1,1,221,0,3.658655," ","integrate(sin(f*x+e)**3*(a+a*sin(f*x+e))**2,x)","\begin{cases} \frac{3 a^{2} x \sin^{4}{\left(e + f x \right)}}{4} + \frac{3 a^{2} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{2} + \frac{3 a^{2} x \cos^{4}{\left(e + f x \right)}}{4} - \frac{a^{2} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{5 a^{2} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{4 f} - \frac{4 a^{2} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{a^{2} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{3 a^{2} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{4 f} - \frac{8 a^{2} \cos^{5}{\left(e + f x \right)}}{15 f} - \frac{2 a^{2} \cos^{3}{\left(e + f x \right)}}{3 f} & \text{for}\: f \neq 0 \\x \left(a \sin{\left(e \right)} + a\right)^{2} \sin^{3}{\left(e \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a**2*x*sin(e + f*x)**4/4 + 3*a**2*x*sin(e + f*x)**2*cos(e + f*x)**2/2 + 3*a**2*x*cos(e + f*x)**4/4 - a**2*sin(e + f*x)**4*cos(e + f*x)/f - 5*a**2*sin(e + f*x)**3*cos(e + f*x)/(4*f) - 4*a**2*sin(e + f*x)**2*cos(e + f*x)**3/(3*f) - a**2*sin(e + f*x)**2*cos(e + f*x)/f - 3*a**2*sin(e + f*x)*cos(e + f*x)**3/(4*f) - 8*a**2*cos(e + f*x)**5/(15*f) - 2*a**2*cos(e + f*x)**3/(3*f), Ne(f, 0)), (x*(a*sin(e) + a)**2*sin(e)**3, True))","A",0
2,1,379,0,6.816400," ","integrate(sin(f*x+e)**3*(a+a*sin(f*x+e))**3,x)","\begin{cases} \frac{5 a^{3} x \sin^{6}{\left(e + f x \right)}}{16} + \frac{15 a^{3} x \sin^{4}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{16} + \frac{9 a^{3} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{15 a^{3} x \sin^{2}{\left(e + f x \right)} \cos^{4}{\left(e + f x \right)}}{16} + \frac{9 a^{3} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{5 a^{3} x \cos^{6}{\left(e + f x \right)}}{16} + \frac{9 a^{3} x \cos^{4}{\left(e + f x \right)}}{8} - \frac{11 a^{3} \sin^{5}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{16 f} - \frac{3 a^{3} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{5 a^{3} \sin^{3}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{6 f} - \frac{15 a^{3} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{4 a^{3} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{f} - \frac{a^{3} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{5 a^{3} \sin{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{16 f} - \frac{9 a^{3} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{8 a^{3} \cos^{5}{\left(e + f x \right)}}{5 f} - \frac{2 a^{3} \cos^{3}{\left(e + f x \right)}}{3 f} & \text{for}\: f \neq 0 \\x \left(a \sin{\left(e \right)} + a\right)^{3} \sin^{3}{\left(e \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((5*a**3*x*sin(e + f*x)**6/16 + 15*a**3*x*sin(e + f*x)**4*cos(e + f*x)**2/16 + 9*a**3*x*sin(e + f*x)**4/8 + 15*a**3*x*sin(e + f*x)**2*cos(e + f*x)**4/16 + 9*a**3*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + 5*a**3*x*cos(e + f*x)**6/16 + 9*a**3*x*cos(e + f*x)**4/8 - 11*a**3*sin(e + f*x)**5*cos(e + f*x)/(16*f) - 3*a**3*sin(e + f*x)**4*cos(e + f*x)/f - 5*a**3*sin(e + f*x)**3*cos(e + f*x)**3/(6*f) - 15*a**3*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 4*a**3*sin(e + f*x)**2*cos(e + f*x)**3/f - a**3*sin(e + f*x)**2*cos(e + f*x)/f - 5*a**3*sin(e + f*x)*cos(e + f*x)**5/(16*f) - 9*a**3*sin(e + f*x)*cos(e + f*x)**3/(8*f) - 8*a**3*cos(e + f*x)**5/(5*f) - 2*a**3*cos(e + f*x)**3/(3*f), Ne(f, 0)), (x*(a*sin(e) + a)**3*sin(e)**3, True))","A",0
3,1,1221,0,5.909785," ","integrate(sin(x)**4/(a+a*sin(x)),x)","- \frac{9 x \tan^{7}{\left(\frac{x}{2} \right)}}{6 a \tan^{7}{\left(\frac{x}{2} \right)} + 6 a \tan^{6}{\left(\frac{x}{2} \right)} + 18 a \tan^{5}{\left(\frac{x}{2} \right)} + 18 a \tan^{4}{\left(\frac{x}{2} \right)} + 18 a \tan^{3}{\left(\frac{x}{2} \right)} + 18 a \tan^{2}{\left(\frac{x}{2} \right)} + 6 a \tan{\left(\frac{x}{2} \right)} + 6 a} - \frac{9 x \tan^{6}{\left(\frac{x}{2} \right)}}{6 a \tan^{7}{\left(\frac{x}{2} \right)} + 6 a \tan^{6}{\left(\frac{x}{2} \right)} + 18 a \tan^{5}{\left(\frac{x}{2} \right)} + 18 a \tan^{4}{\left(\frac{x}{2} \right)} + 18 a \tan^{3}{\left(\frac{x}{2} \right)} + 18 a \tan^{2}{\left(\frac{x}{2} \right)} + 6 a \tan{\left(\frac{x}{2} \right)} + 6 a} - \frac{27 x \tan^{5}{\left(\frac{x}{2} \right)}}{6 a \tan^{7}{\left(\frac{x}{2} \right)} + 6 a \tan^{6}{\left(\frac{x}{2} \right)} + 18 a \tan^{5}{\left(\frac{x}{2} \right)} + 18 a \tan^{4}{\left(\frac{x}{2} \right)} + 18 a \tan^{3}{\left(\frac{x}{2} \right)} + 18 a \tan^{2}{\left(\frac{x}{2} \right)} + 6 a \tan{\left(\frac{x}{2} \right)} + 6 a} - \frac{27 x \tan^{4}{\left(\frac{x}{2} \right)}}{6 a \tan^{7}{\left(\frac{x}{2} \right)} + 6 a \tan^{6}{\left(\frac{x}{2} \right)} + 18 a \tan^{5}{\left(\frac{x}{2} \right)} + 18 a \tan^{4}{\left(\frac{x}{2} \right)} + 18 a \tan^{3}{\left(\frac{x}{2} \right)} + 18 a \tan^{2}{\left(\frac{x}{2} \right)} + 6 a \tan{\left(\frac{x}{2} \right)} + 6 a} - \frac{27 x \tan^{3}{\left(\frac{x}{2} \right)}}{6 a \tan^{7}{\left(\frac{x}{2} \right)} + 6 a \tan^{6}{\left(\frac{x}{2} \right)} + 18 a \tan^{5}{\left(\frac{x}{2} \right)} + 18 a \tan^{4}{\left(\frac{x}{2} \right)} + 18 a \tan^{3}{\left(\frac{x}{2} \right)} + 18 a \tan^{2}{\left(\frac{x}{2} \right)} + 6 a \tan{\left(\frac{x}{2} \right)} + 6 a} - \frac{27 x \tan^{2}{\left(\frac{x}{2} \right)}}{6 a \tan^{7}{\left(\frac{x}{2} \right)} + 6 a \tan^{6}{\left(\frac{x}{2} \right)} + 18 a \tan^{5}{\left(\frac{x}{2} \right)} + 18 a \tan^{4}{\left(\frac{x}{2} \right)} + 18 a \tan^{3}{\left(\frac{x}{2} \right)} + 18 a \tan^{2}{\left(\frac{x}{2} \right)} + 6 a \tan{\left(\frac{x}{2} \right)} + 6 a} - \frac{9 x \tan{\left(\frac{x}{2} \right)}}{6 a \tan^{7}{\left(\frac{x}{2} \right)} + 6 a \tan^{6}{\left(\frac{x}{2} \right)} + 18 a \tan^{5}{\left(\frac{x}{2} \right)} + 18 a \tan^{4}{\left(\frac{x}{2} \right)} + 18 a \tan^{3}{\left(\frac{x}{2} \right)} + 18 a \tan^{2}{\left(\frac{x}{2} \right)} + 6 a \tan{\left(\frac{x}{2} \right)} + 6 a} - \frac{9 x}{6 a \tan^{7}{\left(\frac{x}{2} \right)} + 6 a \tan^{6}{\left(\frac{x}{2} \right)} + 18 a \tan^{5}{\left(\frac{x}{2} \right)} + 18 a \tan^{4}{\left(\frac{x}{2} \right)} + 18 a \tan^{3}{\left(\frac{x}{2} \right)} + 18 a \tan^{2}{\left(\frac{x}{2} \right)} + 6 a \tan{\left(\frac{x}{2} \right)} + 6 a} - \frac{18 \tan^{6}{\left(\frac{x}{2} \right)}}{6 a \tan^{7}{\left(\frac{x}{2} \right)} + 6 a \tan^{6}{\left(\frac{x}{2} \right)} + 18 a \tan^{5}{\left(\frac{x}{2} \right)} + 18 a \tan^{4}{\left(\frac{x}{2} \right)} + 18 a \tan^{3}{\left(\frac{x}{2} \right)} + 18 a \tan^{2}{\left(\frac{x}{2} \right)} + 6 a \tan{\left(\frac{x}{2} \right)} + 6 a} - \frac{18 \tan^{5}{\left(\frac{x}{2} \right)}}{6 a \tan^{7}{\left(\frac{x}{2} \right)} + 6 a \tan^{6}{\left(\frac{x}{2} \right)} + 18 a \tan^{5}{\left(\frac{x}{2} \right)} + 18 a \tan^{4}{\left(\frac{x}{2} \right)} + 18 a \tan^{3}{\left(\frac{x}{2} \right)} + 18 a \tan^{2}{\left(\frac{x}{2} \right)} + 6 a \tan{\left(\frac{x}{2} \right)} + 6 a} - \frac{48 \tan^{4}{\left(\frac{x}{2} \right)}}{6 a \tan^{7}{\left(\frac{x}{2} \right)} + 6 a \tan^{6}{\left(\frac{x}{2} \right)} + 18 a \tan^{5}{\left(\frac{x}{2} \right)} + 18 a \tan^{4}{\left(\frac{x}{2} \right)} + 18 a \tan^{3}{\left(\frac{x}{2} \right)} + 18 a \tan^{2}{\left(\frac{x}{2} \right)} + 6 a \tan{\left(\frac{x}{2} \right)} + 6 a} - \frac{48 \tan^{3}{\left(\frac{x}{2} \right)}}{6 a \tan^{7}{\left(\frac{x}{2} \right)} + 6 a \tan^{6}{\left(\frac{x}{2} \right)} + 18 a \tan^{5}{\left(\frac{x}{2} \right)} + 18 a \tan^{4}{\left(\frac{x}{2} \right)} + 18 a \tan^{3}{\left(\frac{x}{2} \right)} + 18 a \tan^{2}{\left(\frac{x}{2} \right)} + 6 a \tan{\left(\frac{x}{2} \right)} + 6 a} - \frac{78 \tan^{2}{\left(\frac{x}{2} \right)}}{6 a \tan^{7}{\left(\frac{x}{2} \right)} + 6 a \tan^{6}{\left(\frac{x}{2} \right)} + 18 a \tan^{5}{\left(\frac{x}{2} \right)} + 18 a \tan^{4}{\left(\frac{x}{2} \right)} + 18 a \tan^{3}{\left(\frac{x}{2} \right)} + 18 a \tan^{2}{\left(\frac{x}{2} \right)} + 6 a \tan{\left(\frac{x}{2} \right)} + 6 a} - \frac{14 \tan{\left(\frac{x}{2} \right)}}{6 a \tan^{7}{\left(\frac{x}{2} \right)} + 6 a \tan^{6}{\left(\frac{x}{2} \right)} + 18 a \tan^{5}{\left(\frac{x}{2} \right)} + 18 a \tan^{4}{\left(\frac{x}{2} \right)} + 18 a \tan^{3}{\left(\frac{x}{2} \right)} + 18 a \tan^{2}{\left(\frac{x}{2} \right)} + 6 a \tan{\left(\frac{x}{2} \right)} + 6 a} - \frac{32}{6 a \tan^{7}{\left(\frac{x}{2} \right)} + 6 a \tan^{6}{\left(\frac{x}{2} \right)} + 18 a \tan^{5}{\left(\frac{x}{2} \right)} + 18 a \tan^{4}{\left(\frac{x}{2} \right)} + 18 a \tan^{3}{\left(\frac{x}{2} \right)} + 18 a \tan^{2}{\left(\frac{x}{2} \right)} + 6 a \tan{\left(\frac{x}{2} \right)} + 6 a}"," ",0,"-9*x*tan(x/2)**7/(6*a*tan(x/2)**7 + 6*a*tan(x/2)**6 + 18*a*tan(x/2)**5 + 18*a*tan(x/2)**4 + 18*a*tan(x/2)**3 + 18*a*tan(x/2)**2 + 6*a*tan(x/2) + 6*a) - 9*x*tan(x/2)**6/(6*a*tan(x/2)**7 + 6*a*tan(x/2)**6 + 18*a*tan(x/2)**5 + 18*a*tan(x/2)**4 + 18*a*tan(x/2)**3 + 18*a*tan(x/2)**2 + 6*a*tan(x/2) + 6*a) - 27*x*tan(x/2)**5/(6*a*tan(x/2)**7 + 6*a*tan(x/2)**6 + 18*a*tan(x/2)**5 + 18*a*tan(x/2)**4 + 18*a*tan(x/2)**3 + 18*a*tan(x/2)**2 + 6*a*tan(x/2) + 6*a) - 27*x*tan(x/2)**4/(6*a*tan(x/2)**7 + 6*a*tan(x/2)**6 + 18*a*tan(x/2)**5 + 18*a*tan(x/2)**4 + 18*a*tan(x/2)**3 + 18*a*tan(x/2)**2 + 6*a*tan(x/2) + 6*a) - 27*x*tan(x/2)**3/(6*a*tan(x/2)**7 + 6*a*tan(x/2)**6 + 18*a*tan(x/2)**5 + 18*a*tan(x/2)**4 + 18*a*tan(x/2)**3 + 18*a*tan(x/2)**2 + 6*a*tan(x/2) + 6*a) - 27*x*tan(x/2)**2/(6*a*tan(x/2)**7 + 6*a*tan(x/2)**6 + 18*a*tan(x/2)**5 + 18*a*tan(x/2)**4 + 18*a*tan(x/2)**3 + 18*a*tan(x/2)**2 + 6*a*tan(x/2) + 6*a) - 9*x*tan(x/2)/(6*a*tan(x/2)**7 + 6*a*tan(x/2)**6 + 18*a*tan(x/2)**5 + 18*a*tan(x/2)**4 + 18*a*tan(x/2)**3 + 18*a*tan(x/2)**2 + 6*a*tan(x/2) + 6*a) - 9*x/(6*a*tan(x/2)**7 + 6*a*tan(x/2)**6 + 18*a*tan(x/2)**5 + 18*a*tan(x/2)**4 + 18*a*tan(x/2)**3 + 18*a*tan(x/2)**2 + 6*a*tan(x/2) + 6*a) - 18*tan(x/2)**6/(6*a*tan(x/2)**7 + 6*a*tan(x/2)**6 + 18*a*tan(x/2)**5 + 18*a*tan(x/2)**4 + 18*a*tan(x/2)**3 + 18*a*tan(x/2)**2 + 6*a*tan(x/2) + 6*a) - 18*tan(x/2)**5/(6*a*tan(x/2)**7 + 6*a*tan(x/2)**6 + 18*a*tan(x/2)**5 + 18*a*tan(x/2)**4 + 18*a*tan(x/2)**3 + 18*a*tan(x/2)**2 + 6*a*tan(x/2) + 6*a) - 48*tan(x/2)**4/(6*a*tan(x/2)**7 + 6*a*tan(x/2)**6 + 18*a*tan(x/2)**5 + 18*a*tan(x/2)**4 + 18*a*tan(x/2)**3 + 18*a*tan(x/2)**2 + 6*a*tan(x/2) + 6*a) - 48*tan(x/2)**3/(6*a*tan(x/2)**7 + 6*a*tan(x/2)**6 + 18*a*tan(x/2)**5 + 18*a*tan(x/2)**4 + 18*a*tan(x/2)**3 + 18*a*tan(x/2)**2 + 6*a*tan(x/2) + 6*a) - 78*tan(x/2)**2/(6*a*tan(x/2)**7 + 6*a*tan(x/2)**6 + 18*a*tan(x/2)**5 + 18*a*tan(x/2)**4 + 18*a*tan(x/2)**3 + 18*a*tan(x/2)**2 + 6*a*tan(x/2) + 6*a) - 14*tan(x/2)/(6*a*tan(x/2)**7 + 6*a*tan(x/2)**6 + 18*a*tan(x/2)**5 + 18*a*tan(x/2)**4 + 18*a*tan(x/2)**3 + 18*a*tan(x/2)**2 + 6*a*tan(x/2) + 6*a) - 32/(6*a*tan(x/2)**7 + 6*a*tan(x/2)**6 + 18*a*tan(x/2)**5 + 18*a*tan(x/2)**4 + 18*a*tan(x/2)**3 + 18*a*tan(x/2)**2 + 6*a*tan(x/2) + 6*a)","B",0
4,1,665,0,2.787940," ","integrate(sin(x)**3/(a+a*sin(x)),x)","\frac{3 x \tan^{5}{\left(\frac{x}{2} \right)}}{2 a \tan^{5}{\left(\frac{x}{2} \right)} + 2 a \tan^{4}{\left(\frac{x}{2} \right)} + 4 a \tan^{3}{\left(\frac{x}{2} \right)} + 4 a \tan^{2}{\left(\frac{x}{2} \right)} + 2 a \tan{\left(\frac{x}{2} \right)} + 2 a} + \frac{3 x \tan^{4}{\left(\frac{x}{2} \right)}}{2 a \tan^{5}{\left(\frac{x}{2} \right)} + 2 a \tan^{4}{\left(\frac{x}{2} \right)} + 4 a \tan^{3}{\left(\frac{x}{2} \right)} + 4 a \tan^{2}{\left(\frac{x}{2} \right)} + 2 a \tan{\left(\frac{x}{2} \right)} + 2 a} + \frac{6 x \tan^{3}{\left(\frac{x}{2} \right)}}{2 a \tan^{5}{\left(\frac{x}{2} \right)} + 2 a \tan^{4}{\left(\frac{x}{2} \right)} + 4 a \tan^{3}{\left(\frac{x}{2} \right)} + 4 a \tan^{2}{\left(\frac{x}{2} \right)} + 2 a \tan{\left(\frac{x}{2} \right)} + 2 a} + \frac{6 x \tan^{2}{\left(\frac{x}{2} \right)}}{2 a \tan^{5}{\left(\frac{x}{2} \right)} + 2 a \tan^{4}{\left(\frac{x}{2} \right)} + 4 a \tan^{3}{\left(\frac{x}{2} \right)} + 4 a \tan^{2}{\left(\frac{x}{2} \right)} + 2 a \tan{\left(\frac{x}{2} \right)} + 2 a} + \frac{3 x \tan{\left(\frac{x}{2} \right)}}{2 a \tan^{5}{\left(\frac{x}{2} \right)} + 2 a \tan^{4}{\left(\frac{x}{2} \right)} + 4 a \tan^{3}{\left(\frac{x}{2} \right)} + 4 a \tan^{2}{\left(\frac{x}{2} \right)} + 2 a \tan{\left(\frac{x}{2} \right)} + 2 a} + \frac{3 x}{2 a \tan^{5}{\left(\frac{x}{2} \right)} + 2 a \tan^{4}{\left(\frac{x}{2} \right)} + 4 a \tan^{3}{\left(\frac{x}{2} \right)} + 4 a \tan^{2}{\left(\frac{x}{2} \right)} + 2 a \tan{\left(\frac{x}{2} \right)} + 2 a} + \frac{6 \tan^{4}{\left(\frac{x}{2} \right)}}{2 a \tan^{5}{\left(\frac{x}{2} \right)} + 2 a \tan^{4}{\left(\frac{x}{2} \right)} + 4 a \tan^{3}{\left(\frac{x}{2} \right)} + 4 a \tan^{2}{\left(\frac{x}{2} \right)} + 2 a \tan{\left(\frac{x}{2} \right)} + 2 a} + \frac{6 \tan^{3}{\left(\frac{x}{2} \right)}}{2 a \tan^{5}{\left(\frac{x}{2} \right)} + 2 a \tan^{4}{\left(\frac{x}{2} \right)} + 4 a \tan^{3}{\left(\frac{x}{2} \right)} + 4 a \tan^{2}{\left(\frac{x}{2} \right)} + 2 a \tan{\left(\frac{x}{2} \right)} + 2 a} + \frac{10 \tan^{2}{\left(\frac{x}{2} \right)}}{2 a \tan^{5}{\left(\frac{x}{2} \right)} + 2 a \tan^{4}{\left(\frac{x}{2} \right)} + 4 a \tan^{3}{\left(\frac{x}{2} \right)} + 4 a \tan^{2}{\left(\frac{x}{2} \right)} + 2 a \tan{\left(\frac{x}{2} \right)} + 2 a} + \frac{2 \tan{\left(\frac{x}{2} \right)}}{2 a \tan^{5}{\left(\frac{x}{2} \right)} + 2 a \tan^{4}{\left(\frac{x}{2} \right)} + 4 a \tan^{3}{\left(\frac{x}{2} \right)} + 4 a \tan^{2}{\left(\frac{x}{2} \right)} + 2 a \tan{\left(\frac{x}{2} \right)} + 2 a} + \frac{8}{2 a \tan^{5}{\left(\frac{x}{2} \right)} + 2 a \tan^{4}{\left(\frac{x}{2} \right)} + 4 a \tan^{3}{\left(\frac{x}{2} \right)} + 4 a \tan^{2}{\left(\frac{x}{2} \right)} + 2 a \tan{\left(\frac{x}{2} \right)} + 2 a}"," ",0,"3*x*tan(x/2)**5/(2*a*tan(x/2)**5 + 2*a*tan(x/2)**4 + 4*a*tan(x/2)**3 + 4*a*tan(x/2)**2 + 2*a*tan(x/2) + 2*a) + 3*x*tan(x/2)**4/(2*a*tan(x/2)**5 + 2*a*tan(x/2)**4 + 4*a*tan(x/2)**3 + 4*a*tan(x/2)**2 + 2*a*tan(x/2) + 2*a) + 6*x*tan(x/2)**3/(2*a*tan(x/2)**5 + 2*a*tan(x/2)**4 + 4*a*tan(x/2)**3 + 4*a*tan(x/2)**2 + 2*a*tan(x/2) + 2*a) + 6*x*tan(x/2)**2/(2*a*tan(x/2)**5 + 2*a*tan(x/2)**4 + 4*a*tan(x/2)**3 + 4*a*tan(x/2)**2 + 2*a*tan(x/2) + 2*a) + 3*x*tan(x/2)/(2*a*tan(x/2)**5 + 2*a*tan(x/2)**4 + 4*a*tan(x/2)**3 + 4*a*tan(x/2)**2 + 2*a*tan(x/2) + 2*a) + 3*x/(2*a*tan(x/2)**5 + 2*a*tan(x/2)**4 + 4*a*tan(x/2)**3 + 4*a*tan(x/2)**2 + 2*a*tan(x/2) + 2*a) + 6*tan(x/2)**4/(2*a*tan(x/2)**5 + 2*a*tan(x/2)**4 + 4*a*tan(x/2)**3 + 4*a*tan(x/2)**2 + 2*a*tan(x/2) + 2*a) + 6*tan(x/2)**3/(2*a*tan(x/2)**5 + 2*a*tan(x/2)**4 + 4*a*tan(x/2)**3 + 4*a*tan(x/2)**2 + 2*a*tan(x/2) + 2*a) + 10*tan(x/2)**2/(2*a*tan(x/2)**5 + 2*a*tan(x/2)**4 + 4*a*tan(x/2)**3 + 4*a*tan(x/2)**2 + 2*a*tan(x/2) + 2*a) + 2*tan(x/2)/(2*a*tan(x/2)**5 + 2*a*tan(x/2)**4 + 4*a*tan(x/2)**3 + 4*a*tan(x/2)**2 + 2*a*tan(x/2) + 2*a) + 8/(2*a*tan(x/2)**5 + 2*a*tan(x/2)**4 + 4*a*tan(x/2)**3 + 4*a*tan(x/2)**2 + 2*a*tan(x/2) + 2*a)","B",0
5,1,221,0,1.346961," ","integrate(sin(x)**2/(a+a*sin(x)),x)","- \frac{x \tan^{3}{\left(\frac{x}{2} \right)}}{a \tan^{3}{\left(\frac{x}{2} \right)} + a \tan^{2}{\left(\frac{x}{2} \right)} + a \tan{\left(\frac{x}{2} \right)} + a} - \frac{x \tan^{2}{\left(\frac{x}{2} \right)}}{a \tan^{3}{\left(\frac{x}{2} \right)} + a \tan^{2}{\left(\frac{x}{2} \right)} + a \tan{\left(\frac{x}{2} \right)} + a} - \frac{x \tan{\left(\frac{x}{2} \right)}}{a \tan^{3}{\left(\frac{x}{2} \right)} + a \tan^{2}{\left(\frac{x}{2} \right)} + a \tan{\left(\frac{x}{2} \right)} + a} - \frac{x}{a \tan^{3}{\left(\frac{x}{2} \right)} + a \tan^{2}{\left(\frac{x}{2} \right)} + a \tan{\left(\frac{x}{2} \right)} + a} - \frac{2 \tan^{2}{\left(\frac{x}{2} \right)}}{a \tan^{3}{\left(\frac{x}{2} \right)} + a \tan^{2}{\left(\frac{x}{2} \right)} + a \tan{\left(\frac{x}{2} \right)} + a} - \frac{2 \tan{\left(\frac{x}{2} \right)}}{a \tan^{3}{\left(\frac{x}{2} \right)} + a \tan^{2}{\left(\frac{x}{2} \right)} + a \tan{\left(\frac{x}{2} \right)} + a} - \frac{4}{a \tan^{3}{\left(\frac{x}{2} \right)} + a \tan^{2}{\left(\frac{x}{2} \right)} + a \tan{\left(\frac{x}{2} \right)} + a}"," ",0,"-x*tan(x/2)**3/(a*tan(x/2)**3 + a*tan(x/2)**2 + a*tan(x/2) + a) - x*tan(x/2)**2/(a*tan(x/2)**3 + a*tan(x/2)**2 + a*tan(x/2) + a) - x*tan(x/2)/(a*tan(x/2)**3 + a*tan(x/2)**2 + a*tan(x/2) + a) - x/(a*tan(x/2)**3 + a*tan(x/2)**2 + a*tan(x/2) + a) - 2*tan(x/2)**2/(a*tan(x/2)**3 + a*tan(x/2)**2 + a*tan(x/2) + a) - 2*tan(x/2)/(a*tan(x/2)**3 + a*tan(x/2)**2 + a*tan(x/2) + a) - 4/(a*tan(x/2)**3 + a*tan(x/2)**2 + a*tan(x/2) + a)","B",0
6,1,34,0,0.844927," ","integrate(sin(x)/(a+a*sin(x)),x)","\frac{x \tan{\left(\frac{x}{2} \right)}}{a \tan{\left(\frac{x}{2} \right)} + a} + \frac{x}{a \tan{\left(\frac{x}{2} \right)} + a} + \frac{2}{a \tan{\left(\frac{x}{2} \right)} + a}"," ",0,"x*tan(x/2)/(a*tan(x/2) + a) + x/(a*tan(x/2) + a) + 2/(a*tan(x/2) + a)","B",0
7,1,10,0,0.408848," ","integrate(1/(a+a*sin(x)),x)","- \frac{2}{a \tan{\left(\frac{x}{2} \right)} + a}"," ",0,"-2/(a*tan(x/2) + a)","A",0
8,0,0,0,0.000000," ","integrate(csc(x)/(a+a*sin(x)),x)","\frac{\int \frac{\csc{\left(x \right)}}{\sin{\left(x \right)} + 1}\, dx}{a}"," ",0,"Integral(csc(x)/(sin(x) + 1), x)/a","F",0
9,0,0,0,0.000000," ","integrate(csc(x)**2/(a+a*sin(x)),x)","\frac{\int \frac{\csc^{2}{\left(x \right)}}{\sin{\left(x \right)} + 1}\, dx}{a}"," ",0,"Integral(csc(x)**2/(sin(x) + 1), x)/a","F",0
10,0,0,0,0.000000," ","integrate(csc(x)**3/(a+a*sin(x)),x)","\frac{\int \frac{\csc^{3}{\left(x \right)}}{\sin{\left(x \right)} + 1}\, dx}{a}"," ",0,"Integral(csc(x)**3/(sin(x) + 1), x)/a","F",0
11,0,0,0,0.000000," ","integrate(csc(x)**4/(a+a*sin(x)),x)","\frac{\int \frac{\csc^{4}{\left(x \right)}}{\sin{\left(x \right)} + 1}\, dx}{a}"," ",0,"Integral(csc(x)**4/(sin(x) + 1), x)/a","F",0
12,1,1423,0,10.917852," ","integrate(sin(x)**4/(a+a*sin(x))**2,x)","\frac{21 x \tan^{7}{\left(\frac{x}{2} \right)}}{6 a^{2} \tan^{7}{\left(\frac{x}{2} \right)} + 18 a^{2} \tan^{6}{\left(\frac{x}{2} \right)} + 30 a^{2} \tan^{5}{\left(\frac{x}{2} \right)} + 42 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 42 a^{2} \tan^{3}{\left(\frac{x}{2} \right)} + 30 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 18 a^{2} \tan{\left(\frac{x}{2} \right)} + 6 a^{2}} + \frac{63 x \tan^{6}{\left(\frac{x}{2} \right)}}{6 a^{2} \tan^{7}{\left(\frac{x}{2} \right)} + 18 a^{2} \tan^{6}{\left(\frac{x}{2} \right)} + 30 a^{2} \tan^{5}{\left(\frac{x}{2} \right)} + 42 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 42 a^{2} \tan^{3}{\left(\frac{x}{2} \right)} + 30 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 18 a^{2} \tan{\left(\frac{x}{2} \right)} + 6 a^{2}} + \frac{105 x \tan^{5}{\left(\frac{x}{2} \right)}}{6 a^{2} \tan^{7}{\left(\frac{x}{2} \right)} + 18 a^{2} \tan^{6}{\left(\frac{x}{2} \right)} + 30 a^{2} \tan^{5}{\left(\frac{x}{2} \right)} + 42 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 42 a^{2} \tan^{3}{\left(\frac{x}{2} \right)} + 30 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 18 a^{2} \tan{\left(\frac{x}{2} \right)} + 6 a^{2}} + \frac{147 x \tan^{4}{\left(\frac{x}{2} \right)}}{6 a^{2} \tan^{7}{\left(\frac{x}{2} \right)} + 18 a^{2} \tan^{6}{\left(\frac{x}{2} \right)} + 30 a^{2} \tan^{5}{\left(\frac{x}{2} \right)} + 42 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 42 a^{2} \tan^{3}{\left(\frac{x}{2} \right)} + 30 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 18 a^{2} \tan{\left(\frac{x}{2} \right)} + 6 a^{2}} + \frac{147 x \tan^{3}{\left(\frac{x}{2} \right)}}{6 a^{2} \tan^{7}{\left(\frac{x}{2} \right)} + 18 a^{2} \tan^{6}{\left(\frac{x}{2} \right)} + 30 a^{2} \tan^{5}{\left(\frac{x}{2} \right)} + 42 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 42 a^{2} \tan^{3}{\left(\frac{x}{2} \right)} + 30 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 18 a^{2} \tan{\left(\frac{x}{2} \right)} + 6 a^{2}} + \frac{105 x \tan^{2}{\left(\frac{x}{2} \right)}}{6 a^{2} \tan^{7}{\left(\frac{x}{2} \right)} + 18 a^{2} \tan^{6}{\left(\frac{x}{2} \right)} + 30 a^{2} \tan^{5}{\left(\frac{x}{2} \right)} + 42 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 42 a^{2} \tan^{3}{\left(\frac{x}{2} \right)} + 30 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 18 a^{2} \tan{\left(\frac{x}{2} \right)} + 6 a^{2}} + \frac{63 x \tan{\left(\frac{x}{2} \right)}}{6 a^{2} \tan^{7}{\left(\frac{x}{2} \right)} + 18 a^{2} \tan^{6}{\left(\frac{x}{2} \right)} + 30 a^{2} \tan^{5}{\left(\frac{x}{2} \right)} + 42 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 42 a^{2} \tan^{3}{\left(\frac{x}{2} \right)} + 30 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 18 a^{2} \tan{\left(\frac{x}{2} \right)} + 6 a^{2}} + \frac{21 x}{6 a^{2} \tan^{7}{\left(\frac{x}{2} \right)} + 18 a^{2} \tan^{6}{\left(\frac{x}{2} \right)} + 30 a^{2} \tan^{5}{\left(\frac{x}{2} \right)} + 42 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 42 a^{2} \tan^{3}{\left(\frac{x}{2} \right)} + 30 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 18 a^{2} \tan{\left(\frac{x}{2} \right)} + 6 a^{2}} + \frac{42 \tan^{6}{\left(\frac{x}{2} \right)}}{6 a^{2} \tan^{7}{\left(\frac{x}{2} \right)} + 18 a^{2} \tan^{6}{\left(\frac{x}{2} \right)} + 30 a^{2} \tan^{5}{\left(\frac{x}{2} \right)} + 42 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 42 a^{2} \tan^{3}{\left(\frac{x}{2} \right)} + 30 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 18 a^{2} \tan{\left(\frac{x}{2} \right)} + 6 a^{2}} + \frac{126 \tan^{5}{\left(\frac{x}{2} \right)}}{6 a^{2} \tan^{7}{\left(\frac{x}{2} \right)} + 18 a^{2} \tan^{6}{\left(\frac{x}{2} \right)} + 30 a^{2} \tan^{5}{\left(\frac{x}{2} \right)} + 42 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 42 a^{2} \tan^{3}{\left(\frac{x}{2} \right)} + 30 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 18 a^{2} \tan{\left(\frac{x}{2} \right)} + 6 a^{2}} + \frac{196 \tan^{4}{\left(\frac{x}{2} \right)}}{6 a^{2} \tan^{7}{\left(\frac{x}{2} \right)} + 18 a^{2} \tan^{6}{\left(\frac{x}{2} \right)} + 30 a^{2} \tan^{5}{\left(\frac{x}{2} \right)} + 42 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 42 a^{2} \tan^{3}{\left(\frac{x}{2} \right)} + 30 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 18 a^{2} \tan{\left(\frac{x}{2} \right)} + 6 a^{2}} + \frac{252 \tan^{3}{\left(\frac{x}{2} \right)}}{6 a^{2} \tan^{7}{\left(\frac{x}{2} \right)} + 18 a^{2} \tan^{6}{\left(\frac{x}{2} \right)} + 30 a^{2} \tan^{5}{\left(\frac{x}{2} \right)} + 42 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 42 a^{2} \tan^{3}{\left(\frac{x}{2} \right)} + 30 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 18 a^{2} \tan{\left(\frac{x}{2} \right)} + 6 a^{2}} + \frac{194 \tan^{2}{\left(\frac{x}{2} \right)}}{6 a^{2} \tan^{7}{\left(\frac{x}{2} \right)} + 18 a^{2} \tan^{6}{\left(\frac{x}{2} \right)} + 30 a^{2} \tan^{5}{\left(\frac{x}{2} \right)} + 42 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 42 a^{2} \tan^{3}{\left(\frac{x}{2} \right)} + 30 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 18 a^{2} \tan{\left(\frac{x}{2} \right)} + 6 a^{2}} + \frac{150 \tan{\left(\frac{x}{2} \right)}}{6 a^{2} \tan^{7}{\left(\frac{x}{2} \right)} + 18 a^{2} \tan^{6}{\left(\frac{x}{2} \right)} + 30 a^{2} \tan^{5}{\left(\frac{x}{2} \right)} + 42 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 42 a^{2} \tan^{3}{\left(\frac{x}{2} \right)} + 30 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 18 a^{2} \tan{\left(\frac{x}{2} \right)} + 6 a^{2}} + \frac{64}{6 a^{2} \tan^{7}{\left(\frac{x}{2} \right)} + 18 a^{2} \tan^{6}{\left(\frac{x}{2} \right)} + 30 a^{2} \tan^{5}{\left(\frac{x}{2} \right)} + 42 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 42 a^{2} \tan^{3}{\left(\frac{x}{2} \right)} + 30 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 18 a^{2} \tan{\left(\frac{x}{2} \right)} + 6 a^{2}}"," ",0,"21*x*tan(x/2)**7/(6*a**2*tan(x/2)**7 + 18*a**2*tan(x/2)**6 + 30*a**2*tan(x/2)**5 + 42*a**2*tan(x/2)**4 + 42*a**2*tan(x/2)**3 + 30*a**2*tan(x/2)**2 + 18*a**2*tan(x/2) + 6*a**2) + 63*x*tan(x/2)**6/(6*a**2*tan(x/2)**7 + 18*a**2*tan(x/2)**6 + 30*a**2*tan(x/2)**5 + 42*a**2*tan(x/2)**4 + 42*a**2*tan(x/2)**3 + 30*a**2*tan(x/2)**2 + 18*a**2*tan(x/2) + 6*a**2) + 105*x*tan(x/2)**5/(6*a**2*tan(x/2)**7 + 18*a**2*tan(x/2)**6 + 30*a**2*tan(x/2)**5 + 42*a**2*tan(x/2)**4 + 42*a**2*tan(x/2)**3 + 30*a**2*tan(x/2)**2 + 18*a**2*tan(x/2) + 6*a**2) + 147*x*tan(x/2)**4/(6*a**2*tan(x/2)**7 + 18*a**2*tan(x/2)**6 + 30*a**2*tan(x/2)**5 + 42*a**2*tan(x/2)**4 + 42*a**2*tan(x/2)**3 + 30*a**2*tan(x/2)**2 + 18*a**2*tan(x/2) + 6*a**2) + 147*x*tan(x/2)**3/(6*a**2*tan(x/2)**7 + 18*a**2*tan(x/2)**6 + 30*a**2*tan(x/2)**5 + 42*a**2*tan(x/2)**4 + 42*a**2*tan(x/2)**3 + 30*a**2*tan(x/2)**2 + 18*a**2*tan(x/2) + 6*a**2) + 105*x*tan(x/2)**2/(6*a**2*tan(x/2)**7 + 18*a**2*tan(x/2)**6 + 30*a**2*tan(x/2)**5 + 42*a**2*tan(x/2)**4 + 42*a**2*tan(x/2)**3 + 30*a**2*tan(x/2)**2 + 18*a**2*tan(x/2) + 6*a**2) + 63*x*tan(x/2)/(6*a**2*tan(x/2)**7 + 18*a**2*tan(x/2)**6 + 30*a**2*tan(x/2)**5 + 42*a**2*tan(x/2)**4 + 42*a**2*tan(x/2)**3 + 30*a**2*tan(x/2)**2 + 18*a**2*tan(x/2) + 6*a**2) + 21*x/(6*a**2*tan(x/2)**7 + 18*a**2*tan(x/2)**6 + 30*a**2*tan(x/2)**5 + 42*a**2*tan(x/2)**4 + 42*a**2*tan(x/2)**3 + 30*a**2*tan(x/2)**2 + 18*a**2*tan(x/2) + 6*a**2) + 42*tan(x/2)**6/(6*a**2*tan(x/2)**7 + 18*a**2*tan(x/2)**6 + 30*a**2*tan(x/2)**5 + 42*a**2*tan(x/2)**4 + 42*a**2*tan(x/2)**3 + 30*a**2*tan(x/2)**2 + 18*a**2*tan(x/2) + 6*a**2) + 126*tan(x/2)**5/(6*a**2*tan(x/2)**7 + 18*a**2*tan(x/2)**6 + 30*a**2*tan(x/2)**5 + 42*a**2*tan(x/2)**4 + 42*a**2*tan(x/2)**3 + 30*a**2*tan(x/2)**2 + 18*a**2*tan(x/2) + 6*a**2) + 196*tan(x/2)**4/(6*a**2*tan(x/2)**7 + 18*a**2*tan(x/2)**6 + 30*a**2*tan(x/2)**5 + 42*a**2*tan(x/2)**4 + 42*a**2*tan(x/2)**3 + 30*a**2*tan(x/2)**2 + 18*a**2*tan(x/2) + 6*a**2) + 252*tan(x/2)**3/(6*a**2*tan(x/2)**7 + 18*a**2*tan(x/2)**6 + 30*a**2*tan(x/2)**5 + 42*a**2*tan(x/2)**4 + 42*a**2*tan(x/2)**3 + 30*a**2*tan(x/2)**2 + 18*a**2*tan(x/2) + 6*a**2) + 194*tan(x/2)**2/(6*a**2*tan(x/2)**7 + 18*a**2*tan(x/2)**6 + 30*a**2*tan(x/2)**5 + 42*a**2*tan(x/2)**4 + 42*a**2*tan(x/2)**3 + 30*a**2*tan(x/2)**2 + 18*a**2*tan(x/2) + 6*a**2) + 150*tan(x/2)/(6*a**2*tan(x/2)**7 + 18*a**2*tan(x/2)**6 + 30*a**2*tan(x/2)**5 + 42*a**2*tan(x/2)**4 + 42*a**2*tan(x/2)**3 + 30*a**2*tan(x/2)**2 + 18*a**2*tan(x/2) + 6*a**2) + 64/(6*a**2*tan(x/2)**7 + 18*a**2*tan(x/2)**6 + 30*a**2*tan(x/2)**5 + 42*a**2*tan(x/2)**4 + 42*a**2*tan(x/2)**3 + 30*a**2*tan(x/2)**2 + 18*a**2*tan(x/2) + 6*a**2)","B",0
13,1,779,0,6.794493," ","integrate(sin(x)**3/(a+a*sin(x))**2,x)","- \frac{6 x \tan^{5}{\left(\frac{x}{2} \right)}}{3 a^{2} \tan^{5}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 12 a^{2} \tan^{3}{\left(\frac{x}{2} \right)} + 12 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan{\left(\frac{x}{2} \right)} + 3 a^{2}} - \frac{18 x \tan^{4}{\left(\frac{x}{2} \right)}}{3 a^{2} \tan^{5}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 12 a^{2} \tan^{3}{\left(\frac{x}{2} \right)} + 12 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan{\left(\frac{x}{2} \right)} + 3 a^{2}} - \frac{24 x \tan^{3}{\left(\frac{x}{2} \right)}}{3 a^{2} \tan^{5}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 12 a^{2} \tan^{3}{\left(\frac{x}{2} \right)} + 12 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan{\left(\frac{x}{2} \right)} + 3 a^{2}} - \frac{24 x \tan^{2}{\left(\frac{x}{2} \right)}}{3 a^{2} \tan^{5}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 12 a^{2} \tan^{3}{\left(\frac{x}{2} \right)} + 12 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan{\left(\frac{x}{2} \right)} + 3 a^{2}} - \frac{18 x \tan{\left(\frac{x}{2} \right)}}{3 a^{2} \tan^{5}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 12 a^{2} \tan^{3}{\left(\frac{x}{2} \right)} + 12 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan{\left(\frac{x}{2} \right)} + 3 a^{2}} - \frac{6 x}{3 a^{2} \tan^{5}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 12 a^{2} \tan^{3}{\left(\frac{x}{2} \right)} + 12 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan{\left(\frac{x}{2} \right)} + 3 a^{2}} - \frac{12 \tan^{4}{\left(\frac{x}{2} \right)}}{3 a^{2} \tan^{5}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 12 a^{2} \tan^{3}{\left(\frac{x}{2} \right)} + 12 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan{\left(\frac{x}{2} \right)} + 3 a^{2}} - \frac{36 \tan^{3}{\left(\frac{x}{2} \right)}}{3 a^{2} \tan^{5}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 12 a^{2} \tan^{3}{\left(\frac{x}{2} \right)} + 12 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan{\left(\frac{x}{2} \right)} + 3 a^{2}} - \frac{44 \tan^{2}{\left(\frac{x}{2} \right)}}{3 a^{2} \tan^{5}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 12 a^{2} \tan^{3}{\left(\frac{x}{2} \right)} + 12 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan{\left(\frac{x}{2} \right)} + 3 a^{2}} - \frac{48 \tan{\left(\frac{x}{2} \right)}}{3 a^{2} \tan^{5}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 12 a^{2} \tan^{3}{\left(\frac{x}{2} \right)} + 12 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan{\left(\frac{x}{2} \right)} + 3 a^{2}} - \frac{20}{3 a^{2} \tan^{5}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 12 a^{2} \tan^{3}{\left(\frac{x}{2} \right)} + 12 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan{\left(\frac{x}{2} \right)} + 3 a^{2}}"," ",0,"-6*x*tan(x/2)**5/(3*a**2*tan(x/2)**5 + 9*a**2*tan(x/2)**4 + 12*a**2*tan(x/2)**3 + 12*a**2*tan(x/2)**2 + 9*a**2*tan(x/2) + 3*a**2) - 18*x*tan(x/2)**4/(3*a**2*tan(x/2)**5 + 9*a**2*tan(x/2)**4 + 12*a**2*tan(x/2)**3 + 12*a**2*tan(x/2)**2 + 9*a**2*tan(x/2) + 3*a**2) - 24*x*tan(x/2)**3/(3*a**2*tan(x/2)**5 + 9*a**2*tan(x/2)**4 + 12*a**2*tan(x/2)**3 + 12*a**2*tan(x/2)**2 + 9*a**2*tan(x/2) + 3*a**2) - 24*x*tan(x/2)**2/(3*a**2*tan(x/2)**5 + 9*a**2*tan(x/2)**4 + 12*a**2*tan(x/2)**3 + 12*a**2*tan(x/2)**2 + 9*a**2*tan(x/2) + 3*a**2) - 18*x*tan(x/2)/(3*a**2*tan(x/2)**5 + 9*a**2*tan(x/2)**4 + 12*a**2*tan(x/2)**3 + 12*a**2*tan(x/2)**2 + 9*a**2*tan(x/2) + 3*a**2) - 6*x/(3*a**2*tan(x/2)**5 + 9*a**2*tan(x/2)**4 + 12*a**2*tan(x/2)**3 + 12*a**2*tan(x/2)**2 + 9*a**2*tan(x/2) + 3*a**2) - 12*tan(x/2)**4/(3*a**2*tan(x/2)**5 + 9*a**2*tan(x/2)**4 + 12*a**2*tan(x/2)**3 + 12*a**2*tan(x/2)**2 + 9*a**2*tan(x/2) + 3*a**2) - 36*tan(x/2)**3/(3*a**2*tan(x/2)**5 + 9*a**2*tan(x/2)**4 + 12*a**2*tan(x/2)**3 + 12*a**2*tan(x/2)**2 + 9*a**2*tan(x/2) + 3*a**2) - 44*tan(x/2)**2/(3*a**2*tan(x/2)**5 + 9*a**2*tan(x/2)**4 + 12*a**2*tan(x/2)**3 + 12*a**2*tan(x/2)**2 + 9*a**2*tan(x/2) + 3*a**2) - 48*tan(x/2)/(3*a**2*tan(x/2)**5 + 9*a**2*tan(x/2)**4 + 12*a**2*tan(x/2)**3 + 12*a**2*tan(x/2)**2 + 9*a**2*tan(x/2) + 3*a**2) - 20/(3*a**2*tan(x/2)**5 + 9*a**2*tan(x/2)**4 + 12*a**2*tan(x/2)**3 + 12*a**2*tan(x/2)**2 + 9*a**2*tan(x/2) + 3*a**2)","B",0
14,1,321,0,4.264436," ","integrate(sin(x)**2/(a+a*sin(x))**2,x)","\frac{3 x \tan^{3}{\left(\frac{x}{2} \right)}}{3 a^{2} \tan^{3}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan{\left(\frac{x}{2} \right)} + 3 a^{2}} + \frac{9 x \tan^{2}{\left(\frac{x}{2} \right)}}{3 a^{2} \tan^{3}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan{\left(\frac{x}{2} \right)} + 3 a^{2}} + \frac{9 x \tan{\left(\frac{x}{2} \right)}}{3 a^{2} \tan^{3}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan{\left(\frac{x}{2} \right)} + 3 a^{2}} + \frac{3 x}{3 a^{2} \tan^{3}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan{\left(\frac{x}{2} \right)} + 3 a^{2}} + \frac{6 \tan^{2}{\left(\frac{x}{2} \right)}}{3 a^{2} \tan^{3}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan{\left(\frac{x}{2} \right)} + 3 a^{2}} + \frac{18 \tan{\left(\frac{x}{2} \right)}}{3 a^{2} \tan^{3}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan{\left(\frac{x}{2} \right)} + 3 a^{2}} + \frac{8}{3 a^{2} \tan^{3}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan{\left(\frac{x}{2} \right)} + 3 a^{2}}"," ",0,"3*x*tan(x/2)**3/(3*a**2*tan(x/2)**3 + 9*a**2*tan(x/2)**2 + 9*a**2*tan(x/2) + 3*a**2) + 9*x*tan(x/2)**2/(3*a**2*tan(x/2)**3 + 9*a**2*tan(x/2)**2 + 9*a**2*tan(x/2) + 3*a**2) + 9*x*tan(x/2)/(3*a**2*tan(x/2)**3 + 9*a**2*tan(x/2)**2 + 9*a**2*tan(x/2) + 3*a**2) + 3*x/(3*a**2*tan(x/2)**3 + 9*a**2*tan(x/2)**2 + 9*a**2*tan(x/2) + 3*a**2) + 6*tan(x/2)**2/(3*a**2*tan(x/2)**3 + 9*a**2*tan(x/2)**2 + 9*a**2*tan(x/2) + 3*a**2) + 18*tan(x/2)/(3*a**2*tan(x/2)**3 + 9*a**2*tan(x/2)**2 + 9*a**2*tan(x/2) + 3*a**2) + 8/(3*a**2*tan(x/2)**3 + 9*a**2*tan(x/2)**2 + 9*a**2*tan(x/2) + 3*a**2)","B",0
15,1,87,0,2.134376," ","integrate(sin(x)/(a+a*sin(x))**2,x)","- \frac{6 \tan{\left(\frac{x}{2} \right)}}{3 a^{2} \tan^{3}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan{\left(\frac{x}{2} \right)} + 3 a^{2}} - \frac{2}{3 a^{2} \tan^{3}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan{\left(\frac{x}{2} \right)} + 3 a^{2}}"," ",0,"-6*tan(x/2)/(3*a**2*tan(x/2)**3 + 9*a**2*tan(x/2)**2 + 9*a**2*tan(x/2) + 3*a**2) - 2/(3*a**2*tan(x/2)**3 + 9*a**2*tan(x/2)**2 + 9*a**2*tan(x/2) + 3*a**2)","B",0
16,1,134,0,1.019298," ","integrate(1/(a+a*sin(x))**2,x)","- \frac{6 \tan^{2}{\left(\frac{x}{2} \right)}}{3 a^{2} \tan^{3}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan{\left(\frac{x}{2} \right)} + 3 a^{2}} - \frac{6 \tan{\left(\frac{x}{2} \right)}}{3 a^{2} \tan^{3}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan{\left(\frac{x}{2} \right)} + 3 a^{2}} - \frac{4}{3 a^{2} \tan^{3}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan{\left(\frac{x}{2} \right)} + 3 a^{2}}"," ",0,"-6*tan(x/2)**2/(3*a**2*tan(x/2)**3 + 9*a**2*tan(x/2)**2 + 9*a**2*tan(x/2) + 3*a**2) - 6*tan(x/2)/(3*a**2*tan(x/2)**3 + 9*a**2*tan(x/2)**2 + 9*a**2*tan(x/2) + 3*a**2) - 4/(3*a**2*tan(x/2)**3 + 9*a**2*tan(x/2)**2 + 9*a**2*tan(x/2) + 3*a**2)","B",0
17,0,0,0,0.000000," ","integrate(csc(x)/(a+a*sin(x))**2,x)","\frac{\int \frac{\csc{\left(x \right)}}{\sin^{2}{\left(x \right)} + 2 \sin{\left(x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral(csc(x)/(sin(x)**2 + 2*sin(x) + 1), x)/a**2","F",0
18,0,0,0,0.000000," ","integrate(csc(x)**2/(a+a*sin(x))**2,x)","\frac{\int \frac{\csc^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)} + 2 \sin{\left(x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral(csc(x)**2/(sin(x)**2 + 2*sin(x) + 1), x)/a**2","F",0
19,0,0,0,0.000000," ","integrate(csc(x)**3/(a+a*sin(x))**2,x)","\frac{\int \frac{\csc^{3}{\left(x \right)}}{\sin^{2}{\left(x \right)} + 2 \sin{\left(x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral(csc(x)**3/(sin(x)**2 + 2*sin(x) + 1), x)/a**2","F",0
20,0,0,0,0.000000," ","integrate(csc(x)**4/(a+a*sin(x))**2,x)","\frac{\int \frac{\csc^{4}{\left(x \right)}}{\sin^{2}{\left(x \right)} + 2 \sin{\left(x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral(csc(x)**4/(sin(x)**2 + 2*sin(x) + 1), x)/a**2","F",0
