B c^{3} \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{30 B c^{3} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{60 B c^{3} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{36 B c^{3} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{30 B c^{3} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{6 B c^{3}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{120 B c^{2} d \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{60 B c^{2} d \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{132 B c^{2} d \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{60 B c^{2} d \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{12 B c^{2} d}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{45 B c d^{2} f x \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{225 B c d^{2} f x \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{495 B c d^{2} f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{675 B c d^{2} f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{675 B c d^{2} f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{495 B c d^{2} f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{225 B c d^{2} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{45 B c d^{2} f x}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{90 B c d^{2} \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{450 B c d^{2} \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{960 B c d^{2} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{1020 B c d^{2} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{1002 B c d^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{570 B c d^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{132 B c d^{2}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{45 B d^{3} f x \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{225 B d^{3} f x \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{495 B d^{3} f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{675 B d^{3} f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{675 B d^{3} f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{495 B d^{3} f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{225 B d^{3} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{45 B d^{3} f x}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{90 B d^{3} \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{450 B d^{3} \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{960 B d^{3} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{1200 B d^{3} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{1134 B d^{3} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{630 B d^{3} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{144 B d^{3}}{15 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 225 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 165 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right) \left(c + d \sin{\left(e \right)}\right)^{3}}{\left(a \sin{\left(e \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-30*A*c**3*tan(e/2 + f*x/2)**6/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 60*A*c**3*tan(e/2 + f*x/2)**5/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 110*A*c**3*tan(e/2 + f*x/2)**4/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 100*A*c**3*tan(e/2 + f*x/2)**3/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 94*A*c**3*tan(e/2 + f*x/2)**2/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 40*A*c**3*tan(e/2 + f*x/2)/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 14*A*c**3/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 90*A*c**2*d*tan(e/2 + f*x/2)**5/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 90*A*c**2*d*tan(e/2 + f*x/2)**4/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 180*A*c**2*d*tan(e/2 + f*x/2)**3/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 108*A*c**2*d*tan(e/2 + f*x/2)**2/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 90*A*c**2*d*tan(e/2 + f*x/2)/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 18*A*c**2*d/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 120*A*c*d**2*tan(e/2 + f*x/2)**4/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 60*A*c*d**2*tan(e/2 + f*x/2)**3/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 132*A*c*d**2*tan(e/2 + f*x/2)**2/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 60*A*c*d**2*tan(e/2 + f*x/2)/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 12*A*c*d**2/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 15*A*d**3*f*x*tan(e/2 + f*x/2)**7/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 75*A*d**3*f*x*tan(e/2 + f*x/2)**6/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 165*A*d**3*f*x*tan(e/2 + f*x/2)**5/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 225*A*d**3*f*x*tan(e/2 + f*x/2)**4/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 225*A*d**3*f*x*tan(e/2 + f*x/2)**3/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 165*A*d**3*f*x*tan(e/2 + f*x/2)**2/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 75*A*d**3*f*x*tan(e/2 + f*x/2)/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 15*A*d**3*f*x/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 30*A*d**3*tan(e/2 + f*x/2)**6/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 150*A*d**3*tan(e/2 + f*x/2)**5/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 320*A*d**3*tan(e/2 + f*x/2)**4/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 340*A*d**3*tan(e/2 + f*x/2)**3/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 334*A*d**3*tan(e/2 + f*x/2)**2/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 190*A*d**3*tan(e/2 + f*x/2)/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 44*A*d**3/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 30*B*c**3*tan(e/2 + f*x/2)**5/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 30*B*c**3*tan(e/2 + f*x/2)**4/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 60*B*c**3*tan(e/2 + f*x/2)**3/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 36*B*c**3*tan(e/2 + f*x/2)**2/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 30*B*c**3*tan(e/2 + f*x/2)/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 6*B*c**3/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 120*B*c**2*d*tan(e/2 + f*x/2)**4/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 60*B*c**2*d*tan(e/2 + f*x/2)**3/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 132*B*c**2*d*tan(e/2 + f*x/2)**2/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 60*B*c**2*d*tan(e/2 + f*x/2)/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 12*B*c**2*d/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 45*B*c*d**2*f*x*tan(e/2 + f*x/2)**7/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 225*B*c*d**2*f*x*tan(e/2 + f*x/2)**6/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 495*B*c*d**2*f*x*tan(e/2 + f*x/2)**5/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 675*B*c*d**2*f*x*tan(e/2 + f*x/2)**4/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 675*B*c*d**2*f*x*tan(e/2 + f*x/2)**3/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 495*B*c*d**2*f*x*tan(e/2 + f*x/2)**2/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 225*B*c*d**2*f*x*tan(e/2 + f*x/2)/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 45*B*c*d**2*f*x/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 90*B*c*d**2*tan(e/2 + f*x/2)**6/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 450*B*c*d**2*tan(e/2 + f*x/2)**5/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 960*B*c*d**2*tan(e/2 + f*x/2)**4/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 1020*B*c*d**2*tan(e/2 + f*x/2)**3/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 1002*B*c*d**2*tan(e/2 + f*x/2)**2/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 570*B*c*d**2*tan(e/2 + f*x/2)/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 132*B*c*d**2/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 45*B*d**3*f*x*tan(e/2 + f*x/2)**7/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 225*B*d**3*f*x*tan(e/2 + f*x/2)**6/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 495*B*d**3*f*x*tan(e/2 + f*x/2)**5/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 675*B*d**3*f*x*tan(e/2 + f*x/2)**4/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 675*B*d**3*f*x*tan(e/2 + f*x/2)**3/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 495*B*d**3*f*x*tan(e/2 + f*x/2)**2/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 225*B*d**3*f*x*tan(e/2 + f*x/2)/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 45*B*d**3*f*x/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 90*B*d**3*tan(e/2 + f*x/2)**6/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 450*B*d**3*tan(e/2 + f*x/2)**5/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 960*B*d**3*tan(e/2 + f*x/2)**4/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 1200*B*d**3*tan(e/2 + f*x/2)**3/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 1134*B*d**3*tan(e/2 + f*x/2)**2/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 630*B*d**3*tan(e/2 + f*x/2)/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 144*B*d**3/(15*a**3*f*tan(e/2 + f*x/2)**7 + 75*a**3*f*tan(e/2 + f*x/2)**6 + 165*a**3*f*tan(e/2 + f*x/2)**5 + 225*a**3*f*tan(e/2 + f*x/2)**4 + 225*a**3*f*tan(e/2 + f*x/2)**3 + 165*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f), Ne(f, 0)), (x*(A + B*sin(e))*(c + d*sin(e))**3/(a*sin(e) + a)**3, True))","A",0
280,1,3468,0,33.402815," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))**2/(a+a*sin(f*x+e))**3,x)","\begin{cases} - \frac{30 A c^{2} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{60 A c^{2} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{80 A c^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{40 A c^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{14 A c^{2}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{60 A c d \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{60 A c d \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{60 A c d \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{12 A c d}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{40 A d^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{20 A d^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{4 A d^{2}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{30 B c^{2} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{30 B c^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{30 B c^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{6 B c^{2}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{80 B c d \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{40 B c d \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{8 B c d}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{15 B d^{2} f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{75 B d^{2} f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{150 B d^{2} f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{150 B d^{2} f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{75 B d^{2} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{15 B d^{2} f x}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{30 B d^{2} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{150 