21,1,3288,0,50.536386," ","integrate(sin(x)**6/(a+a*sin(x))**3,x)","- \frac{345 x \tan^{11}{\left(\frac{x}{2} \right)}}{30 a^{3} \tan^{11}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{10}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{9}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan{\left(\frac{x}{2} \right)} + 30 a^{3}} - \frac{1725 x \tan^{10}{\left(\frac{x}{2} \right)}}{30 a^{3} \tan^{11}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{10}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{9}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan{\left(\frac{x}{2} \right)} + 30 a^{3}} - \frac{4485 x \tan^{9}{\left(\frac{x}{2} \right)}}{30 a^{3} \tan^{11}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{10}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{9}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan{\left(\frac{x}{2} \right)} + 30 a^{3}} - \frac{8625 x \tan^{8}{\left(\frac{x}{2} \right)}}{30 a^{3} \tan^{11}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{10}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{9}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan{\left(\frac{x}{2} \right)} + 30 a^{3}} - \frac{13110 x \tan^{7}{\left(\frac{x}{2} \right)}}{30 a^{3} \tan^{11}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{10}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{9}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan{\left(\frac{x}{2} \right)} + 30 a^{3}} - \frac{15870 x \tan^{6}{\left(\frac{x}{2} \right)}}{30 a^{3} \tan^{11}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{10}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{9}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan{\left(\frac{x}{2} \right)} + 30 a^{3}} - \frac{15870 x \tan^{5}{\left(\frac{x}{2} \right)}}{30 a^{3} \tan^{11}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{10}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{9}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan{\left(\frac{x}{2} \right)} + 30 a^{3}} - \frac{13110 x \tan^{4}{\left(\frac{x}{2} \right)}}{30 a^{3} \tan^{11}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{10}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{9}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan{\left(\frac{x}{2} \right)} + 30 a^{3}} - \frac{8625 x \tan^{3}{\left(\frac{x}{2} \right)}}{30 a^{3} \tan^{11}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{10}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{9}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan{\left(\frac{x}{2} \right)} + 30 a^{3}} - \frac{4485 x \tan^{2}{\left(\frac{x}{2} \right)}}{30 a^{3} \tan^{11}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{10}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{9}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan{\left(\frac{x}{2} \right)} + 30 a^{3}} - \frac{1725 x \tan{\left(\frac{x}{2} \right)}}{30 a^{3} \tan^{11}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{10}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{9}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan{\left(\frac{x}{2} \right)} + 30 a^{3}} - \frac{345 x}{30 a^{3} \tan^{11}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{10}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{9}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan{\left(\frac{x}{2} \right)} + 30 a^{3}} - \frac{690 \tan^{10}{\left(\frac{x}{2} \right)}}{30 a^{3} \tan^{11}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{10}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{9}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan{\left(\frac{x}{2} \right)} + 30 a^{3}} - \frac{3450 \tan^{9}{\left(\frac{x}{2} \right)}}{30 a^{3} \tan^{11}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{10}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{9}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan{\left(\frac{x}{2} \right)} + 30 a^{3}} - \frac{8740 \tan^{8}{\left(\frac{x}{2} \right)}}{30 a^{3} \tan^{11}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{10}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{9}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan{\left(\frac{x}{2} \right)} + 30 a^{3}} - \frac{16100 \tan^{7}{\left(\frac{x}{2} \right)}}{30 a^{3} \tan^{11}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{10}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{9}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan{\left(\frac{x}{2} \right)} + 30 a^{3}} - \frac{23368 \tan^{6}{\left(\frac{x}{2} \right)}}{30 a^{3} \tan^{11}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{10}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{9}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan{\left(\frac{x}{2} \right)} + 30 a^{3}} - \frac{26680 \tan^{5}{\left(\frac{x}{2} \right)}}{30 a^{3} \tan^{11}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{10}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{9}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan{\left(\frac{x}{2} \right)} + 30 a^{3}} - \frac{25244 \tan^{4}{\left(\frac{x}{2} \right)}}{30 a^{3} \tan^{11}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{10}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{9}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan{\left(\frac{x}{2} \right)} + 30 a^{3}} - \frac{18460 \tan^{3}{\left(\frac{x}{2} \right)}}{30 a^{3} \tan^{11}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{10}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{9}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan{\left(\frac{x}{2} \right)} + 30 a^{3}} - \frac{10694 \tan^{2}{\left(\frac{x}{2} \right)}}{30 a^{3} \tan^{11}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{10}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{9}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan{\left(\frac{x}{2} \right)} + 30 a^{3}} - \frac{4750 \tan{\left(\frac{x}{2} \right)}}{30 a^{3} \tan^{11}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{10}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{9}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan{\left(\frac{x}{2} \right)} + 30 a^{3}} - \frac{1088}{30 a^{3} \tan^{11}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{10}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{9}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 1380 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 1140 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 750 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 390 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan{\left(\frac{x}{2} \right)} + 30 a^{3}}"," ",0,"-345*x*tan(x/2)**11/(30*a**3*tan(x/2)**11 + 150*a**3*tan(x/2)**10 + 390*a**3*tan(x/2)**9 + 750*a**3*tan(x/2)**8 + 1140*a**3*tan(x/2)**7 + 1380*a**3*tan(x/2)**6 + 1380*a**3*tan(x/2)**5 + 1140*a**3*tan(x/2)**4 + 750*a**3*tan(x/2)**3 + 390*a**3*tan(x/2)**2 + 150*a**3*tan(x/2) + 30*a**3) - 1725*x*tan(x/2)**10/(30*a**3*tan(x/2)**11 + 150*a**3*tan(x/2)**10 + 390*a**3*tan(x/2)**9 + 750*a**3*tan(x/2)**8 + 1140*a**3*tan(x/2)**7 + 1380*a**3*tan(x/2)**6 + 1380*a**3*tan(x/2)**5 + 1140*a**3*tan(x/2)**4 + 750*a**3*tan(x/2)**3 + 390*a**3*tan(x/2)**2 + 150*a**3*tan(x/2) + 30*a**3) - 4485*x*tan(x/2)**9/(30*a**3*tan(x/2)**11 + 150*a**3*tan(x/2)**10 + 390*a**3*tan(x/2)**9 + 750*a**3*tan(x/2)**8 + 1140*a**3*tan(x/2)**7 + 1380*a**3*tan(x/2)**6 + 1380*a**3*tan(x/2)**5 + 1140*a**3*tan(x/2)**4 + 750*a**3*tan(x/2)**3 + 390*a**3*tan(x/2)**2 + 150*a**3*tan(x/2) + 30*a**3) - 8625*x*tan(x/2)**8/(30*a**3*tan(x/2)**11 + 150*a**3*tan(x/2)**10 + 390*a**3*tan(x/2)**9 + 750*a**3*tan(x/2)**8 + 1140*a**3*tan(x/2)**7 + 1380*a**3*tan(x/2)**6 + 1380*a**3*tan(x/2)**5 + 1140*a**3*tan(x/2)**4 + 750*a**3*tan(x/2)**3 + 390*a**3*tan(x/2)**2 + 150*a**3*tan(x/2) + 30*a**3) - 13110*x*tan(x/2)**7/(30*a**3*tan(x/2)**11 + 150*a**3*tan(x/2)**10 + 390*a**3*tan(x/2)**9 + 750*a**3*tan(x/2)**8 + 1140*a**3*tan(x/2)**7 + 1380*a**3*tan(x/2)**6 + 1380*a**3*tan(x/2)**5 + 1140*a**3*tan(x/2)**4 + 750*a**3*tan(x/2)**3 + 390*a**3*tan(x/2)**2 + 150*a**3*tan(x/2) + 30*a**3) - 15870*x*tan(x/2)**6/(30*a**3*tan(x/2)**11 + 150*a**3*tan(x/2)**10 + 390*a**3*tan(x/2)**9 + 750*a**3*tan(x/2)**8 + 1140*a**3*tan(x/2)**7 + 1380*a**3*tan(x/2)**6 + 1380*a**3*tan(x/2)**5 + 1140*a**3*tan(x/2)**4 + 750*a**3*tan(x/2)**3 + 390*a**3*tan(x/2)**2 + 150*a**3*tan(x/2) + 30*a**3) - 15870*x*tan(x/2)**5/(30*a**3*tan(x/2)**11 + 150*a**3*tan(x/2)**10 + 390*a**3*tan(x/2)**9 + 750*a**3*tan(x/2)**8 + 1140*a**3*tan(x/2)**7 + 1380*a**3*tan(x/2)**6 + 1380*a**3*tan(x/2)**5 + 1140*a**3*tan(x/2)**4 + 750*a**3*tan(x/2)**3 + 390*a**3*tan(x/2)**2 + 150*a**3*tan(x/2) + 30*a**3) - 13110*x*tan(x/2)**4/(30*a**3*tan(x/2)**11 + 150*a**3*tan(x/2)**10 + 390*a**3*tan(x/2)**9 + 750*a**3*tan(x/2)**8 + 1140*a**3*tan(x/2)**7 + 1380*a**3*tan(x/2)**6 + 1380*a**3*tan(x/2)**5 + 1140*a**3*tan(x/2)**4 + 750*a**3*tan(x/2)**3 + 390*a**3*tan(x/2)**2 + 150*a**3*tan(x/2) + 30*a**3) - 8625*x*tan(x/2)**3/(30*a**3*tan(x/2)**11 + 150*a**3*tan(x/2)**10 + 390*a**3*tan(x/2)**9 + 750*a**3*tan(x/2)**8 + 1140*a**3*tan(x/2)**7 + 1380*a**3*tan(x/2)**6 + 1380*a**3*tan(x/2)**5 + 1140*a**3*tan(x/2)**4 + 750*a**3*tan(x/2)**3 + 390*a**3*tan(x/2)**2 + 150*a**3*tan(x/2) + 30*a**3) - 4485*x*tan(x/2)**2/(30*a**3*tan(x/2)**11 + 150*a**3*tan(x/2)**10 + 390*a**3*tan(x/2)**9 + 750*a**3*tan(x/2)**8 + 1140*a**3*tan(x/2)**7 + 1380*a**3*tan(x/2)**6 + 1380*a**3*tan(x/2)**5 + 1140*a**3*tan(x/2)**4 + 750*a**3*tan(x/2)**3 + 390*a**3*tan(x/2)**2 + 150*a**3*tan(x/2) + 30*a**3) - 1725*x*tan(x/2)/(30*a**3*tan(x/2)**11 + 150*a**3*tan(x/2)**10 + 390*a**3*tan(x/2)**9 + 750*a**3*tan(x/2)**8 + 1140*a**3*tan(x/2)**7 + 1380*a**3*tan(x/2)**6 + 1380*a**3*tan(x/2)**5 + 1140*a**3*tan(x/2)**4 + 750*a**3*tan(x/2)**3 + 390*a**3*tan(x/2)**2 + 150*a**3*tan(x/2) + 30*a**3) - 345*x/(30*a**3*tan(x/2)**11 + 150*a**3*tan(x/2)**10 + 390*a**3*tan(x/2)**9 + 750*a**3*tan(x/2)**8 + 1140*a**3*tan(x/2)**7 + 1380*a**3*tan(x/2)**6 + 1380*a**3*tan(x/2)**5 + 1140*a**3*tan(x/2)**4 + 750*a**3*tan(x/2)**3 + 390*a**3*tan(x/2)**2 + 150*a**3*tan(x/2) + 30*a**3) - 690*tan(x/2)**10/(30*a**3*tan(x/2)**11 + 150*a**3*tan(x/2)**10 + 390*a**3*tan(x/2)**9 + 750*a**3*tan(x/2)**8 + 1140*a**3*tan(x/2)**7 + 1380*a**3*tan(x/2)**6 + 1380*a**3*tan(x/2)**5 + 1140*a**3*tan(x/2)**4 + 750*a**3*tan(x/2)**3 + 390*a**3*tan(x/2)**2 + 150*a**3*tan(x/2) + 30*a**3) - 3450*tan(x/2)**9/(30*a**3*tan(x/2)**11 + 150*a**3*tan(x/2)**10 + 390*a**3*tan(x/2)**9 + 750*a**3*tan(x/2)**8 + 1140*a**3*tan(x/2)**7 + 1380*a**3*tan(x/2)**6 + 1380*a**3*tan(x/2)**5 + 1140*a**3*tan(x/2)**4 + 750*a**3*tan(x/2)**3 + 390*a**3*tan(x/2)**2 + 150*a**3*tan(x/2) + 30*a**3) - 8740*tan(x/2)**8/(30*a**3*tan(x/2)**11 + 150*a**3*tan(x/2)**10 + 390*a**3*tan(x/2)**9 + 750*a**3*tan(x/2)**8 + 1140*a**3*tan(x/2)**7 + 1380*a**3*tan(x/2)**6 + 1380*a**3*tan(x/2)**5 + 1140*a**3*tan(x/2)**4 + 750*a**3*tan(x/2)**3 + 390*a**3*tan(x/2)**2 + 150*a**3*tan(x/2) + 30*a**3) - 16100*tan(x/2)**7/(30*a**3*tan(x/2)**11 + 150*a**3*tan(x/2)**10 + 390*a**3*tan(x/2)**9 + 750*a**3*tan(x/2)**8 + 1140*a**3*tan(x/2)**7 + 1380*a**3*tan(x/2)**6 + 1380*a**3*tan(x/2)**5 + 1140*a**3*tan(x/2)**4 + 750*a**3*tan(x/2)**3 + 390*a**3*tan(x/2)**2 + 150*a**3*tan(x/2) + 30*a**3) - 23368*tan(x/2)**6/(30*a**3*tan(x/2)**11 + 150*a**3*tan(x/2)**10 + 390*a**3*tan(x/2)**9 + 750*a**3*tan(x/2)**8 + 1140*a**3*tan(x/2)**7 + 1380*a**3*tan(x/2)**6 + 1380*a**3*tan(x/2)**5 + 1140*a**3*tan(x/2)**4 + 750*a**3*tan(x/2)**3 + 390*a**3*tan(x/2)**2 + 150*a**3*tan(x/2) + 30*a**3) - 26680*tan(x/2)**5/(30*a**3*tan(x/2)**11 + 150*a**3*tan(x/2)**10 + 390*a**3*tan(x/2)**9 + 750*a**3*tan(x/2)**8 + 1140*a**3*tan(x/2)**7 + 1380*a**3*tan(x/2)**6 + 1380*a**3*tan(x/2)**5 + 1140*a**3*tan(x/2)**4 + 750*a**3*tan(x/2)**3 + 390*a**3*tan(x/2)**2 + 150*a**3*tan(x/2) + 30*a**3) - 25244*tan(x/2)**4/(30*a**3*tan(x/2)**11 + 150*a**3*tan(x/2)**10 + 390*a**3*tan(x/2)**9 + 750*a**3*tan(x/2)**8 + 1140*a**3*tan(x/2)**7 + 1380*a**3*tan(x/2)**6 + 1380*a**3*tan(x/2)**5 + 1140*a**3*tan(x/2)**4 + 750*a**3*tan(x/2)**3 + 390*a**3*tan(x/2)**2 + 150*a**3*tan(x/2) + 30*a**3) - 18460*tan(x/2)**3/(30*a**3*tan(x/2)**11 + 150*a**3*tan(x/2)**10 + 390*a**3*tan(x/2)**9 + 750*a**3*tan(x/2)**8 + 1140*a**3*tan(x/2)**7 + 1380*a**3*tan(x/2)**6 + 1380*a**3*tan(x/2)**5 + 1140*a**3*tan(x/2)**4 + 750*a**3*tan(x/2)**3 + 390*a**3*tan(x/2)**2 + 150*a**3*tan(x/2) + 30*a**3) - 10694*tan(x/2)**2/(30*a**3*tan(x/2)**11 + 150*a**3*tan(x/2)**10 + 390*a**3*tan(x/2)**9 + 750*a**3*tan(x/2)**8 + 1140*a**3*tan(x/2)**7 + 1380*a**3*tan(x/2)**6 + 1380*a**3*tan(x/2)**5 + 1140*a**3*tan(x/2)**4 + 750*a**3*tan(x/2)**3 + 390*a**3*tan(x/2)**2 + 150*a**3*tan(x/2) + 30*a**3) - 4750*tan(x/2)/(30*a**3*tan(x/2)**11 + 150*a**3*tan(x/2)**10 + 390*a**3*tan(x/2)**9 + 750*a**3*tan(x/2)**8 + 1140*a**3*tan(x/2)**7 + 1380*a**3*tan(x/2)**6 + 1380*a**3*tan(x/2)**5 + 1140*a**3*tan(x/2)**4 + 750*a**3*tan(x/2)**3 + 390*a**3*tan(x/2)**2 + 150*a**3*tan(x/2) + 30*a**3) - 1088/(30*a**3*tan(x/2)**11 + 150*a**3*tan(x/2)**10 + 390*a**3*tan(x/2)**9 + 750*a**3*tan(x/2)**8 + 1140*a**3*tan(x/2)**7 + 1380*a**3*tan(x/2)**6 + 1380*a**3*tan(x/2)**5 + 1140*a**3*tan(x/2)**4 + 750*a**3*tan(x/2)**3 + 390*a**3*tan(x/2)**2 + 150*a**3*tan(x/2) + 30*a**3)","B",0
22,1,2259,0,33.590553," ","integrate(sin(x)**5/(a+a*sin(x))**3,x)","\frac{195 x \tan^{9}{\left(\frac{x}{2} \right)}}{30 a^{3} \tan^{9}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 360 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 600 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 780 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 780 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 600 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 360 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan{\left(\frac{x}{2} \right)} + 30 a^{3}} + \frac{975 x \tan^{8}{\left(\frac{x}{2} \right)}}{30 a^{3} \tan^{9}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 360 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 600 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 780 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 780 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 600 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 360 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan{\left(\frac{x}{2} \right)} + 30 a^{3}} + \frac{2340 x \tan^{7}{\left(\frac{x}{2} \right)}}{30 a^{3} \tan^{9}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 360 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 600 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 780 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 780 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 600 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 360 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan{\left(\frac{x}{2} \right)} + 30 a^{3}} + \frac{3900 x \tan^{6}{\left(\frac{x}{2} \right)}}{30 a^{3} \tan^{9}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 360 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 600 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 780 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 780 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 600 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 360 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan{\left(\frac{x}{2} \right)} + 30 a^{3}} + \frac{5070 x \tan^{5}{\left(\frac{x}{2} \right)}}{30 a^{3} \tan^{9}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 360 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 600 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 780 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 780 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 600 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 360 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan{\left(\frac{x}{2} \right)} + 30 a^{3}} + \frac{5070 x \tan^{4}{\left(\frac{x}{2} \right)}}{30 a^{3} \tan^{9}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 360 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 600 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 780 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 780 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 600 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 360 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan{\left(\frac{x}{2} \right)} + 30 a^{3}} + \frac{3900 x \tan^{3}{\left(\frac{x}{2} \right)}}{30 a^{3} \tan^{9}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 360 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 600 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 780 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 780 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 600 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 360 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan{\left(\frac{x}{2} \right)} + 30 a^{3}} + \frac{2340 x \tan^{2}{\left(\frac{x}{2} \right)}}{30 a^{3} \tan^{9}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 360 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 600 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 780 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 780 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 600 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 360 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan{\left(\frac{x}{2} \right)} + 30 a^{3}} + \frac{975 x \tan{\left(\frac{x}{2} \right)}}{30 a^{3} \tan^{9}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 360 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 600 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 780 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 780 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 600 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 360 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan{\left(\frac{x}{2} \right)} + 30 a^{3}} + \frac{195 x}{30 a^{3} \tan^{9}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 360 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 600 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 780 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 780 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 600 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 360 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan{\left(\frac{x}{2} \right)} + 30 a^{3}} + \frac{390 \tan^{8}{\left(\frac{x}{2} \right)}}{30 a^{3} \tan^{9}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 360 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 600 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 780 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 780 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 600 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 360 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan{\left(\frac{x}{2} \right)} + 30 a^{3}} + \frac{1950 \tan^{7}{\left(\frac{x}{2} \right)}}{30 a^{3} \tan^{9}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 360 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 600 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 780 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 780 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 600 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 360 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan{\left(\frac{x}{2} \right)} + 30 a^{3}} + \frac{4550 \tan^{6}{\left(\frac{x}{2} \right)}}{30 a^{3} \tan^{9}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 360 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 600 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 780 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 780 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 600 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 360 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan{\left(\frac{x}{2} \right)} + 30 a^{3}} + \frac{7150 \tan^{5}{\left(\frac{x}{2} \right)}}{30 a^{3} \tan^{9}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 360 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 600 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 780 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 780 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 600 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 360 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan{\left(\frac{x}{2} \right)} + 30 a^{3}} + \frac{8658 \tan^{4}{\left(\frac{x}{2} \right)}}{30 a^{3} \tan^{9}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 360 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 600 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 780 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 780 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 600 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 360 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan{\left(\frac{x}{2} \right)} + 30 a^{3}} + \frac{7610 \tan^{3}{\left(\frac{x}{2} \right)}}{30 a^{3} \tan^{9}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 360 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 600 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 780 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 780 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 600 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 360 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan{\left(\frac{x}{2} \right)} + 30 a^{3}} + \frac{5346 \tan^{2}{\left(\frac{x}{2} \right)}}{30 a^{3} \tan^{9}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 360 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 600 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 780 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 780 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 600 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 360 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan{\left(\frac{x}{2} \right)} + 30 a^{3}} + \frac{2650 \tan{\left(\frac{x}{2} \right)}}{30 a^{3} \tan^{9}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 360 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 600 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 780 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 780 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 600 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 360 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan{\left(\frac{x}{2} \right)} + 30 a^{3}} + \frac{608}{30 a^{3} \tan^{9}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 360 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 600 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 780 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 780 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 600 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 360 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan{\left(\frac{x}{2} \right)} + 30 a^{3}}"," ",0,"195*x*tan(x/2)**9/(30*a**3*tan(x/2)**9 + 150*a**3*tan(x/2)**8 + 360*a**3*tan(x/2)**7 + 600*a**3*tan(x/2)**6 + 780*a**3*tan(x/2)**5 + 780*a**3*tan(x/2)**4 + 600*a**3*tan(x/2)**3 + 360*a**3*tan(x/2)**2 + 150*a**3*tan(x/2) + 30*a**3) + 975*x*tan(x/2)**8/(30*a**3*tan(x/2)**9 + 150*a**3*tan(x/2)**8 + 360*a**3*tan(x/2)**7 + 600*a**3*tan(x/2)**6 + 780*a**3*tan(x/2)**5 + 780*a**3*tan(x/2)**4 + 600*a**3*tan(x/2)**3 + 360*a**3*tan(x/2)**2 + 150*a**3*tan(x/2) + 30*a**3) + 2340*x*tan(x/2)**7/(30*a**3*tan(x/2)**9 + 150*a**3*tan(x/2)**8 + 360*a**3*tan(x/2)**7 + 600*a**3*tan(x/2)**6 + 780*a**3*tan(x/2)**5 + 780*a**3*tan(x/2)**4 + 600*a**3*tan(x/2)**3 + 360*a**3*tan(x/2)**2 + 150*a**3*tan(x/2) + 30*a**3) + 3900*x*tan(x/2)**6/(30*a**3*tan(x/2)**9 + 150*a**3*tan(x/2)**8 + 360*a**3*tan(x/2)**7 + 600*a**3*tan(x/2)**6 + 780*a**3*tan(x/2)**5 + 780*a**3*tan(x/2)**4 + 600*a**3*tan(x/2)**3 + 360*a**3*tan(x/2)**2 + 150*a**3*tan(x/2) + 30*a**3) + 5070*x*tan(x/2)**5/(30*a**3*tan(x/2)**9 + 150*a**3*tan(x/2)**8 + 360*a**3*tan(x/2)**7 + 600*a**3*tan(x/2)**6 + 780*a**3*tan(x/2)**5 + 780*a**3*tan(x/2)**4 + 600*a**3*tan(x/2)**3 + 360*a**3*tan(x/2)**2 + 150*a**3*tan(x/2) + 30*a**3) + 5070*x*tan(x/2)**4/(30*a**3*tan(x/2)**9 + 150*a**3*tan(x/2)**8 + 360*a**3*tan(x/2)**7 + 600*a**3*tan(x/2)**6 + 780*a**3*tan(x/2)**5 + 780*a**3*tan(x/2)**4 + 600*a**3*tan(x/2)**3 + 360*a**3*tan(x/2)**2 + 150*a**3*tan(x/2) + 30*a**3) + 3900*x*tan(x/2)**3/(30*a**3*tan(x/2)**9 + 150*a**3*tan(x/2)**8 + 360*a**3*tan(x/2)**7 + 600*a**3*tan(x/2)**6 + 780*a**3*tan(x/2)**5 + 780*a**3*tan(x/2)**4 + 600*a**3*tan(x/2)**3 + 360*a**3*tan(x/2)**2 + 150*a**3*tan(x/2) + 30*a**3) + 2340*x*tan(x/2)**2/(30*a**3*tan(x/2)**9 + 150*a**3*tan(x/2)**8 + 360*a**3*tan(x/2)**7 + 600*a**3*tan(x/2)**6 + 780*a**3*tan(x/2)**5 + 780*a**3*tan(x/2)**4 + 600*a**3*tan(x/2)**3 + 360*a**3*tan(x/2)**2 + 150*a**3*tan(x/2) + 30*a**3) + 975*x*tan(x/2)/(30*a**3*tan(x/2)**9 + 150*a**3*tan(x/2)**8 + 360*a**3*tan(x/2)**7 + 600*a**3*tan(x/2)**6 + 780*a**3*tan(x/2)**5 + 780*a**3*tan(x/2)**4 + 600*a**3*tan(x/2)**3 + 360*a**3*tan(x/2)**2 + 150*a**3*tan(x/2) + 30*a**3) + 195*x/(30*a**3*tan(x/2)**9 + 150*a**3*tan(x/2)**8 + 360*a**3*tan(x/2)**7 + 600*a**3*tan(x/2)**6 + 780*a**3*tan(x/2)**5 + 780*a**3*tan(x/2)**4 + 600*a**3*tan(x/2)**3 + 360*a**3*tan(x/2)**2 + 150*a**3*tan(x/2) + 30*a**3) + 390*tan(x/2)**8/(30*a**3*tan(x/2)**9 + 150*a**3*tan(x/2)**8 + 360*a**3*tan(x/2)**7 + 600*a**3*tan(x/2)**6 + 780*a**3*tan(x/2)**5 + 780*a**3*tan(x/2)**4 + 600*a**3*tan(x/2)**3 + 360*a**3*tan(x/2)**2 + 150*a**3*tan(x/2) + 30*a**3) + 1950*tan(x/2)**7/(30*a**3*tan(x/2)**9 + 150*a**3*tan(x/2)**8 + 360*a**3*tan(x/2)**7 + 600*a**3*tan(x/2)**6 + 780*a**3*tan(x/2)**5 + 780*a**3*tan(x/2)**4 + 600*a**3*tan(x/2)**3 + 360*a**3*tan(x/2)**2 + 150*a**3*tan(x/2) + 30*a**3) + 4550*tan(x/2)**6/(30*a**3*tan(x/2)**9 + 150*a**3*tan(x/2)**8 + 360*a**3*tan(x/2)**7 + 600*a**3*tan(x/2)**6 + 780*a**3*tan(x/2)**5 + 780*a**3*tan(x/2)**4 + 600*a**3*tan(x/2)**3 + 360*a**3*tan(x/2)**2 + 150*a**3*tan(x/2) + 30*a**3) + 7150*tan(x/2)**5/(30*a**3*tan(x/2)**9 + 150*a**3*tan(x/2)**8 + 360*a**3*tan(x/2)**7 + 600*a**3*tan(x/2)**6 + 780*a**3*tan(x/2)**5 + 780*a**3*tan(x/2)**4 + 600*a**3*tan(x/2)**3 + 360*a**3*tan(x/2)**2 + 150*a**3*tan(x/2) + 30*a**3) + 8658*tan(x/2)**4/(30*a**3*tan(x/2)**9 + 150*a**3*tan(x/2)**8 + 360*a**3*tan(x/2)**7 + 600*a**3*tan(x/2)**6 + 780*a**3*tan(x/2)**5 + 780*a**3*tan(x/2)**4 + 600*a**3*tan(x/2)**3 + 360*a**3*tan(x/2)**2 + 150*a**3*tan(x/2) + 30*a**3) + 7610*tan(x/2)**3/(30*a**3*tan(x/2)**9 + 150*a**3*tan(x/2)**8 + 360*a**3*tan(x/2)**7 + 600*a**3*tan(x/2)**6 + 780*a**3*tan(x/2)**5 + 780*a**3*tan(x/2)**4 + 600*a**3*tan(x/2)**3 + 360*a**3*tan(x/2)**2 + 150*a**3*tan(x/2) + 30*a**3) + 5346*tan(x/2)**2/(30*a**3*tan(x/2)**9 + 150*a**3*tan(x/2)**8 + 360*a**3*tan(x/2)**7 + 600*a**3*tan(x/2)**6 + 780*a**3*tan(x/2)**5 + 780*a**3*tan(x/2)**4 + 600*a**3*tan(x/2)**3 + 360*a**3*tan(x/2)**2 + 150*a**3*tan(x/2) + 30*a**3) + 2650*tan(x/2)/(30*a**3*tan(x/2)**9 + 150*a**3*tan(x/2)**8 + 360*a**3*tan(x/2)**7 + 600*a**3*tan(x/2)**6 + 780*a**3*tan(x/2)**5 + 780*a**3*tan(x/2)**4 + 600*a**3*tan(x/2)**3 + 360*a**3*tan(x/2)**2 + 150*a**3*tan(x/2) + 30*a**3) + 608/(30*a**3*tan(x/2)**9 + 150*a**3*tan(x/2)**8 + 360*a**3*tan(x/2)**7 + 600*a**3*tan(x/2)**6 + 780*a**3*tan(x/2)**5 + 780*a**3*tan(x/2)**4 + 600*a**3*tan(x/2)**3 + 360*a**3*tan(x/2)**2 + 150*a**3*tan(x/2) + 30*a**3)","B",0
23,1,1425,0,19.639972," ","integrate(sin(x)**4/(a+a*sin(x))**3,x)","- \frac{15 x \tan^{7}{\left(\frac{x}{2} \right)}}{5 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 25 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 55 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 55 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 25 a^{3} \tan{\left(\frac{x}{2} \right)} + 5 a^{3}} - \frac{75 x \tan^{6}{\left(\frac{x}{2} \right)}}{5 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 25 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 55 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 55 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 25 a^{3} \tan{\left(\frac{x}{2} \right)} + 5 a^{3}} - \frac{165 x \tan^{5}{\left(\frac{x}{2} \right)}}{5 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 25 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 55 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 55 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 25 a^{3} \tan{\left(\frac{x}{2} \right)} + 5 a^{3}} - \frac{225 x \tan^{4}{\left(\frac{x}{2} \right)}}{5 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 25 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 55 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 55 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 25 a^{3} \tan{\left(\frac{x}{2} \right)} + 5 a^{3}} - \frac{225 x \tan^{3}{\left(\frac{x}{2} \right)}}{5 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 25 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 55 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 55 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 25 a^{3} \tan{\left(\frac{x}{2} \right)} + 5 a^{3}} - \frac{165 x \tan^{2}{\left(\frac{x}{2} \right)}}{5 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 25 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 55 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 55 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 25 a^{3} \tan{\left(\frac{x}{2} \right)} + 5 a^{3}} - \frac{75 x \tan{\left(\frac{x}{2} \right)}}{5 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 25 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 55 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 55 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 25 a^{3} \tan{\left(\frac{x}{2} \right)} + 5 a^{3}} - \frac{15 x}{5 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 25 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 55 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 55 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 25 a^{3} \tan{\left(\frac{x}{2} \right)} + 5 a^{3}} - \frac{30 \tan^{6}{\left(\frac{x}{2} \right)}}{5 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 25 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 55 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 55 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 25 a^{3} \tan{\left(\frac{x}{2} \right)} + 5 a^{3}} - \frac{150 \tan^{5}{\left(\frac{x}{2} \right)}}{5 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 25 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 55 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 55 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 25 a^{3} \tan{\left(\frac{x}{2} \right)} + 5 a^{3}} - \frac{320 \tan^{4}{\left(\frac{x}{2} \right)}}{5 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 25 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 55 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 55 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 25 a^{3} \tan{\left(\frac{x}{2} \right)} + 5 a^{3}} - \frac{400 \tan^{3}{\left(\frac{x}{2} \right)}}{5 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 25 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 55 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 55 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 25 a^{3} \tan{\left(\frac{x}{2} \right)} + 5 a^{3}} - \frac{378 \tan^{2}{\left(\frac{x}{2} \right)}}{5 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 25 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 55 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 55 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 25 a^{3} \tan{\left(\frac{x}{2} \right)} + 5 a^{3}} - \frac{210 \tan{\left(\frac{x}{2} \right)}}{5 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 25 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 55 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 55 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 25 a^{3} \tan{\left(\frac{x}{2} \right)} + 5 a^{3}} - \frac{48}{5 a^{3} \tan^{7}{\left(\frac{x}{2} \right)} + 25 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} + 55 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 55 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 25 a^{3} \tan{\left(\frac{x}{2} \right)} + 5 a^{3}}"," ",0,"-15*x*tan(x/2)**7/(5*a**3*tan(x/2)**7 + 25*a**3*tan(x/2)**6 + 55*a**3*tan(x/2)**5 + 75*a**3*tan(x/2)**4 + 75*a**3*tan(x/2)**3 + 55*a**3*tan(x/2)**2 + 25*a**3*tan(x/2) + 5*a**3) - 75*x*tan(x/2)**6/(5*a**3*tan(x/2)**7 + 25*a**3*tan(x/2)**6 + 55*a**3*tan(x/2)**5 + 75*a**3*tan(x/2)**4 + 75*a**3*tan(x/2)**3 + 55*a**3*tan(x/2)**2 + 25*a**3*tan(x/2) + 5*a**3) - 165*x*tan(x/2)**5/(5*a**3*tan(x/2)**7 + 25*a**3*tan(x/2)**6 + 55*a**3*tan(x/2)**5 + 75*a**3*tan(x/2)**4 + 75*a**3*tan(x/2)**3 + 55*a**3*tan(x/2)**2 + 25*a**3*tan(x/2) + 5*a**3) - 225*x*tan(x/2)**4/(5*a**3*tan(x/2)**7 + 25*a**3*tan(x/2)**6 + 55*a**3*tan(x/2)**5 + 75*a**3*tan(x/2)**4 + 75*a**3*tan(x/2)**3 + 55*a**3*tan(x/2)**2 + 25*a**3*tan(x/2) + 5*a**3) - 225*x*tan(x/2)**3/(5*a**3*tan(x/2)**7 + 25*a**3*tan(x/2)**6 + 55*a**3*tan(x/2)**5 + 75*a**3*tan(x/2)**4 + 75*a**3*tan(x/2)**3 + 55*a**3*tan(x/2)**2 + 25*a**3*tan(x/2) + 5*a**3) - 165*x*tan(x/2)**2/(5*a**3*tan(x/2)**7 + 25*a**3*tan(x/2)**6 + 55*a**3*tan(x/2)**5 + 75*a**3*tan(x/2)**4 + 75*a**3*tan(x/2)**3 + 55*a**3*tan(x/2)**2 + 25*a**3*tan(x/2) + 5*a**3) - 75*x*tan(x/2)/(5*a**3*tan(x/2)**7 + 25*a**3*tan(x/2)**6 + 55*a**3*tan(x/2)**5 + 75*a**3*tan(x/2)**4 + 75*a**3*tan(x/2)**3 + 55*a**3*tan(x/2)**2 + 25*a**3*tan(x/2) + 5*a**3) - 15*x/(5*a**3*tan(x/2)**7 + 25*a**3*tan(x/2)**6 + 55*a**3*tan(x/2)**5 + 75*a**3*tan(x/2)**4 + 75*a**3*tan(x/2)**3 + 55*a**3*tan(x/2)**2 + 25*a**3*tan(x/2) + 5*a**3) - 30*tan(x/2)**6/(5*a**3*tan(x/2)**7 + 25*a**3*tan(x/2)**6 + 55*a**3*tan(x/2)**5 + 75*a**3*tan(x/2)**4 + 75*a**3*tan(x/2)**3 + 55*a**3*tan(x/2)**2 + 25*a**3*tan(x/2) + 5*a**3) - 150*tan(x/2)**5/(5*a**3*tan(x/2)**7 + 25*a**3*tan(x/2)**6 + 55*a**3*tan(x/2)**5 + 75*a**3*tan(x/2)**4 + 75*a**3*tan(x/2)**3 + 55*a**3*tan(x/2)**2 + 25*a**3*tan(x/2) + 5*a**3) - 320*tan(x/2)**4/(5*a**3*tan(x/2)**7 + 25*a**3*tan(x/2)**6 + 55*a**3*tan(x/2)**5 + 75*a**3*tan(x/2)**4 + 75*a**3*tan(x/2)**3 + 55*a**3*tan(x/2)**2 + 25*a**3*tan(x/2) + 5*a**3) - 400*tan(x/2)**3/(5*a**3*tan(x/2)**7 + 25*a**3*tan(x/2)**6 + 55*a**3*tan(x/2)**5 + 75*a**3*tan(x/2)**4 + 75*a**3*tan(x/2)**3 + 55*a**3*tan(x/2)**2 + 25*a**3*tan(x/2) + 5*a**3) - 378*tan(x/2)**2/(5*a**3*tan(x/2)**7 + 25*a**3*tan(x/2)**6 + 55*a**3*tan(x/2)**5 + 75*a**3*tan(x/2)**4 + 75*a**3*tan(x/2)**3 + 55*a**3*tan(x/2)**2 + 25*a**3*tan(x/2) + 5*a**3) - 210*tan(x/2)/(5*a**3*tan(x/2)**7 + 25*a**3*tan(x/2)**6 + 55*a**3*tan(x/2)**5 + 75*a**3*tan(x/2)**4 + 75*a**3*tan(x/2)**3 + 55*a**3*tan(x/2)**2 + 25*a**3*tan(x/2) + 5*a**3) - 48/(5*a**3*tan(x/2)**7 + 25*a**3*tan(x/2)**6 + 55*a**3*tan(x/2)**5 + 75*a**3*tan(x/2)**4 + 75*a**3*tan(x/2)**3 + 55*a**3*tan(x/2)**2 + 25*a**3*tan(x/2) + 5*a**3)","B",0
24,1,777,0,11.815420," ","integrate(sin(x)**3/(a+a*sin(x))**3,x)","\frac{15 x \tan^{5}{\left(\frac{x}{2} \right)}}{15 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan{\left(\frac{x}{2} \right)} + 15 a^{3}} + \frac{75 x \tan^{4}{\left(\frac{x}{2} \right)}}{15 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan{\left(\frac{x}{2} \right)} + 15 a^{3}} + \frac{150 x \tan^{3}{\left(\frac{x}{2} \right)}}{15 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan{\left(\frac{x}{2} \right)} + 15 a^{3}} + \frac{150 x \tan^{2}{\left(\frac{x}{2} \right)}}{15 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan{\left(\frac{x}{2} \right)} + 15 a^{3}} + \frac{75 x \tan{\left(\frac{x}{2} \right)}}{15 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan{\left(\frac{x}{2} \right)} + 15 a^{3}} + \frac{15 x}{15 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan{\left(\frac{x}{2} \right)} + 15 a^{3}} + \frac{30 \tan^{4}{\left(\frac{x}{2} \right)}}{15 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan{\left(\frac{x}{2} \right)} + 15 a^{3}} + \frac{150 \tan^{3}{\left(\frac{x}{2} \right)}}{15 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan{\left(\frac{x}{2} \right)} + 15 a^{3}} + \frac{290 \tan^{2}{\left(\frac{x}{2} \right)}}{15 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan{\left(\frac{x}{2} \right)} + 15 a^{3}} + \frac{190 \tan{\left(\frac{x}{2} \right)}}{15 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan{\left(\frac{x}{2} \right)} + 15 a^{3}} + \frac{44}{15 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan{\left(\frac{x}{2} \right)} + 15 a^{3}}"," ",0,"15*x*tan(x/2)**5/(15*a**3*tan(x/2)**5 + 75*a**3*tan(x/2)**4 + 150*a**3*tan(x/2)**3 + 150*a**3*tan(x/2)**2 + 75*a**3*tan(x/2) + 15*a**3) + 75*x*tan(x/2)**4/(15*a**3*tan(x/2)**5 + 75*a**3*tan(x/2)**4 + 150*a**3*tan(x/2)**3 + 150*a**3*tan(x/2)**2 + 75*a**3*tan(x/2) + 15*a**3) + 150*x*tan(x/2)**3/(15*a**3*tan(x/2)**5 + 75*a**3*tan(x/2)**4 + 150*a**3*tan(x/2)**3 + 150*a**3*tan(x/2)**2 + 75*a**3*tan(x/2) + 15*a**3) + 150*x*tan(x/2)**2/(15*a**3*tan(x/2)**5 + 75*a**3*tan(x/2)**4 + 150*a**3*tan(x/2)**3 + 150*a**3*tan(x/2)**2 + 75*a**3*tan(x/2) + 15*a**3) + 75*x*tan(x/2)/(15*a**3*tan(x/2)**5 + 75*a**3*tan(x/2)**4 + 150*a**3*tan(x/2)**3 + 150*a**3*tan(x/2)**2 + 75*a**3*tan(x/2) + 15*a**3) + 15*x/(15*a**3*tan(x/2)**5 + 75*a**3*tan(x/2)**4 + 150*a**3*tan(x/2)**3 + 150*a**3*tan(x/2)**2 + 75*a**3*tan(x/2) + 15*a**3) + 30*tan(x/2)**4/(15*a**3*tan(x/2)**5 + 75*a**3*tan(x/2)**4 + 150*a**3*tan(x/2)**3 + 150*a**3*tan(x/2)**2 + 75*a**3*tan(x/2) + 15*a**3) + 150*tan(x/2)**3/(15*a**3*tan(x/2)**5 + 75*a**3*tan(x/2)**4 + 150*a**3*tan(x/2)**3 + 150*a**3*tan(x/2)**2 + 75*a**3*tan(x/2) + 15*a**3) + 290*tan(x/2)**2/(15*a**3*tan(x/2)**5 + 75*a**3*tan(x/2)**4 + 150*a**3*tan(x/2)**3 + 150*a**3*tan(x/2)**2 + 75*a**3*tan(x/2) + 15*a**3) + 190*tan(x/2)/(15*a**3*tan(x/2)**5 + 75*a**3*tan(x/2)**4 + 150*a**3*tan(x/2)**3 + 150*a**3*tan(x/2)**2 + 75*a**3*tan(x/2) + 15*a**3) + 44/(15*a**3*tan(x/2)**5 + 75*a**3*tan(x/2)**4 + 150*a**3*tan(x/2)**3 + 150*a**3*tan(x/2)**2 + 75*a**3*tan(x/2) + 15*a**3)","B",0
25,1,206,0,6.920543," ","integrate(sin(x)**2/(a+a*sin(x))**3,x)","- \frac{40 \tan^{2}{\left(\frac{x}{2} \right)}}{15 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan{\left(\frac{x}{2} \right)} + 15 a^{3}} - \frac{20 \tan{\left(\frac{x}{2} \right)}}{15 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan{\left(\frac{x}{2} \right)} + 15 a^{3}} - \frac{4}{15 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan{\left(\frac{x}{2} \right)} + 15 a^{3}}"," ",0,"-40*tan(x/2)**2/(15*a**3*tan(x/2)**5 + 75*a**3*tan(x/2)**4 + 150*a**3*tan(x/2)**3 + 150*a**3*tan(x/2)**2 + 75*a**3*tan(x/2) + 15*a**3) - 20*tan(x/2)/(15*a**3*tan(x/2)**5 + 75*a**3*tan(x/2)**4 + 150*a**3*tan(x/2)**3 + 150*a**3*tan(x/2)**2 + 75*a**3*tan(x/2) + 15*a**3) - 4/(15*a**3*tan(x/2)**5 + 75*a**3*tan(x/2)**4 + 150*a**3*tan(x/2)**3 + 150*a**3*tan(x/2)**2 + 75*a**3*tan(x/2) + 15*a**3)","B",0
26,1,277,0,4.740700," ","integrate(sin(x)/(a+a*sin(x))**3,x)","- \frac{10 \tan^{3}{\left(\frac{x}{2} \right)}}{5 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 25 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 50 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 50 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 25 a^{3} \tan{\left(\frac{x}{2} \right)} + 5 a^{3}} - \frac{10 \tan^{2}{\left(\frac{x}{2} \right)}}{5 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 25 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 50 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 50 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 25 a^{3} \tan{\left(\frac{x}{2} \right)} + 5 a^{3}} - \frac{10 \tan{\left(\frac{x}{2} \right)}}{5 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 25 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 50 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 50 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 25 a^{3} \tan{\left(\frac{x}{2} \right)} + 5 a^{3}} - \frac{2}{5 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 25 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 50 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 50 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 25 a^{3} \tan{\left(\frac{x}{2} \right)} + 5 a^{3}}"," ",0,"-10*tan(x/2)**3/(5*a**3*tan(x/2)**5 + 25*a**3*tan(x/2)**4 + 50*a**3*tan(x/2)**3 + 50*a**3*tan(x/2)**2 + 25*a**3*tan(x/2) + 5*a**3) - 10*tan(x/2)**2/(5*a**3*tan(x/2)**5 + 25*a**3*tan(x/2)**4 + 50*a**3*tan(x/2)**3 + 50*a**3*tan(x/2)**2 + 25*a**3*tan(x/2) + 5*a**3) - 10*tan(x/2)/(5*a**3*tan(x/2)**5 + 25*a**3*tan(x/2)**4 + 50*a**3*tan(x/2)**3 + 50*a**3*tan(x/2)**2 + 25*a**3*tan(x/2) + 5*a**3) - 2/(5*a**3*tan(x/2)**5 + 25*a**3*tan(x/2)**4 + 50*a**3*tan(x/2)**3 + 50*a**3*tan(x/2)**2 + 25*a**3*tan(x/2) + 5*a**3)","B",0
27,1,348,0,2.225804," ","integrate(1/(a+a*sin(x))**3,x)","- \frac{30 \tan^{4}{\left(\frac{x}{2} \right)}}{15 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan{\left(\frac{x}{2} \right)} + 15 a^{3}} - \frac{60 \tan^{3}{\left(\frac{x}{2} \right)}}{15 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan{\left(\frac{x}{2} \right)} + 15 a^{3}} - \frac{80 \tan^{2}{\left(\frac{x}{2} \right)}}{15 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan{\left(\frac{x}{2} \right)} + 15 a^{3}} - \frac{40 \tan{\left(\frac{x}{2} \right)}}{15 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan{\left(\frac{x}{2} \right)} + 15 a^{3}} - \frac{14}{15 a^{3} \tan^{5}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{3}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan{\left(\frac{x}{2} \right)} + 15 a^{3}}"," ",0,"-30*tan(x/2)**4/(15*a**3*tan(x/2)**5 + 75*a**3*tan(x/2)**4 + 150*a**3*tan(x/2)**3 + 150*a**3*tan(x/2)**2 + 75*a**3*tan(x/2) + 15*a**3) - 60*tan(x/2)**3/(15*a**3*tan(x/2)**5 + 75*a**3*tan(x/2)**4 + 150*a**3*tan(x/2)**3 + 150*a**3*tan(x/2)**2 + 75*a**3*tan(x/2) + 15*a**3) - 80*tan(x/2)**2/(15*a**3*tan(x/2)**5 + 75*a**3*tan(x/2)**4 + 150*a**3*tan(x/2)**3 + 150*a**3*tan(x/2)**2 + 75*a**3*tan(x/2) + 15*a**3) - 40*tan(x/2)/(15*a**3*tan(x/2)**5 + 75*a**3*tan(x/2)**4 + 150*a**3*tan(x/2)**3 + 150*a**3*tan(x/2)**2 + 75*a**3*tan(x/2) + 15*a**3) - 14/(15*a**3*tan(x/2)**5 + 75*a**3*tan(x/2)**4 + 150*a**3*tan(x/2)**3 + 150*a**3*tan(x/2)**2 + 75*a**3*tan(x/2) + 15*a**3)","B",0
28,0,0,0,0.000000," ","integrate(csc(x)/(a+a*sin(x))**3,x)","\frac{\int \frac{\csc{\left(x \right)}}{\sin^{3}{\left(x \right)} + 3 \sin^{2}{\left(x \right)} + 3 \sin{\left(x \right)} + 1}\, dx}{a^{3}}"," ",0,"Integral(csc(x)/(sin(x)**3 + 3*sin(x)**2 + 3*sin(x) + 1), x)/a**3","F",0
29,0,0,0,0.000000," ","integrate(csc(x)**2/(a+a*sin(x))**3,x)","\frac{\int \frac{\csc^{2}{\left(x \right)}}{\sin^{3}{\left(x \right)} + 3 \sin^{2}{\left(x \right)} + 3 \sin{\left(x \right)} + 1}\, dx}{a^{3}}"," ",0,"Integral(csc(x)**2/(sin(x)**3 + 3*sin(x)**2 + 3*sin(x) + 1), x)/a**3","F",0
30,0,0,0,0.000000," ","integrate(csc(x)**3/(a+a*sin(x))**3,x)","\frac{\int \frac{\csc^{3}{\left(x \right)}}{\sin^{3}{\left(x \right)} + 3 \sin^{2}{\left(x \right)} + 3 \sin{\left(x \right)} + 1}\, dx}{a^{3}}"," ",0,"Integral(csc(x)**3/(sin(x)**3 + 3*sin(x)**2 + 3*sin(x) + 1), x)/a**3","F",0
31,0,0,0,0.000000," ","integrate(csc(x)**4/(a+a*sin(x))**3,x)","\frac{\int \frac{\csc^{4}{\left(x \right)}}{\sin^{3}{\left(x \right)} + 3 \sin^{2}{\left(x \right)} + 3 \sin{\left(x \right)} + 1}\, dx}{a^{3}}"," ",0,"Integral(csc(x)**4/(sin(x)**3 + 3*sin(x)**2 + 3*sin(x) + 1), x)/a**3","F",0
32,0,0,0,0.000000," ","integrate(sin(d*x+c)**4*(a+a*sin(d*x+c))**(1/2),x)","\int \sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)} \sin^{4}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a*(sin(c + d*x) + 1))*sin(c + d*x)**4, x)","F",0
33,-1,0,0,0.000000," ","integrate(sin(d*x+c)**3*(a+a*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
34,0,0,0,0.000000," ","integrate(sin(d*x+c)**2*(a+a*sin(d*x+c))**(1/2),x)","\int \sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)} \sin^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a*(sin(c + d*x) + 1))*sin(c + d*x)**2, x)","F",0
35,0,0,0,0.000000," ","integrate(sin(d*x+c)*(a+a*sin(d*x+c))**(1/2),x)","\int \sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)} \sin{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a*(sin(c + d*x) + 1))*sin(c + d*x), x)","F",0
36,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**(1/2),x)","\int \sqrt{a \sin{\left(c + d x \right)} + a}\, dx"," ",0,"Integral(sqrt(a*sin(c + d*x) + a), x)","F",0
37,0,0,0,0.000000," ","integrate(csc(d*x+c)*(a+a*sin(d*x+c))**(1/2),x)","\int \sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)} \csc{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a*(sin(c + d*x) + 1))*csc(c + d*x), x)","F",0