B d^{2} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{290 B d^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{190 B d^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} + \frac{44 B d^{2}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right) \left(c + d \sin{\left(e \right)}\right)^{2}}{\left(a \sin{\left(e \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-30*A*c**2*tan(e/2 + f*x/2)**4/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 60*A*c**2*tan(e/2 + f*x/2)**3/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 80*A*c**2*tan(e/2 + f*x/2)**2/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 40*A*c**2*tan(e/2 + f*x/2)/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 14*A*c**2/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 60*A*c*d*tan(e/2 + f*x/2)**3/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 60*A*c*d*tan(e/2 + f*x/2)**2/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 60*A*c*d*tan(e/2 + f*x/2)/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 12*A*c*d/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 40*A*d**2*tan(e/2 + f*x/2)**2/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 20*A*d**2*tan(e/2 + f*x/2)/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 4*A*d**2/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 30*B*c**2*tan(e/2 + f*x/2)**3/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 30*B*c**2*tan(e/2 + f*x/2)**2/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 30*B*c**2*tan(e/2 + f*x/2)/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 6*B*c**2/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 80*B*c*d*tan(e/2 + f*x/2)**2/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 40*B*c*d*tan(e/2 + f*x/2)/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 8*B*c*d/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 15*B*d**2*f*x*tan(e/2 + f*x/2)**5/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 75*B*d**2*f*x*tan(e/2 + f*x/2)**4/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 150*B*d**2*f*x*tan(e/2 + f*x/2)**3/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 150*B*d**2*f*x*tan(e/2 + f*x/2)**2/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 75*B*d**2*f*x*tan(e/2 + f*x/2)/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 15*B*d**2*f*x/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 30*B*d**2*tan(e/2 + f*x/2)**4/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 150*B*d**2*tan(e/2 + f*x/2)**3/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 290*B*d**2*tan(e/2 + f*x/2)**2/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 190*B*d**2*tan(e/2 + f*x/2)/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) + 44*B*d**2/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f), Ne(f, 0)), (x*(A + B*sin(e))*(c + d*sin(e))**2/(a*sin(e) + a)**3, True))","A",0
281,1,1819,0,15.102391," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))/(a+a*sin(f*x+e))**3,x)","\begin{cases} - \frac{30 A c \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{60 A c \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{80 A c \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{40 A c \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{14 A c}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{30 A d \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{30 A d \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{30 A d \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{6 A d}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{30 B c \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{30 B c \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{30 B c \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{6 B c}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{40 B d \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{20 B d \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{4 B d}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right) \left(c + d \sin{\left(e \right)}\right)}{\left(a \sin{\left(e \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-30*A*c*tan(e/2 + f*x/2)**4/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 60*A*c*tan(e/2 + f*x/2)**3/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 80*A*c*tan(e/2 + f*x/2)**2/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 40*A*c*tan(e/2 + f*x/2)/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 14*A*c/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 30*A*d*tan(e/2 + f*x/2)**3/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 30*A*d*tan(e/2 + f*x/2)**2/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 30*A*d*tan(e/2 + f*x/2)/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 6*A*d/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 30*B*c*tan(e/2 + f*x/2)**3/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 30*B*c*tan(e/2 + f*x/2)**2/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 30*B*c*tan(e/2 + f*x/2)/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 6*B*c/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 40*B*d*tan(e/2 + f*x/2)**2/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 20*B*d*tan(e/2 + f*x/2)/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 4*B*d/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f), Ne(f, 0)), (x*(A + B*sin(e))*(c + d*sin(e))/(a*sin(e) + a)**3, True))","A",0
282,1,1015,0,8.341605," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))**3,x)","\begin{cases} - \frac{30 A \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{60 A \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{80 A \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{40 A \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{14 A}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{30 B \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{30 B \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{30 B \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} - \frac{6 B}{15 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 150 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 75 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 15 a^{3} f} & \text{for}\: f \neq 0 \\\frac{x \left(A + B \sin{\left(e \right)}\right)}{\left(a \sin{\left(e \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-30*A*tan(e/2 + f*x/2)**4/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 60*A*tan(e/2 + f*x/2)**3/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 80*A*tan(e/2 + f*x/2)**2/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 40*A*tan(e/2 + f*x/2)/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 14*A/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 30*B*tan(e/2 + f*x/2)**3/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 30*B*tan(e/2 + f*x/2)**2/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 30*B*tan(e/2 + f*x/2)/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f) - 6*B/(15*a**3*f*tan(e/2 + f*x/2)**5 + 75*a**3*f*tan(e/2 + f*x/2)**4 + 150*a**3*f*tan(e/2 + f*x/2)**3 + 150*a**3*f*tan(e/2 + f*x/2)**2 + 75*a**3*f*tan(e/2 + f*x/2) + 15*a**3*f), Ne(f, 0)), (x*(A + B*sin(e))/(a*sin(e) + a)**3, True))","A",0
283,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))**3/(c+d*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
284,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))**3/(c+d*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
285,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))**3/(c+d*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
286,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))**3*(a+a*sin(f*x+e))**(1/2),x)","\int \sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)} \left(A + B \sin{\left(e + f x \right)}\right) \left(c + d \sin{\left(e + f x \right)}\right)^{3}\, dx"," ",0,"Integral(sqrt(a*(sin(e + f*x) + 1))*(A + B*sin(e + f*x))*(c + d*sin(e + f*x))**3, x)","F",0
287,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))**2*(a+a*sin(f*x+e))**(1/2),x)","\int \sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)} \left(A + B \sin{\left(e + f x \right)}\right) \left(c + d \sin{\left(e + f x \right)}\right)^{2}\, dx"," ",0,"Integral(sqrt(a*(sin(e + f*x) + 1))*(A + B*sin(e + f*x))*(c + d*sin(e + f*x))**2, x)","F",0
288,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))*(a+a*sin(f*x+e))**(1/2),x)","\int \sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)} \left(A + B \sin{\left(e + f x \right)}\right) \left(c + d \sin{\left(e + f x \right)}\right)\, dx"," ",0,"Integral(sqrt(a*(sin(e + f*x) + 1))*(A + B*sin(e + f*x))*(c + d*sin(e + f*x)), x)","F",0
289,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(a+a*sin(f*x+e))**(1/2),x)","\int \sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)} \left(A + B \sin{\left(e + f x \right)}\right)\, dx"," ",0,"Integral(sqrt(a*(sin(e + f*x) + 1))*(A + B*sin(e + f*x)), x)","F",0
290,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(a+a*sin(f*x+e))**(1/2)/(c+d*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
291,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(a+a*sin(f*x+e))**(1/2)/(c+d*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
292,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(a+a*sin(f*x+e))**(1/2)/(c+d*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
293,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(3/2)*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
294,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(3/2)*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))**2,x)","\int \left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}} \left(A + B \sin{\left(e + f x \right)}\right) \left(c + d \sin{\left(e + f x \right)}\right)^{2}\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**(3/2)*(A + B*sin(e + f*x))*(c + d*sin(e + f*x))**2, x)","F",0
295,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(3/2)*(A+B*sin(f*x+e))*(c+d*sin(f*x+e)),x)","\int \left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}} \left(A + B \sin{\left(e + f x \right)}\right) \left(c + d \sin{\left(e + f x \right)}\right)\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**(3/2)*(A + B*sin(e + f*x))*(c + d*sin(e + f*x)), x)","F",0
296,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(3/2)*(A+B*sin(f*x+e)),x)","\int \left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}} \left(A + B \sin{\left(e + f x \right)}\right)\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**(3/2)*(A + B*sin(e + f*x)), x)","F",0
297,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(3/2)*(A+B*sin(f*x+e))/(c+d*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
298,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(3/2)*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
299,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(3/2)*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
300,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(5/2)*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
301,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(5/2)*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
302,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(5/2)*(A+B*sin(f*x+e))*(c+d*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