38,0,0,0,0.000000," ","integrate(csc(d*x+c)**2*(a+a*sin(d*x+c))**(1/2),x)","\int \sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)} \csc^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a*(sin(c + d*x) + 1))*csc(c + d*x)**2, x)","F",0
39,0,0,0,0.000000," ","integrate(csc(d*x+c)**3*(a+a*sin(d*x+c))**(1/2),x)","\int \sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)} \csc^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a*(sin(c + d*x) + 1))*csc(c + d*x)**3, x)","F",0
40,0,0,0,0.000000," ","integrate(csc(d*x+c)**4*(a+a*sin(d*x+c))**(1/2),x)","\int \sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)} \csc^{4}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a*(sin(c + d*x) + 1))*csc(c + d*x)**4, x)","F",0
41,0,0,0,0.000000," ","integrate(csc(d*x+c)*(a-a*sin(d*x+c))**(1/2),x)","\int \sqrt{- a \left(\sin{\left(c + d x \right)} - 1\right)} \csc{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(-a*(sin(c + d*x) - 1))*csc(c + d*x), x)","F",0
42,0,0,0,0.000000," ","integrate(csc(d*x+c)*(-a+a*sin(d*x+c))**(1/2),x)","\int \sqrt{a \left(\sin{\left(c + d x \right)} - 1\right)} \csc{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a*(sin(c + d*x) - 1))*csc(c + d*x), x)","F",0
43,0,0,0,0.000000," ","integrate(csc(d*x+c)*(-a-a*sin(d*x+c))**(1/2),x)","\int \sqrt{- a \left(\sin{\left(c + d x \right)} + 1\right)} \csc{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(-a*(sin(c + d*x) + 1))*csc(c + d*x), x)","F",0
44,-1,0,0,0.000000," ","integrate(sin(d*x+c)**3*(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
45,0,0,0,0.000000," ","integrate(sin(d*x+c)**2*(a+a*sin(d*x+c))**(3/2),x)","\int \left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}} \sin^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((a*(sin(c + d*x) + 1))**(3/2)*sin(c + d*x)**2, x)","F",0
46,0,0,0,0.000000," ","integrate(sin(d*x+c)*(a+a*sin(d*x+c))**(3/2),x)","\int \left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}} \sin{\left(c + d x \right)}\, dx"," ",0,"Integral((a*(sin(c + d*x) + 1))**(3/2)*sin(c + d*x), x)","F",0
47,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**(3/2),x)","\int \left(a \sin{\left(c + d x \right)} + a\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a*sin(c + d*x) + a)**(3/2), x)","F",0
48,0,0,0,0.000000," ","integrate(csc(d*x+c)*(a+a*sin(d*x+c))**(3/2),x)","\int \left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}} \csc{\left(c + d x \right)}\, dx"," ",0,"Integral((a*(sin(c + d*x) + 1))**(3/2)*csc(c + d*x), x)","F",0
49,-1,0,0,0.000000," ","integrate(csc(d*x+c)**2*(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
50,-1,0,0,0.000000," ","integrate(csc(d*x+c)**3*(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
51,-1,0,0,0.000000," ","integrate(csc(d*x+c)**4*(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
52,-1,0,0,0.000000," ","integrate(sin(d*x+c)**3*(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
53,-1,0,0,0.000000," ","integrate(sin(d*x+c)**2*(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
54,0,0,0,0.000000," ","integrate(sin(d*x+c)*(a+a*sin(d*x+c))**(5/2),x)","\int \left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{5}{2}} \sin{\left(c + d x \right)}\, dx"," ",0,"Integral((a*(sin(c + d*x) + 1))**(5/2)*sin(c + d*x), x)","F",0
55,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**(5/2),x)","\int \left(a \sin{\left(c + d x \right)} + a\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a*sin(c + d*x) + a)**(5/2), x)","F",0
56,-1,0,0,0.000000," ","integrate(csc(d*x+c)*(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
57,-1,0,0,0.000000," ","integrate(csc(d*x+c)**2*(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
58,-1,0,0,0.000000," ","integrate(csc(d*x+c)**3*(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
59,-1,0,0,0.000000," ","integrate(csc(d*x+c)**4*(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
60,-1,0,0,0.000000," ","integrate(csc(d*x+c)**5*(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
61,-1,0,0,0.000000," ","integrate(sin(d*x+c)**3/(a+a*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
62,0,0,0,0.000000," ","integrate(sin(d*x+c)**2/(a+a*sin(d*x+c))**(1/2),x)","\int \frac{\sin^{2}{\left(c + d x \right)}}{\sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral(sin(c + d*x)**2/sqrt(a*(sin(c + d*x) + 1)), x)","F",0
63,0,0,0,0.000000," ","integrate(sin(d*x+c)/(a+a*sin(d*x+c))**(1/2),x)","\int \frac{\sin{\left(c + d x \right)}}{\sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral(sin(c + d*x)/sqrt(a*(sin(c + d*x) + 1)), x)","F",0
64,0,0,0,0.000000," ","integrate(1/(a+a*sin(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{a \sin{\left(c + d x \right)} + a}}\, dx"," ",0,"Integral(1/sqrt(a*sin(c + d*x) + a), x)","F",0
65,0,0,0,0.000000," ","integrate(csc(d*x+c)/(a+a*sin(d*x+c))**(1/2),x)","\int \frac{\csc{\left(c + d x \right)}}{\sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral(csc(c + d*x)/sqrt(a*(sin(c + d*x) + 1)), x)","F",0
66,0,0,0,0.000000," ","integrate(csc(d*x+c)**2/(a+a*sin(d*x+c))**(1/2),x)","\int \frac{\csc^{2}{\left(c + d x \right)}}{\sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral(csc(c + d*x)**2/sqrt(a*(sin(c + d*x) + 1)), x)","F",0
67,0,0,0,0.000000," ","integrate(csc(d*x+c)**3/(a+a*sin(d*x+c))**(1/2),x)","\int \frac{\csc^{3}{\left(c + d x \right)}}{\sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral(csc(c + d*x)**3/sqrt(a*(sin(c + d*x) + 1)), x)","F",0
68,0,0,0,0.000000," ","integrate(sin(d*x+c)**4/(a+a*sin(d*x+c))**(3/2),x)","\int \frac{\sin^{4}{\left(c + d x \right)}}{\left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sin(c + d*x)**4/(a*(sin(c + d*x) + 1))**(3/2), x)","F",0
69,-1,0,0,0.000000," ","integrate(sin(d*x+c)**3/(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
70,0,0,0,0.000000," ","integrate(sin(d*x+c)**2/(a+a*sin(d*x+c))**(3/2),x)","\int \frac{\sin^{2}{\left(c + d x \right)}}{\left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sin(c + d*x)**2/(a*(sin(c + d*x) + 1))**(3/2), x)","F",0
71,0,0,0,0.000000," ","integrate(sin(d*x+c)/(a+a*sin(d*x+c))**(3/2),x)","\int \frac{\sin{\left(c + d x \right)}}{\left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sin(c + d*x)/(a*(sin(c + d*x) + 1))**(3/2), x)","F",0
72,0,0,0,0.000000," ","integrate(1/(a+a*sin(d*x+c))**(3/2),x)","\int \frac{1}{\left(a \sin{\left(c + d x \right)} + a\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a*sin(c + d*x) + a)**(-3/2), x)","F",0
73,0,0,0,0.000000," ","integrate(csc(d*x+c)/(a+a*sin(d*x+c))**(3/2),x)","\int \frac{\csc{\left(c + d x \right)}}{\left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(csc(c + d*x)/(a*(sin(c + d*x) + 1))**(3/2), x)","F",0
74,0,0,0,0.000000," ","integrate(csc(d*x+c)**2/(a+a*sin(d*x+c))**(3/2),x)","\int \frac{\csc^{2}{\left(c + d x \right)}}{\left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(csc(c + d*x)**2/(a*(sin(c + d*x) + 1))**(3/2), x)","F",0
75,0,0,0,0.000000," ","integrate(csc(d*x+c)**3/(a+a*sin(d*x+c))**(3/2),x)","\int \frac{\csc^{3}{\left(c + d x \right)}}{\left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(csc(c + d*x)**3/(a*(sin(c + d*x) + 1))**(3/2), x)","F",0
76,-1,0,0,0.000000," ","integrate(sin(d*x+c)**5/(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
77,-1,0,0,0.000000," ","integrate(sin(d*x+c)**4/(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
78,-1,0,0,0.000000," ","integrate(sin(d*x+c)**3/(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
79,0,0,0,0.000000," ","integrate(sin(d*x+c)**2/(a+a*sin(d*x+c))**(5/2),x)","\int \frac{\sin^{2}{\left(c + d x \right)}}{\left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sin(c + d*x)**2/(a*(sin(c + d*x) + 1))**(5/2), x)","F",0
80,0,0,0,0.000000," ","integrate(sin(d*x+c)/(a+a*sin(d*x+c))**(5/2),x)","\int \frac{\sin{\left(c + d x \right)}}{\left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sin(c + d*x)/(a*(sin(c + d*x) + 1))**(5/2), x)","F",0
81,0,0,0,0.000000," ","integrate(1/(a+a*sin(d*x+c))**(5/2),x)","\int \frac{1}{\left(a \sin{\left(c + d x \right)} + a\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a*sin(c + d*x) + a)**(-5/2), x)","F",0
82,0,0,0,0.000000," ","integrate(csc(d*x+c)/(a+a*sin(d*x+c))**(5/2),x)","\int \frac{\csc{\left(c + d x \right)}}{\left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(csc(c + d*x)/(a*(sin(c + d*x) + 1))**(5/2), x)","F",0
83,0,0,0,0.000000," ","integrate(csc(d*x+c)**2/(a+a*sin(d*x+c))**(5/2),x)","\int \frac{\csc^{2}{\left(c + d x \right)}}{\left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(csc(c + d*x)**2/(a*(sin(c + d*x) + 1))**(5/2), x)","F",0
84,0,0,0,0.000000," ","integrate(csc(d*x+c)**3/(a+a*sin(d*x+c))**(5/2),x)","\int \frac{\csc^{3}{\left(c + d x \right)}}{\left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(csc(c + d*x)**3/(a*(sin(c + d*x) + 1))**(5/2), x)","F",0
85,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(1/2)/sin(f*x+e)**(1/2),x)","\int \frac{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)}}{\sqrt{\sin{\left(e + f x \right)}}}\, dx"," ",0,"Integral(sqrt(a*(sin(e + f*x) + 1))/sqrt(sin(e + f*x)), x)","F",0
86,0,0,0,0.000000," ","integrate((a-a*sin(f*x+e))**(1/2)/(-sin(f*x+e))**(1/2),x)","\int \frac{\sqrt{- a \left(\sin{\left(e + f x \right)} - 1\right)}}{\sqrt{- \sin{\left(e + f x \right)}}}\, dx"," ",0,"Integral(sqrt(-a*(sin(e + f*x) - 1))/sqrt(-sin(e + f*x)), x)","F",0
87,0,0,0,0.000000," ","integrate(1/sin(x)**(1/2)/(1+sin(x))**(1/2),x)","\int \frac{1}{\sqrt{\sin{\left(x \right)} + 1} \sqrt{\sin{\left(x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(sin(x) + 1)*sqrt(sin(x))), x)","F",0
88,0,0,0,0.000000," ","integrate(1/sin(x)**(1/2)/(a+a*sin(x))**(1/2),x)","\int \frac{1}{\sqrt{a \left(\sin{\left(x \right)} + 1\right)} \sqrt{\sin{\left(x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(a*(sin(x) + 1))*sqrt(sin(x))), x)","F",0
89,0,0,0,0.000000," ","integrate(1/(1-sin(x))**(1/2)/sin(x)**(1/2),x)","\int \frac{1}{\sqrt{1 - \sin{\left(x \right)}} \sqrt{\sin{\left(x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(1 - sin(x))*sqrt(sin(x))), x)","F",0
90,0,0,0,0.000000," ","integrate(1/sin(x)**(1/2)/(a-a*sin(x))**(1/2),x)","\int \frac{1}{\sqrt{- a \left(\sin{\left(x \right)} - 1\right)} \sqrt{\sin{\left(x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(-a*(sin(x) - 1))*sqrt(sin(x))), x)","F",0
91,0,0,0,0.000000," ","integrate(sin(d*x+c)**(1/3)/(a+a*sin(d*x+c))**2,x)","\frac{\int \frac{\sqrt[3]{\sin{\left(c + d x \right)}}}{\sin^{2}{\left(c + d x \right)} + 2 \sin{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral(sin(c + d*x)**(1/3)/(sin(c + d*x)**2 + 2*sin(c + d*x) + 1), x)/a**2","F",0
92,-1,0,0,0.000000," ","integrate(sin(d*x+c)**3*(a+a*sin(d*x+c))**(2/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
93,0,0,0,0.000000," ","integrate(sin(d*x+c)**2*(a+a*sin(d*x+c))**(2/3),x)","\int \left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{2}{3}} \sin^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((a*(sin(c + d*x) + 1))**(2/3)*sin(c + d*x)**2, x)","F",0
94,0,0,0,0.000000," ","integrate(sin(d*x+c)*(a+a*sin(d*x+c))**(2/3),x)","\int \left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{2}{3}} \sin{\left(c + d x \right)}\, dx"," ",0,"Integral((a*(sin(c + d*x) + 1))**(2/3)*sin(c + d*x), x)","F",0
95,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**(2/3),x)","\int \left(a \sin{\left(c + d x \right)} + a\right)^{\frac{2}{3}}\, dx"," ",0,"Integral((a*sin(c + d*x) + a)**(2/3), x)","F",0
96,0,0,0,0.000000," ","integrate(csc(d*x+c)*(a+a*sin(d*x+c))**(2/3),x)","\int \left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{2}{3}} \csc{\left(c + d x \right)}\, dx"," ",0,"Integral((a*(sin(c + d*x) + 1))**(2/3)*csc(c + d*x), x)","F",0
97,0,0,0,0.000000," ","integrate(csc(d*x+c)**2*(a+a*sin(d*x+c))**(2/3),x)","\int \left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{2}{3}} \csc^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((a*(sin(c + d*x) + 1))**(2/3)*csc(c + d*x)**2, x)","F",0
98,-1,0,0,0.000000," ","integrate(sin(d*x+c)**3*(a+a*sin(d*x+c))**(4/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
99,0,0,0,0.000000," ","integrate(sin(d*x+c)**2*(a+a*sin(d*x+c))**(4/3),x)","\int \left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{4}{3}} \sin^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((a*(sin(c + d*x) + 1))**(4/3)*sin(c + d*x)**2, x)","F",0
100,0,0,0,0.000000," ","integrate(sin(d*x+c)*(a+a*sin(d*x+c))**(4/3),x)","\int \left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{4}{3}} \sin{\left(c + d x \right)}\, dx"," ",0,"Integral((a*(sin(c + d*x) + 1))**(4/3)*sin(c + d*x), x)","F",0
101,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**(4/3),x)","\int \left(a \sin{\left(c + d x \right)} + a\right)^{\frac{4}{3}}\, dx"," ",0,"Integral((a*sin(c + d*x) + a)**(4/3), x)","F",0
102,-1,0,0,0.000000," ","integrate(csc(d*x+c)*(a+a*sin(d*x+c))**(4/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
103,-1,0,0,0.000000," ","integrate(csc(d*x+c)**2*(a+a*sin(d*x+c))**(4/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
104,-1,0,0,0.000000," ","integrate(sin(d*x+c)**3/(a+a*sin(d*x+c))**(1/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
105,0,0,0,0.000000," ","integrate(sin(d*x+c)**2/(a+a*sin(d*x+c))**(1/3),x)","\int \frac{\sin^{2}{\left(c + d x \right)}}{\sqrt[3]{a \left(\sin{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral(sin(c + d*x)**2/(a*(sin(c + d*x) + 1))**(1/3), x)","F",0
106,0,0,0,0.000000," ","integrate(sin(d*x+c)/(a+a*sin(d*x+c))**(1/3),x)","\int \frac{\sin{\left(c + d x \right)}}{\sqrt[3]{a \left(\sin{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral(sin(c + d*x)/(a*(sin(c + d*x) + 1))**(1/3), x)","F",0
107,0,0,0,0.000000," ","integrate(1/(a+a*sin(d*x+c))**(1/3),x)","\int \frac{1}{\sqrt[3]{a \sin{\left(c + d x \right)} + a}}\, dx"," ",0,"Integral((a*sin(c + d*x) + a)**(-1/3), x)","F",0
108,0,0,0,0.000000," ","integrate(csc(d*x+c)/(a+a*sin(d*x+c))**(1/3),x)","\int \frac{\csc{\left(c + d x \right)}}{\sqrt[3]{a \left(\sin{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral(csc(c + d*x)/(a*(sin(c + d*x) + 1))**(1/3), x)","F",0
109,0,0,0,0.000000," ","integrate(csc(d*x+c)**2/(a+a*sin(d*x+c))**(1/3),x)","\int \frac{\csc^{2}{\left(c + d x \right)}}{\sqrt[3]{a \left(\sin{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral(csc(c + d*x)**2/(a*(sin(c + d*x) + 1))**(1/3), x)","F",0
110,-1,0,0,0.000000," ","integrate(sin(d*x+c)**3/(a+a*sin(d*x+c))**(4/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
111,0,0,0,0.000000," ","integrate(sin(d*x+c)**2/(a+a*sin(d*x+c))**(4/3),x)","\int \frac{\sin^{2}{\left(c + d x \right)}}{\left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral(sin(c + d*x)**2/(a*(sin(c + d*x) + 1))**(4/3), x)","F",0
112,0,0,0,0.000000," ","integrate(sin(d*x+c)/(a+a*sin(d*x+c))**(4/3),x)","\int \frac{\sin{\left(c + d x \right)}}{\left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral(sin(c + d*x)/(a*(sin(c + d*x) + 1))**(4/3), x)","F",0
113,0,0,0,0.000000," ","integrate(1/(a+a*sin(d*x+c))**(4/3),x)","\int \frac{1}{\left(a \sin{\left(c + d x \right)} + a\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral((a*sin(c + d*x) + a)**(-4/3), x)","F",0
114,0,0,0,0.000000," ","integrate(csc(d*x+c)/(a+a*sin(d*x+c))**(4/3),x)","\int \frac{\csc{\left(c + d x \right)}}{\left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral(csc(c + d*x)/(a*(sin(c + d*x) + 1))**(4/3), x)","F",0
115,0,0,0,0.000000," ","integrate(csc(d*x+c)**2/(a+a*sin(d*x+c))**(4/3),x)","\int \frac{\csc^{2}{\left(c + d x \right)}}{\left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral(csc(c + d*x)**2/(a*(sin(c + d*x) + 1))**(4/3), x)","F",0
116,0,0,0,0.000000," ","integrate(sin(f*x+e)**n*(1+sin(f*x+e))**(3/2),x)","\int \left(\sin{\left(e + f x \right)} + 1\right)^{\frac{3}{2}} \sin^{n}{\left(e + f x \right)}\, dx"," ",0,"Integral((sin(e + f*x) + 1)**(3/2)*sin(e + f*x)**n, x)","F",0
117,0,0,0,0.000000," ","integrate(sin(f*x+e)**n*(1+sin(f*x+e))**(1/2),x)","\int \sqrt{\sin{\left(e + f x \right)} + 1} \sin^{n}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(sin(e + f*x) + 1)*sin(e + f*x)**n, x)","F",0
118,0,0,0,0.000000," ","integrate(sin(f*x+e)**n/(1+sin(f*x+e))**(1/2),x)","\int \frac{\sin^{n}{\left(e + f x \right)}}{\sqrt{\sin{\left(e + f x \right)} + 1}}\, dx"," ",0,"Integral(sin(e + f*x)**n/sqrt(sin(e + f*x) + 1), x)","F",0
119,0,0,0,0.000000," ","integrate(sin(f*x+e)**n/(1+sin(f*x+e))**(3/2),x)","\int \frac{\sin^{n}{\left(e + f x \right)}}{\left(\sin{\left(e + f x \right)} + 1\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sin(e + f*x)**n/(sin(e + f*x) + 1)**(3/2), x)","F",0
120,0,0,0,0.000000," ","integrate(sin(f*x+e)**n*(a+a*sin(f*x+e))**(3/2),x)","\int \left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}} \sin^{n}{\left(e + f x \right)}\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**(3/2)*sin(e + f*x)**n, x)","F",0
121,0,0,0,0.000000," ","integrate(sin(f*x+e)**n*(a+a*sin(f*x+e))**(1/2),x)","\int \sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)} \sin^{n}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a*(sin(e + f*x) + 1))*sin(e + f*x)**n, x)","F",0
122,0,0,0,0.000000," ","integrate(sin(f*x+e)**n/(a+a*sin(f*x+e))**(1/2),x)","\int \frac{\sin^{n}{\left(e + f x \right)}}{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)}}\, dx"," ",0,"Integral(sin(e + f*x)**n/sqrt(a*(sin(e + f*x) + 1)), x)","F",0
123,0,0,0,0.000000," ","integrate(sin(f*x+e)**n/(a+a*sin(f*x+e))**(3/2),x)","\int \frac{\sin^{n}{\left(e + f x \right)}}{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sin(e + f*x)**n/(a*(sin(e + f*x) + 1))**(3/2), x)","F",0
124,0,0,0,0.000000," ","integrate((d*sin(f*x+e))**n*(1+sin(f*x+e))**(3/2),x)","\int \left(d \sin{\left(e + f x \right)}\right)^{n} \left(\sin{\left(e + f x \right)} + 1\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((d*sin(e + f*x))**n*(sin(e + f*x) + 1)**(3/2), x)","F",0
125,0,0,0,0.000000," ","integrate((d*sin(f*x+e))**n*(1+sin(f*x+e))**(1/2),x)","\int \left(d \sin{\left(e + f x \right)}\right)^{n} \sqrt{\sin{\left(e + f x \right)} + 1}\, dx"," ",0,"Integral((d*sin(e + f*x))**n*sqrt(sin(e + f*x) + 1), x)","F",0
126,0,0,0,0.000000," ","integrate((d*sin(f*x+e))**n/(1+sin(f*x+e))**(1/2),x)","\int \frac{\left(d \sin{\left(e + f x \right)}\right)^{n}}{\sqrt{\sin{\left(e + f x \right)} + 1}}\, dx"," ",0,"Integral((d*sin(e + f*x))**n/sqrt(sin(e + f*x) + 1), x)","F",0
127,0,0,0,0.000000," ","integrate((d*sin(f*x+e))**n/(1+sin(f*x+e))**(3/2),x)","\int \frac{\left(d \sin{\left(e + f x \right)}\right)^{n}}{\left(\sin{\left(e + f x \right)} + 1\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d*sin(e + f*x))**n/(sin(e + f*x) + 1)**(3/2), x)","F",0
128,0,0,0,0.000000," ","integrate((d*sin(f*x+e))**n*(a+a*sin(f*x+e))**(3/2),x)","\int \left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}} \left(d \sin{\left(e + f x \right)}\right)^{n}\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**(3/2)*(d*sin(e + f*x))**n, x)","F",0
129,0,0,0,0.000000," ","integrate((d*sin(f*x+e))**n*(a+a*sin(f*x+e))**(1/2),x)","\int \sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)} \left(d \sin{\left(e + f x \right)}\right)^{n}\, dx"," ",0,"Integral(sqrt(a*(sin(e + f*x) + 1))*(d*sin(e + f*x))**n, x)","F",0
130,0,0,0,0.000000," ","integrate((d*sin(f*x+e))**n/(a+a*sin(f*x+e))**(1/2),x)","\int \frac{\left(d \sin{\left(e + f x \right)}\right)^{n}}{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)}}\, dx"," ",0,"Integral((d*sin(e + f*x))**n/sqrt(a*(sin(e + f*x) + 1)), x)","F",0
131,0,0,0,0.000000," ","integrate((d*sin(f*x+e))**n/(a+a*sin(f*x+e))**(3/2),x)","\int \frac{\left(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((d*sin(e + f*x))**n/(a*(sin(e + f*x) + 1))**(3/2), x)","F",0
132,0,0,0,0.000000," ","integrate(sin(f*x+e)**n*(1+sin(f*x+e))**m,x)","\int \left(\sin{\left(e + f x \right)} + 1\right)^{m} \sin^{n}{\left(e + f x \right)}\, dx"," ",0,"Integral((sin(e + f*x) + 1)**m*sin(e + f*x)**n, x)","F",0
133,0,0,0,0.000000," ","integrate((1-sin(f*x+e))**m*(-sin(f*x+e))**n,x)","\int \left(- \sin{\left(e + f x \right)}\right)^{n} \left(1 - \sin{\left(e + f x \right)}\right)^{m}\, dx"," ",0,"Integral((-sin(e + f*x))**n*(1 - sin(e + f*x))**m, x)","F",0
134,0,0,0,0.000000," ","integrate((d*sin(f*x+e))**n*(1+sin(f*x+e))**m,x)","\int \left(d \sin{\left(e + f x \right)}\right)^{n} \left(\sin{\left(e + f x \right)} + 1\right)^{m}\, dx"," ",0,"Integral((d*sin(e + f*x))**n*(sin(e + f*x) + 1)**m, x)","F",0
135,0,0,0,0.000000," ","integrate((1-sin(f*x+e))**m*(d*sin(f*x+e))**n,x)","\int \left(d \sin{\left(e + f x \right)}\right)^{n} \left(1 - \sin{\left(e + f x \right)}\right)^{m}\, dx"," ",0,"Integral((d*sin(e + f*x))**n*(1 - sin(e + f*x))**m, x)","F",0
136,0,0,0,0.000000," ","integrate(sin(f*x+e)**n*(a+a*sin(f*x+e))**m,x)","\int \left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{m} \sin^{n}{\left(e + f x \right)}\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**m*sin(e + f*x)**n, x)","F",0
137,0,0,0,0.000000," ","integrate((-sin(f*x+e))**n*(a-a*sin(f*x+e))**m,x)","\int \left(- \sin{\left(e + f x \right)}\right)^{n} \left(- a \left(\sin{\left(e + f x \right)} - 1\right)\right)^{m}\, dx"," ",0,"Integral((-sin(e + f*x))**n*(-a*(sin(e + f*x) - 1))**m, x)","F",0
138,0,0,0,0.000000," ","integrate((d*sin(f*x+e))**n*(a+a*sin(f*x+e))**m,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}\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**m*(d*sin(e + f*x))**n, x)","F",0
139,0,0,0,0.000000," ","integrate((d*sin(f*x+e))**n*(a-a*sin(f*x+e))**m,x)","\int \left(d \sin{\left(e + f x \right)}\right)^{n} \left(- a \left(\sin{\left(e + f x \right)} - 1\right)\right)^{m}\, dx"," ",0,"Integral((d*sin(e + f*x))**n*(-a*(sin(e + f*x) - 1))**m, x)","F",0
140,0,0,0,0.000000," ","integrate(sin(d*x+c)**4*(a+a*sin(d*x+c))**n,x)","\int \left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{n} \sin^{4}{\left(c + d x \right)}\, dx"," ",0,"Integral((a*(sin(c + d*x) + 1))**n*sin(c + d*x)**4, x)","F",0
141,-1,0,0,0.000000," ","integrate(sin(d*x+c)**3*(a+a*sin(d*x+c))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
142,0,0,0,0.000000," ","integrate(sin(d*x+c)**2*(a+a*sin(d*x+c))**n,x)","\int \left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{n} \sin^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((a*(sin(c + d*x) + 1))**n*sin(c + d*x)**2, x)","F",0
143,0,0,0,0.000000," ","integrate(sin(d*x+c)*(a+a*sin(d*x+c))**n,x)","\int \left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{n} \sin{\left(c + d x \right)}\, dx"," ",0,"Integral((a*(sin(c + d*x) + 1))**n*sin(c + d*x), x)","F",0
144,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**n,x)","\int \left(a \sin{\left(c + d x \right)} + a\right)^{n}\, dx"," ",0,"Integral((a*sin(c + d*x) + a)**n, x)","F",0
145,0,0,0,0.000000," ","integrate(csc(d*x+c)*(a+a*sin(d*x+c))**n,x)","\int \left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{n} \csc{\left(c + d x \right)}\, dx"," ",0,"Integral((a*(sin(c + d*x) + 1))**n*csc(c + d*x), x)","F",0
146,0,0,0,0.000000," ","integrate(csc(d*x+c)**2*(a+a*sin(d*x+c))**n,x)","\int \left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{n} \csc^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((a*(sin(c + d*x) + 1))**n*csc(c + d*x)**2, x)","F",0
147,0,0,0,0.000000," ","integrate((1+sin(d*x+c))**n,x)","\int \left(\sin{\left(c + d x \right)} + 1\right)^{n}\, dx"," ",0,"Integral((sin(c + d*x) + 1)**n, x)","F",0
148,0,0,0,0.000000," ","integrate((1-sin(d*x+c))**n,x)","\int \left(1 - \sin{\left(c + d x \right)}\right)^{n}\, dx"," ",0,"Integral((1 - sin(c + d*x))**n, x)","F",0
149,1,144,0,1.341455," ","integrate(sin(f*x+e)**3*(a+b*sin(f*x+e)),x)","\begin{cases} - \frac{a \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{2 a \cos^{3}{\left(e + f x \right)}}{3 f} + \frac{3 b x \sin^{4}{\left(e + f x \right)}}{8} + \frac{3 b x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{3 b x \cos^{4}{\left(e + f x \right)}}{8} - \frac{5 b \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{3 b \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} & \text{for}\: f \neq 0 \\x \left(a + b \sin{\left(e \right)}\right) \sin^{3}{\left(e \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*sin(e + f*x)**2*cos(e + f*x)/f - 2*a*cos(e + f*x)**3/(3*f) + 3*b*x*sin(e + f*x)**4/8 + 3*b*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + 3*b*x*cos(e + f*x)**4/8 - 5*b*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 3*b*sin(e + f*x)*cos(e + f*x)**3/(8*f), Ne(f, 0)), (x*(a + b*sin(e))*sin(e)**3, True))","A",0
150,1,92,0,0.740807," ","integrate(sin(f*x+e)**2*(a+b*sin(f*x+e)),x)","\begin{cases} \frac{a x \sin^{2}{\left(e + f x \right)}}{2} + \frac{a x \cos^{2}{\left(e + f x \right)}}{2} - \frac{a \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{b \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{2 b \cos^{3}{\left(e + f x \right)}}{3 f} & \text{for}\: f \neq 0 \\x \left(a + b \sin{\left(e \right)}\right) \sin^{2}{\left(e \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x*sin(e + f*x)**2/2 + a*x*cos(e + f*x)**2/2 - a*sin(e + f*x)*cos(e + f*x)/(2*f) - b*sin(e + f*x)**2*cos(e + f*x)/f - 2*b*cos(e + f*x)**3/(3*f), Ne(f, 0)), (x*(a + b*sin(e))*sin(e)**2, True))","A",0
151,1,66,0,0.308172," ","integrate(sin(f*x+e)*(a+b*sin(f*x+e)),x)","\begin{cases} - \frac{a \cos{\left(e + f x \right)}}{f} + \frac{b x \sin^{2}{\left(e + f x \right)}}{2} + \frac{b x \cos^{2}{\left(e + f x \right)}}{2} - \frac{b \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} & \text{for}\: f \neq 0 \\x \left(a + b \sin{\left(e \right)}\right) \sin{\left(e \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*cos(e + f*x)/f + b*x*sin(e + f*x)**2/2 + b*x*cos(e + f*x)**2/2 - b*sin(e + f*x)*cos(e + f*x)/(2*f), Ne(f, 0)), (x*(a + b*sin(e))*sin(e), True))","A",0
152,1,19,0,0.157480," ","integrate(a+b*sin(f*x+e),x)","a x + b \left(\begin{cases} - \frac{\cos{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \sin{\left(e \right)} & \text{otherwise} \end{cases}\right)"," ",0,"a*x + b*Piecewise((-cos(e + f*x)/f, Ne(f, 0)), (x*sin(e), True))","A",0
153,1,51,0,6.757786," ","integrate(csc(f*x+e)*(a+b*sin(f*x+e)),x)","a \left(\begin{cases} \frac{x \cot{\left(e \right)} \csc{\left(e \right)}}{\cot{\left(e \right)} + \csc{\left(e \right)}} + \frac{x \csc^{2}{\left(e \right)}}{\cot{\left(e \right)} + \csc{\left(e \right)}} & \text{for}\: f = 0 \\- \frac{\log{\left(\cot{\left(e + f x \right)} + \csc{\left(e + f x \right)} \right)}}{f} & \text{otherwise} \end{cases}\right) + b x"," ",0,"a*Piecewise((x*cot(e)*csc(e)/(cot(e) + csc(e)) + x*csc(e)**2/(cot(e) + csc(e)), Eq(f, 0)), (-log(cot(e + f*x) + csc(e + f*x))/f, True)) + b*x","B",0
154,0,0,0,0.000000," ","integrate(csc(f*x+e)**2*(a+b*sin(f*x+e)),x)","\int \left(a + b \sin{\left(e + f x \right)}\right) \csc^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*sin(e + f*x))*csc(e + f*x)**2, x)","F",0
155,0,0,0,0.000000," ","integrate(csc(f*x+e)**3*(a+b*sin(f*x+e)),x)","\int \left(a + b \sin{\left(e + f x \right)}\right) \csc^{3}{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*sin(e + f*x))*csc(e + f*x)**3, x)","F",0
156,0,0,0,0.000000," ","integrate(csc(f*x+e)**4*(a+b*sin(f*x+e)),x)","\int \left(a + b \sin{\left(e + f x \right)}\right) \csc^{4}{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*sin(e + f*x))*csc(e + f*x)**4, x)","F",0
157,1,221,0,3.104886," ","integrate(sin(f*x+e)**3*(a+b*sin(f*x+e))**2,x)","\begin{cases} - \frac{a^{2} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{2 a^{2} \cos^{3}{\left(e + f x \right)}}{3 f} + \frac{3 a b x \sin^{4}{\left(e + f x \right)}}{4} + \frac{3 a b x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{2} + \frac{3 a b x \cos^{4}{\left(e + f x \right)}}{4} - \frac{5 a b \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{4 f} - \frac{3 a b \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{4 f} - \frac{b^{2} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{4 b^{2} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{8 b^{2} \cos^{5}{\left(e + f x \right)}}{15 f} & \text{for}\: f \neq 0 \\x \left(a + b \sin{\left(e \right)}\right)^{2} \sin^{3}{\left(e \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*sin(e + f*x)**2*cos(e + f*x)/f - 2*a**2*cos(e + f*x)**3/(3*f) + 3*a*b*x*sin(e + f*x)**4/4 + 3*a*b*x*sin(e + f*x)**2*cos(e + f*x)**2/2 + 3*a*b*x*cos(e + f*x)**4/4 - 5*a*b*sin(e + f*x)**3*cos(e + f*x)/(4*f) - 3*a*b*sin(e + f*x)*cos(e + f*x)**3/(4*f) - b**2*sin(e + f*x)**4*cos(e + f*x)/f - 4*b**2*sin(e + f*x)**2*cos(e + f*x)**3/(3*f) - 8*b**2*cos(e + f*x)**5/(15*f), Ne(f, 0)), (x*(a + b*sin(e))**2*sin(e)**3, True))","A",0
158,1,211,0,1.731656," ","integrate(sin(f*x+e)**2*(a+b*sin(f*x+e))**2,x)","\begin{cases} \frac{a^{2} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{a^{2} x \cos^{2}{\left(e + f x \right)}}{2} - \frac{a^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{2 a b \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{4 a b \cos^{3}{\left(e + f x \right)}}{3 f} + \frac{3 b^{2} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{3 b^{2} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{3 b^{2} x \cos^{4}{\left(e + f x \right)}}{8} - \frac{5 b^{2} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{3 b^{2} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} & \text{for}\: f \neq 0 \\x \left(a + b \sin{\left(e \right)}\right)^{2} \sin^{2}{\left(e \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x*sin(e + f*x)**2/2 + a**2*x*cos(e + f*x)**2/2 - a**2*sin(e + f*x)*cos(e + f*x)/(2*f) - 2*a*b*sin(e + f*x)**2*cos(e + f*x)/f - 4*a*b*cos(e + f*x)**3/(3*f) + 3*b**2*x*sin(e + f*x)**4/8 + 3*b**2*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + 3*b**2*x*cos(e + f*x)**4/8 - 5*b**2*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 3*b**2*sin(e + f*x)*cos(e + f*x)**3/(8*f), Ne(f, 0)), (x*(a + b*sin(e))**2*sin(e)**2, True))","A",0
159,1,107,0,0.718480," ","integrate(sin(f*x+e)*(a+b*sin(f*x+e))**2,x)","\begin{cases} - \frac{a^{2} \cos{\left(e + f x \right)}}{f} + a b x \sin^{2}{\left(e + f x \right)} + a b x \cos^{2}{\left(e + f x \right)} - \frac{a b \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{b^{2} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{2 b^{2} \cos^{3}{\left(e + f x \right)}}{3 f} & \text{for}\: f \neq 0 \\x \left(a + b \sin{\left(e \right)}\right)^{2} \sin{\left(e \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*cos(e + f*x)/f + a*b*x*sin(e + f*x)**2 + a*b*x*cos(e + f*x)**2 - a*b*sin(e + f*x)*cos(e + f*x)/f - b**2*sin(e + f*x)**2*cos(e + f*x)/f - 2*b**2*cos(e + f*x)**3/(3*f), Ne(f, 0)), (x*(a + b*sin(e))**2*sin(e), True))","A",0
160,1,78,0,0.400197," ","integrate((a+b*sin(f*x+e))**2,x)","\begin{cases} a^{2} x - \frac{2 a b \cos{\left(e + f x \right)}}{f} + \frac{b^{2} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{b^{2} x \cos^{2}{\left(e + f x \right)}}{2} - \frac{b^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} & \text{for}\: f \neq 0 \\x \left(a + b \sin{\left(e \right)}\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x - 2*a*b*cos(e + f*x)/f + b**2*x*sin(e + f*x)**2/2 + b**2*x*cos(e + f*x)**2/2 - b**2*sin(e + f*x)*cos(e + f*x)/(2*f), Ne(f, 0)), (x*(a + b*sin(e))**2, True))","A",0
161,0,0,0,0.000000," ","integrate(csc(f*x+e)*(a+b*sin(f*x+e))**2,x)","\int \left(a + b \sin{\left(e + f x \right)}\right)^{2} \csc{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*sin(e + f*x))**2*csc(e + f*x), x)","F",0
162,0,0,0,0.000000," ","integrate(csc(f*x+e)**2*(a+b*sin(f*x+e))**2,x)","\int \left(a + b \sin{\left(e + f x \right)}\right)^{2} \csc^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*sin(e + f*x))**2*csc(e + f*x)**2, x)","F",0
163,0,0,0,0.000000," ","integrate(csc(f*x+e)**3*(a+b*sin(f*x+e))**2,x)","\int \left(a + b \sin{\left(e + f x \right)}\right)^{2} \csc^{3}{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*sin(e + f*x))**2*csc(e + f*x)**3, x)","F",0
164,0,0,0,0.000000," ","integrate(csc(f*x+e)**4*(a+b*sin(f*x+e))**2,x)","\int \left(a + b \sin{\left(e + f x \right)}\right)^{2} \csc^{4}{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*sin(e + f*x))**2*csc(e + f*x)**4, x)","F",0
165,-1,0,0,0.000000," ","integrate(csc(f*x+e)**5*(a+b*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
166,1,393,0,5.552394," ","integrate(sin(f*x+e)**3*(a+b*sin(f*x+e))**3,x)","\begin{cases} - \frac{a^{3} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{2 a^{3} \cos^{3}{\left(e + f x \right)}}{3 f} + \frac{9 a^{2} b x \sin^{4}{\left(e + f x \right)}}{8} + \frac{9 a^{2} b x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{9 a^{2} b x \cos^{4}{\left(e + f x \right)}}{8} - \frac{15 a^{2} b \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{9 a^{2} b \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{3 a b^{2} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{4 a b^{2} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{f} - \frac{8 a b^{2} \cos^{5}{\left(e + f x \right)}}{5 f} + \frac{5 b^{3} x \sin^{6}{\left(e + f x \right)}}{16} + \frac{15 b^{3} x \sin^{4}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{16} + \frac{15 b^{3} x \sin^{2}{\left(e + f x \right)} \cos^{4}{\left(e + f x \right)}}{16} + \frac{5 b^{3} x \cos^{6}{\left(e + f x \right)}}{16} - \frac{11 b^{3} \sin^{5}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{16 f} - \frac{5 b^{3} \sin^{3}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{6 f} - \frac{5 b^{3} \sin{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{16 f} & \text{for}\: f \neq 0 \\x \left(a + b \sin{\left(e \right)}\right)^{3} \sin^{3}{\left(e \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**3*sin(e + f*x)**2*cos(e + f*x)/f - 2*a**3*cos(e + f*x)**3/(3*f) + 9*a**2*b*x*sin(e + f*x)**4/8 + 9*a**2*b*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + 9*a**2*b*x*cos(e + f*x)**4/8 - 15*a**2*b*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 9*a**2*b*sin(e + f*x)*cos(e + f*x)**3/(8*f) - 3*a*b**2*sin(e + f*x)**4*cos(e + f*x)/f - 4*a*b**2*sin(e + f*x)**2*cos(e + f*x)**3/f - 8*a*b**2*cos(e + f*x)**5/(5*f) + 5*b**3*x*sin(e + f*x)**6/16 + 15*b**3*x*sin(e + f*x)**4*cos(e + f*x)**2/16 + 15*b**3*x*sin(e + f*x)**2*cos(e + f*x)**4/16 + 5*b**3*x*cos(e + f*x)**6/16 - 11*b**3*sin(e + f*x)**5*cos(e + f*x)/(16*f) - 5*b**3*sin(e + f*x)**3*cos(e + f*x)**3/(6*f) - 5*b**3*sin(e + f*x)*cos(e + f*x)**5/(16*f), Ne(f, 0)), (x*(a + b*sin(e))**3*sin(e)**3, True))","A",0
167,1,284,0,2.851638," ","integrate(sin(f*x+e)**2*(a+b*sin(f*x+e))**3,x)","\begin{cases} \frac{a^{3} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{a^{3} x \cos^{2}{\left(e + f x \right)}}{2} - \frac{a^{3} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{3 a^{2} b \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{2 a^{2} b \cos^{3}{\left(e + f x \right)}}{f} + \frac{9 a b^{2} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{9 a b^{2} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{9 a b^{2} x \cos^{4}{\left(e + f x \right)}}{8} - \frac{15 a b^{2} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{9 a b^{2} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{b^{3} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{4 b^{3} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{8 b^{3} \cos^{5}{\left(e + f x \right)}}{15 f} & \text{for}\: f \neq 0 \\x \left(a + b \sin{\left(e \right)}\right)^{3} \sin^{2}{\left(e \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*x*sin(e + f*x)**2/2 + a**3*x*cos(e + f*x)**2/2 - a**3*sin(e + f*x)*cos(e + f*x)/(2*f) - 3*a**2*b*sin(e + f*x)**2*cos(e + f*x)/f - 2*a**2*b*cos(e + f*x)**3/f + 9*a*b**2*x*sin(e + f*x)**4/8 + 9*a*b**2*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + 9*a*b**2*x*cos(e + f*x)**4/8 - 15*a*b**2*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 9*a*b**2*sin(e + f*x)*cos(e + f*x)**3/(8*f) - b**3*sin(e + f*x)**4*cos(e + f*x)/f - 4*b**3*sin(e + f*x)**2*cos(e + f*x)**3/(3*f) - 8*b**3*cos(e + f*x)**5/(15*f), Ne(f, 0)), (x*(a + b*sin(e))**3*sin(e)**2, True))","A",0
168,1,233,0,1.659207," ","integrate(sin(f*x+e)*(a+b*sin(f*x+e))**3,x)","\begin{cases} - \frac{a^{3} \cos{\left(e + f x \right)}}{f} + \frac{3 a^{2} b x \sin^{2}{\left(e + f x \right)}}{2} + \frac{3 a^{2} b x \cos^{2}{\left(e + f x \right)}}{2} - \frac{3 a^{2} b \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{3 a b^{2} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{2 a b^{2} \cos^{3}{\left(e + f x \right)}}{f} + \frac{3 b^{3} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{3 b^{3} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{3 b^{3} x \cos^{4}{\left(e + f x \right)}}{8} - \frac{5 b^{3} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{3 b^{3} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} & \text{for}\: f \neq 0 \\x \left(a + b \sin{\left(e \right)}\right)^{3} \sin{\left(e \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**3*cos(e + f*x)/f + 3*a**2*b*x*sin(e + f*x)**2/2 + 3*a**2*b*x*cos(e + f*x)**2/2 - 3*a**2*b*sin(e + f*x)*cos(e + f*x)/(2*f) - 3*a*b**2*sin(e + f*x)**2*cos(e + f*x)/f - 2*a*b**2*cos(e + f*x)**3/f + 3*b**3*x*sin(e + f*x)**4/8 + 3*b**3*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + 3*b**3*x*cos(e + f*x)**4/8 - 5*b**3*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 3*b**3*sin(e + f*x)*cos(e + f*x)**3/(8*f), Ne(f, 0)), (x*(a + b*sin(e))**3*sin(e), True))","A",0
169,1,128,0,0.736882," ","integrate((a+b*sin(f*x+e))**3,x)","\begin{cases} a^{3} x - \frac{3 a^{2} b \cos{\left(e + f x \right)}}{f} + \frac{3 a b^{2} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{3 a b^{2} x \cos^{2}{\left(e + f x \right)}}{2} - \frac{3 a b^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{b^{3} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{2 b^{3} \cos^{3}{\left(e + f x \right)}}{3 f} & \text{for}\: f \neq 0 \\x \left(a + b \sin{\left(e \right)}\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*x - 3*a**2*b*cos(e + f*x)/f + 3*a*b**2*x*sin(e + f*x)**2/2 + 3*a*b**2*x*cos(e + f*x)**2/2 - 3*a*b**2*sin(e + f*x)*cos(e + f*x)/(2*f) - b**3*sin(e + f*x)**2*cos(e + f*x)/f - 2*b**3*cos(e + f*x)**3/(3*f), Ne(f, 0)), (x*(a + b*sin(e))**3, True))","A",0
170,0,0,0,0.000000," ","integrate(csc(f*x+e)*(a+b*sin(f*x+e))**3,x)","\int \left(a + b \sin{\left(e + f x \right)}\right)^{3} \csc{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*sin(e + f*x))**3*csc(e + f*x), x)","F",0
171,0,0,0,0.000000," ","integrate(csc(f*x+e)**2*(a+b*sin(f*x+e))**3,x)","\int \left(a + b \sin{\left(e + f x \right)}\right)^{3} \csc^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*sin(e + f*x))**3*csc(e + f*x)**2, x)","F",0
172,0,0,0,0.000000," ","integrate(csc(f*x+e)**3*(a+b*sin(f*x+e))**3,x)","\int \left(a + b \sin{\left(e + f x \right)}\right)^{3} \csc^{3}{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*sin(e + f*x))**3*csc(e + f*x)**3, x)","F",0
173,-1,0,0,0.000000," ","integrate(csc(f*x+e)**4*(a+b*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
174,-1,0,0,0.000000," ","integrate(csc(f*x+e)**5*(a+b*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