303,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(5/2)*(A+B*sin(f*x+e)),x)","\int \left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{5}{2}} \left(A + B \sin{\left(e + f x \right)}\right)\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**(5/2)*(A + B*sin(e + f*x)), x)","F",0
304,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(5/2)*(A+B*sin(f*x+e))/(c+d*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
305,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(5/2)*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
306,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(5/2)*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
307,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))**3/(a+a*sin(f*x+e))**(1/2),x)","\int \frac{\left(A + B \sin{\left(e + f x \right)}\right) \left(c + d \sin{\left(e + f x \right)}\right)^{3}}{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)}}\, dx"," ",0,"Integral((A + B*sin(e + f*x))*(c + d*sin(e + f*x))**3/sqrt(a*(sin(e + f*x) + 1)), x)","F",0
308,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))**2/(a+a*sin(f*x+e))**(1/2),x)","\int \frac{\left(A + B \sin{\left(e + f x \right)}\right) \left(c + d \sin{\left(e + f x \right)}\right)^{2}}{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)}}\, dx"," ",0,"Integral((A + B*sin(e + f*x))*(c + d*sin(e + f*x))**2/sqrt(a*(sin(e + f*x) + 1)), x)","F",0
309,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))/(a+a*sin(f*x+e))**(1/2),x)","\int \frac{\left(A + B \sin{\left(e + f x \right)}\right) \left(c + d \sin{\left(e + f x \right)}\right)}{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)}}\, dx"," ",0,"Integral((A + B*sin(e + f*x))*(c + d*sin(e + f*x))/sqrt(a*(sin(e + f*x) + 1)), x)","F",0
310,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))**(1/2),x)","\int \frac{A + B \sin{\left(e + f x \right)}}{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)}}\, dx"," ",0,"Integral((A + B*sin(e + f*x))/sqrt(a*(sin(e + f*x) + 1)), x)","F",0
311,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(c+d*sin(f*x+e))/(a+a*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
312,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(c+d*sin(f*x+e))**2/(a+a*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
313,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(c+d*sin(f*x+e))**3/(a+a*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
314,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))**3/(a+a*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
315,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))**2/(a+a*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
316,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))/(a+a*sin(f*x+e))**(3/2),x)","\int \frac{\left(A + B \sin{\left(e + f x \right)}\right) \left(c + d \sin{\left(e + f x \right)}\right)}{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*sin(e + f*x))*(c + d*sin(e + f*x))/(a*(sin(e + f*x) + 1))**(3/2), x)","F",0
317,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))**(3/2),x)","\int \frac{A + B \sin{\left(e + f x \right)}}{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*sin(e + f*x))/(a*(sin(e + f*x) + 1))**(3/2), x)","F",0
318,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))**(3/2)/(c+d*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
319,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))**(3/2)/(c+d*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
320,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))**(3/2)/(c+d*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
321,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))**3/(a+a*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
322,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))**2/(a+a*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
323,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))/(a+a*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
324,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))**(5/2),x)","\int \frac{A + B \sin{\left(e + f x \right)}}{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*sin(e + f*x))/(a*(sin(e + f*x) + 1))**(5/2), x)","F",0
325,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))**(5/2)/(c+d*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
326,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))**(5/2)/(c+d*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
327,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))**(5/2)/(c+d*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
328,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**2*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
329,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
330,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))**n/(a+a*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
331,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))**n/(a+a*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
332,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(3/2)*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
333,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(1/2)*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))**n,x)","\int \sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)} \left(A + B \sin{\left(e + f x \right)}\right) \left(c + d \sin{\left(e + f x \right)}\right)^{n}\, dx"," ",0,"Integral(sqrt(a*(sin(e + f*x) + 1))*(A + B*sin(e + f*x))*(c + d*sin(e + f*x))**n, x)","F",0