175,1,240,0,1.669699," ","integrate((a+b*sin(f*x+e))**4,x)","\begin{cases} a^{4} x - \frac{4 a^{3} b \cos{\left(e + f x \right)}}{f} + 3 a^{2} b^{2} x \sin^{2}{\left(e + f x \right)} + 3 a^{2} b^{2} x \cos^{2}{\left(e + f x \right)} - \frac{3 a^{2} b^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{4 a b^{3} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{8 a b^{3} \cos^{3}{\left(e + f x \right)}}{3 f} + \frac{3 b^{4} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{3 b^{4} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{3 b^{4} x \cos^{4}{\left(e + f x \right)}}{8} - \frac{5 b^{4} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{3 b^{4} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} & \text{for}\: f \neq 0 \\x \left(a + b \sin{\left(e \right)}\right)^{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*x - 4*a**3*b*cos(e + f*x)/f + 3*a**2*b**2*x*sin(e + f*x)**2 + 3*a**2*b**2*x*cos(e + f*x)**2 - 3*a**2*b**2*sin(e + f*x)*cos(e + f*x)/f - 4*a*b**3*sin(e + f*x)**2*cos(e + f*x)/f - 8*a*b**3*cos(e + f*x)**3/(3*f) + 3*b**4*x*sin(e + f*x)**4/8 + 3*b**4*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + 3*b**4*x*cos(e + f*x)**4/8 - 5*b**4*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 3*b**4*sin(e + f*x)*cos(e + f*x)**3/(8*f), Ne(f, 0)), (x*(a + b*sin(e))**4, True))","A",0
176,-1,0,0,0.000000," ","integrate(sin(x)**4/(a+b*sin(x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
177,-1,0,0,0.000000," ","integrate(sin(x)**3/(a+b*sin(x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
178,-1,0,0,0.000000," ","integrate(sin(x)**2/(a+b*sin(x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
179,1,236,0,80.939292," ","integrate(sin(x)/(a+b*sin(x)),x)","\begin{cases} \tilde{\infty} x & \text{for}\: a = 0 \wedge b = 0 \\\frac{b x \tan{\left(\frac{x}{2} \right)}}{b^{2} \tan{\left(\frac{x}{2} \right)} - b \sqrt{b^{2}}} + \frac{2 b}{b^{2} \tan{\left(\frac{x}{2} \right)} - b \sqrt{b^{2}}} - \frac{x \sqrt{b^{2}}}{b^{2} \tan{\left(\frac{x}{2} \right)} - b \sqrt{b^{2}}} & \text{for}\: a = - \sqrt{b^{2}} \\\frac{b x \tan{\left(\frac{x}{2} \right)}}{b^{2} \tan{\left(\frac{x}{2} \right)} + b \sqrt{b^{2}}} + \frac{2 b}{b^{2} \tan{\left(\frac{x}{2} \right)} + b \sqrt{b^{2}}} + \frac{x \sqrt{b^{2}}}{b^{2} \tan{\left(\frac{x}{2} \right)} + b \sqrt{b^{2}}} & \text{for}\: a = \sqrt{b^{2}} \\- \frac{\cos{\left(x \right)}}{a} & \text{for}\: b = 0 \\\frac{x}{b} & \text{for}\: a = 0 \\- \frac{a \log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{b}{a} - \frac{\sqrt{- a^{2} + b^{2}}}{a} \right)}}{b \sqrt{- a^{2} + b^{2}}} + \frac{a \log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{b}{a} + \frac{\sqrt{- a^{2} + b^{2}}}{a} \right)}}{b \sqrt{- a^{2} + b^{2}}} + \frac{x}{b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x, Eq(a, 0) & Eq(b, 0)), (b*x*tan(x/2)/(b**2*tan(x/2) - b*sqrt(b**2)) + 2*b/(b**2*tan(x/2) - b*sqrt(b**2)) - x*sqrt(b**2)/(b**2*tan(x/2) - b*sqrt(b**2)), Eq(a, -sqrt(b**2))), (b*x*tan(x/2)/(b**2*tan(x/2) + b*sqrt(b**2)) + 2*b/(b**2*tan(x/2) + b*sqrt(b**2)) + x*sqrt(b**2)/(b**2*tan(x/2) + b*sqrt(b**2)), Eq(a, sqrt(b**2))), (-cos(x)/a, Eq(b, 0)), (x/b, Eq(a, 0)), (-a*log(tan(x/2) + b/a - sqrt(-a**2 + b**2)/a)/(b*sqrt(-a**2 + b**2)) + a*log(tan(x/2) + b/a + sqrt(-a**2 + b**2)/a)/(b*sqrt(-a**2 + b**2)) + x/b, True))","A",0
180,1,133,0,9.660777," ","integrate(1/(a+b*sin(x)),x)","\begin{cases} \frac{2 \sqrt{b^{2}}}{b^{2} \tan{\left(\frac{x}{2} \right)} - b \sqrt{b^{2}}} & \text{for}\: a = - \sqrt{b^{2}} \\- \frac{2 \sqrt{b^{2}}}{b^{2} \tan{\left(\frac{x}{2} \right)} + b \sqrt{b^{2}}} & \text{for}\: a = \sqrt{b^{2}} \\\frac{\log{\left(\tan{\left(\frac{x}{2} \right)} \right)}}{b} & \text{for}\: a = 0 \\\frac{\log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{b}{a} - \frac{\sqrt{- a^{2} + b^{2}}}{a} \right)}}{\sqrt{- a^{2} + b^{2}}} - \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{b}{a} + \frac{\sqrt{- a^{2} + b^{2}}}{a} \right)}}{\sqrt{- a^{2} + b^{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*sqrt(b**2)/(b**2*tan(x/2) - b*sqrt(b**2)), Eq(a, -sqrt(b**2))), (-2*sqrt(b**2)/(b**2*tan(x/2) + b*sqrt(b**2)), Eq(a, sqrt(b**2))), (log(tan(x/2))/b, Eq(a, 0)), (log(tan(x/2) + b/a - sqrt(-a**2 + b**2)/a)/sqrt(-a**2 + b**2) - log(tan(x/2) + b/a + sqrt(-a**2 + b**2)/a)/sqrt(-a**2 + b**2), True))","A",0
181,0,0,0,0.000000," ","integrate(csc(x)/(a+b*sin(x)),x)","\int \frac{\csc{\left(x \right)}}{a + b \sin{\left(x \right)}}\, dx"," ",0,"Integral(csc(x)/(a + b*sin(x)), x)","F",0
182,0,0,0,0.000000," ","integrate(csc(x)**2/(a+b*sin(x)),x)","\int \frac{\csc^{2}{\left(x \right)}}{a + b \sin{\left(x \right)}}\, dx"," ",0,"Integral(csc(x)**2/(a + b*sin(x)), x)","F",0
183,0,0,0,0.000000," ","integrate(csc(x)**3/(a+b*sin(x)),x)","\int \frac{\csc^{3}{\left(x \right)}}{a + b \sin{\left(x \right)}}\, dx"," ",0,"Integral(csc(x)**3/(a + b*sin(x)), x)","F",0
184,0,0,0,0.000000," ","integrate(csc(x)**4/(a+b*sin(x)),x)","\int \frac{\csc^{4}{\left(x \right)}}{a + b \sin{\left(x \right)}}\, dx"," ",0,"Integral(csc(x)**4/(a + b*sin(x)), x)","F",0
185,-1,0,0,0.000000," ","integrate(sin(x)**4/(a+b*sin(x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
186,-1,0,0,0.000000," ","integrate(sin(x)**3/(a+b*sin(x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
187,-1,0,0,0.000000," ","integrate(sin(x)**2/(a+b*sin(x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
188,-1,0,0,0.000000," ","integrate(sin(x)/(a+b*sin(x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
189,0,0,0,0.000000," ","integrate(1/(a+b*sin(x))**2,x)","\int \frac{1}{\left(a + b \sin{\left(x \right)}\right)^{2}}\, dx"," ",0,"Integral((a + b*sin(x))**(-2), x)","F",0
190,0,0,0,0.000000," ","integrate(csc(x)/(a+b*sin(x))**2,x)","\int \frac{\csc{\left(x \right)}}{\left(a + b \sin{\left(x \right)}\right)^{2}}\, dx"," ",0,"Integral(csc(x)/(a + b*sin(x))**2, x)","F",0
191,0,0,0,0.000000," ","integrate(csc(x)**2/(a+b*sin(x))**2,x)","\int \frac{\csc^{2}{\left(x \right)}}{\left(a + b \sin{\left(x \right)}\right)^{2}}\, dx"," ",0,"Integral(csc(x)**2/(a + b*sin(x))**2, x)","F",0
192,0,0,0,0.000000," ","integrate(csc(x)**3/(a+b*sin(x))**2,x)","\int \frac{\csc^{3}{\left(x \right)}}{\left(a + b \sin{\left(x \right)}\right)^{2}}\, dx"," ",0,"Integral(csc(x)**3/(a + b*sin(x))**2, x)","F",0
193,-1,0,0,0.000000," ","integrate(sin(x)**5/(a+b*sin(x))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
194,-1,0,0,0.000000," ","integrate(sin(x)**4/(a+b*sin(x))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
195,-1,0,0,0.000000," ","integrate(sin(x)**3/(a+b*sin(x))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
196,-1,0,0,0.000000," ","integrate(sin(x)**2/(a+b*sin(x))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
197,-1,0,0,0.000000," ","integrate(sin(x)/(a+b*sin(x))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
198,-1,0,0,0.000000," ","integrate(1/(a+b*sin(x))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
199,0,0,0,0.000000," ","integrate(csc(x)/(a+b*sin(x))**3,x)","\int \frac{\csc{\left(x \right)}}{\left(a + b \sin{\left(x \right)}\right)^{3}}\, dx"," ",0,"Integral(csc(x)/(a + b*sin(x))**3, x)","F",0
200,0,0,0,0.000000," ","integrate(csc(x)**2/(a+b*sin(x))**3,x)","\int \frac{\csc^{2}{\left(x \right)}}{\left(a + b \sin{\left(x \right)}\right)^{3}}\, dx"," ",0,"Integral(csc(x)**2/(a + b*sin(x))**3, x)","F",0
201,0,0,0,0.000000," ","integrate(csc(x)**3/(a+b*sin(x))**3,x)","\int \frac{\csc^{3}{\left(x \right)}}{\left(a + b \sin{\left(x \right)}\right)^{3}}\, dx"," ",0,"Integral(csc(x)**3/(a + b*sin(x))**3, x)","F",0
202,-1,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
203,0,0,0,0.000000," ","integrate(sin(f*x+e)*(a+b*sin(f*x+e))**(1/2),x)","\int \sqrt{a + b \sin{\left(e + f x \right)}} \sin{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*sin(e + f*x))*sin(e + f*x), x)","F",0
204,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**(1/2),x)","\int \sqrt{a + b \sin{\left(e + f x \right)}}\, dx"," ",0,"Integral(sqrt(a + b*sin(e + f*x)), x)","F",0
205,0,0,0,0.000000," ","integrate(csc(f*x+e)*(a+b*sin(f*x+e))**(1/2),x)","\int \sqrt{a + b \sin{\left(e + f x \right)}} \csc{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*sin(e + f*x))*csc(e + f*x), x)","F",0
206,0,0,0,0.000000," ","integrate(csc(f*x+e)**2*(a+b*sin(f*x+e))**(1/2),x)","\int \sqrt{a + b \sin{\left(e + f x \right)}} \csc^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*sin(e + f*x))*csc(e + f*x)**2, x)","F",0
207,0,0,0,0.000000," ","integrate(sin(f*x+e)/(a+b*sin(f*x+e))**(1/2),x)","\int \frac{\sin{\left(e + f x \right)}}{\sqrt{a + b \sin{\left(e + f x \right)}}}\, dx"," ",0,"Integral(sin(e + f*x)/sqrt(a + b*sin(e + f*x)), x)","F",0
208,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))**(1/2),x)","\int \frac{1}{\sqrt{a + b \sin{\left(e + f x \right)}}}\, dx"," ",0,"Integral(1/sqrt(a + b*sin(e + f*x)), x)","F",0
209,0,0,0,0.000000," ","integrate(csc(f*x+e)/(a+b*sin(f*x+e))**(1/2),x)","\int \frac{\csc{\left(e + f x \right)}}{\sqrt{a + b \sin{\left(e + f x \right)}}}\, dx"," ",0,"Integral(csc(e + f*x)/sqrt(a + b*sin(e + f*x)), x)","F",0
210,0,0,0,0.000000," ","integrate(csc(f*x+e)**2/(a+b*sin(f*x+e))**(1/2),x)","\int \frac{\csc^{2}{\left(e + f x \right)}}{\sqrt{a + b \sin{\left(e + f x \right)}}}\, dx"," ",0,"Integral(csc(e + f*x)**2/sqrt(a + b*sin(e + f*x)), x)","F",0
211,0,0,0,0.000000," ","integrate(sin(d*x+c)**(1/2)*(a+b*sin(d*x+c))**(1/2),x)","\int \sqrt{a + b \sin{\left(c + d x \right)}} \sqrt{\sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(a + b*sin(c + d*x))*sqrt(sin(c + d*x)), x)","F",0
212,0,0,0,0.000000," ","integrate(1/sin(d*x+c)**(1/2)/(a+b*sin(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{a + b \sin{\left(c + d x \right)}} \sqrt{\sin{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(a + b*sin(c + d*x))*sqrt(sin(c + d*x))), x)","F",0
213,-1,0,0,0.000000," ","integrate((d*sin(f*x+e))**m*(a+b*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
214,-1,0,0,0.000000," ","integrate((d*sin(f*x+e))**m*(a+b*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
215,-1,0,0,0.000000," ","integrate((d*sin(f*x+e))**m*(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
216,-1,0,0,0.000000," ","integrate((d*sin(f*x+e))**m/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
217,-1,0,0,0.000000," ","integrate((d*sin(f*x+e))**m/(a+b*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
218,-1,0,0,0.000000," ","integrate((d*sin(f*x+e))**m/(a+b*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
219,0,0,0,0.000000," ","integrate(sin(d*x+c)**(-1-a**2/(a**2+b**2))*(a+b*sin(d*x+c))**2,x)","\int \left(a + b \sin{\left(c + d x \right)}\right)^{2} \sin^{- \frac{a^{2}}{a^{2} + b^{2}} - 1}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*sin(c + d*x))**2*sin(c + d*x)**(-a**2/(a**2 + b**2) - 1), x)","F",0
220,-1,0,0,0.000000," ","integrate((1+2*sin(d*x+c))**2/sin(d*x+c)**(6/5),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
221,0,0,0,0.000000," ","integrate(sin(d*x+c)**m*(a+b*sin(d*x+c))**n,x)","\int \left(a + b \sin{\left(c + d x \right)}\right)^{n} \sin^{m}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*sin(c + d*x))**n*sin(c + d*x)**m, x)","F",0
222,-1,0,0,0.000000," ","integrate(sin(d*x+c)**3*(a+b*sin(d*x+c))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
223,-1,0,0,0.000000," ","integrate(sin(d*x+c)**2*(a+b*sin(d*x+c))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
224,-1,0,0,0.000000," ","integrate(sin(d*x+c)*(a+b*sin(d*x+c))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
225,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))**n,x)","\int \left(a + b \sin{\left(c + d x \right)}\right)^{n}\, dx"," ",0,"Integral((a + b*sin(c + d*x))**n, x)","F",0
226,0,0,0,0.000000," ","integrate(csc(d*x+c)*(a+b*sin(d*x+c))**n,x)","\int \left(a + b \sin{\left(c + d x \right)}\right)^{n} \csc{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*sin(c + d*x))**n*csc(c + d*x), x)","F",0
227,1,314,0,3.638067," ","integrate((a+a*sin(f*x+e))*(c-c*sin(f*x+e))**4,x)","\begin{cases} - \frac{9 a c^{4} x \sin^{4}{\left(e + f x \right)}}{8} - \frac{9 a c^{4} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + a c^{4} x \sin^{2}{\left(e + f x \right)} - \frac{9 a c^{4} x \cos^{4}{\left(e + f x \right)}}{8} + a c^{4} x \cos^{2}{\left(e + f x \right)} + a c^{4} x - \frac{a c^{4} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{15 a c^{4} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{4 a c^{4} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{2 a c^{4} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{9 a c^{4} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{a c^{4} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{8 a c^{4} \cos^{5}{\left(e + f x \right)}}{15 f} - \frac{4 a c^{4} \cos^{3}{\left(e + f x \right)}}{3 f} + \frac{3 a c^{4} \cos{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \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*c**4*x*sin(e + f*x)**4/8 - 9*a*c**4*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + a*c**4*x*sin(e + f*x)**2 - 9*a*c**4*x*cos(e + f*x)**4/8 + a*c**4*x*cos(e + f*x)**2 + a*c**4*x - a*c**4*sin(e + f*x)**4*cos(e + f*x)/f + 15*a*c**4*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 4*a*c**4*sin(e + f*x)**2*cos(e + f*x)**3/(3*f) - 2*a*c**4*sin(e + f*x)**2*cos(e + f*x)/f + 9*a*c**4*sin(e + f*x)*cos(e + f*x)**3/(8*f) - a*c**4*sin(e + f*x)*cos(e + f*x)/f - 8*a*c**4*cos(e + f*x)**5/(15*f) - 4*a*c**4*cos(e + f*x)**3/(3*f) + 3*a*c**4*cos(e + f*x)/f, Ne(f, 0)), (x*(a*sin(e) + a)*(-c*sin(e) + c)**4, True))","A",0
228,1,196,0,1.368849," ","integrate((a+a*sin(f*x+e))*(c-c*sin(f*x+e))**3,x)","\begin{cases} - \frac{3 a c^{3} x \sin^{4}{\left(e + f x \right)}}{8} - \frac{3 a c^{3} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} - \frac{3 a c^{3} x \cos^{4}{\left(e + f x \right)}}{8} + a c^{3} x + \frac{5 a c^{3} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{2 a c^{3} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{3 a c^{3} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{4 a c^{3} \cos^{3}{\left(e + f x \right)}}{3 f} + \frac{2 a c^{3} \cos{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \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*c**3*x*sin(e + f*x)**4/8 - 3*a*c**3*x*sin(e + f*x)**2*cos(e + f*x)**2/4 - 3*a*c**3*x*cos(e + f*x)**4/8 + a*c**3*x + 5*a*c**3*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 2*a*c**3*sin(e + f*x)**2*cos(e + f*x)/f + 3*a*c**3*sin(e + f*x)*cos(e + f*x)**3/(8*f) - 4*a*c**3*cos(e + f*x)**3/(3*f) + 2*a*c**3*cos(e + f*x)/f, Ne(f, 0)), (x*(a*sin(e) + a)*(-c*sin(e) + c)**3, True))","A",0
229,1,133,0,0.903870," ","integrate((a+a*sin(f*x+e))*(c-c*sin(f*x+e))**2,x)","\begin{cases} - \frac{a c^{2} x \sin^{2}{\left(e + f x \right)}}{2} - \frac{a c^{2} x \cos^{2}{\left(e + f x \right)}}{2} + a c^{2} x - \frac{a c^{2} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{a c^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{2 a c^{2} \cos^{3}{\left(e + f x \right)}}{3 f} + \frac{a c^{2} \cos{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \left(a \sin{\left(e \right)} + a\right) \left(- c \sin{\left(e \right)} + c\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*c**2*x*sin(e + f*x)**2/2 - a*c**2*x*cos(e + f*x)**2/2 + a*c**2*x - a*c**2*sin(e + f*x)**2*cos(e + f*x)/f + a*c**2*sin(e + f*x)*cos(e + f*x)/(2*f) - 2*a*c**2*cos(e + f*x)**3/(3*f) + a*c**2*cos(e + f*x)/f, Ne(f, 0)), (x*(a*sin(e) + a)*(-c*sin(e) + c)**2, True))","A",0
230,1,70,0,0.300330," ","integrate((a+a*sin(f*x+e))*(c-c*sin(f*x+e)),x)","\begin{cases} - \frac{a c x \sin^{2}{\left(e + f x \right)}}{2} - \frac{a c x \cos^{2}{\left(e + f x \right)}}{2} + a c x + \frac{a c \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} & \text{for}\: f \neq 0 \\x \left(a \sin{\left(e \right)} + a\right) \left(- c \sin{\left(e \right)} + c\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*c*x*sin(e + f*x)**2/2 - a*c*x*cos(e + f*x)**2/2 + a*c*x + a*c*sin(e + f*x)*cos(e + f*x)/(2*f), Ne(f, 0)), (x*(a*sin(e) + a)*(-c*sin(e) + c), True))","A",0
231,1,88,0,1.605358," ","integrate((a+a*sin(f*x+e))/(c-c*sin(f*x+e)),x)","\begin{cases} - \frac{a f x \tan{\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 f x}{c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - c f} - \frac{4 a}{c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - c f} & \text{for}\: f \neq 0 \\\frac{x \left(a \sin{\left(e \right)} + a\right)}{- c \sin{\left(e \right)} + c} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*f*x*tan(e/2 + f*x/2)/(c*f*tan(e/2 + f*x/2) - c*f) + a*f*x/(c*f*tan(e/2 + f*x/2) - c*f) - 4*a/(c*f*tan(e/2 + f*x/2) - c*f), Ne(f, 0)), (x*(a*sin(e) + a)/(-c*sin(e) + c), True))","A",0
232,1,158,0,3.713441," ","integrate((a+a*sin(f*x+e))/(c-c*sin(f*x+e))**2,x)","\begin{cases} - \frac{6 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}{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 \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)**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/(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*sin(e) + a)/(-c*sin(e) + c)**2, True))","A",0
233,1,571,0,7.490695," ","integrate((a+a*sin(f*x+e))/(c-c*sin(f*x+e))**3,x)","\begin{cases} - \frac{30 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 \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 \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 \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}{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 \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)**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*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*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*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/(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*sin(e) + a)/(-c*sin(e) + c)**3, True))","A",0
234,1,1061,0,16.671531," ","integrate((a+a*sin(f*x+e))/(c-c*sin(f*x+e))**4,x)","\begin{cases} - \frac{210 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 \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 \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 \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 \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 \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}{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 \sin{\left(e \right)} + a\right)}{\left(- c \sin{\left(e \right)} + c\right)^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-210*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*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*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*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*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*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/(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*sin(e) + a)/(-c*sin(e) + c)**4, True))","A",0
235,1,1700,0,33.029443," ","integrate((a+a*sin(f*x+e))/(c-c*sin(f*x+e))**5,x)","\begin{cases} - \frac{630 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 \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 \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 \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 \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 \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 \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 \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}{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 \sin{\left(e \right)} + a\right)}{\left(- c \sin{\left(e \right)} + c\right)^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-630*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*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*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*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*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*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*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*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/(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*sin(e) + a)/(-c*sin(e) + c)**5, True))","A",0
236,1,629,0,10.577111," ","integrate((a+a*sin(f*x+e))**2*(c-c*sin(f*x+e))**5,x)","\begin{cases} \frac{15 a^{2} c^{5} x \sin^{6}{\left(e + f x \right)}}{16} + \frac{45 a^{2} c^{5} x \sin^{4}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{16} - \frac{15 a^{2} c^{5} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{45 a^{2} c^{5} x \sin^{2}{\left(e + f x \right)} \cos^{4}{\left(e + f x \right)}}{16} - \frac{15 a^{2} c^{5} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{a^{2} c^{5} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{15 a^{2} c^{5} x \cos^{6}{\left(e + f x \right)}}{16} - \frac{15 a^{2} c^{5} x \cos^{4}{\left(e + f x \right)}}{8} + \frac{a^{2} c^{5} x \cos^{2}{\left(e + f x \right)}}{2} + a^{2} c^{5} x + \frac{a^{2} c^{5} \sin^{6}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{33 a^{2} c^{5} \sin^{5}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{16 f} + \frac{2 a^{2} c^{5} \sin^{4}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{f} + \frac{a^{2} c^{5} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{5 a^{2} c^{5} \sin^{3}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{2 f} + \frac{25 a^{2} c^{5} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} + \frac{8 a^{2} c^{5} \sin^{2}{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{5 f} + \frac{4 a^{2} c^{5} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{5 a^{2} c^{5} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{15 a^{2} c^{5} \sin{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{16 f} + \frac{15 a^{2} c^{5} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{a^{2} c^{5} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} + \frac{16 a^{2} c^{5} \cos^{7}{\left(e + f x \right)}}{35 f} + \frac{8 a^{2} c^{5} \cos^{5}{\left(e + f x \right)}}{15 f} - \frac{10 a^{2} c^{5} \cos^{3}{\left(e + f x \right)}}{3 f} + \frac{3 a^{2} c^{5} \cos{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \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**2*c**5*x*sin(e + f*x)**6/16 + 45*a**2*c**5*x*sin(e + f*x)**4*cos(e + f*x)**2/16 - 15*a**2*c**5*x*sin(e + f*x)**4/8 + 45*a**2*c**5*x*sin(e + f*x)**2*cos(e + f*x)**4/16 - 15*a**2*c**5*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + a**2*c**5*x*sin(e + f*x)**2/2 + 15*a**2*c**5*x*cos(e + f*x)**6/16 - 15*a**2*c**5*x*cos(e + f*x)**4/8 + a**2*c**5*x*cos(e + f*x)**2/2 + a**2*c**5*x + a**2*c**5*sin(e + f*x)**6*cos(e + f*x)/f - 33*a**2*c**5*sin(e + f*x)**5*cos(e + f*x)/(16*f) + 2*a**2*c**5*sin(e + f*x)**4*cos(e + f*x)**3/f + a**2*c**5*sin(e + f*x)**4*cos(e + f*x)/f - 5*a**2*c**5*sin(e + f*x)**3*cos(e + f*x)**3/(2*f) + 25*a**2*c**5*sin(e + f*x)**3*cos(e + f*x)/(8*f) + 8*a**2*c**5*sin(e + f*x)**2*cos(e + f*x)**5/(5*f) + 4*a**2*c**5*sin(e + f*x)**2*cos(e + f*x)**3/(3*f) - 5*a**2*c**5*sin(e + f*x)**2*cos(e + f*x)/f - 15*a**2*c**5*sin(e + f*x)*cos(e + f*x)**5/(16*f) + 15*a**2*c**5*sin(e + f*x)*cos(e + f*x)**3/(8*f) - a**2*c**5*sin(e + f*x)*cos(e + f*x)/(2*f) + 16*a**2*c**5*cos(e + f*x)**7/(35*f) + 8*a**2*c**5*cos(e + f*x)**5/(15*f) - 10*a**2*c**5*cos(e + f*x)**3/(3*f) + 3*a**2*c**5*cos(e + f*x)/f, Ne(f, 0)), (x*(a*sin(e) + a)**2*(-c*sin(e) + c)**5, True))","A",0
237,1,530,0,6.932419," ","integrate((a+a*sin(f*x+e))**2*(c-c*sin(f*x+e))**4,x)","\begin{cases} \frac{5 a^{2} c^{4} x \sin^{6}{\left(e + f x \right)}}{16} + \frac{15 a^{2} c^{4} x \sin^{4}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{16} - \frac{3 a^{2} c^{4} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{15 a^{2} c^{4} x \sin^{2}{\left(e + f x \right)} \cos^{4}{\left(e + f x \right)}}{16} - \frac{3 a^{2} c^{4} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} - \frac{a^{2} c^{4} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{5 a^{2} c^{4} x \cos^{6}{\left(e + f x \right)}}{16} - \frac{3 a^{2} c^{4} x \cos^{4}{\left(e + f x \right)}}{8} - \frac{a^{2} c^{4} x \cos^{2}{\left(e + f x \right)}}{2} + a^{2} c^{4} x - \frac{11 a^{2} c^{4} \sin^{5}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{16 f} + \frac{2 a^{2} c^{4} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{5 a^{2} c^{4} \sin^{3}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{6 f} + \frac{5 a^{2} c^{4} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} + \frac{8 a^{2} c^{4} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{4 a^{2} c^{4} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{5 a^{2} c^{4} \sin{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{16 f} + \frac{3 a^{2} c^{4} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} + \frac{a^{2} c^{4} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} + \frac{16 a^{2} c^{4} \cos^{5}{\left(e + f x \right)}}{15 f} - \frac{8 a^{2} c^{4} \cos^{3}{\left(e + f x \right)}}{3 f} + \frac{2 a^{2} c^{4} \cos{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \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**2*c**4*x*sin(e + f*x)**6/16 + 15*a**2*c**4*x*sin(e + f*x)**4*cos(e + f*x)**2/16 - 3*a**2*c**4*x*sin(e + f*x)**4/8 + 15*a**2*c**4*x*sin(e + f*x)**2*cos(e + f*x)**4/16 - 3*a**2*c**4*x*sin(e + f*x)**2*cos(e + f*x)**2/4 - a**2*c**4*x*sin(e + f*x)**2/2 + 5*a**2*c**4*x*cos(e + f*x)**6/16 - 3*a**2*c**4*x*cos(e + f*x)**4/8 - a**2*c**4*x*cos(e + f*x)**2/2 + a**2*c**4*x - 11*a**2*c**4*sin(e + f*x)**5*cos(e + f*x)/(16*f) + 2*a**2*c**4*sin(e + f*x)**4*cos(e + f*x)/f - 5*a**2*c**4*sin(e + f*x)**3*cos(e + f*x)**3/(6*f) + 5*a**2*c**4*sin(e + f*x)**3*cos(e + f*x)/(8*f) + 8*a**2*c**4*sin(e + f*x)**2*cos(e + f*x)**3/(3*f) - 4*a**2*c**4*sin(e + f*x)**2*cos(e + f*x)/f - 5*a**2*c**4*sin(e + f*x)*cos(e + f*x)**5/(16*f) + 3*a**2*c**4*sin(e + f*x)*cos(e + f*x)**3/(8*f) + a**2*c**4*sin(e + f*x)*cos(e + f*x)/(2*f) + 16*a**2*c**4*cos(e + f*x)**5/(15*f) - 8*a**2*c**4*cos(e + f*x)**3/(3*f) + 2*a**2*c**4*cos(e + f*x)/f, Ne(f, 0)), (x*(a*sin(e) + a)**2*(-c*sin(e) + c)**4, True))","A",0
238,1,340,0,3.039093," ","integrate((a+a*sin(f*x+e))**2*(c-c*sin(f*x+e))**3,x)","\begin{cases} \frac{3 a^{2} c^{3} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{3 a^{2} c^{3} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} - a^{2} c^{3} x \sin^{2}{\left(e + f x \right)} + \frac{3 a^{2} c^{3} x \cos^{4}{\left(e + f x \right)}}{8} - a^{2} c^{3} x \cos^{2}{\left(e + f x \right)} + a^{2} c^{3} x + \frac{a^{2} c^{3} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{5 a^{2} c^{3} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} + \frac{4 a^{2} c^{3} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{2 a^{2} c^{3} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{3 a^{2} c^{3} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} + \frac{a^{2} c^{3} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{8 a^{2} c^{3} \cos^{5}{\left(e + f x \right)}}{15 f} - \frac{4 a^{2} c^{3} \cos^{3}{\left(e + f x \right)}}{3 f} + \frac{a^{2} c^{3} \cos{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \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**2*c**3*x*sin(e + f*x)**4/8 + 3*a**2*c**3*x*sin(e + f*x)**2*cos(e + f*x)**2/4 - a**2*c**3*x*sin(e + f*x)**2 + 3*a**2*c**3*x*cos(e + f*x)**4/8 - a**2*c**3*x*cos(e + f*x)**2 + a**2*c**3*x + a**2*c**3*sin(e + f*x)**4*cos(e + f*x)/f - 5*a**2*c**3*sin(e + f*x)**3*cos(e + f*x)/(8*f) + 4*a**2*c**3*sin(e + f*x)**2*cos(e + f*x)**3/(3*f) - 2*a**2*c**3*sin(e + f*x)**2*cos(e + f*x)/f - 3*a**2*c**3*sin(e + f*x)*cos(e + f*x)**3/(8*f) + a**2*c**3*sin(e + f*x)*cos(e + f*x)/f + 8*a**2*c**3*cos(e + f*x)**5/(15*f) - 4*a**2*c**3*cos(e + f*x)**3/(3*f) + a**2*c**3*cos(e + f*x)/f, Ne(f, 0)), (x*(a*sin(e) + a)**2*(-c*sin(e) + c)**3, True))","A",0
239,1,206,0,1.468695," ","integrate((a+a*sin(f*x+e))**2*(c-c*sin(f*x+e))**2,x)","\begin{cases} \frac{3 a^{2} c^{2} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{3 a^{2} c^{2} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} - a^{2} c^{2} x \sin^{2}{\left(e + f x \right)} + \frac{3 a^{2} c^{2} x \cos^{4}{\left(e + f x \right)}}{8} - a^{2} c^{2} x \cos^{2}{\left(e + f x \right)} + a^{2} c^{2} x - \frac{5 a^{2} c^{2} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{3 a^{2} c^{2} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} + \frac{a^{2} c^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \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**2*c**2*x*sin(e + f*x)**4/8 + 3*a**2*c**2*x*sin(e + f*x)**2*cos(e + f*x)**2/4 - a**2*c**2*x*sin(e + f*x)**2 + 3*a**2*c**2*x*cos(e + f*x)**4/8 - a**2*c**2*x*cos(e + f*x)**2 + a**2*c**2*x - 5*a**2*c**2*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 3*a**2*c**2*sin(e + f*x)*cos(e + f*x)**3/(8*f) + a**2*c**2*sin(e + f*x)*cos(e + f*x)/f, Ne(f, 0)), (x*(a*sin(e) + a)**2*(-c*sin(e) + c)**2, True))","A",0
240,1,133,0,0.893048," ","integrate((a+a*sin(f*x+e))**2*(c-c*sin(f*x+e)),x)","\begin{cases} - \frac{a^{2} c x \sin^{2}{\left(e + f x \right)}}{2} - \frac{a^{2} c x \cos^{2}{\left(e + f x \right)}}{2} + a^{2} c x + \frac{a^{2} c \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{a^{2} c \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} + \frac{2 a^{2} c \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{a^{2} c \cos{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \left(a \sin{\left(e \right)} + a\right)^{2} \left(- c \sin{\left(e \right)} + c\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*c*x*sin(e + f*x)**2/2 - a**2*c*x*cos(e + f*x)**2/2 + a**2*c*x + a**2*c*sin(e + f*x)**2*cos(e + f*x)/f + a**2*c*sin(e + f*x)*cos(e + f*x)/(2*f) + 2*a**2*c*cos(e + f*x)**3/(3*f) - a**2*c*cos(e + f*x)/f, Ne(f, 0)), (x*(a*sin(e) + a)**2*(-c*sin(e) + c), True))","A",0
241,1,454,0,4.197399," ","integrate((a+a*sin(f*x+e))**2/(c-c*sin(f*x+e)),x)","\begin{cases} - \frac{3 a^{2} 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{3 a^{2} 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{3 a^{2} 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{3 a^{2} 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{8 a^{2} \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 a^{2} \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{10 a^{2}}{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 \sin{\left(e \right)} + a\right)^{2}}{- c \sin{\left(e \right)} + c} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*a**2*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) + 3*a**2*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) - 3*a**2*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) + 3*a**2*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) - 8*a**2*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*a**2*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) - 10*a**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), Ne(f, 0)), (x*(a*sin(e) + a)**2/(-c*sin(e) + c), True))","A",0
242,1,473,0,8.243138," ","integrate((a+a*sin(f*x+e))**2/(c-c*sin(f*x+e))**2,x)","\begin{cases} \frac{3 a^{2} 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 a^{2} 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 a^{2} 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 a^{2} 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{24 a^{2} \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{8 a^{2}}{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 \sin{\left(e \right)} + a\right)^{2}}{\left(- c \sin{\left(e \right)} + c\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a**2*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*a**2*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*a**2*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*a**2*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) - 24*a**2*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) + 8*a**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), Ne(f, 0)), (x*(a*sin(e) + a)**2/(-c*sin(e) + c)**2, True))","A",0
243,1,354,0,14.875748," ","integrate((a+a*sin(f*x+e))**2/(c-c*sin(f*x+e))**3,x)","\begin{cases} - \frac{10 a^{2} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{5 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 25 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 50 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 25 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5 c^{3} f} - \frac{20 a^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{5 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 25 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 50 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 25 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5 c^{3} f} - \frac{2 a^{2}}{5 c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 25 c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 c^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 50 c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 25 c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5 c^{3} f} & \text{for}\: f \neq 0 \\\frac{x \left(a \sin{\left(e \right)} + a\right)^{2}}{\left(- c \sin{\left(e \right)} + c\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-10*a**2*tan(e/2 + f*x/2)**4/(5*c**3*f*tan(e/2 + f*x/2)**5 - 25*c**3*f*tan(e/2 + f*x/2)**4 + 50*c**3*f*tan(e/2 + f*x/2)**3 - 50*c**3*f*tan(e/2 + f*x/2)**2 + 25*c**3*f*tan(e/2 + f*x/2) - 5*c**3*f) - 20*a**2*tan(e/2 + f*x/2)**2/(5*c**3*f*tan(e/2 + f*x/2)**5 - 25*c**3*f*tan(e/2 + f*x/2)**4 + 50*c**3*f*tan(e/2 + f*x/2)**3 - 50*c**3*f*tan(e/2 + f*x/2)**2 + 25*c**3*f*tan(e/2 + f*x/2) - 5*c**3*f) - 2*a**2/(5*c**3*f*tan(e/2 + f*x/2)**5 - 25*c**3*f*tan(e/2 + f*x/2)**4 + 50*c**3*f*tan(e/2 + f*x/2)**3 - 50*c**3*f*tan(e/2 + f*x/2)**2 + 25*c**3*f*tan(e/2 + f*x/2) - 5*c**3*f), Ne(f, 0)), (x*(a*sin(e) + a)**2/(-c*sin(e) + c)**3, True))","A",0
244,1,1074,0,25.117813," ","integrate((a+a*sin(f*x+e))**2/(c-c*sin(f*x+e))**4,x)","\begin{cases} - \frac{70 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^{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^{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^{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^{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^{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^{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 \sin{\left(e \right)} + a\right)^{2}}{\left(- c \sin{\left(e \right)} + c\right)^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-70*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**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**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**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**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**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**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*sin(e) + a)**2/(-c*sin(e) + c)**4, True))","A",0
245,1,1717,0,50.689965," ","integrate((a+a*sin(f*x+e))**2/(c-c*sin(f*x+e))**5,x)","\begin{cases} - \frac{630 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^{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^{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^{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^{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^{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^{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^{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^{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 \sin{\left(e \right)} + a\right)^{2}}{\left(- c \sin{\left(e \right)} + c\right)^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-630*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**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**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**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**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**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**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**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**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*sin(e) + a)**2/(-c*sin(e) + c)**5, True))","A",0