334,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))**n/(a+a*sin(f*x+e))**(1/2),x)","\int \frac{\left(A + B \sin{\left(e + f x \right)}\right) \left(c + d \sin{\left(e + f x \right)}\right)^{n}}{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)}}\, dx"," ",0,"Integral((A + B*sin(e + f*x))*(c + d*sin(e + f*x))**n/sqrt(a*(sin(e + f*x) + 1)), x)","F",0
335,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))**n/(a+a*sin(f*x+e))**(3/2),x)","\int \frac{\left(A + B \sin{\left(e + f x \right)}\right) \left(c + d \sin{\left(e + f x \right)}\right)^{n}}{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*sin(e + f*x))*(c + d*sin(e + f*x))**n/(a*(sin(e + f*x) + 1))**(3/2), x)","F",0
336,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))**2,x)","\int \left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{m} \left(A + B \sin{\left(e + f x \right)}\right) \left(c + d \sin{\left(e + f x \right)}\right)^{2}\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**m*(A + B*sin(e + f*x))*(c + d*sin(e + f*x))**2, x)","F",0
337,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(A+B*sin(f*x+e))*(c+d*sin(f*x+e)),x)","\int \left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{m} \left(A + B \sin{\left(e + f x \right)}\right) \left(c + d \sin{\left(e + f x \right)}\right)\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**m*(A + B*sin(e + f*x))*(c + d*sin(e + f*x)), x)","F",0
338,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(A+B*sin(f*x+e)),x)","\int \left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{m} \left(A + B \sin{\left(e + f x \right)}\right)\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**m*(A + B*sin(e + f*x)), x)","F",0
339,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(A+B*sin(f*x+e))/(c+d*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
340,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
341,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
342,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
343,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))**(1/2),x)","\int \left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{m} \left(A + B \sin{\left(e + f x \right)}\right) \sqrt{c + d \sin{\left(e + f x \right)}}\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**m*(A + B*sin(e + f*x))*sqrt(c + d*sin(e + f*x)), x)","F",0
344,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))**(1/2),x)","\int \frac{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{m} \left(A + B \sin{\left(e + f x \right)}\right)}{\sqrt{c + d \sin{\left(e + f x \right)}}}\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**m*(A + B*sin(e + f*x))/sqrt(c + d*sin(e + f*x)), x)","F",0
345,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))**(3/2),x)","\int \frac{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{m} \left(A + B \sin{\left(e + f x \right)}\right)}{\left(c + d \sin{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**m*(A + B*sin(e + f*x))/(c + d*sin(e + f*x))**(3/2), x)","F",0
346,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
347,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))**(-1-m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
348,-1,0,0,0.000000," ","integrate((a-a*sin(f*x+e))*(a+a*sin(f*x+e))**m*(c+d*sin(f*x+e))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
349,-1,0,0,0.000000," ","integrate((a-a*sin(f*x+e))*(a+a*sin(f*x+e))**m*(c+d*sin(f*x+e))**(-1-m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
350,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(c+d*sin(f*x+e))**(-2-m)*(d-(c-d)*m+(c+(c-d)*m)*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
351,-1,0,0,0.000000," ","integrate((a-a*sin(f*x+e))**m*(c+d*sin(f*x+e))**(-2-m)*(d+(c+d)*m+(c+(c+d)*m)*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
352,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**2*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
353,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))**(3/2)/(a+b*sin(f*x+e))**(3/2),x)","\int \frac{\left(A + B \sin{\left(e + f x \right)}\right) \left(c + d \sin{\left(e + f x \right)}\right)^{\frac{3}{2}}}{\left(a + b \sin{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*sin(e + f*x))*(c + d*sin(e + f*x))**(3/2)/(a + b*sin(e + f*x))**(3/2), x)","F",0
354,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))**(1/2)/(a+b*sin(f*x+e))**(3/2),x)","\int \frac{\left(A + B \sin{\left(e + f x \right)}\right) \sqrt{c + d \sin{\left(e + f x \right)}}}{\left(a + b \sin{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*sin(e + f*x))*sqrt(c + d*sin(e + f*x))/(a + b*sin(e + f*x))**(3/2), x)","F",0
355,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+b*sin(f*x+e))**(3/2)/(c+d*sin(f*x+e))**(1/2),x)","\int \frac{A + B \sin{\left(e + f x \right)}}{\left(a + b \sin{\left(e + f x \right)}\right)^{\frac{3}{2}} \sqrt{c + d \sin{\left(e + f x \right)}}}\, dx"," ",0,"Integral((A + B*sin(e + f*x))/((a + b*sin(e + f*x))**(3/2)*sqrt(c + d*sin(e + f*x))), x)","F",0
356,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+b*sin(f*x+e))**(3/2)/(c+d*sin(f*x+e))**(3/2),x)","\int \frac{A + B \sin{\left(e + f x \right)}}{\left(a + b \sin{\left(e + f x \right)}\right)^{\frac{3}{2}} \left(c + d \sin{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*sin(e + f*x))/((a + b*sin(e + f*x))**(3/2)*(c + d*sin(e + f*x))**(3/2)), x)","F",0
357,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+b*sin(f*x+e))**(3/2)/(c+d*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
358,-2,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**m*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))**n,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