246,1,2509,0,84.940755," ","integrate((a+a*sin(f*x+e))**2/(c-c*sin(f*x+e))**6,x)","\begin{cases} - \frac{2310 a^{2} \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{1155 c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 12705 c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 63525 c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 190575 c^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 381150 c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 533610 c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 533610 c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 381150 c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 190575 c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63525 c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12705 c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1155 c^{6} f} + \frac{6930 a^{2} \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{1155 c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 12705 c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 63525 c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 190575 c^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 381150 c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 533610 c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 533610 c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 381150 c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 190575 c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63525 c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12705 c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1155 c^{6} f} - \frac{27720 a^{2} \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{1155 c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 12705 c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 63525 c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 190575 c^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 381150 c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 533610 c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 533610 c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 381150 c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 190575 c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63525 c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12705 c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1155 c^{6} f} + \frac{46200 a^{2} \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{1155 c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 12705 c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 63525 c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 190575 c^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 381150 c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 533610 c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 533610 c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 381150 c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 190575 c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63525 c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12705 c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1155 c^{6} f} - \frac{74844 a^{2} \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{1155 c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 12705 c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 63525 c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 190575 c^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 381150 c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 533610 c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 533610 c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 381150 c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 190575 c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63525 c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12705 c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1155 c^{6} f} + \frac{65604 a^{2} \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{1155 c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 12705 c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 63525 c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 190575 c^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 381150 c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 533610 c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 533610 c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 381150 c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 190575 c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63525 c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12705 c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1155 c^{6} f} - \frac{54120 a^{2} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{1155 c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 12705 c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 63525 c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 190575 c^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 381150 c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 533610 c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 533610 c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 381150 c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 190575 c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63525 c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12705 c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1155 c^{6} f} + \frac{22440 a^{2} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{1155 c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 12705 c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 63525 c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 190575 c^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 381150 c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 533610 c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 533610 c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 381150 c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 190575 c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63525 c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12705 c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1155 c^{6} f} - \frac{9790 a^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{1155 c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 12705 c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 63525 c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 190575 c^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 381150 c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 533610 c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 533610 c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 381150 c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 190575 c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63525 c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12705 c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1155 c^{6} f} + \frac{1034 a^{2} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{1155 c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 12705 c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 63525 c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 190575 c^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 381150 c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 533610 c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 533610 c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 381150 c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 190575 c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63525 c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12705 c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1155 c^{6} f} - \frac{304 a^{2}}{1155 c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 12705 c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 63525 c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 190575 c^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 381150 c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 533610 c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 533610 c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 381150 c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 190575 c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63525 c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 12705 c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 1155 c^{6} f} & \text{for}\: f \neq 0 \\\frac{x \left(a \sin{\left(e \right)} + a\right)^{2}}{\left(- c \sin{\left(e \right)} + c\right)^{6}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2310*a**2*tan(e/2 + f*x/2)**10/(1155*c**6*f*tan(e/2 + f*x/2)**11 - 12705*c**6*f*tan(e/2 + f*x/2)**10 + 63525*c**6*f*tan(e/2 + f*x/2)**9 - 190575*c**6*f*tan(e/2 + f*x/2)**8 + 381150*c**6*f*tan(e/2 + f*x/2)**7 - 533610*c**6*f*tan(e/2 + f*x/2)**6 + 533610*c**6*f*tan(e/2 + f*x/2)**5 - 381150*c**6*f*tan(e/2 + f*x/2)**4 + 190575*c**6*f*tan(e/2 + f*x/2)**3 - 63525*c**6*f*tan(e/2 + f*x/2)**2 + 12705*c**6*f*tan(e/2 + f*x/2) - 1155*c**6*f) + 6930*a**2*tan(e/2 + f*x/2)**9/(1155*c**6*f*tan(e/2 + f*x/2)**11 - 12705*c**6*f*tan(e/2 + f*x/2)**10 + 63525*c**6*f*tan(e/2 + f*x/2)**9 - 190575*c**6*f*tan(e/2 + f*x/2)**8 + 381150*c**6*f*tan(e/2 + f*x/2)**7 - 533610*c**6*f*tan(e/2 + f*x/2)**6 + 533610*c**6*f*tan(e/2 + f*x/2)**5 - 381150*c**6*f*tan(e/2 + f*x/2)**4 + 190575*c**6*f*tan(e/2 + f*x/2)**3 - 63525*c**6*f*tan(e/2 + f*x/2)**2 + 12705*c**6*f*tan(e/2 + f*x/2) - 1155*c**6*f) - 27720*a**2*tan(e/2 + f*x/2)**8/(1155*c**6*f*tan(e/2 + f*x/2)**11 - 12705*c**6*f*tan(e/2 + f*x/2)**10 + 63525*c**6*f*tan(e/2 + f*x/2)**9 - 190575*c**6*f*tan(e/2 + f*x/2)**8 + 381150*c**6*f*tan(e/2 + f*x/2)**7 - 533610*c**6*f*tan(e/2 + f*x/2)**6 + 533610*c**6*f*tan(e/2 + f*x/2)**5 - 381150*c**6*f*tan(e/2 + f*x/2)**4 + 190575*c**6*f*tan(e/2 + f*x/2)**3 - 63525*c**6*f*tan(e/2 + f*x/2)**2 + 12705*c**6*f*tan(e/2 + f*x/2) - 1155*c**6*f) + 46200*a**2*tan(e/2 + f*x/2)**7/(1155*c**6*f*tan(e/2 + f*x/2)**11 - 12705*c**6*f*tan(e/2 + f*x/2)**10 + 63525*c**6*f*tan(e/2 + f*x/2)**9 - 190575*c**6*f*tan(e/2 + f*x/2)**8 + 381150*c**6*f*tan(e/2 + f*x/2)**7 - 533610*c**6*f*tan(e/2 + f*x/2)**6 + 533610*c**6*f*tan(e/2 + f*x/2)**5 - 381150*c**6*f*tan(e/2 + f*x/2)**4 + 190575*c**6*f*tan(e/2 + f*x/2)**3 - 63525*c**6*f*tan(e/2 + f*x/2)**2 + 12705*c**6*f*tan(e/2 + f*x/2) - 1155*c**6*f) - 74844*a**2*tan(e/2 + f*x/2)**6/(1155*c**6*f*tan(e/2 + f*x/2)**11 - 12705*c**6*f*tan(e/2 + f*x/2)**10 + 63525*c**6*f*tan(e/2 + f*x/2)**9 - 190575*c**6*f*tan(e/2 + f*x/2)**8 + 381150*c**6*f*tan(e/2 + f*x/2)**7 - 533610*c**6*f*tan(e/2 + f*x/2)**6 + 533610*c**6*f*tan(e/2 + f*x/2)**5 - 381150*c**6*f*tan(e/2 + f*x/2)**4 + 190575*c**6*f*tan(e/2 + f*x/2)**3 - 63525*c**6*f*tan(e/2 + f*x/2)**2 + 12705*c**6*f*tan(e/2 + f*x/2) - 1155*c**6*f) + 65604*a**2*tan(e/2 + f*x/2)**5/(1155*c**6*f*tan(e/2 + f*x/2)**11 - 12705*c**6*f*tan(e/2 + f*x/2)**10 + 63525*c**6*f*tan(e/2 + f*x/2)**9 - 190575*c**6*f*tan(e/2 + f*x/2)**8 + 381150*c**6*f*tan(e/2 + f*x/2)**7 - 533610*c**6*f*tan(e/2 + f*x/2)**6 + 533610*c**6*f*tan(e/2 + f*x/2)**5 - 381150*c**6*f*tan(e/2 + f*x/2)**4 + 190575*c**6*f*tan(e/2 + f*x/2)**3 - 63525*c**6*f*tan(e/2 + f*x/2)**2 + 12705*c**6*f*tan(e/2 + f*x/2) - 1155*c**6*f) - 54120*a**2*tan(e/2 + f*x/2)**4/(1155*c**6*f*tan(e/2 + f*x/2)**11 - 12705*c**6*f*tan(e/2 + f*x/2)**10 + 63525*c**6*f*tan(e/2 + f*x/2)**9 - 190575*c**6*f*tan(e/2 + f*x/2)**8 + 381150*c**6*f*tan(e/2 + f*x/2)**7 - 533610*c**6*f*tan(e/2 + f*x/2)**6 + 533610*c**6*f*tan(e/2 + f*x/2)**5 - 381150*c**6*f*tan(e/2 + f*x/2)**4 + 190575*c**6*f*tan(e/2 + f*x/2)**3 - 63525*c**6*f*tan(e/2 + f*x/2)**2 + 12705*c**6*f*tan(e/2 + f*x/2) - 1155*c**6*f) + 22440*a**2*tan(e/2 + f*x/2)**3/(1155*c**6*f*tan(e/2 + f*x/2)**11 - 12705*c**6*f*tan(e/2 + f*x/2)**10 + 63525*c**6*f*tan(e/2 + f*x/2)**9 - 190575*c**6*f*tan(e/2 + f*x/2)**8 + 381150*c**6*f*tan(e/2 + f*x/2)**7 - 533610*c**6*f*tan(e/2 + f*x/2)**6 + 533610*c**6*f*tan(e/2 + f*x/2)**5 - 381150*c**6*f*tan(e/2 + f*x/2)**4 + 190575*c**6*f*tan(e/2 + f*x/2)**3 - 63525*c**6*f*tan(e/2 + f*x/2)**2 + 12705*c**6*f*tan(e/2 + f*x/2) - 1155*c**6*f) - 9790*a**2*tan(e/2 + f*x/2)**2/(1155*c**6*f*tan(e/2 + f*x/2)**11 - 12705*c**6*f*tan(e/2 + f*x/2)**10 + 63525*c**6*f*tan(e/2 + f*x/2)**9 - 190575*c**6*f*tan(e/2 + f*x/2)**8 + 381150*c**6*f*tan(e/2 + f*x/2)**7 - 533610*c**6*f*tan(e/2 + f*x/2)**6 + 533610*c**6*f*tan(e/2 + f*x/2)**5 - 381150*c**6*f*tan(e/2 + f*x/2)**4 + 190575*c**6*f*tan(e/2 + f*x/2)**3 - 63525*c**6*f*tan(e/2 + f*x/2)**2 + 12705*c**6*f*tan(e/2 + f*x/2) - 1155*c**6*f) + 1034*a**2*tan(e/2 + f*x/2)/(1155*c**6*f*tan(e/2 + f*x/2)**11 - 12705*c**6*f*tan(e/2 + f*x/2)**10 + 63525*c**6*f*tan(e/2 + f*x/2)**9 - 190575*c**6*f*tan(e/2 + f*x/2)**8 + 381150*c**6*f*tan(e/2 + f*x/2)**7 - 533610*c**6*f*tan(e/2 + f*x/2)**6 + 533610*c**6*f*tan(e/2 + f*x/2)**5 - 381150*c**6*f*tan(e/2 + f*x/2)**4 + 190575*c**6*f*tan(e/2 + f*x/2)**3 - 63525*c**6*f*tan(e/2 + f*x/2)**2 + 12705*c**6*f*tan(e/2 + f*x/2) - 1155*c**6*f) - 304*a**2/(1155*c**6*f*tan(e/2 + f*x/2)**11 - 12705*c**6*f*tan(e/2 + f*x/2)**10 + 63525*c**6*f*tan(e/2 + f*x/2)**9 - 190575*c**6*f*tan(e/2 + f*x/2)**8 + 381150*c**6*f*tan(e/2 + f*x/2)**7 - 533610*c**6*f*tan(e/2 + f*x/2)**6 + 533610*c**6*f*tan(e/2 + f*x/2)**5 - 381150*c**6*f*tan(e/2 + f*x/2)**4 + 190575*c**6*f*tan(e/2 + f*x/2)**3 - 63525*c**6*f*tan(e/2 + f*x/2)**2 + 12705*c**6*f*tan(e/2 + f*x/2) - 1155*c**6*f), Ne(f, 0)), (x*(a*sin(e) + a)**2/(-c*sin(e) + c)**6, True))","A",0
247,1,838,0,26.385946," ","integrate((a+a*sin(f*x+e))**3*(c-c*sin(f*x+e))**6,x)","\begin{cases} - \frac{105 a^{3} c^{6} x \sin^{8}{\left(e + f x \right)}}{128} - \frac{105 a^{3} c^{6} x \sin^{6}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{32} + \frac{5 a^{3} c^{6} x \sin^{6}{\left(e + f x \right)}}{2} - \frac{315 a^{3} c^{6} x \sin^{4}{\left(e + f x \right)} \cos^{4}{\left(e + f x \right)}}{64} + \frac{15 a^{3} c^{6} x \sin^{4}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{2} - \frac{9 a^{3} c^{6} x \sin^{4}{\left(e + f x \right)}}{4} - \frac{105 a^{3} c^{6} x \sin^{2}{\left(e + f x \right)} \cos^{6}{\left(e + f x \right)}}{32} + \frac{15 a^{3} c^{6} x \sin^{2}{\left(e + f x \right)} \cos^{4}{\left(e + f x \right)}}{2} - \frac{9 a^{3} c^{6} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{2} - \frac{105 a^{3} c^{6} x \cos^{8}{\left(e + f x \right)}}{128} + \frac{5 a^{3} c^{6} x \cos^{6}{\left(e + f x \right)}}{2} - \frac{9 a^{3} c^{6} x \cos^{4}{\left(e + f x \right)}}{4} + a^{3} c^{6} x - \frac{a^{3} c^{6} \sin^{8}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{279 a^{3} c^{6} \sin^{7}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{128 f} - \frac{8 a^{3} c^{6} \sin^{6}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{3 f} + \frac{511 a^{3} c^{6} \sin^{5}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{128 f} - \frac{11 a^{3} c^{6} \sin^{5}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{16 a^{3} c^{6} \sin^{4}{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{5 f} + \frac{6 a^{3} c^{6} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{385 a^{3} c^{6} \sin^{3}{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{128 f} - \frac{20 a^{3} c^{6} \sin^{3}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{3 f} + \frac{15 a^{3} c^{6} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{4 f} - \frac{64 a^{3} c^{6} \sin^{2}{\left(e + f x \right)} \cos^{7}{\left(e + f x \right)}}{35 f} + \frac{8 a^{3} c^{6} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{f} - \frac{8 a^{3} c^{6} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{105 a^{3} c^{6} \sin{\left(e + f x \right)} \cos^{7}{\left(e + f x \right)}}{128 f} - \frac{5 a^{3} c^{6} \sin{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{2 f} + \frac{9 a^{3} c^{6} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{4 f} - \frac{128 a^{3} c^{6} \cos^{9}{\left(e + f x \right)}}{315 f} + \frac{16 a^{3} c^{6} \cos^{5}{\left(e + f x \right)}}{5 f} - \frac{16 a^{3} c^{6} \cos^{3}{\left(e + f x \right)}}{3 f} + \frac{3 a^{3} c^{6} \cos{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \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**3*c**6*x*sin(e + f*x)**8/128 - 105*a**3*c**6*x*sin(e + f*x)**6*cos(e + f*x)**2/32 + 5*a**3*c**6*x*sin(e + f*x)**6/2 - 315*a**3*c**6*x*sin(e + f*x)**4*cos(e + f*x)**4/64 + 15*a**3*c**6*x*sin(e + f*x)**4*cos(e + f*x)**2/2 - 9*a**3*c**6*x*sin(e + f*x)**4/4 - 105*a**3*c**6*x*sin(e + f*x)**2*cos(e + f*x)**6/32 + 15*a**3*c**6*x*sin(e + f*x)**2*cos(e + f*x)**4/2 - 9*a**3*c**6*x*sin(e + f*x)**2*cos(e + f*x)**2/2 - 105*a**3*c**6*x*cos(e + f*x)**8/128 + 5*a**3*c**6*x*cos(e + f*x)**6/2 - 9*a**3*c**6*x*cos(e + f*x)**4/4 + a**3*c**6*x - a**3*c**6*sin(e + f*x)**8*cos(e + f*x)/f + 279*a**3*c**6*sin(e + f*x)**7*cos(e + f*x)/(128*f) - 8*a**3*c**6*sin(e + f*x)**6*cos(e + f*x)**3/(3*f) + 511*a**3*c**6*sin(e + f*x)**5*cos(e + f*x)**3/(128*f) - 11*a**3*c**6*sin(e + f*x)**5*cos(e + f*x)/(2*f) - 16*a**3*c**6*sin(e + f*x)**4*cos(e + f*x)**5/(5*f) + 6*a**3*c**6*sin(e + f*x)**4*cos(e + f*x)/f + 385*a**3*c**6*sin(e + f*x)**3*cos(e + f*x)**5/(128*f) - 20*a**3*c**6*sin(e + f*x)**3*cos(e + f*x)**3/(3*f) + 15*a**3*c**6*sin(e + f*x)**3*cos(e + f*x)/(4*f) - 64*a**3*c**6*sin(e + f*x)**2*cos(e + f*x)**7/(35*f) + 8*a**3*c**6*sin(e + f*x)**2*cos(e + f*x)**3/f - 8*a**3*c**6*sin(e + f*x)**2*cos(e + f*x)/f + 105*a**3*c**6*sin(e + f*x)*cos(e + f*x)**7/(128*f) - 5*a**3*c**6*sin(e + f*x)*cos(e + f*x)**5/(2*f) + 9*a**3*c**6*sin(e + f*x)*cos(e + f*x)**3/(4*f) - 128*a**3*c**6*cos(e + f*x)**9/(315*f) + 16*a**3*c**6*cos(e + f*x)**5/(5*f) - 16*a**3*c**6*cos(e + f*x)**3/(3*f) + 3*a**3*c**6*cos(e + f*x)/f, Ne(f, 0)), (x*(a*sin(e) + a)**3*(-c*sin(e) + c)**6, True))","A",0
248,1,740,0,15.628894," ","integrate((a+a*sin(f*x+e))**3*(c-c*sin(f*x+e))**5,x)","\begin{cases} - \frac{35 a^{3} c^{5} x \sin^{8}{\left(e + f x \right)}}{128} - \frac{35 a^{3} c^{5} x \sin^{6}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{32} + \frac{5 a^{3} c^{5} x \sin^{6}{\left(e + f x \right)}}{8} - \frac{105 a^{3} c^{5} x \sin^{4}{\left(e + f x \right)} \cos^{4}{\left(e + f x \right)}}{64} + \frac{15 a^{3} c^{5} x \sin^{4}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{8} - \frac{35 a^{3} c^{5} x \sin^{2}{\left(e + f x \right)} \cos^{6}{\left(e + f x \right)}}{32} + \frac{15 a^{3} c^{5} x \sin^{2}{\left(e + f x \right)} \cos^{4}{\left(e + f x \right)}}{8} - a^{3} c^{5} x \sin^{2}{\left(e + f x \right)} - \frac{35 a^{3} c^{5} x \cos^{8}{\left(e + f x \right)}}{128} + \frac{5 a^{3} c^{5} x \cos^{6}{\left(e + f x \right)}}{8} - a^{3} c^{5} x \cos^{2}{\left(e + f x \right)} + a^{3} c^{5} x + \frac{93 a^{3} c^{5} \sin^{7}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{128 f} - \frac{2 a^{3} c^{5} \sin^{6}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{511 a^{3} c^{5} \sin^{5}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{384 f} - \frac{11 a^{3} c^{5} \sin^{5}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{4 a^{3} c^{5} \sin^{4}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{f} + \frac{6 a^{3} c^{5} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{385 a^{3} c^{5} \sin^{3}{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{384 f} - \frac{5 a^{3} c^{5} \sin^{3}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{16 a^{3} c^{5} \sin^{2}{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{5 f} + \frac{8 a^{3} c^{5} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{f} - \frac{6 a^{3} c^{5} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{35 a^{3} c^{5} \sin{\left(e + f x \right)} \cos^{7}{\left(e + f x \right)}}{128 f} - \frac{5 a^{3} c^{5} \sin{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{8 f} + \frac{a^{3} c^{5} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{32 a^{3} c^{5} \cos^{7}{\left(e + f x \right)}}{35 f} + \frac{16 a^{3} c^{5} \cos^{5}{\left(e + f x \right)}}{5 f} - \frac{4 a^{3} c^{5} \cos^{3}{\left(e + f x \right)}}{f} + \frac{2 a^{3} c^{5} \cos{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \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**3*c**5*x*sin(e + f*x)**8/128 - 35*a**3*c**5*x*sin(e + f*x)**6*cos(e + f*x)**2/32 + 5*a**3*c**5*x*sin(e + f*x)**6/8 - 105*a**3*c**5*x*sin(e + f*x)**4*cos(e + f*x)**4/64 + 15*a**3*c**5*x*sin(e + f*x)**4*cos(e + f*x)**2/8 - 35*a**3*c**5*x*sin(e + f*x)**2*cos(e + f*x)**6/32 + 15*a**3*c**5*x*sin(e + f*x)**2*cos(e + f*x)**4/8 - a**3*c**5*x*sin(e + f*x)**2 - 35*a**3*c**5*x*cos(e + f*x)**8/128 + 5*a**3*c**5*x*cos(e + f*x)**6/8 - a**3*c**5*x*cos(e + f*x)**2 + a**3*c**5*x + 93*a**3*c**5*sin(e + f*x)**7*cos(e + f*x)/(128*f) - 2*a**3*c**5*sin(e + f*x)**6*cos(e + f*x)/f + 511*a**3*c**5*sin(e + f*x)**5*cos(e + f*x)**3/(384*f) - 11*a**3*c**5*sin(e + f*x)**5*cos(e + f*x)/(8*f) - 4*a**3*c**5*sin(e + f*x)**4*cos(e + f*x)**3/f + 6*a**3*c**5*sin(e + f*x)**4*cos(e + f*x)/f + 385*a**3*c**5*sin(e + f*x)**3*cos(e + f*x)**5/(384*f) - 5*a**3*c**5*sin(e + f*x)**3*cos(e + f*x)**3/(3*f) - 16*a**3*c**5*sin(e + f*x)**2*cos(e + f*x)**5/(5*f) + 8*a**3*c**5*sin(e + f*x)**2*cos(e + f*x)**3/f - 6*a**3*c**5*sin(e + f*x)**2*cos(e + f*x)/f + 35*a**3*c**5*sin(e + f*x)*cos(e + f*x)**7/(128*f) - 5*a**3*c**5*sin(e + f*x)*cos(e + f*x)**5/(8*f) + a**3*c**5*sin(e + f*x)*cos(e + f*x)/f - 32*a**3*c**5*cos(e + f*x)**7/(35*f) + 16*a**3*c**5*cos(e + f*x)**5/(5*f) - 4*a**3*c**5*cos(e + f*x)**3/f + 2*a**3*c**5*cos(e + f*x)/f, Ne(f, 0)), (x*(a*sin(e) + a)**3*(-c*sin(e) + c)**5, True))","A",0
249,1,631,0,9.274471," ","integrate((a+a*sin(f*x+e))**3*(c-c*sin(f*x+e))**4,x)","\begin{cases} - \frac{5 a^{3} c^{4} x \sin^{6}{\left(e + f x \right)}}{16} - \frac{15 a^{3} c^{4} x \sin^{4}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{16} + \frac{9 a^{3} c^{4} x \sin^{4}{\left(e + f x \right)}}{8} - \frac{15 a^{3} c^{4} x \sin^{2}{\left(e + f x \right)} \cos^{4}{\left(e + f x \right)}}{16} + \frac{9 a^{3} c^{4} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} - \frac{3 a^{3} c^{4} x \sin^{2}{\left(e + f x \right)}}{2} - \frac{5 a^{3} c^{4} x \cos^{6}{\left(e + f x \right)}}{16} + \frac{9 a^{3} c^{4} x \cos^{4}{\left(e + f x \right)}}{8} - \frac{3 a^{3} c^{4} x \cos^{2}{\left(e + f x \right)}}{2} + a^{3} c^{4} x - \frac{a^{3} c^{4} \sin^{6}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{11 a^{3} c^{4} \sin^{5}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{16 f} - \frac{2 a^{3} c^{4} \sin^{4}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{f} + \frac{3 a^{3} c^{4} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{5 a^{3} c^{4} \sin^{3}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{6 f} - \frac{15 a^{3} c^{4} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{8 a^{3} c^{4} \sin^{2}{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{5 f} + \frac{4 a^{3} c^{4} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{f} - \frac{3 a^{3} c^{4} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{5 a^{3} c^{4} \sin{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{16 f} - \frac{9 a^{3} c^{4} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} + \frac{3 a^{3} c^{4} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{16 a^{3} c^{4} \cos^{7}{\left(e + f x \right)}}{35 f} + \frac{8 a^{3} c^{4} \cos^{5}{\left(e + f x \right)}}{5 f} - \frac{2 a^{3} c^{4} \cos^{3}{\left(e + f x \right)}}{f} + \frac{a^{3} c^{4} \cos{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \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**3*c**4*x*sin(e + f*x)**6/16 - 15*a**3*c**4*x*sin(e + f*x)**4*cos(e + f*x)**2/16 + 9*a**3*c**4*x*sin(e + f*x)**4/8 - 15*a**3*c**4*x*sin(e + f*x)**2*cos(e + f*x)**4/16 + 9*a**3*c**4*x*sin(e + f*x)**2*cos(e + f*x)**2/4 - 3*a**3*c**4*x*sin(e + f*x)**2/2 - 5*a**3*c**4*x*cos(e + f*x)**6/16 + 9*a**3*c**4*x*cos(e + f*x)**4/8 - 3*a**3*c**4*x*cos(e + f*x)**2/2 + a**3*c**4*x - a**3*c**4*sin(e + f*x)**6*cos(e + f*x)/f + 11*a**3*c**4*sin(e + f*x)**5*cos(e + f*x)/(16*f) - 2*a**3*c**4*sin(e + f*x)**4*cos(e + f*x)**3/f + 3*a**3*c**4*sin(e + f*x)**4*cos(e + f*x)/f + 5*a**3*c**4*sin(e + f*x)**3*cos(e + f*x)**3/(6*f) - 15*a**3*c**4*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 8*a**3*c**4*sin(e + f*x)**2*cos(e + f*x)**5/(5*f) + 4*a**3*c**4*sin(e + f*x)**2*cos(e + f*x)**3/f - 3*a**3*c**4*sin(e + f*x)**2*cos(e + f*x)/f + 5*a**3*c**4*sin(e + f*x)*cos(e + f*x)**5/(16*f) - 9*a**3*c**4*sin(e + f*x)*cos(e + f*x)**3/(8*f) + 3*a**3*c**4*sin(e + f*x)*cos(e + f*x)/(2*f) - 16*a**3*c**4*cos(e + f*x)**7/(35*f) + 8*a**3*c**4*cos(e + f*x)**5/(5*f) - 2*a**3*c**4*cos(e + f*x)**3/f + a**3*c**4*cos(e + f*x)/f, Ne(f, 0)), (x*(a*sin(e) + a)**3*(-c*sin(e) + c)**4, True))","A",0
250,1,398,0,5.416555," ","integrate((a+a*sin(f*x+e))**3*(c-c*sin(f*x+e))**3,x)","\begin{cases} - \frac{5 a^{3} c^{3} x \sin^{6}{\left(e + f x \right)}}{16} - \frac{15 a^{3} c^{3} x \sin^{4}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{16} + \frac{9 a^{3} c^{3} x \sin^{4}{\left(e + f x \right)}}{8} - \frac{15 a^{3} c^{3} x \sin^{2}{\left(e + f x \right)} \cos^{4}{\left(e + f x \right)}}{16} + \frac{9 a^{3} c^{3} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} - \frac{3 a^{3} c^{3} x \sin^{2}{\left(e + f x \right)}}{2} - \frac{5 a^{3} c^{3} x \cos^{6}{\left(e + f x \right)}}{16} + \frac{9 a^{3} c^{3} x \cos^{4}{\left(e + f x \right)}}{8} - \frac{3 a^{3} c^{3} x \cos^{2}{\left(e + f x \right)}}{2} + a^{3} c^{3} x + \frac{11 a^{3} c^{3} \sin^{5}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{16 f} + \frac{5 a^{3} c^{3} \sin^{3}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{6 f} - \frac{15 a^{3} c^{3} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} + \frac{5 a^{3} c^{3} \sin{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{16 f} - \frac{9 a^{3} c^{3} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} + \frac{3 a^{3} c^{3} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} & \text{for}\: f \neq 0 \\x \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**3*c**3*x*sin(e + f*x)**6/16 - 15*a**3*c**3*x*sin(e + f*x)**4*cos(e + f*x)**2/16 + 9*a**3*c**3*x*sin(e + f*x)**4/8 - 15*a**3*c**3*x*sin(e + f*x)**2*cos(e + f*x)**4/16 + 9*a**3*c**3*x*sin(e + f*x)**2*cos(e + f*x)**2/4 - 3*a**3*c**3*x*sin(e + f*x)**2/2 - 5*a**3*c**3*x*cos(e + f*x)**6/16 + 9*a**3*c**3*x*cos(e + f*x)**4/8 - 3*a**3*c**3*x*cos(e + f*x)**2/2 + a**3*c**3*x + 11*a**3*c**3*sin(e + f*x)**5*cos(e + f*x)/(16*f) + 5*a**3*c**3*sin(e + f*x)**3*cos(e + f*x)**3/(6*f) - 15*a**3*c**3*sin(e + f*x)**3*cos(e + f*x)/(8*f) + 5*a**3*c**3*sin(e + f*x)*cos(e + f*x)**5/(16*f) - 9*a**3*c**3*sin(e + f*x)*cos(e + f*x)**3/(8*f) + 3*a**3*c**3*sin(e + f*x)*cos(e + f*x)/(2*f), Ne(f, 0)), (x*(a*sin(e) + a)**3*(-c*sin(e) + c)**3, True))","A",0
251,1,340,0,3.324198," ","integrate((a+a*sin(f*x+e))**3*(c-c*sin(f*x+e))**2,x)","\begin{cases} \frac{3 a^{3} c^{2} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{3 a^{3} c^{2} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} - a^{3} c^{2} x \sin^{2}{\left(e + f x \right)} + \frac{3 a^{3} c^{2} x \cos^{4}{\left(e + f x \right)}}{8} - a^{3} c^{2} x \cos^{2}{\left(e + f x \right)} + a^{3} c^{2} x - \frac{a^{3} c^{2} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{5 a^{3} c^{2} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{4 a^{3} c^{2} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{3 f} + \frac{2 a^{3} c^{2} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{3 a^{3} c^{2} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} + \frac{a^{3} c^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{8 a^{3} c^{2} \cos^{5}{\left(e + f x \right)}}{15 f} + \frac{4 a^{3} c^{2} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{a^{3} c^{2} \cos{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \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**3*c**2*x*sin(e + f*x)**4/8 + 3*a**3*c**2*x*sin(e + f*x)**2*cos(e + f*x)**2/4 - a**3*c**2*x*sin(e + f*x)**2 + 3*a**3*c**2*x*cos(e + f*x)**4/8 - a**3*c**2*x*cos(e + f*x)**2 + a**3*c**2*x - a**3*c**2*sin(e + f*x)**4*cos(e + f*x)/f - 5*a**3*c**2*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 4*a**3*c**2*sin(e + f*x)**2*cos(e + f*x)**3/(3*f) + 2*a**3*c**2*sin(e + f*x)**2*cos(e + f*x)/f - 3*a**3*c**2*sin(e + f*x)*cos(e + f*x)**3/(8*f) + a**3*c**2*sin(e + f*x)*cos(e + f*x)/f - 8*a**3*c**2*cos(e + f*x)**5/(15*f) + 4*a**3*c**2*cos(e + f*x)**3/(3*f) - a**3*c**2*cos(e + f*x)/f, Ne(f, 0)), (x*(a*sin(e) + a)**3*(-c*sin(e) + c)**2, True))","A",0
252,1,196,0,1.491703," ","integrate((a+a*sin(f*x+e))**3*(c-c*sin(f*x+e)),x)","\begin{cases} - \frac{3 a^{3} c x \sin^{4}{\left(e + f x \right)}}{8} - \frac{3 a^{3} c x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} - \frac{3 a^{3} c x \cos^{4}{\left(e + f x \right)}}{8} + a^{3} c x + \frac{5 a^{3} c \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} + \frac{2 a^{3} c \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{3 a^{3} c \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} + \frac{4 a^{3} c \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{2 a^{3} c \cos{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \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**3*c*x*sin(e + f*x)**4/8 - 3*a**3*c*x*sin(e + f*x)**2*cos(e + f*x)**2/4 - 3*a**3*c*x*cos(e + f*x)**4/8 + a**3*c*x + 5*a**3*c*sin(e + f*x)**3*cos(e + f*x)/(8*f) + 2*a**3*c*sin(e + f*x)**2*cos(e + f*x)/f + 3*a**3*c*sin(e + f*x)*cos(e + f*x)**3/(8*f) + 4*a**3*c*cos(e + f*x)**3/(3*f) - 2*a**3*c*cos(e + f*x)/f, Ne(f, 0)), (x*(a*sin(e) + a)**3*(-c*sin(e) + c), True))","A",0
253,1,1168,0,7.425201," ","integrate((a+a*sin(f*x+e))**3/(c-c*sin(f*x+e)),x)","\begin{cases} - \frac{15 a^{3} 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{15 a^{3} 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{30 a^{3} 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{30 a^{3} 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{15 a^{3} 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{15 a^{3} 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{34 a^{3} \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 a^{3} \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{78 a^{3} \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{14 a^{3} \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{48 a^{3}}{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 \sin{\left(e \right)} + a\right)^{3}}{- c \sin{\left(e \right)} + c} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-15*a**3*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) + 15*a**3*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) - 30*a**3*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) + 30*a**3*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) - 15*a**3*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) + 15*a**3*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) - 34*a**3*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*a**3*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) - 78*a**3*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) + 14*a**3*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) - 48*a**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), Ne(f, 0)), (x*(a*sin(e) + a)**3/(-c*sin(e) + c), True))","A",0
254,1,1282,0,13.649338," ","integrate((a+a*sin(f*x+e))**3/(c-c*sin(f*x+e))**2,x)","\begin{cases} \frac{15 a^{3} 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{45 a^{3} 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{60 a^{3} 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{60 a^{3} 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{45 a^{3} 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{15 a^{3} 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^{3} \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{102 a^{3} \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{82 a^{3} \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{114 a^{3} \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{46 a^{3}}{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 \sin{\left(e \right)} + a\right)^{3}}{\left(- c \sin{\left(e \right)} + c\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((15*a**3*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) - 45*a**3*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) + 60*a**3*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) - 60*a**3*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) + 45*a**3*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) - 15*a**3*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**3*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) - 102*a**3*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) + 82*a**3*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) - 114*a**3*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) + 46*a**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), Ne(f, 0)), (x*(a*sin(e) + a)**3/(-c*sin(e) + c)**2, True))","A",0
255,1,1282,0,26.029691," ","integrate((a+a*sin(f*x+e))**3/(c-c*sin(f*x+e))**3,x)","\begin{cases} - \frac{15 a^{3} 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 a^{3} 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 a^{3} 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 a^{3} 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 a^{3} 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 a^{3} 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{60 a^{3} \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 a^{3} \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{400 a^{3} \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 a^{3} \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{52 a^{3}}{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 \sin{\left(e \right)} + a\right)^{3}}{\left(- c \sin{\left(e \right)} + c\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-15*a**3*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*a**3*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*a**3*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*a**3*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*a**3*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*a**3*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) - 60*a**3*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*a**3*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) - 400*a**3*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*a**3*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) - 52*a**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), Ne(f, 0)), (x*(a*sin(e) + a)**3/(-c*sin(e) + c)**3, True))","A",0
256,1,619,0,41.605809," ","integrate((a+a*sin(f*x+e))**3/(c-c*sin(f*x+e))**4,x)","\begin{cases} - \frac{14 a^{3} \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{7 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 49 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 147 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 245 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 245 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 147 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 49 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 7 c^{4} f} - \frac{70 a^{3} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{7 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 49 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 147 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 245 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 245 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 147 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 49 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 7 c^{4} f} - \frac{42 a^{3} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{7 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 49 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 147 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 245 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 245 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 147 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 49 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 7 c^{4} f} - \frac{2 a^{3}}{7 c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 49 c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 147 c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 245 c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 245 c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 147 c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 49 c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 7 c^{4} f} & \text{for}\: f \neq 0 \\\frac{x \left(a \sin{\left(e \right)} + a\right)^{3}}{\left(- c \sin{\left(e \right)} + c\right)^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-14*a**3*tan(e/2 + f*x/2)**6/(7*c**4*f*tan(e/2 + f*x/2)**7 - 49*c**4*f*tan(e/2 + f*x/2)**6 + 147*c**4*f*tan(e/2 + f*x/2)**5 - 245*c**4*f*tan(e/2 + f*x/2)**4 + 245*c**4*f*tan(e/2 + f*x/2)**3 - 147*c**4*f*tan(e/2 + f*x/2)**2 + 49*c**4*f*tan(e/2 + f*x/2) - 7*c**4*f) - 70*a**3*tan(e/2 + f*x/2)**4/(7*c**4*f*tan(e/2 + f*x/2)**7 - 49*c**4*f*tan(e/2 + f*x/2)**6 + 147*c**4*f*tan(e/2 + f*x/2)**5 - 245*c**4*f*tan(e/2 + f*x/2)**4 + 245*c**4*f*tan(e/2 + f*x/2)**3 - 147*c**4*f*tan(e/2 + f*x/2)**2 + 49*c**4*f*tan(e/2 + f*x/2) - 7*c**4*f) - 42*a**3*tan(e/2 + f*x/2)**2/(7*c**4*f*tan(e/2 + f*x/2)**7 - 49*c**4*f*tan(e/2 + f*x/2)**6 + 147*c**4*f*tan(e/2 + f*x/2)**5 - 245*c**4*f*tan(e/2 + f*x/2)**4 + 245*c**4*f*tan(e/2 + f*x/2)**3 - 147*c**4*f*tan(e/2 + f*x/2)**2 + 49*c**4*f*tan(e/2 + f*x/2) - 7*c**4*f) - 2*a**3/(7*c**4*f*tan(e/2 + f*x/2)**7 - 49*c**4*f*tan(e/2 + f*x/2)**6 + 147*c**4*f*tan(e/2 + f*x/2)**5 - 245*c**4*f*tan(e/2 + f*x/2)**4 + 245*c**4*f*tan(e/2 + f*x/2)**3 - 147*c**4*f*tan(e/2 + f*x/2)**2 + 49*c**4*f*tan(e/2 + f*x/2) - 7*c**4*f), Ne(f, 0)), (x*(a*sin(e) + a)**3/(-c*sin(e) + c)**4, True))","A",0
257,1,1717,0,72.339023," ","integrate((a+a*sin(f*x+e))**3/(c-c*sin(f*x+e))**5,x)","\begin{cases} - \frac{126 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^{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^{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^{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^{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^{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^{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^{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^{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 \sin{\left(e \right)} + a\right)^{3}}{\left(- c \sin{\left(e \right)} + c\right)^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-126*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**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**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**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**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**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**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**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**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*sin(e) + a)**3/(-c*sin(e) + c)**5, True))","A",0
258,1,2509,0,118.535414," ","integrate((a+a*sin(f*x+e))**3/(c-c*sin(f*x+e))**6,x)","\begin{cases} - \frac{1386 a^{3} \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{693 c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 7623 c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 38115 c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 114345 c^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 228690 c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 320166 c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 320166 c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 228690 c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 114345 c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 38115 c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 7623 c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 693 c^{6} f} + \frac{2772 a^{3} \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{693 c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 7623 c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 38115 c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 114345 c^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 228690 c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 320166 c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 320166 c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 228690 c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 114345 c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 38115 c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 7623 c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 693 c^{6} f} - \frac{16170 a^{3} \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{693 c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 7623 c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 38115 c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 114345 c^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 228690 c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 320166 c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 320166 c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 228690 c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 114345 c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 38115 c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 7623 c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 693 c^{6} f} + \frac{21252 a^{3} \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{693 c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 7623 c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 38115 c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 114345 c^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 228690 c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 320166 c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 320166 c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 228690 c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 114345 c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 38115 c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 7623 c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 693 c^{6} f} - \frac{42504 a^{3} \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{693 c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 7623 c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 38115 c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 114345 c^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 228690 c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 320166 c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 320166 c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 228690 c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 114345 c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 38115 c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 7623 c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 693 c^{6} f} + \frac{30492 a^{3} \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{693 c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 7623 c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 38115 c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 114345 c^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 228690 c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 320166 c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 320166 c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 228690 c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 114345 c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 38115 c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 7623 c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 693 c^{6} f} - \frac{30888 a^{3} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{693 c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 7623 c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 38115 c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 114345 c^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 228690 c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 320166 c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 320166 c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 228690 c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 114345 c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 38115 c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 7623 c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 693 c^{6} f} + \frac{9900 a^{3} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{693 c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 7623 c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 38115 c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 114345 c^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 228690 c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 320166 c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 320166 c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 228690 c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 114345 c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 38115 c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 7623 c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 693 c^{6} f} - \frac{5918 a^{3} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{693 c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 7623 c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 38115 c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 114345 c^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 228690 c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 320166 c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 320166 c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 228690 c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 114345 c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 38115 c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 7623 c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 693 c^{6} f} + \frac{352 a^{3} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{693 c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 7623 c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 38115 c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 114345 c^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 228690 c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 320166 c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 320166 c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 228690 c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 114345 c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 38115 c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 7623 c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 693 c^{6} f} - \frac{158 a^{3}}{693 c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 7623 c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 38115 c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 114345 c^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 228690 c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 320166 c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 320166 c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 228690 c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 114345 c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 38115 c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 7623 c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 693 c^{6} f} & \text{for}\: f \neq 0 \\\frac{x \left(a \sin{\left(e \right)} + a\right)^{3}}{\left(- c \sin{\left(e \right)} + c\right)^{6}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-1386*a**3*tan(e/2 + f*x/2)**10/(693*c**6*f*tan(e/2 + f*x/2)**11 - 7623*c**6*f*tan(e/2 + f*x/2)**10 + 38115*c**6*f*tan(e/2 + f*x/2)**9 - 114345*c**6*f*tan(e/2 + f*x/2)**8 + 228690*c**6*f*tan(e/2 + f*x/2)**7 - 320166*c**6*f*tan(e/2 + f*x/2)**6 + 320166*c**6*f*tan(e/2 + f*x/2)**5 - 228690*c**6*f*tan(e/2 + f*x/2)**4 + 114345*c**6*f*tan(e/2 + f*x/2)**3 - 38115*c**6*f*tan(e/2 + f*x/2)**2 + 7623*c**6*f*tan(e/2 + f*x/2) - 693*c**6*f) + 2772*a**3*tan(e/2 + f*x/2)**9/(693*c**6*f*tan(e/2 + f*x/2)**11 - 7623*c**6*f*tan(e/2 + f*x/2)**10 + 38115*c**6*f*tan(e/2 + f*x/2)**9 - 114345*c**6*f*tan(e/2 + f*x/2)**8 + 228690*c**6*f*tan(e/2 + f*x/2)**7 - 320166*c**6*f*tan(e/2 + f*x/2)**6 + 320166*c**6*f*tan(e/2 + f*x/2)**5 - 228690*c**6*f*tan(e/2 + f*x/2)**4 + 114345*c**6*f*tan(e/2 + f*x/2)**3 - 38115*c**6*f*tan(e/2 + f*x/2)**2 + 7623*c**6*f*tan(e/2 + f*x/2) - 693*c**6*f) - 16170*a**3*tan(e/2 + f*x/2)**8/(693*c**6*f*tan(e/2 + f*x/2)**11 - 7623*c**6*f*tan(e/2 + f*x/2)**10 + 38115*c**6*f*tan(e/2 + f*x/2)**9 - 114345*c**6*f*tan(e/2 + f*x/2)**8 + 228690*c**6*f*tan(e/2 + f*x/2)**7 - 320166*c**6*f*tan(e/2 + f*x/2)**6 + 320166*c**6*f*tan(e/2 + f*x/2)**5 - 228690*c**6*f*tan(e/2 + f*x/2)**4 + 114345*c**6*f*tan(e/2 + f*x/2)**3 - 38115*c**6*f*tan(e/2 + f*x/2)**2 + 7623*c**6*f*tan(e/2 + f*x/2) - 693*c**6*f) + 21252*a**3*tan(e/2 + f*x/2)**7/(693*c**6*f*tan(e/2 + f*x/2)**11 - 7623*c**6*f*tan(e/2 + f*x/2)**10 + 38115*c**6*f*tan(e/2 + f*x/2)**9 - 114345*c**6*f*tan(e/2 + f*x/2)**8 + 228690*c**6*f*tan(e/2 + f*x/2)**7 - 320166*c**6*f*tan(e/2 + f*x/2)**6 + 320166*c**6*f*tan(e/2 + f*x/2)**5 - 228690*c**6*f*tan(e/2 + f*x/2)**4 + 114345*c**6*f*tan(e/2 + f*x/2)**3 - 38115*c**6*f*tan(e/2 + f*x/2)**2 + 7623*c**6*f*tan(e/2 + f*x/2) - 693*c**6*f) - 42504*a**3*tan(e/2 + f*x/2)**6/(693*c**6*f*tan(e/2 + f*x/2)**11 - 7623*c**6*f*tan(e/2 + f*x/2)**10 + 38115*c**6*f*tan(e/2 + f*x/2)**9 - 114345*c**6*f*tan(e/2 + f*x/2)**8 + 228690*c**6*f*tan(e/2 + f*x/2)**7 - 320166*c**6*f*tan(e/2 + f*x/2)**6 + 320166*c**6*f*tan(e/2 + f*x/2)**5 - 228690*c**6*f*tan(e/2 + f*x/2)**4 + 114345*c**6*f*tan(e/2 + f*x/2)**3 - 38115*c**6*f*tan(e/2 + f*x/2)**2 + 7623*c**6*f*tan(e/2 + f*x/2) - 693*c**6*f) + 30492*a**3*tan(e/2 + f*x/2)**5/(693*c**6*f*tan(e/2 + f*x/2)**11 - 7623*c**6*f*tan(e/2 + f*x/2)**10 + 38115*c**6*f*tan(e/2 + f*x/2)**9 - 114345*c**6*f*tan(e/2 + f*x/2)**8 + 228690*c**6*f*tan(e/2 + f*x/2)**7 - 320166*c**6*f*tan(e/2 + f*x/2)**6 + 320166*c**6*f*tan(e/2 + f*x/2)**5 - 228690*c**6*f*tan(e/2 + f*x/2)**4 + 114345*c**6*f*tan(e/2 + f*x/2)**3 - 38115*c**6*f*tan(e/2 + f*x/2)**2 + 7623*c**6*f*tan(e/2 + f*x/2) - 693*c**6*f) - 30888*a**3*tan(e/2 + f*x/2)**4/(693*c**6*f*tan(e/2 + f*x/2)**11 - 7623*c**6*f*tan(e/2 + f*x/2)**10 + 38115*c**6*f*tan(e/2 + f*x/2)**9 - 114345*c**6*f*tan(e/2 + f*x/2)**8 + 228690*c**6*f*tan(e/2 + f*x/2)**7 - 320166*c**6*f*tan(e/2 + f*x/2)**6 + 320166*c**6*f*tan(e/2 + f*x/2)**5 - 228690*c**6*f*tan(e/2 + f*x/2)**4 + 114345*c**6*f*tan(e/2 + f*x/2)**3 - 38115*c**6*f*tan(e/2 + f*x/2)**2 + 7623*c**6*f*tan(e/2 + f*x/2) - 693*c**6*f) + 9900*a**3*tan(e/2 + f*x/2)**3/(693*c**6*f*tan(e/2 + f*x/2)**11 - 7623*c**6*f*tan(e/2 + f*x/2)**10 + 38115*c**6*f*tan(e/2 + f*x/2)**9 - 114345*c**6*f*tan(e/2 + f*x/2)**8 + 228690*c**6*f*tan(e/2 + f*x/2)**7 - 320166*c**6*f*tan(e/2 + f*x/2)**6 + 320166*c**6*f*tan(e/2 + f*x/2)**5 - 228690*c**6*f*tan(e/2 + f*x/2)**4 + 114345*c**6*f*tan(e/2 + f*x/2)**3 - 38115*c**6*f*tan(e/2 + f*x/2)**2 + 7623*c**6*f*tan(e/2 + f*x/2) - 693*c**6*f) - 5918*a**3*tan(e/2 + f*x/2)**2/(693*c**6*f*tan(e/2 + f*x/2)**11 - 7623*c**6*f*tan(e/2 + f*x/2)**10 + 38115*c**6*f*tan(e/2 + f*x/2)**9 - 114345*c**6*f*tan(e/2 + f*x/2)**8 + 228690*c**6*f*tan(e/2 + f*x/2)**7 - 320166*c**6*f*tan(e/2 + f*x/2)**6 + 320166*c**6*f*tan(e/2 + f*x/2)**5 - 228690*c**6*f*tan(e/2 + f*x/2)**4 + 114345*c**6*f*tan(e/2 + f*x/2)**3 - 38115*c**6*f*tan(e/2 + f*x/2)**2 + 7623*c**6*f*tan(e/2 + f*x/2) - 693*c**6*f) + 352*a**3*tan(e/2 + f*x/2)/(693*c**6*f*tan(e/2 + f*x/2)**11 - 7623*c**6*f*tan(e/2 + f*x/2)**10 + 38115*c**6*f*tan(e/2 + f*x/2)**9 - 114345*c**6*f*tan(e/2 + f*x/2)**8 + 228690*c**6*f*tan(e/2 + f*x/2)**7 - 320166*c**6*f*tan(e/2 + f*x/2)**6 + 320166*c**6*f*tan(e/2 + f*x/2)**5 - 228690*c**6*f*tan(e/2 + f*x/2)**4 + 114345*c**6*f*tan(e/2 + f*x/2)**3 - 38115*c**6*f*tan(e/2 + f*x/2)**2 + 7623*c**6*f*tan(e/2 + f*x/2) - 693*c**6*f) - 158*a**3/(693*c**6*f*tan(e/2 + f*x/2)**11 - 7623*c**6*f*tan(e/2 + f*x/2)**10 + 38115*c**6*f*tan(e/2 + f*x/2)**9 - 114345*c**6*f*tan(e/2 + f*x/2)**8 + 228690*c**6*f*tan(e/2 + f*x/2)**7 - 320166*c**6*f*tan(e/2 + f*x/2)**6 + 320166*c**6*f*tan(e/2 + f*x/2)**5 - 228690*c**6*f*tan(e/2 + f*x/2)**4 + 114345*c**6*f*tan(e/2 + f*x/2)**3 - 38115*c**6*f*tan(e/2 + f*x/2)**2 + 7623*c**6*f*tan(e/2 + f*x/2) - 693*c**6*f), Ne(f, 0)), (x*(a*sin(e) + a)**3/(-c*sin(e) + c)**6, True))","A",0
259,1,3451,0,178.922071," ","integrate((a+a*sin(f*x+e))**3/(c-c*sin(f*x+e))**7,x)","\begin{cases} - \frac{6006 a^{3} \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3003 c^{7} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39039 c^{7} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 234234 c^{7} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 858858 c^{7} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2147145 c^{7} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3864861 c^{7} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5153148 c^{7} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5153148 c^{7} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3864861 c^{7} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2147145 c^{7} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 858858 c^{7} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 234234 c^{7} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39039 c^{7} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3003 c^{7} f} + \frac{18018 a^{3} \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3003 c^{7} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39039 c^{7} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 234234 c^{7} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 858858 c^{7} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2147145 c^{7} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3864861 c^{7} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5153148 c^{7} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5153148 c^{7} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3864861 c^{7} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2147145 c^{7} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 858858 c^{7} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 234234 c^{7} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39039 c^{7} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3003 c^{7} f} - \frac{102102 a^{3} \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3003 c^{7} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39039 c^{7} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 234234 c^{7} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 858858 c^{7} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2147145 c^{7} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3864861 c^{7} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5153148 c^{7} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5153148 c^{7} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3864861 c^{7} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2147145 c^{7} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 858858 c^{7} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 234234 c^{7} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39039 c^{7} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3003 c^{7} f} + \frac{198198 a^{3} \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3003 c^{7} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39039 c^{7} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 234234 c^{7} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 858858 c^{7} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2147145 c^{7} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3864861 c^{7} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5153148 c^{7} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5153148 c^{7} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3864861 c^{7} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2147145 c^{7} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 858858 c^{7} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 234234 c^{7} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39039 c^{7} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3003 c^{7} f} - \frac{432432 a^{3} \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3003 c^{7} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39039 c^{7} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 234234 c^{7} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 858858 c^{7} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2147145 c^{7} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3864861 c^{7} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5153148 c^{7} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5153148 c^{7} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3864861 c^{7} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2147145 c^{7} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 858858 c^{7} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 234234 c^{7} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39039 c^{7} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3003 c^{7} f} + \frac{492492 a^{3} \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3003 c^{7} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39039 c^{7} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 234234 c^{7} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 858858 c^{7} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2147145 c^{7} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3864861 c^{7} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5153148 c^{7} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5153148 c^{7} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3864861 c^{7} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2147145 c^{7} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 858858 c^{7} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 234234 c^{7} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39039 c^{7} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3003 c^{7} f} - \frac{571428 a^{3} \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3003 c^{7} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39039 c^{7} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 234234 c^{7} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 858858 c^{7} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2147145 c^{7} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3864861 c^{7} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5153148 c^{7} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5153148 c^{7} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3864861 c^{7} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2147145 c^{7} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 858858 c^{7} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 234234 c^{7} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39039 c^{7} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3003 c^{7} f} + \frac{365508 a^{3} \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3003 c^{7} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39039 c^{7} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 234234 c^{7} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 858858 c^{7} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2147145 c^{7} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3864861 c^{7} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5153148 c^{7} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5153148 c^{7} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3864861 c^{7} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2147145 c^{7} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 858858 c^{7} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 234234 c^{7} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39039 c^{7} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3003 c^{7} f} - \frac{245102 a^{3} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3003 c^{7} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39039 c^{7} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 234234 c^{7} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 858858 c^{7} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2147145 c^{7} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3864861 c^{7} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5153148 c^{7} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5153148 c^{7} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3864861 c^{7} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2147145 c^{7} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 858858 c^{7} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 234234 c^{7} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39039 c^{7} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3003 c^{7} f} + \frac{75218 a^{3} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3003 c^{7} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39039 c^{7} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 234234 c^{7} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 858858 c^{7} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2147145 c^{7} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3864861 c^{7} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5153148 c^{7} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5153148 c^{7} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3864861 c^{7} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2147145 c^{7} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 858858 c^{7} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 234234 c^{7} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39039 c^{7} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3003 c^{7} f} - \frac{30342 a^{3} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3003 c^{7} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39039 c^{7} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 234234 c^{7} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 858858 c^{7} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2147145 c^{7} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3864861 c^{7} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5153148 c^{7} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5153148 c^{7} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3864861 c^{7} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2147145 c^{7} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 858858 c^{7} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 234234 c^{7} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39039 c^{7} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3003 c^{7} f} + \frac{2054 a^{3} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3003 c^{7} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39039 c^{7} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 234234 c^{7} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 858858 c^{7} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2147145 c^{7} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3864861 c^{7} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5153148 c^{7} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5153148 c^{7} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3864861 c^{7} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2147145 c^{7} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 858858 c^{7} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 234234 c^{7} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39039 c^{7} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3003 c^{7} f} - \frac{620 a^{3}}{3003 c^{7} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 39039 c^{7} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 234234 c^{7} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 858858 c^{7} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2147145 c^{7} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3864861 c^{7} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5153148 c^{7} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5153148 c^{7} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3864861 c^{7} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2147145 c^{7} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 858858 c^{7} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 234234 c^{7} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39039 c^{7} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 3003 c^{7} f} & \text{for}\: f \neq 0 \\\frac{x \left(a \sin{\left(e \right)} + a\right)^{3}}{\left(- c \sin{\left(e \right)} + c\right)^{7}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-6006*a**3*tan(e/2 + f*x/2)**12/(3003*c**7*f*tan(e/2 + f*x/2)**13 - 39039*c**7*f*tan(e/2 + f*x/2)**12 + 234234*c**7*f*tan(e/2 + f*x/2)**11 - 858858*c**7*f*tan(e/2 + f*x/2)**10 + 2147145*c**7*f*tan(e/2 + f*x/2)**9 - 3864861*c**7*f*tan(e/2 + f*x/2)**8 + 5153148*c**7*f*tan(e/2 + f*x/2)**7 - 5153148*c**7*f*tan(e/2 + f*x/2)**6 + 3864861*c**7*f*tan(e/2 + f*x/2)**5 - 2147145*c**7*f*tan(e/2 + f*x/2)**4 + 858858*c**7*f*tan(e/2 + f*x/2)**3 - 234234*c**7*f*tan(e/2 + f*x/2)**2 + 39039*c**7*f*tan(e/2 + f*x/2) - 3003*c**7*f) + 18018*a**3*tan(e/2 + f*x/2)**11/(3003*c**7*f*tan(e/2 + f*x/2)**13 - 39039*c**7*f*tan(e/2 + f*x/2)**12 + 234234*c**7*f*tan(e/2 + f*x/2)**11 - 858858*c**7*f*tan(e/2 + f*x/2)**10 + 2147145*c**7*f*tan(e/2 + f*x/2)**9 - 3864861*c**7*f*tan(e/2 + f*x/2)**8 + 5153148*c**7*f*tan(e/2 + f*x/2)**7 - 5153148*c**7*f*tan(e/2 + f*x/2)**6 + 3864861*c**7*f*tan(e/2 + f*x/2)**5 - 2147145*c**7*f*tan(e/2 + f*x/2)**4 + 858858*c**7*f*tan(e/2 + f*x/2)**3 - 234234*c**7*f*tan(e/2 + f*x/2)**2 + 39039*c**7*f*tan(e/2 + f*x/2) - 3003*c**7*f) - 102102*a**3*tan(e/2 + f*x/2)**10/(3003*c**7*f*tan(e/2 + f*x/2)**13 - 39039*c**7*f*tan(e/2 + f*x/2)**12 + 234234*c**7*f*tan(e/2 + f*x/2)**11 - 858858*c**7*f*tan(e/2 + f*x/2)**10 + 2147145*c**7*f*tan(e/2 + f*x/2)**9 - 3864861*c**7*f*tan(e/2 + f*x/2)**8 + 5153148*c**7*f*tan(e/2 + f*x/2)**7 - 5153148*c**7*f*tan(e/2 + f*x/2)**6 + 3864861*c**7*f*tan(e/2 + f*x/2)**5 - 2147145*c**7*f*tan(e/2 + f*x/2)**4 + 858858*c**7*f*tan(e/2 + f*x/2)**3 - 234234*c**7*f*tan(e/2 + f*x/2)**2 + 39039*c**7*f*tan(e/2 + f*x/2) - 3003*c**7*f) + 198198*a**3*tan(e/2 + f*x/2)**9/(3003*c**7*f*tan(e/2 + f*x/2)**13 - 39039*c**7*f*tan(e/2 + f*x/2)**12 + 234234*c**7*f*tan(e/2 + f*x/2)**11 - 858858*c**7*f*tan(e/2 + f*x/2)**10 + 2147145*c**7*f*tan(e/2 + f*x/2)**9 - 3864861*c**7*f*tan(e/2 + f*x/2)**8 + 5153148*c**7*f*tan(e/2 + f*x/2)**7 - 5153148*c**7*f*tan(e/2 + f*x/2)**6 + 3864861*c**7*f*tan(e/2 + f*x/2)**5 - 2147145*c**7*f*tan(e/2 + f*x/2)**4 + 858858*c**7*f*tan(e/2 + f*x/2)**3 - 234234*c**7*f*tan(e/2 + f*x/2)**2 + 39039*c**7*f*tan(e/2 + f*x/2) - 3003*c**7*f) - 432432*a**3*tan(e/2 + f*x/2)**8/(3003*c**7*f*tan(e/2 + f*x/2)**13 - 39039*c**7*f*tan(e/2 + f*x/2)**12 + 234234*c**7*f*tan(e/2 + f*x/2)**11 - 858858*c**7*f*tan(e/2 + f*x/2)**10 + 2147145*c**7*f*tan(e/2 + f*x/2)**9 - 3864861*c**7*f*tan(e/2 + f*x/2)**8 + 5153148*c**7*f*tan(e/2 + f*x/2)**7 - 5153148*c**7*f*tan(e/2 + f*x/2)**6 + 3864861*c**7*f*tan(e/2 + f*x/2)**5 - 2147145*c**7*f*tan(e/2 + f*x/2)**4 + 858858*c**7*f*tan(e/2 + f*x/2)**3 - 234234*c**7*f*tan(e/2 + f*x/2)**2 + 39039*c**7*f*tan(e/2 + f*x/2) - 3003*c**7*f) + 492492*a**3*tan(e/2 + f*x/2)**7/(3003*c**7*f*tan(e/2 + f*x/2)**13 - 39039*c**7*f*tan(e/2 + f*x/2)**12 + 234234*c**7*f*tan(e/2 + f*x/2)**11 - 858858*c**7*f*tan(e/2 + f*x/2)**10 + 2147145*c**7*f*tan(e/2 + f*x/2)**9 - 3864861*c**7*f*tan(e/2 + f*x/2)**8 + 5153148*c**7*f*tan(e/2 + f*x/2)**7 - 5153148*c**7*f*tan(e/2 + f*x/2)**6 + 3864861*c**7*f*tan(e/2 + f*x/2)**5 - 2147145*c**7*f*tan(e/2 + f*x/2)**4 + 858858*c**7*f*tan(e/2 + f*x/2)**3 - 234234*c**7*f*tan(e/2 + f*x/2)**2 + 39039*c**7*f*tan(e/2 + f*x/2) - 3003*c**7*f) - 571428*a**3*tan(e/2 + f*x/2)**6/(3003*c**7*f*tan(e/2 + f*x/2)**13 - 39039*c**7*f*tan(e/2 + f*x/2)**12 + 234234*c**7*f*tan(e/2 + f*x/2)**11 - 858858*c**7*f*tan(e/2 + f*x/2)**10 + 2147145*c**7*f*tan(e/2 + f*x/2)**9 - 3864861*c**7*f*tan(e/2 + f*x/2)**8 + 5153148*c**7*f*tan(e/2 + f*x/2)**7 - 5153148*c**7*f*tan(e/2 + f*x/2)**6 + 3864861*c**7*f*tan(e/2 + f*x/2)**5 - 2147145*c**7*f*tan(e/2 + f*x/2)**4 + 858858*c**7*f*tan(e/2 + f*x/2)**3 - 234234*c**7*f*tan(e/2 + f*x/2)**2 + 39039*c**7*f*tan(e/2 + f*x/2) - 3003*c**7*f) + 365508*a**3*tan(e/2 + f*x/2)**5/(3003*c**7*f*tan(e/2 + f*x/2)**13 - 39039*c**7*f*tan(e/2 + f*x/2)**12 + 234234*c**7*f*tan(e/2 + f*x/2)**11 - 858858*c**7*f*tan(e/2 + f*x/2)**10 + 2147145*c**7*f*tan(e/2 + f*x/2)**9 - 3864861*c**7*f*tan(e/2 + f*x/2)**8 + 5153148*c**7*f*tan(e/2 + f*x/2)**7 - 5153148*c**7*f*tan(e/2 + f*x/2)**6 + 3864861*c**7*f*tan(e/2 + f*x/2)**5 - 2147145*c**7*f*tan(e/2 + f*x/2)**4 + 858858*c**7*f*tan(e/2 + f*x/2)**3 - 234234*c**7*f*tan(e/2 + f*x/2)**2 + 39039*c**7*f*tan(e/2 + f*x/2) - 3003*c**7*f) - 245102*a**3*tan(e/2 + f*x/2)**4/(3003*c**7*f*tan(e/2 + f*x/2)**13 - 39039*c**7*f*tan(e/2 + f*x/2)**12 + 234234*c**7*f*tan(e/2 + f*x/2)**11 - 858858*c**7*f*tan(e/2 + f*x/2)**10 + 2147145*c**7*f*tan(e/2 + f*x/2)**9 - 3864861*c**7*f*tan(e/2 + f*x/2)**8 + 5153148*c**7*f*tan(e/2 + f*x/2)**7 - 5153148*c**7*f*tan(e/2 + f*x/2)**6 + 3864861*c**7*f*tan(e/2 + f*x/2)**5 - 2147145*c**7*f*tan(e/2 + f*x/2)**4 + 858858*c**7*f*tan(e/2 + f*x/2)**3 - 234234*c**7*f*tan(e/2 + f*x/2)**2 + 39039*c**7*f*tan(e/2 + f*x/2) - 3003*c**7*f) + 75218*a**3*tan(e/2 + f*x/2)**3/(3003*c**7*f*tan(e/2 + f*x/2)**13 - 39039*c**7*f*tan(e/2 + f*x/2)**12 + 234234*c**7*f*tan(e/2 + f*x/2)**11 - 858858*c**7*f*tan(e/2 + f*x/2)**10 + 2147145*c**7*f*tan(e/2 + f*x/2)**9 - 3864861*c**7*f*tan(e/2 + f*x/2)**8 + 5153148*c**7*f*tan(e/2 + f*x/2)**7 - 5153148*c**7*f*tan(e/2 + f*x/2)**6 + 3864861*c**7*f*tan(e/2 + f*x/2)**5 - 2147145*c**7*f*tan(e/2 + f*x/2)**4 + 858858*c**7*f*tan(e/2 + f*x/2)**3 - 234234*c**7*f*tan(e/2 + f*x/2)**2 + 39039*c**7*f*tan(e/2 + f*x/2) - 3003*c**7*f) - 30342*a**3*tan(e/2 + f*x/2)**2/(3003*c**7*f*tan(e/2 + f*x/2)**13 - 39039*c**7*f*tan(e/2 + f*x/2)**12 + 234234*c**7*f*tan(e/2 + f*x/2)**11 - 858858*c**7*f*tan(e/2 + f*x/2)**10 + 2147145*c**7*f*tan(e/2 + f*x/2)**9 - 3864861*c**7*f*tan(e/2 + f*x/2)**8 + 5153148*c**7*f*tan(e/2 + f*x/2)**7 - 5153148*c**7*f*tan(e/2 + f*x/2)**6 + 3864861*c**7*f*tan(e/2 + f*x/2)**5 - 2147145*c**7*f*tan(e/2 + f*x/2)**4 + 858858*c**7*f*tan(e/2 + f*x/2)**3 - 234234*c**7*f*tan(e/2 + f*x/2)**2 + 39039*c**7*f*tan(e/2 + f*x/2) - 3003*c**7*f) + 2054*a**3*tan(e/2 + f*x/2)/(3003*c**7*f*tan(e/2 + f*x/2)**13 - 39039*c**7*f*tan(e/2 + f*x/2)**12 + 234234*c**7*f*tan(e/2 + f*x/2)**11 - 858858*c**7*f*tan(e/2 + f*x/2)**10 + 2147145*c**7*f*tan(e/2 + f*x/2)**9 - 3864861*c**7*f*tan(e/2 + f*x/2)**8 + 5153148*c**7*f*tan(e/2 + f*x/2)**7 - 5153148*c**7*f*tan(e/2 + f*x/2)**6 + 3864861*c**7*f*tan(e/2 + f*x/2)**5 - 2147145*c**7*f*tan(e/2 + f*x/2)**4 + 858858*c**7*f*tan(e/2 + f*x/2)**3 - 234234*c**7*f*tan(e/2 + f*x/2)**2 + 39039*c**7*f*tan(e/2 + f*x/2) - 3003*c**7*f) - 620*a**3/(3003*c**7*f*tan(e/2 + f*x/2)**13 - 39039*c**7*f*tan(e/2 + f*x/2)**12 + 234234*c**7*f*tan(e/2 + f*x/2)**11 - 858858*c**7*f*tan(e/2 + f*x/2)**10 + 2147145*c**7*f*tan(e/2 + f*x/2)**9 - 3864861*c**7*f*tan(e/2 + f*x/2)**8 + 5153148*c**7*f*tan(e/2 + f*x/2)**7 - 5153148*c**7*f*tan(e/2 + f*x/2)**6 + 3864861*c**7*f*tan(e/2 + f*x/2)**5 - 2147145*c**7*f*tan(e/2 + f*x/2)**4 + 858858*c**7*f*tan(e/2 + f*x/2)**3 - 234234*c**7*f*tan(e/2 + f*x/2)**2 + 39039*c**7*f*tan(e/2 + f*x/2) - 3003*c**7*f), Ne(f, 0)), (x*(a*sin(e) + a)**3/(-c*sin(e) + c)**7, True))","A",0
260,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**3/(c-c*sin(f*x+e))**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
261,1,2108,0,14.000141," ","integrate((c-c*sin(f*x+e))**4/(a+a*sin(f*x+e)),x)","\begin{cases} - \frac{105 c^{4} 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{105 c^{4} 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{315 c^{4} 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{315 c^{4} 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{315 c^{4} 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{315 c^{4} 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{105 c^{4} 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{105 c^{4} 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{222 c^{4} \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{162 c^{4} \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{708 c^{4} \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{288 c^{4} \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{834 c^{4} \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{110 c^{4} \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{332 c^{4}}{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(- c \sin{\left(e \right)} + c\right)^{4}}{a \sin{\left(e \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-105*c**4*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) - 105*c**4*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) - 315*c**4*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) - 315*c**4*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) - 315*c**4*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) - 315*c**4*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) - 105*c**4*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) - 105*c**4*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) - 222*c**4*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) - 162*c**4*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) - 708*c**4*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) - 288*c**4*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) - 834*c**4*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) - 110*c**4*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) - 332*c**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), Ne(f, 0)), (x*(-c*sin(e) + c)**4/(a*sin(e) + a), True))","A",0
262,1,1170,0,7.444209," ","integrate((c-c*sin(f*x+e))**3/(a+a*sin(f*x+e)),x)","\begin{cases} - \frac{15 c^{3} 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{15 c^{3} 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{30 c^{3} 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{30 c^{3} 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{15 c^{3} 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{15 c^{3} 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{34 c^{3} \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 c^{3} \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{78 c^{3} \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{14 c^{3} \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{48 c^{3}}{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(- c \sin{\left(e \right)} + c\right)^{3}}{a \sin{\left(e \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-15*c**3*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) - 15*c**3*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) - 30*c**3*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) - 30*c**3*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) - 15*c**3*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) - 15*c**3*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) - 34*c**3*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*c**3*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) - 78*c**3*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) - 14*c**3*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) - 48*c**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), Ne(f, 0)), (x*(-c*sin(e) + c)**3/(a*sin(e) + a), True))","A",0
263,1,456,0,3.894067," ","integrate((c-c*sin(f*x+e))**2/(a+a*sin(f*x+e)),x)","\begin{cases} - \frac{3 c^{2} 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{3 c^{2} 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{3 c^{2} 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{3 c^{2} 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{8 c^{2} \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 c^{2} \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{10 c^{2}}{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(- c \sin{\left(e \right)} + c\right)^{2}}{a \sin{\left(e \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*c**2*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) - 3*c**2*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) - 3*c**2*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) - 3*c**2*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) - 8*c**2*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*c**2*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) - 10*c**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), Ne(f, 0)), (x*(-c*sin(e) + c)**2/(a*sin(e) + a), True))","A",0
264,1,90,0,1.817993," ","integrate((c-c*sin(f*x+e))/(a+a*sin(f*x+e)),x)","\begin{cases} - \frac{c 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{c f x}{a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f} - \frac{4 c}{a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f} & \text{for}\: f \neq 0 \\\frac{x \left(- c \sin{\left(e \right)} + c\right)}{a \sin{\left(e \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-c*f*x*tan(e/2 + f*x/2)/(a*f*tan(e/2 + f*x/2) + a*f) - c*f*x/(a*f*tan(e/2 + f*x/2) + a*f) - 4*c/(a*f*tan(e/2 + f*x/2) + a*f), Ne(f, 0)), (x*(-c*sin(e) + c)/(a*sin(e) + a), True))","A",0
265,1,49,0,1.650473," ","integrate(1/(a+a*sin(f*x+e))/(c-c*sin(f*x+e)),x)","\begin{cases} - \frac{2 \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} & \text{for}\: f \neq 0 \\\frac{x}{\left(a \sin{\left(e \right)} + a\right) \left(- c \sin{\left(e \right)} + c\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*tan(e/2 + f*x/2)/(a*c*f*tan(e/2 + f*x/2)**2 - a*c*f), Ne(f, 0)), (x/((a*sin(e) + a)*(-c*sin(e) + c)), True))","A",0
266,1,328,0,4.020446," ","integrate(1/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))**2,x)","\begin{cases} - \frac{6 \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 \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 \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}{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 \sin{\left(e \right)} + a\right) \left(- c \sin{\left(e \right)} + c\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-6*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*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*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/(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*sin(e) + a)*(-c*sin(e) + c)**2), True))","A",0
267,1,614,0,8.433899," ","integrate(1/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))**3,x)","\begin{cases} - \frac{10 \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{5 a c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 20 a c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 25 a c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 25 a c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 20 a c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5 a c^{3} f} + \frac{20 \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{5 a c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 20 a c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 25 a c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 25 a c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 20 a c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5 a c^{3} f} - \frac{20 \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{5 a c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 20 a c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 25 a c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 25 a c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 20 a c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5 a c^{3} f} + \frac{6 \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{5 a c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 20 a c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 25 a c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 25 a c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 20 a c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5 a c^{3} f} - \frac{4}{5 a c^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 20 a c^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 25 a c^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 25 a c^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 20 a c^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5 a c^{3} f} & \text{for}\: f \neq 0 \\\frac{x}{\left(a \sin{\left(e \right)} + a\right) \left(- c \sin{\left(e \right)} + c\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-10*tan(e/2 + f*x/2)**5/(5*a*c**3*f*tan(e/2 + f*x/2)**6 - 20*a*c**3*f*tan(e/2 + f*x/2)**5 + 25*a*c**3*f*tan(e/2 + f*x/2)**4 - 25*a*c**3*f*tan(e/2 + f*x/2)**2 + 20*a*c**3*f*tan(e/2 + f*x/2) - 5*a*c**3*f) + 20*tan(e/2 + f*x/2)**4/(5*a*c**3*f*tan(e/2 + f*x/2)**6 - 20*a*c**3*f*tan(e/2 + f*x/2)**5 + 25*a*c**3*f*tan(e/2 + f*x/2)**4 - 25*a*c**3*f*tan(e/2 + f*x/2)**2 + 20*a*c**3*f*tan(e/2 + f*x/2) - 5*a*c**3*f) - 20*tan(e/2 + f*x/2)**3/(5*a*c**3*f*tan(e/2 + f*x/2)**6 - 20*a*c**3*f*tan(e/2 + f*x/2)**5 + 25*a*c**3*f*tan(e/2 + f*x/2)**4 - 25*a*c**3*f*tan(e/2 + f*x/2)**2 + 20*a*c**3*f*tan(e/2 + f*x/2) - 5*a*c**3*f) + 6*tan(e/2 + f*x/2)/(5*a*c**3*f*tan(e/2 + f*x/2)**6 - 20*a*c**3*f*tan(e/2 + f*x/2)**5 + 25*a*c**3*f*tan(e/2 + f*x/2)**4 - 25*a*c**3*f*tan(e/2 + f*x/2)**2 + 20*a*c**3*f*tan(e/2 + f*x/2) - 5*a*c**3*f) - 4/(5*a*c**3*f*tan(e/2 + f*x/2)**6 - 20*a*c**3*f*tan(e/2 + f*x/2)**5 + 25*a*c**3*f*tan(e/2 + f*x/2)**4 - 25*a*c**3*f*tan(e/2 + f*x/2)**2 + 20*a*c**3*f*tan(e/2 + f*x/2) - 5*a*c**3*f), Ne(f, 0)), (x/((a*sin(e) + a)*(-c*sin(e) + c)**3), True))","A",0
268,1,1307,0,13.732915," ","integrate(1/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))**4,x)","\begin{cases} - \frac{70 \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 \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 \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 \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 \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 \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 \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}{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 \sin{\left(e \right)} + a\right) \left(- c \sin{\left(e \right)} + c\right)^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-70*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*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*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*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*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*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*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/(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*sin(e) + a)*(-c*sin(e) + c)**4), True))","A",0
269,1,3641,0,41.194027," ","integrate((c-c*sin(f*x+e))**5/(a+a*sin(f*x+e))**2,x)","\begin{cases} \frac{315 c^{5} 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{945 c^{5} 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{1890 c^{5} 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{3150 c^{5} 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{3780 c^{5} 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{3780 c^{5} 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{3150 c^{5} 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{1890 c^{5} 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{945 c^{5} 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{315 c^{5} 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{618 c^{5} \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{1938 c^{5} \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{3386 c^{5} \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{6054 c^{5} \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{5802 c^{5} \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{6494 c^{5} \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{3990 c^{5} \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{2346 c^{5} \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{988 c^{5}}{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(- c \sin{\left(e \right)} + c\right)^{5}}{\left(a \sin{\left(e \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((315*c**5*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) + 945*c**5*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) + 1890*c**5*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) + 3150*c**5*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) + 3780*c**5*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) + 3780*c**5*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) + 3150*c**5*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) + 1890*c**5*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) + 945*c**5*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) + 315*c**5*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) + 618*c**5*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) + 1938*c**5*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) + 3386*c**5*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) + 6054*c**5*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) + 5802*c**5*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) + 6494*c**5*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) + 3990*c**5*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) + 2346*c**5*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) + 988*c**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), Ne(f, 0)), (x*(-c*sin(e) + c)**5/(a*sin(e) + a)**2, True))","A",0
270,1,2312,0,23.376900," ","integrate((c-c*sin(f*x+e))**4/(a+a*sin(f*x+e))**2,x)","\begin{cases} \frac{105 c^{4} 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{315 c^{4} 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{525 c^{4} 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{735 c^{4} 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{735 c^{4} 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{525 c^{4} 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{315 c^{4} 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{105 c^{4} 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{198 c^{4} \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{666 c^{4} \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{868 c^{4} \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{1428 c^{4} \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{974 c^{4} \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{786 c^{4} \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{328 c^{4}}{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(- c \sin{\left(e \right)} + c\right)^{4}}{\left(a \sin{\left(e \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((105*c**4*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) + 315*c**4*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) + 525*c**4*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) + 735*c**4*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) + 735*c**4*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) + 525*c**4*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) + 315*c**4*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) + 105*c**4*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) + 198*c**4*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) + 666*c**4*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) + 868*c**4*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) + 1428*c**4*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) + 974*c**4*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) + 786*c**4*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) + 328*c**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), Ne(f, 0)), (x*(-c*sin(e) + c)**4/(a*sin(e) + a)**2, True))","A",0
271,1,1282,0,12.757354," ","integrate((c-c*sin(f*x+e))**3/(a+a*sin(f*x+e))**2,x)","\begin{cases} \frac{15 c^{3} 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{45 c^{3} 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{60 c^{3} 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{60 c^{3} 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{45 c^{3} 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{15 c^{3} 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 c^{3} \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{102 c^{3} \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{82 c^{3} \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{114 c^{3} \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{46 c^{3}}{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(- c \sin{\left(e \right)} + c\right)^{3}}{\left(a \sin{\left(e \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((15*c**3*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) + 45*c**3*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) + 60*c**3*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) + 60*c**3*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) + 45*c**3*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) + 15*c**3*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*c**3*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) + 102*c**3*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) + 82*c**3*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) + 114*c**3*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) + 46*c**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), Ne(f, 0)), (x*(-c*sin(e) + c)**3/(a*sin(e) + a)**2, True))","A",0
272,1,473,0,7.687676," ","integrate((c-c*sin(f*x+e))**2/(a+a*sin(f*x+e))**2,x)","\begin{cases} \frac{3 c^{2} 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 c^{2} 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 c^{2} 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 c^{2} 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{24 c^{2} \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 c^{2}}{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(- c \sin{\left(e \right)} + c\right)^{2}}{\left(a \sin{\left(e \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*c**2*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*c**2*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*c**2*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*c**2*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) + 24*c**2*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*c**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), Ne(f, 0)), (x*(-c*sin(e) + c)**2/(a*sin(e) + a)**2, True))","A",0
273,1,158,0,3.856838," ","integrate((c-c*sin(f*x+e))/(a+a*sin(f*x+e))**2,x)","\begin{cases} - \frac{6 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 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(- c \sin{\left(e \right)} + c\right)}{\left(a \sin{\left(e \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-6*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*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*(-c*sin(e) + c)/(a*sin(e) + a)**2, True))","A",0
274,1,328,0,3.920135," ","integrate(1/(a+a*sin(f*x+e))**2/(c-c*sin(f*x+e)),x)","\begin{cases} - \frac{6 \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 \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 \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}{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 \sin{\left(e \right)} + a\right)^{2} \left(- c \sin{\left(e \right)} + c\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-6*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*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*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/(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*sin(e) + a)**2*(-c*sin(e) + c)), True))","A",0
275,1,286,0,5.069715," ","integrate(1/(a+a*sin(f*x+e))**2/(c-c*sin(f*x+e))**2,x)","\begin{cases} - \frac{6 \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 \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 \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} & \text{for}\: f \neq 0 \\\frac{x}{\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*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*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*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), Ne(f, 0)), (x/((a*sin(e) + a)**2*(-c*sin(e) + c)**2), True))","A",0
276,1,1418,0,15.884083," ","integrate(1/(a+a*sin(f*x+e))**2/(c-c*sin(f*x+e))**3,x)","\begin{cases} - \frac{30 \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 \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 \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 \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 \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 \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 \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}{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 \sin{\left(e \right)} + a\right)^{2} \left(- c \sin{\left(e \right)} + c\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-30*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*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*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*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*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*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*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/(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*sin(e) + a)**2*(-c*sin(e) + c)**3), True))","A",0
277,1,2213,0,30.149429," ","integrate(1/(a+a*sin(f*x+e))**2/(c-c*sin(f*x+e))**4,x)","\begin{cases} - \frac{42 \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{21 a^{2} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 84 a^{2} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 63 a^{2} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 294 a^{2} c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 294 a^{2} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 168 a^{2} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 a^{2} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 84 a^{2} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 21 a^{2} c^{4} f} + \frac{84 \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{21 a^{2} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 84 a^{2} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 63 a^{2} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 294 a^{2} c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 294 a^{2} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 168 a^{2} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 a^{2} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 84 a^{2} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 21 a^{2} c^{4} f} - \frac{56 \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{21 a^{2} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 84 a^{2} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 63 a^{2} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 294 a^{2} c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 294 a^{2} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 168 a^{2} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 a^{2} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 84 a^{2} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 21 a^{2} c^{4} f} - \frac{112 \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{21 a^{2} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 84 a^{2} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 63 a^{2} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 294 a^{2} c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 294 a^{2} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 168 a^{2} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 a^{2} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 84 a^{2} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 21 a^{2} c^{4} f} + \frac{84 \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{21 a^{2} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 84 a^{2} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 63 a^{2} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 294 a^{2} c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 294 a^{2} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 168 a^{2} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 a^{2} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 84 a^{2} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 21 a^{2} c^{4} f} + \frac{56 \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{21 a^{2} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 84 a^{2} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 63 a^{2} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 294 a^{2} c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 294 a^{2} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 168 a^{2} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 a^{2} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 84 a^{2} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 21 a^{2} c^{4} f} - \frac{152 \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{21 a^{2} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 84 a^{2} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 63 a^{2} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 294 a^{2} c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 294 a^{2} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 168 a^{2} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 a^{2} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 84 a^{2} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 21 a^{2} c^{4} f} + \frac{48 \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{21 a^{2} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 84 a^{2} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 63 a^{2} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 294 a^{2} c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 294 a^{2} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 168 a^{2} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 a^{2} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 84 a^{2} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 21 a^{2} c^{4} f} + \frac{6 \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{21 a^{2} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 84 a^{2} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 63 a^{2} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 294 a^{2} c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 294 a^{2} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 168 a^{2} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 a^{2} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 84 a^{2} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 21 a^{2} c^{4} f} - \frac{12}{21 a^{2} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 84 a^{2} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 63 a^{2} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 168 a^{2} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 294 a^{2} c^{4} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 294 a^{2} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 168 a^{2} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 63 a^{2} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 84 a^{2} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 21 a^{2} c^{4} f} & \text{for}\: f \neq 0 \\\frac{x}{\left(a \sin{\left(e \right)} + a\right)^{2} \left(- c \sin{\left(e \right)} + c\right)^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-42*tan(e/2 + f*x/2)**9/(21*a**2*c**4*f*tan(e/2 + f*x/2)**10 - 84*a**2*c**4*f*tan(e/2 + f*x/2)**9 + 63*a**2*c**4*f*tan(e/2 + f*x/2)**8 + 168*a**2*c**4*f*tan(e/2 + f*x/2)**7 - 294*a**2*c**4*f*tan(e/2 + f*x/2)**6 + 294*a**2*c**4*f*tan(e/2 + f*x/2)**4 - 168*a**2*c**4*f*tan(e/2 + f*x/2)**3 - 63*a**2*c**4*f*tan(e/2 + f*x/2)**2 + 84*a**2*c**4*f*tan(e/2 + f*x/2) - 21*a**2*c**4*f) + 84*tan(e/2 + f*x/2)**8/(21*a**2*c**4*f*tan(e/2 + f*x/2)**10 - 84*a**2*c**4*f*tan(e/2 + f*x/2)**9 + 63*a**2*c**4*f*tan(e/2 + f*x/2)**8 + 168*a**2*c**4*f*tan(e/2 + f*x/2)**7 - 294*a**2*c**4*f*tan(e/2 + f*x/2)**6 + 294*a**2*c**4*f*tan(e/2 + f*x/2)**4 - 168*a**2*c**4*f*tan(e/2 + f*x/2)**3 - 63*a**2*c**4*f*tan(e/2 + f*x/2)**2 + 84*a**2*c**4*f*tan(e/2 + f*x/2) - 21*a**2*c**4*f) - 56*tan(e/2 + f*x/2)**7/(21*a**2*c**4*f*tan(e/2 + f*x/2)**10 - 84*a**2*c**4*f*tan(e/2 + f*x/2)**9 + 63*a**2*c**4*f*tan(e/2 + f*x/2)**8 + 168*a**2*c**4*f*tan(e/2 + f*x/2)**7 - 294*a**2*c**4*f*tan(e/2 + f*x/2)**6 + 294*a**2*c**4*f*tan(e/2 + f*x/2)**4 - 168*a**2*c**4*f*tan(e/2 + f*x/2)**3 - 63*a**2*c**4*f*tan(e/2 + f*x/2)**2 + 84*a**2*c**4*f*tan(e/2 + f*x/2) - 21*a**2*c**4*f) - 112*tan(e/2 + f*x/2)**6/(21*a**2*c**4*f*tan(e/2 + f*x/2)**10 - 84*a**2*c**4*f*tan(e/2 + f*x/2)**9 + 63*a**2*c**4*f*tan(e/2 + f*x/2)**8 + 168*a**2*c**4*f*tan(e/2 + f*x/2)**7 - 294*a**2*c**4*f*tan(e/2 + f*x/2)**6 + 294*a**2*c**4*f*tan(e/2 + f*x/2)**4 - 168*a**2*c**4*f*tan(e/2 + f*x/2)**3 - 63*a**2*c**4*f*tan(e/2 + f*x/2)**2 + 84*a**2*c**4*f*tan(e/2 + f*x/2) - 21*a**2*c**4*f) + 84*tan(e/2 + f*x/2)**5/(21*a**2*c**4*f*tan(e/2 + f*x/2)**10 - 84*a**2*c**4*f*tan(e/2 + f*x/2)**9 + 63*a**2*c**4*f*tan(e/2 + f*x/2)**8 + 168*a**2*c**4*f*tan(e/2 + f*x/2)**7 - 294*a**2*c**4*f*tan(e/2 + f*x/2)**6 + 294*a**2*c**4*f*tan(e/2 + f*x/2)**4 - 168*a**2*c**4*f*tan(e/2 + f*x/2)**3 - 63*a**2*c**4*f*tan(e/2 + f*x/2)**2 + 84*a**2*c**4*f*tan(e/2 + f*x/2) - 21*a**2*c**4*f) + 56*tan(e/2 + f*x/2)**4/(21*a**2*c**4*f*tan(e/2 + f*x/2)**10 - 84*a**2*c**4*f*tan(e/2 + f*x/2)**9 + 63*a**2*c**4*f*tan(e/2 + f*x/2)**8 + 168*a**2*c**4*f*tan(e/2 + f*x/2)**7 - 294*a**2*c**4*f*tan(e/2 + f*x/2)**6 + 294*a**2*c**4*f*tan(e/2 + f*x/2)**4 - 168*a**2*c**4*f*tan(e/2 + f*x/2)**3 - 63*a**2*c**4*f*tan(e/2 + f*x/2)**2 + 84*a**2*c**4*f*tan(e/2 + f*x/2) - 21*a**2*c**4*f) - 152*tan(e/2 + f*x/2)**3/(21*a**2*c**4*f*tan(e/2 + f*x/2)**10 - 84*a**2*c**4*f*tan(e/2 + f*x/2)**9 + 63*a**2*c**4*f*tan(e/2 + f*x/2)**8 + 168*a**2*c**4*f*tan(e/2 + f*x/2)**7 - 294*a**2*c**4*f*tan(e/2 + f*x/2)**6 + 294*a**2*c**4*f*tan(e/2 + f*x/2)**4 - 168*a**2*c**4*f*tan(e/2 + f*x/2)**3 - 63*a**2*c**4*f*tan(e/2 + f*x/2)**2 + 84*a**2*c**4*f*tan(e/2 + f*x/2) - 21*a**2*c**4*f) + 48*tan(e/2 + f*x/2)**2/(21*a**2*c**4*f*tan(e/2 + f*x/2)**10 - 84*a**2*c**4*f*tan(e/2 + f*x/2)**9 + 63*a**2*c**4*f*tan(e/2 + f*x/2)**8 + 168*a**2*c**4*f*tan(e/2 + f*x/2)**7 - 294*a**2*c**4*f*tan(e/2 + f*x/2)**6 + 294*a**2*c**4*f*tan(e/2 + f*x/2)**4 - 168*a**2*c**4*f*tan(e/2 + f*x/2)**3 - 63*a**2*c**4*f*tan(e/2 + f*x/2)**2 + 84*a**2*c**4*f*tan(e/2 + f*x/2) - 21*a**2*c**4*f) + 6*tan(e/2 + f*x/2)/(21*a**2*c**4*f*tan(e/2 + f*x/2)**10 - 84*a**2*c**4*f*tan(e/2 + f*x/2)**9 + 63*a**2*c**4*f*tan(e/2 + f*x/2)**8 + 168*a**2*c**4*f*tan(e/2 + f*x/2)**7 - 294*a**2*c**4*f*tan(e/2 + f*x/2)**6 + 294*a**2*c**4*f*tan(e/2 + f*x/2)**4 - 168*a**2*c**4*f*tan(e/2 + f*x/2)**3 - 63*a**2*c**4*f*tan(e/2 + f*x/2)**2 + 84*a**2*c**4*f*tan(e/2 + f*x/2) - 21*a**2*c**4*f) - 12/(21*a**2*c**4*f*tan(e/2 + f*x/2)**10 - 84*a**2*c**4*f*tan(e/2 + f*x/2)**9 + 63*a**2*c**4*f*tan(e/2 + f*x/2)**8 + 168*a**2*c**4*f*tan(e/2 + f*x/2)**7 - 294*a**2*c**4*f*tan(e/2 + f*x/2)**6 + 294*a**2*c**4*f*tan(e/2 + f*x/2)**4 - 168*a**2*c**4*f*tan(e/2 + f*x/2)**3 - 63*a**2*c**4*f*tan(e/2 + f*x/2)**2 + 84*a**2*c**4*f*tan(e/2 + f*x/2) - 21*a**2*c**4*f), Ne(f, 0)), (x/((a*sin(e) + a)**2*(-c*sin(e) + c)**4), True))","A",0
278,1,3186,0,56.786834," ","integrate(1/(a+a*sin(f*x+e))**2/(c-c*sin(f*x+e))**5,x)","\begin{cases} - \frac{126 \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 \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 \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 \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 \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 \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 \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 \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 \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 \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 \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}{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 \sin{\left(e \right)} + a\right)^{2} \left(- c \sin{\left(e \right)} + c\right)^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-126*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*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*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*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*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*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*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*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*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*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*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/(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*sin(e) + a)**2*(-c*sin(e) + c)**5), True))","A",0
279,1,3643,0,72.500963," ","integrate((c-c*sin(f*x+e))**5/(a+a*sin(f*x+e))**3,x)","\begin{cases} - \frac{315 c^{5} f x \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{10 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 120 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 200 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 260 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 260 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 200 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 120 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 10 a^{3} f} - \frac{1575 c^{5} f x \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{10 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 120 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 200 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 260 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 260 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 200 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 120 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 10 a^{3} f} - \frac{3780 c^{5} f x \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{10 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 120 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 200 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 260 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 260 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 200 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 120 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 10 a^{3} f} - \frac{6300 c^{5} f x \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{10 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 120 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 200 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 260 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 260 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 200 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 120 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 10 a^{3} f} - \frac{8190 c^{5} f x \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{10 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 120 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 200 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 260 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 260 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 200 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 120 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 10 a^{3} f} - \frac{8190 c^{5} f x \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{10 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 120 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 200 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 260 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 260 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 200 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 120 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 10 a^{3} f} - \frac{6300 c^{5} f x \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{10 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 120 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 200 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 260 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 260 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 200 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 120 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 10 a^{3} f} - \frac{3780 c^{5} f x \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{10 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 120 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 200 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 260 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 260 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 200 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 120 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 10 a^{3} f} - \frac{1575 c^{5} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{10 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 120 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 200 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 260 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 260 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 200 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 120 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 10 a^{3} f} - \frac{315 c^{5} f x}{10 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 120 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 200 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 260 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 260 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 200 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 120 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 10 a^{3} f} - \frac{650 c^{5} \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{10 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 120 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 200 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 260 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 260 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 200 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 120 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 10 a^{3} f} - \frac{3090 c^{5} \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{10 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 120 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 200 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 260 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 260 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 200 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 120 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 10 a^{3} f} - \frac{7610 c^{5} \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{10 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 120 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 200 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 260 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 260 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 200 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 120 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 10 a^{3} f} - \frac{11090 c^{5} \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{10 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 120 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 200 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 260 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 260 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 200 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 120 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 10 a^{3} f} - \frac{14702 c^{5} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{10 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 120 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 200 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 260 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 260 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 200 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 120 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 10 a^{3} f} - \frac{12230 c^{5} \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{10 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 120 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 200 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 260 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 260 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 200 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 120 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 10 a^{3} f} - \frac{8814 c^{5} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{10 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 120 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 200 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 260 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 260 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 200 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 120 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 10 a^{3} f} - \frac{4310 c^{5} \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{10 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 120 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 200 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 260 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 260 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 200 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 120 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 10 a^{3} f} - \frac{992 c^{5}}{10 a^{3} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 a^{3} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 120 a^{3} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 200 a^{3} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 260 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 260 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 200 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 120 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 10 a^{3} f} & \text{for}\: f \neq 0 \\\frac{x \left(- c \sin{\left(e \right)} + c\right)^{5}}{\left(a \sin{\left(e \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-315*c**5*f*x*tan(e/2 + f*x/2)**9/(10*a**3*f*tan(e/2 + f*x/2)**9 + 50*a**3*f*tan(e/2 + f*x/2)**8 + 120*a**3*f*tan(e/2 + f*x/2)**7 + 200*a**3*f*tan(e/2 + f*x/2)**6 + 260*a**3*f*tan(e/2 + f*x/2)**5 + 260*a**3*f*tan(e/2 + f*x/2)**4 + 200*a**3*f*tan(e/2 + f*x/2)**3 + 120*a**3*f*tan(e/2 + f*x/2)**2 + 50*a**3*f*tan(e/2 + f*x/2) + 10*a**3*f) - 1575*c**5*f*x*tan(e/2 + f*x/2)**8/(10*a**3*f*tan(e/2 + f*x/2)**9 + 50*a**3*f*tan(e/2 + f*x/2)**8 + 120*a**3*f*tan(e/2 + f*x/2)**7 + 200*a**3*f*tan(e/2 + f*x/2)**6 + 260*a**3*f*tan(e/2 + f*x/2)**5 + 260*a**3*f*tan(e/2 + f*x/2)**4 + 200*a**3*f*tan(e/2 + f*x/2)**3 + 120*a**3*f*tan(e/2 + f*x/2)**2 + 50*a**3*f*tan(e/2 + f*x/2) + 10*a**3*f) - 3780*c**5*f*x*tan(e/2 + f*x/2)**7/(10*a**3*f*tan(e/2 + f*x/2)**9 + 50*a**3*f*tan(e/2 + f*x/2)**8 + 120*a**3*f*tan(e/2 + f*x/2)**7 + 200*a**3*f*tan(e/2 + f*x/2)**6 + 260*a**3*f*tan(e/2 + f*x/2)**5 + 260*a**3*f*tan(e/2 + f*x/2)**4 + 200*a**3*f*tan(e/2 + f*x/2)**3 + 120*a**3*f*tan(e/2 + f*x/2)**2 + 50*a**3*f*tan(e/2 + f*x/2) + 10*a**3*f) - 6300*c**5*f*x*tan(e/2 + f*x/2)**6/(10*a**3*f*tan(e/2 + f*x/2)**9 + 50*a**3*f*tan(e/2 + f*x/2)**8 + 120*a**3*f*tan(e/2 + f*x/2)**7 + 200*a**3*f*tan(e/2 + f*x/2)**6 + 260*a**3*f*tan(e/2 + f*x/2)**5 + 260*a**3*f*tan(e/2 + f*x/2)**4 + 200*a**3*f*tan(e/2 + f*x/2)**3 + 120*a**3*f*tan(e/2 + f*x/2)**2 + 50*a**3*f*tan(e/2 + f*x/2) + 10*a**3*f) - 8190*c**5*f*x*tan(e/2 + f*x/2)**5/(10*a**3*f*tan(e/2 + f*x/2)**9 + 50*a**3*f*tan(e/2 + f*x/2)**8 + 120*a**3*f*tan(e/2 + f*x/2)**7 + 200*a**3*f*tan(e/2 + f*x/2)**6 + 260*a**3*f*tan(e/2 + f*x/2)**5 + 260*a**3*f*tan(e/2 + f*x/2)**4 + 200*a**3*f*tan(e/2 + f*x/2)**3 + 120*a**3*f*tan(e/2 + f*x/2)**2 + 50*a**3*f*tan(e/2 + f*x/2) + 10*a**3*f) - 8190*c**5*f*x*tan(e/2 + f*x/2)**4/(10*a**3*f*tan(e/2 + f*x/2)**9 + 50*a**3*f*tan(e/2 + f*x/2)**8 + 120*a**3*f*tan(e/2 + f*x/2)**7 + 200*a**3*f*tan(e/2 + f*x/2)**6 + 260*a**3*f*tan(e/2 + f*x/2)**5 + 260*a**3*f*tan(e/2 + f*x/2)**4 + 200*a**3*f*tan(e/2 + f*x/2)**3 + 120*a**3*f*tan(e/2 + f*x/2)**2 + 50*a**3*f*tan(e/2 + f*x/2) + 10*a**3*f) - 6300*c**5*f*x*tan(e/2 + f*x/2)**3/(10*a**3*f*tan(e/2 + f*x/2)**9 + 50*a**3*f*tan(e/2 + f*x/2)**8 + 120*a**3*f*tan(e/2 + f*x/2)**7 + 200*a**3*f*tan(e/2 + f*x/2)**6 + 260*a**3*f*tan(e/2 + f*x/2)**5 + 260*a**3*f*tan(e/2 + f*x/2)**4 + 200*a**3*f*tan(e/2 + f*x/2)**3 + 120*a**3*f*tan(e/2 + f*x/2)**2 + 50*a**3*f*tan(e/2 + f*x/2) + 10*a**3*f) - 3780*c**5*f*x*tan(e/2 + f*x/2)**2/(10*a**3*f*tan(e/2 + f*x/2)**9 + 50*a**3*f*tan(e/2 + f*x/2)**8 + 120*a**3*f*tan(e/2 + f*x/2)**7 + 200*a**3*f*tan(e/2 + f*x/2)**6 + 260*a**3*f*tan(e/2 + f*x/2)**5 + 260*a**3*f*tan(e/2 + f*x/2)**4 + 200*a**3*f*tan(e/2 + f*x/2)**3 + 120*a**3*f*tan(e/2 + f*x/2)**2 + 50*a**3*f*tan(e/2 + f*x/2) + 10*a**3*f) - 1575*c**5*f*x*tan(e/2 + f*x/2)/(10*a**3*f*tan(e/2 + f*x/2)**9 + 50*a**3*f*tan(e/2 + f*x/2)**8 + 120*a**3*f*tan(e/2 + f*x/2)**7 + 200*a**3*f*tan(e/2 + f*x/2)**6 + 260*a**3*f*tan(e/2 + f*x/2)**5 + 260*a**3*f*tan(e/2 + f*x/2)**4 + 200*a**3*f*tan(e/2 + f*x/2)**3 + 120*a**3*f*tan(e/2 + f*x/2)**2 + 50*a**3*f*tan(e/2 + f*x/2) + 10*a**3*f) - 315*c**5*f*x/(10*a**3*f*tan(e/2 + f*x/2)**9 + 50*a**3*f*tan(e/2 + f*x/2)**8 + 120*a**3*f*tan(e/2 + f*x/2)**7 + 200*a**3*f*tan(e/2 + f*x/2)**6 + 260*a**3*f*tan(e/2 + f*x/2)**5 + 260*a**3*f*tan(e/2 + f*x/2)**4 + 200*a**3*f*tan(e/2 + f*x/2)**3 + 120*a**3*f*tan(e/2 + f*x/2)**2 + 50*a**3*f*tan(e/2 + f*x/2) + 10*a**3*f) - 650*c**5*tan(e/2 + f*x/2)**8/(10*a**3*f*tan(e/2 + f*x/2)**9 + 50*a**3*f*tan(e/2 + f*x/2)**8 + 120*a**3*f*tan(e/2 + f*x/2)**7 + 200*a**3*f*tan(e/2 + f*x/2)**6 + 260*a**3*f*tan(e/2 + f*x/2)**5 + 260*a**3*f*tan(e/2 + f*x/2)**4 + 200*a**3*f*tan(e/2 + f*x/2)**3 + 120*a**3*f*tan(e/2 + f*x/2)**2 + 50*a**3*f*tan(e/2 + f*x/2) + 10*a**3*f) - 3090*c**5*tan(e/2 + f*x/2)**7/(10*a**3*f*tan(e/2 + f*x/2)**9 + 50*a**3*f*tan(e/2 + f*x/2)**8 + 120*a**3*f*tan(e/2 + f*x/2)**7 + 200*a**3*f*tan(e/2 + f*x/2)**6 + 260*a**3*f*tan(e/2 + f*x/2)**5 + 260*a**3*f*tan(e/2 + f*x/2)**4 + 200*a**3*f*tan(e/2 + f*x/2)**3 + 120*a**3*f*tan(e/2 + f*x/2)**2 + 50*a**3*f*tan(e/2 + f*x/2) + 10*a**3*f) - 7610*c**5*tan(e/2 + f*x/2)**6/(10*a**3*f*tan(e/2 + f*x/2)**9 + 50*a**3*f*tan(e/2 + f*x/2)**8 + 120*a**3*f*tan(e/2 + f*x/2)**7 + 200*a**3*f*tan(e/2 + f*x/2)**6 + 260*a**3*f*tan(e/2 + f*x/2)**5 + 260*a**3*f*tan(e/2 + f*x/2)**4 + 200*a**3*f*tan(e/2 + f*x/2)**3 + 120*a**3*f*tan(e/2 + f*x/2)**2 + 50*a**3*f*tan(e/2 + f*x/2) + 10*a**3*f) - 11090*c**5*tan(e/2 + f*x/2)**5/(10*a**3*f*tan(e/2 + f*x/2)**9 + 50*a**3*f*tan(e/2 + f*x/2)**8 + 120*a**3*f*tan(e/2 + f*x/2)**7 + 200*a**3*f*tan(e/2 + f*x/2)**6 + 260*a**3*f*tan(e/2 + f*x/2)**5 + 260*a**3*f*tan(e/2 + f*x/2)**4 + 200*a**3*f*tan(e/2 + f*x/2)**3 + 120*a**3*f*tan(e/2 + f*x/2)**2 + 50*a**3*f*tan(e/2 + f*x/2) + 10*a**3*f) - 14702*c**5*tan(e/2 + f*x/2)**4/(10*a**3*f*tan(e/2 + f*x/2)**9 + 50*a**3*f*tan(e/2 + f*x/2)**8 + 120*a**3*f*tan(e/2 + f*x/2)**7 + 200*a**3*f*tan(e/2 + f*x/2)**6 + 260*a**3*f*tan(e/2 + f*x/2)**5 + 260*a**3*f*tan(e/2 + f*x/2)**4 + 200*a**3*f*tan(e/2 + f*x/2)**3 + 120*a**3*f*tan(e/2 + f*x/2)**2 + 50*a**3*f*tan(e/2 + f*x/2) + 10*a**3*f) - 12230*c**5*tan(e/2 + f*x/2)**3/(10*a**3*f*tan(e/2 + f*x/2)**9 + 50*a**3*f*tan(e/2 + f*x/2)**8 + 120*a**3*f*tan(e/2 + f*x/2)**7 + 200*a**3*f*tan(e/2 + f*x/2)**6 + 260*a**3*f*tan(e/2 + f*x/2)**5 + 260*a**3*f*tan(e/2 + f*x/2)**4 + 200*a**3*f*tan(e/2 + f*x/2)**3 + 120*a**3*f*tan(e/2 + f*x/2)**2 + 50*a**3*f*tan(e/2 + f*x/2) + 10*a**3*f) - 8814*c**5*tan(e/2 + f*x/2)**2/(10*a**3*f*tan(e/2 + f*x/2)**9 + 50*a**3*f*tan(e/2 + f*x/2)**8 + 120*a**3*f*tan(e/2 + f*x/2)**7 + 200*a**3*f*tan(e/2 + f*x/2)**6 + 260*a**3*f*tan(e/2 + f*x/2)**5 + 260*a**3*f*tan(e/2 + f*x/2)**4 + 200*a**3*f*tan(e/2 + f*x/2)**3 + 120*a**3*f*tan(e/2 + f*x/2)**2 + 50*a**3*f*tan(e/2 + f*x/2) + 10*a**3*f) - 4310*c**5*tan(e/2 + f*x/2)/(10*a**3*f*tan(e/2 + f*x/2)**9 + 50*a**3*f*tan(e/2 + f*x/2)**8 + 120*a**3*f*tan(e/2 + f*x/2)**7 + 200*a**3*f*tan(e/2 + f*x/2)**6 + 260*a**3*f*tan(e/2 + f*x/2)**5 + 260*a**3*f*tan(e/2 + f*x/2)**4 + 200*a**3*f*tan(e/2 + f*x/2)**3 + 120*a**3*f*tan(e/2 + f*x/2)**2 + 50*a**3*f*tan(e/2 + f*x/2) + 10*a**3*f) - 992*c**5/(10*a**3*f*tan(e/2 + f*x/2)**9 + 50*a**3*f*tan(e/2 + f*x/2)**8 + 120*a**3*f*tan(e/2 + f*x/2)**7 + 200*a**3*f*tan(e/2 + f*x/2)**6 + 260*a**3*f*tan(e/2 + f*x/2)**5 + 260*a**3*f*tan(e/2 + f*x/2)**4 + 200*a**3*f*tan(e/2 + f*x/2)**3 + 120*a**3*f*tan(e/2 + f*x/2)**2 + 50*a**3*f*tan(e/2 + f*x/2) + 10*a**3*f), Ne(f, 0)), (x*(-c*sin(e) + c)**5/(a*sin(e) + a)**3, True))","A",0
280,1,2314,0,44.740439," ","integrate((c-c*sin(f*x+e))**4/(a+a*sin(f*x+e))**3,x)","\begin{cases} - \frac{105 c^{4} 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{525 c^{4} 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{1155 c^{4} 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{1575 c^{4} 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{1575 c^{4} 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{1155 c^{4} 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{525 c^{4} 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{105 c^{4} 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{240 c^{4} \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 c^{4} \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{2470 c^{4} \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{2540 c^{4} \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{2684 c^{4} \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{1430 c^{4} \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{334 c^{4}}{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(- c \sin{\left(e \right)} + c\right)^{4}}{\left(a \sin{\left(e \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-105*c**4*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) - 525*c**4*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) - 1155*c**4*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) - 1575*c**4*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) - 1575*c**4*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) - 1155*c**4*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) - 525*c**4*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) - 105*c**4*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) - 240*c**4*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*c**4*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) - 2470*c**4*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) - 2540*c**4*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) - 2684*c**4*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) - 1430*c**4*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) - 334*c**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), Ne(f, 0)), (x*(-c*sin(e) + c)**4/(a*sin(e) + a)**3, True))","A",0
281,1,1284,0,26.241206," ","integrate((c-c*sin(f*x+e))**3/(a+a*sin(f*x+e))**3,x)","\begin{cases} - \frac{15 c^{3} 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 c^{3} 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 c^{3} 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 c^{3} 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 c^{3} 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 c^{3} 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{60 c^{3} \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 c^{3} \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{400 c^{3} \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 c^{3} \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{52 c^{3}}{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(- c \sin{\left(e \right)} + c\right)^{3}}{\left(a \sin{\left(e \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-15*c**3*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*c**3*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*c**3*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*c**3*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*c**3*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*c**3*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) - 60*c**3*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*c**3*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) - 400*c**3*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*c**3*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) - 52*c**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), Ne(f, 0)), (x*(-c*sin(e) + c)**3/(a*sin(e) + a)**3, True))","A",0
282,1,354,0,14.472859," ","integrate((c-c*sin(f*x+e))**2/(a+a*sin(f*x+e))**3,x)","\begin{cases} - \frac{10 c^{2} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{5 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 25 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 25 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5 a^{3} f} - \frac{20 c^{2} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{5 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 25 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 25 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5 a^{3} f} - \frac{2 c^{2}}{5 a^{3} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 25 a^{3} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 a^{3} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 50 a^{3} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 25 a^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 5 a^{3} f} & \text{for}\: f \neq 0 \\\frac{x \left(- c \sin{\left(e \right)} + c\right)^{2}}{\left(a \sin{\left(e \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-10*c**2*tan(e/2 + f*x/2)**4/(5*a**3*f*tan(e/2 + f*x/2)**5 + 25*a**3*f*tan(e/2 + f*x/2)**4 + 50*a**3*f*tan(e/2 + f*x/2)**3 + 50*a**3*f*tan(e/2 + f*x/2)**2 + 25*a**3*f*tan(e/2 + f*x/2) + 5*a**3*f) - 20*c**2*tan(e/2 + f*x/2)**2/(5*a**3*f*tan(e/2 + f*x/2)**5 + 25*a**3*f*tan(e/2 + f*x/2)**4 + 50*a**3*f*tan(e/2 + f*x/2)**3 + 50*a**3*f*tan(e/2 + f*x/2)**2 + 25*a**3*f*tan(e/2 + f*x/2) + 5*a**3*f) - 2*c**2/(5*a**3*f*tan(e/2 + f*x/2)**5 + 25*a**3*f*tan(e/2 + f*x/2)**4 + 50*a**3*f*tan(e/2 + f*x/2)**3 + 50*a**3*f*tan(e/2 + f*x/2)**2 + 25*a**3*f*tan(e/2 + f*x/2) + 5*a**3*f), Ne(f, 0)), (x*(-c*sin(e) + c)**2/(a*sin(e) + a)**3, True))","A",0
283,1,573,0,8.426176," ","integrate((c-c*sin(f*x+e))/(a+a*sin(f*x+e))**3,x)","\begin{cases} - \frac{30 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 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 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 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 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(- c \sin{\left(e \right)} + c\right)}{\left(a \sin{\left(e \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-30*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*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*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*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*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*(-c*sin(e) + c)/(a*sin(e) + a)**3, True))","A",0
284,1,614,0,8.243042," ","integrate(1/(a+a*sin(f*x+e))**3/(c-c*sin(f*x+e)),x)","\begin{cases} - \frac{10 \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{5 a^{3} c f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 20 a^{3} c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 25 a^{3} c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 25 a^{3} c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 20 a^{3} c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5 a^{3} c f} - \frac{20 \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{5 a^{3} c f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 20 a^{3} c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 25 a^{3} c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 25 a^{3} c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 20 a^{3} c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5 a^{3} c f} - \frac{20 \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{5 a^{3} c f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 20 a^{3} c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 25 a^{3} c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 25 a^{3} c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 20 a^{3} c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5 a^{3} c f} + \frac{6 \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{5 a^{3} c f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 20 a^{3} c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 25 a^{3} c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 25 a^{3} c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 20 a^{3} c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5 a^{3} c f} + \frac{4}{5 a^{3} c f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 20 a^{3} c f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 25 a^{3} c f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 25 a^{3} c f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 20 a^{3} c f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 5 a^{3} c f} & \text{for}\: f \neq 0 \\\frac{x}{\left(a \sin{\left(e \right)} + a\right)^{3} \left(- c \sin{\left(e \right)} + c\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-10*tan(e/2 + f*x/2)**5/(5*a**3*c*f*tan(e/2 + f*x/2)**6 + 20*a**3*c*f*tan(e/2 + f*x/2)**5 + 25*a**3*c*f*tan(e/2 + f*x/2)**4 - 25*a**3*c*f*tan(e/2 + f*x/2)**2 - 20*a**3*c*f*tan(e/2 + f*x/2) - 5*a**3*c*f) - 20*tan(e/2 + f*x/2)**4/(5*a**3*c*f*tan(e/2 + f*x/2)**6 + 20*a**3*c*f*tan(e/2 + f*x/2)**5 + 25*a**3*c*f*tan(e/2 + f*x/2)**4 - 25*a**3*c*f*tan(e/2 + f*x/2)**2 - 20*a**3*c*f*tan(e/2 + f*x/2) - 5*a**3*c*f) - 20*tan(e/2 + f*x/2)**3/(5*a**3*c*f*tan(e/2 + f*x/2)**6 + 20*a**3*c*f*tan(e/2 + f*x/2)**5 + 25*a**3*c*f*tan(e/2 + f*x/2)**4 - 25*a**3*c*f*tan(e/2 + f*x/2)**2 - 20*a**3*c*f*tan(e/2 + f*x/2) - 5*a**3*c*f) + 6*tan(e/2 + f*x/2)/(5*a**3*c*f*tan(e/2 + f*x/2)**6 + 20*a**3*c*f*tan(e/2 + f*x/2)**5 + 25*a**3*c*f*tan(e/2 + f*x/2)**4 - 25*a**3*c*f*tan(e/2 + f*x/2)**2 - 20*a**3*c*f*tan(e/2 + f*x/2) - 5*a**3*c*f) + 4/(5*a**3*c*f*tan(e/2 + f*x/2)**6 + 20*a**3*c*f*tan(e/2 + f*x/2)**5 + 25*a**3*c*f*tan(e/2 + f*x/2)**4 - 25*a**3*c*f*tan(e/2 + f*x/2)**2 - 20*a**3*c*f*tan(e/2 + f*x/2) - 5*a**3*c*f), Ne(f, 0)), (x/((a*sin(e) + a)**3*(-c*sin(e) + c)), True))","A",0
285,1,1418,0,15.763721," ","integrate(1/(a+a*sin(f*x+e))**3/(c-c*sin(f*x+e))**2,x)","\begin{cases} - \frac{30 \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 \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 \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 \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 \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 \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 \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}{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 \sin{\left(e \right)} + a\right)^{3} \left(- c \sin{\left(e \right)} + c\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-30*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*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*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*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*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*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*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/(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*sin(e) + a)**3*(-c*sin(e) + c)**2), True))","A",0
286,1,687,0,14.793962," ","integrate(1/(a+a*sin(f*x+e))**3/(c-c*sin(f*x+e))**3,x)","\begin{cases} - \frac{30 \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 \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 \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 \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 \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} & \text{for}\: f \neq 0 \\\frac{x}{\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*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*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*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*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*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), Ne(f, 0)), (x/((a*sin(e) + a)**3*(-c*sin(e) + c)**3), True))","A",0
287,1,3186,0,55.959381," ","integrate(1/(a+a*sin(f*x+e))**3/(c-c*sin(f*x+e))**4,x)","\begin{cases} - \frac{70 \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{35 a^{3} c^{4} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 70 a^{3} c^{4} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 140 a^{3} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 350 a^{3} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 175 a^{3} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 700 a^{3} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 700 a^{3} c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 175 a^{3} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 350 a^{3} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 140 a^{3} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 70 a^{3} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 35 a^{3} c^{4} f} + \frac{70 \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{35 a^{3} c^{4} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 70 a^{3} c^{4} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 140 a^{3} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 350 a^{3} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 175 a^{3} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 700 a^{3} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 700 a^{3} c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 175 a^{3} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 350 a^{3} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 140 a^{3} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 70 a^{3} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 35 a^{3} c^{4} f} + \frac{70 \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{35 a^{3} c^{4} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 70 a^{3} c^{4} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 140 a^{3} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 350 a^{3} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 175 a^{3} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 700 a^{3} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 700 a^{3} c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 175 a^{3} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 350 a^{3} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 140 a^{3} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 70 a^{3} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 35 a^{3} c^{4} f} - \frac{210 \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{35 a^{3} c^{4} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 70 a^{3} c^{4} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 140 a^{3} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 350 a^{3} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 175 a^{3} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 700 a^{3} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 700 a^{3} c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 175 a^{3} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 350 a^{3} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 140 a^{3} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 70 a^{3} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 35 a^{3} c^{4} f} - \frac{252 \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{35 a^{3} c^{4} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 70 a^{3} c^{4} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 140 a^{3} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 350 a^{3} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 175 a^{3} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 700 a^{3} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 700 a^{3} c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 175 a^{3} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 350 a^{3} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 140 a^{3} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 70 a^{3} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 35 a^{3} c^{4} f} + \frac{364 \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{35 a^{3} c^{4} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 70 a^{3} c^{4} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 140 a^{3} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 350 a^{3} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 175 a^{3} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 700 a^{3} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 700 a^{3} c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 175 a^{3} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 350 a^{3} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 140 a^{3} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 70 a^{3} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 35 a^{3} c^{4} f} - \frac{52 \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{35 a^{3} c^{4} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 70 a^{3} c^{4} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 140 a^{3} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 350 a^{3} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 175 a^{3} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 700 a^{3} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 700 a^{3} c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 175 a^{3} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 350 a^{3} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 140 a^{3} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 70 a^{3} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 35 a^{3} c^{4} f} - \frac{260 \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{35 a^{3} c^{4} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 70 a^{3} c^{4} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 140 a^{3} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 350 a^{3} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 175 a^{3} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 700 a^{3} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 700 a^{3} c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 175 a^{3} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 350 a^{3} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 140 a^{3} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 70 a^{3} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 35 a^{3} c^{4} f} - \frac{30 \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{35 a^{3} c^{4} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 70 a^{3} c^{4} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 140 a^{3} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 350 a^{3} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 175 a^{3} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 700 a^{3} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 700 a^{3} c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 175 a^{3} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 350 a^{3} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 140 a^{3} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 70 a^{3} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 35 a^{3} c^{4} f} + \frac{110 \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{35 a^{3} c^{4} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 70 a^{3} c^{4} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 140 a^{3} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 350 a^{3} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 175 a^{3} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 700 a^{3} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 700 a^{3} c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 175 a^{3} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 350 a^{3} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 140 a^{3} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 70 a^{3} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 35 a^{3} c^{4} f} - \frac{50 \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{35 a^{3} c^{4} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 70 a^{3} c^{4} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 140 a^{3} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 350 a^{3} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 175 a^{3} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 700 a^{3} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 700 a^{3} c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 175 a^{3} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 350 a^{3} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 140 a^{3} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 70 a^{3} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 35 a^{3} c^{4} f} - \frac{10}{35 a^{3} c^{4} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 70 a^{3} c^{4} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 140 a^{3} c^{4} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 350 a^{3} c^{4} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 175 a^{3} c^{4} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 700 a^{3} c^{4} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 700 a^{3} c^{4} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 175 a^{3} c^{4} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 350 a^{3} c^{4} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 140 a^{3} c^{4} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 70 a^{3} c^{4} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 35 a^{3} c^{4} f} & \text{for}\: f \neq 0 \\\frac{x}{\left(a \sin{\left(e \right)} + a\right)^{3} \left(- c \sin{\left(e \right)} + c\right)^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-70*tan(e/2 + f*x/2)**11/(35*a**3*c**4*f*tan(e/2 + f*x/2)**12 - 70*a**3*c**4*f*tan(e/2 + f*x/2)**11 - 140*a**3*c**4*f*tan(e/2 + f*x/2)**10 + 350*a**3*c**4*f*tan(e/2 + f*x/2)**9 + 175*a**3*c**4*f*tan(e/2 + f*x/2)**8 - 700*a**3*c**4*f*tan(e/2 + f*x/2)**7 + 700*a**3*c**4*f*tan(e/2 + f*x/2)**5 - 175*a**3*c**4*f*tan(e/2 + f*x/2)**4 - 350*a**3*c**4*f*tan(e/2 + f*x/2)**3 + 140*a**3*c**4*f*tan(e/2 + f*x/2)**2 + 70*a**3*c**4*f*tan(e/2 + f*x/2) - 35*a**3*c**4*f) + 70*tan(e/2 + f*x/2)**10/(35*a**3*c**4*f*tan(e/2 + f*x/2)**12 - 70*a**3*c**4*f*tan(e/2 + f*x/2)**11 - 140*a**3*c**4*f*tan(e/2 + f*x/2)**10 + 350*a**3*c**4*f*tan(e/2 + f*x/2)**9 + 175*a**3*c**4*f*tan(e/2 + f*x/2)**8 - 700*a**3*c**4*f*tan(e/2 + f*x/2)**7 + 700*a**3*c**4*f*tan(e/2 + f*x/2)**5 - 175*a**3*c**4*f*tan(e/2 + f*x/2)**4 - 350*a**3*c**4*f*tan(e/2 + f*x/2)**3 + 140*a**3*c**4*f*tan(e/2 + f*x/2)**2 + 70*a**3*c**4*f*tan(e/2 + f*x/2) - 35*a**3*c**4*f) + 70*tan(e/2 + f*x/2)**9/(35*a**3*c**4*f*tan(e/2 + f*x/2)**12 - 70*a**3*c**4*f*tan(e/2 + f*x/2)**11 - 140*a**3*c**4*f*tan(e/2 + f*x/2)**10 + 350*a**3*c**4*f*tan(e/2 + f*x/2)**9 + 175*a**3*c**4*f*tan(e/2 + f*x/2)**8 - 700*a**3*c**4*f*tan(e/2 + f*x/2)**7 + 700*a**3*c**4*f*tan(e/2 + f*x/2)**5 - 175*a**3*c**4*f*tan(e/2 + f*x/2)**4 - 350*a**3*c**4*f*tan(e/2 + f*x/2)**3 + 140*a**3*c**4*f*tan(e/2 + f*x/2)**2 + 70*a**3*c**4*f*tan(e/2 + f*x/2) - 35*a**3*c**4*f) - 210*tan(e/2 + f*x/2)**8/(35*a**3*c**4*f*tan(e/2 + f*x/2)**12 - 70*a**3*c**4*f*tan(e/2 + f*x/2)**11 - 140*a**3*c**4*f*tan(e/2 + f*x/2)**10 + 350*a**3*c**4*f*tan(e/2 + f*x/2)**9 + 175*a**3*c**4*f*tan(e/2 + f*x/2)**8 - 700*a**3*c**4*f*tan(e/2 + f*x/2)**7 + 700*a**3*c**4*f*tan(e/2 + f*x/2)**5 - 175*a**3*c**4*f*tan(e/2 + f*x/2)**4 - 350*a**3*c**4*f*tan(e/2 + f*x/2)**3 + 140*a**3*c**4*f*tan(e/2 + f*x/2)**2 + 70*a**3*c**4*f*tan(e/2 + f*x/2) - 35*a**3*c**4*f) - 252*tan(e/2 + f*x/2)**7/(35*a**3*c**4*f*tan(e/2 + f*x/2)**12 - 70*a**3*c**4*f*tan(e/2 + f*x/2)**11 - 140*a**3*c**4*f*tan(e/2 + f*x/2)**10 + 350*a**3*c**4*f*tan(e/2 + f*x/2)**9 + 175*a**3*c**4*f*tan(e/2 + f*x/2)**8 - 700*a**3*c**4*f*tan(e/2 + f*x/2)**7 + 700*a**3*c**4*f*tan(e/2 + f*x/2)**5 - 175*a**3*c**4*f*tan(e/2 + f*x/2)**4 - 350*a**3*c**4*f*tan(e/2 + f*x/2)**3 + 140*a**3*c**4*f*tan(e/2 + f*x/2)**2 + 70*a**3*c**4*f*tan(e/2 + f*x/2) - 35*a**3*c**4*f) + 364*tan(e/2 + f*x/2)**6/(35*a**3*c**4*f*tan(e/2 + f*x/2)**12 - 70*a**3*c**4*f*tan(e/2 + f*x/2)**11 - 140*a**3*c**4*f*tan(e/2 + f*x/2)**10 + 350*a**3*c**4*f*tan(e/2 + f*x/2)**9 + 175*a**3*c**4*f*tan(e/2 + f*x/2)**8 - 700*a**3*c**4*f*tan(e/2 + f*x/2)**7 + 700*a**3*c**4*f*tan(e/2 + f*x/2)**5 - 175*a**3*c**4*f*tan(e/2 + f*x/2)**4 - 350*a**3*c**4*f*tan(e/2 + f*x/2)**3 + 140*a**3*c**4*f*tan(e/2 + f*x/2)**2 + 70*a**3*c**4*f*tan(e/2 + f*x/2) - 35*a**3*c**4*f) - 52*tan(e/2 + f*x/2)**5/(35*a**3*c**4*f*tan(e/2 + f*x/2)**12 - 70*a**3*c**4*f*tan(e/2 + f*x/2)**11 - 140*a**3*c**4*f*tan(e/2 + f*x/2)**10 + 350*a**3*c**4*f*tan(e/2 + f*x/2)**9 + 175*a**3*c**4*f*tan(e/2 + f*x/2)**8 - 700*a**3*c**4*f*tan(e/2 + f*x/2)**7 + 700*a**3*c**4*f*tan(e/2 + f*x/2)**5 - 175*a**3*c**4*f*tan(e/2 + f*x/2)**4 - 350*a**3*c**4*f*tan(e/2 + f*x/2)**3 + 140*a**3*c**4*f*tan(e/2 + f*x/2)**2 + 70*a**3*c**4*f*tan(e/2 + f*x/2) - 35*a**3*c**4*f) - 260*tan(e/2 + f*x/2)**4/(35*a**3*c**4*f*tan(e/2 + f*x/2)**12 - 70*a**3*c**4*f*tan(e/2 + f*x/2)**11 - 140*a**3*c**4*f*tan(e/2 + f*x/2)**10 + 350*a**3*c**4*f*tan(e/2 + f*x/2)**9 + 175*a**3*c**4*f*tan(e/2 + f*x/2)**8 - 700*a**3*c**4*f*tan(e/2 + f*x/2)**7 + 700*a**3*c**4*f*tan(e/2 + f*x/2)**5 - 175*a**3*c**4*f*tan(e/2 + f*x/2)**4 - 350*a**3*c**4*f*tan(e/2 + f*x/2)**3 + 140*a**3*c**4*f*tan(e/2 + f*x/2)**2 + 70*a**3*c**4*f*tan(e/2 + f*x/2) - 35*a**3*c**4*f) - 30*tan(e/2 + f*x/2)**3/(35*a**3*c**4*f*tan(e/2 + f*x/2)**12 - 70*a**3*c**4*f*tan(e/2 + f*x/2)**11 - 140*a**3*c**4*f*tan(e/2 + f*x/2)**10 + 350*a**3*c**4*f*tan(e/2 + f*x/2)**9 + 175*a**3*c**4*f*tan(e/2 + f*x/2)**8 - 700*a**3*c**4*f*tan(e/2 + f*x/2)**7 + 700*a**3*c**4*f*tan(e/2 + f*x/2)**5 - 175*a**3*c**4*f*tan(e/2 + f*x/2)**4 - 350*a**3*c**4*f*tan(e/2 + f*x/2)**3 + 140*a**3*c**4*f*tan(e/2 + f*x/2)**2 + 70*a**3*c**4*f*tan(e/2 + f*x/2) - 35*a**3*c**4*f) + 110*tan(e/2 + f*x/2)**2/(35*a**3*c**4*f*tan(e/2 + f*x/2)**12 - 70*a**3*c**4*f*tan(e/2 + f*x/2)**11 - 140*a**3*c**4*f*tan(e/2 + f*x/2)**10 + 350*a**3*c**4*f*tan(e/2 + f*x/2)**9 + 175*a**3*c**4*f*tan(e/2 + f*x/2)**8 - 700*a**3*c**4*f*tan(e/2 + f*x/2)**7 + 700*a**3*c**4*f*tan(e/2 + f*x/2)**5 - 175*a**3*c**4*f*tan(e/2 + f*x/2)**4 - 350*a**3*c**4*f*tan(e/2 + f*x/2)**3 + 140*a**3*c**4*f*tan(e/2 + f*x/2)**2 + 70*a**3*c**4*f*tan(e/2 + f*x/2) - 35*a**3*c**4*f) - 50*tan(e/2 + f*x/2)/(35*a**3*c**4*f*tan(e/2 + f*x/2)**12 - 70*a**3*c**4*f*tan(e/2 + f*x/2)**11 - 140*a**3*c**4*f*tan(e/2 + f*x/2)**10 + 350*a**3*c**4*f*tan(e/2 + f*x/2)**9 + 175*a**3*c**4*f*tan(e/2 + f*x/2)**8 - 700*a**3*c**4*f*tan(e/2 + f*x/2)**7 + 700*a**3*c**4*f*tan(e/2 + f*x/2)**5 - 175*a**3*c**4*f*tan(e/2 + f*x/2)**4 - 350*a**3*c**4*f*tan(e/2 + f*x/2)**3 + 140*a**3*c**4*f*tan(e/2 + f*x/2)**2 + 70*a**3*c**4*f*tan(e/2 + f*x/2) - 35*a**3*c**4*f) - 10/(35*a**3*c**4*f*tan(e/2 + f*x/2)**12 - 70*a**3*c**4*f*tan(e/2 + f*x/2)**11 - 140*a**3*c**4*f*tan(e/2 + f*x/2)**10 + 350*a**3*c**4*f*tan(e/2 + f*x/2)**9 + 175*a**3*c**4*f*tan(e/2 + f*x/2)**8 - 700*a**3*c**4*f*tan(e/2 + f*x/2)**7 + 700*a**3*c**4*f*tan(e/2 + f*x/2)**5 - 175*a**3*c**4*f*tan(e/2 + f*x/2)**4 - 350*a**3*c**4*f*tan(e/2 + f*x/2)**3 + 140*a**3*c**4*f*tan(e/2 + f*x/2)**2 + 70*a**3*c**4*f*tan(e/2 + f*x/2) - 35*a**3*c**4*f), Ne(f, 0)), (x/((a*sin(e) + a)**3*(-c*sin(e) + c)**4), True))","A",0
288,1,4335,0,98.598056," ","integrate(1/(a+a*sin(f*x+e))**3/(c-c*sin(f*x+e))**5,x)","\begin{cases} - \frac{90 \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{45 a^{3} c^{5} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 180 a^{3} c^{5} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 45 a^{3} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 720 a^{3} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 855 a^{3} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 900 a^{3} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2025 a^{3} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2025 a^{3} c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 900 a^{3} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 855 a^{3} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 720 a^{3} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 45 a^{3} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 180 a^{3} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 45 a^{3} c^{5} f} + \frac{180 \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{45 a^{3} c^{5} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 180 a^{3} c^{5} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 45 a^{3} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 720 a^{3} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 855 a^{3} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 900 a^{3} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2025 a^{3} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2025 a^{3} c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 900 a^{3} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 855 a^{3} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 720 a^{3} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 45 a^{3} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 180 a^{3} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 45 a^{3} c^{5} f} - \frac{60 \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{45 a^{3} c^{5} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 180 a^{3} c^{5} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 45 a^{3} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 720 a^{3} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 855 a^{3} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 900 a^{3} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2025 a^{3} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2025 a^{3} c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 900 a^{3} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 855 a^{3} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 720 a^{3} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 45 a^{3} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 180 a^{3} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 45 a^{3} c^{5} f} - \frac{480 \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{45 a^{3} c^{5} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 180 a^{3} c^{5} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 45 a^{3} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 720 a^{3} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 855 a^{3} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 900 a^{3} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2025 a^{3} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2025 a^{3} c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 900 a^{3} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 855 a^{3} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 720 a^{3} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 45 a^{3} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 180 a^{3} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 45 a^{3} c^{5} f} + \frac{138 \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{45 a^{3} c^{5} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 180 a^{3} c^{5} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 45 a^{3} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 720 a^{3} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 855 a^{3} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 900 a^{3} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2025 a^{3} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2025 a^{3} c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 900 a^{3} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 855 a^{3} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 720 a^{3} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 45 a^{3} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 180 a^{3} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 45 a^{3} c^{5} f} + \frac{708 \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{45 a^{3} c^{5} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 180 a^{3} c^{5} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 45 a^{3} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 720 a^{3} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 855 a^{3} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 900 a^{3} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2025 a^{3} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2025 a^{3} c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 900 a^{3} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 855 a^{3} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 720 a^{3} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 45 a^{3} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 180 a^{3} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 45 a^{3} c^{5} f} - \frac{1032 \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{45 a^{3} c^{5} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 180 a^{3} c^{5} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 45 a^{3} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 720 a^{3} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 855 a^{3} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 900 a^{3} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2025 a^{3} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2025 a^{3} c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 900 a^{3} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 855 a^{3} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 720 a^{3} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 45 a^{3} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 180 a^{3} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 45 a^{3} c^{5} f} - \frac{192 \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{45 a^{3} c^{5} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 180 a^{3} c^{5} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 45 a^{3} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 720 a^{3} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 855 a^{3} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 900 a^{3} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2025 a^{3} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2025 a^{3} c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 900 a^{3} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 855 a^{3} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 720 a^{3} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 45 a^{3} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 180 a^{3} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 45 a^{3} c^{5} f} + \frac{538 \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{45 a^{3} c^{5} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 180 a^{3} c^{5} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 45 a^{3} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 720 a^{3} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 855 a^{3} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 900 a^{3} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2025 a^{3} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2025 a^{3} c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 900 a^{3} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 855 a^{3} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 720 a^{3} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 45 a^{3} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 180 a^{3} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 45 a^{3} c^{5} f} - \frac{100 \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{45 a^{3} c^{5} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 180 a^{3} c^{5} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 45 a^{3} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 720 a^{3} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 855 a^{3} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 900 a^{3} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2025 a^{3} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2025 a^{3} c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 900 a^{3} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 855 a^{3} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 720 a^{3} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 45 a^{3} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 180 a^{3} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 45 a^{3} c^{5} f} - \frac{380 \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{45 a^{3} c^{5} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 180 a^{3} c^{5} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 45 a^{3} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 720 a^{3} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 855 a^{3} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 900 a^{3} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2025 a^{3} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2025 a^{3} c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 900 a^{3} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 855 a^{3} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 720 a^{3} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 45 a^{3} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 180 a^{3} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 45 a^{3} c^{5} f} + \frac{160 \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{45 a^{3} c^{5} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 180 a^{3} c^{5} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 45 a^{3} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 720 a^{3} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 855 a^{3} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 900 a^{3} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2025 a^{3} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2025 a^{3} c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 900 a^{3} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 855 a^{3} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 720 a^{3} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 45 a^{3} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 180 a^{3} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 45 a^{3} c^{5} f} - \frac{10 \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{45 a^{3} c^{5} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 180 a^{3} c^{5} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 45 a^{3} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 720 a^{3} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 855 a^{3} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 900 a^{3} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2025 a^{3} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2025 a^{3} c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 900 a^{3} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 855 a^{3} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 720 a^{3} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 45 a^{3} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 180 a^{3} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 45 a^{3} c^{5} f} - \frac{20}{45 a^{3} c^{5} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 180 a^{3} c^{5} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 45 a^{3} c^{5} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 720 a^{3} c^{5} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 855 a^{3} c^{5} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 900 a^{3} c^{5} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2025 a^{3} c^{5} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2025 a^{3} c^{5} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 900 a^{3} c^{5} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 855 a^{3} c^{5} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 720 a^{3} c^{5} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 45 a^{3} c^{5} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 180 a^{3} c^{5} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 45 a^{3} c^{5} f} & \text{for}\: f \neq 0 \\\frac{x}{\left(a \sin{\left(e \right)} + a\right)^{3} \left(- c \sin{\left(e \right)} + c\right)^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-90*tan(e/2 + f*x/2)**13/(45*a**3*c**5*f*tan(e/2 + f*x/2)**14 - 180*a**3*c**5*f*tan(e/2 + f*x/2)**13 + 45*a**3*c**5*f*tan(e/2 + f*x/2)**12 + 720*a**3*c**5*f*tan(e/2 + f*x/2)**11 - 855*a**3*c**5*f*tan(e/2 + f*x/2)**10 - 900*a**3*c**5*f*tan(e/2 + f*x/2)**9 + 2025*a**3*c**5*f*tan(e/2 + f*x/2)**8 - 2025*a**3*c**5*f*tan(e/2 + f*x/2)**6 + 900*a**3*c**5*f*tan(e/2 + f*x/2)**5 + 855*a**3*c**5*f*tan(e/2 + f*x/2)**4 - 720*a**3*c**5*f*tan(e/2 + f*x/2)**3 - 45*a**3*c**5*f*tan(e/2 + f*x/2)**2 + 180*a**3*c**5*f*tan(e/2 + f*x/2) - 45*a**3*c**5*f) + 180*tan(e/2 + f*x/2)**12/(45*a**3*c**5*f*tan(e/2 + f*x/2)**14 - 180*a**3*c**5*f*tan(e/2 + f*x/2)**13 + 45*a**3*c**5*f*tan(e/2 + f*x/2)**12 + 720*a**3*c**5*f*tan(e/2 + f*x/2)**11 - 855*a**3*c**5*f*tan(e/2 + f*x/2)**10 - 900*a**3*c**5*f*tan(e/2 + f*x/2)**9 + 2025*a**3*c**5*f*tan(e/2 + f*x/2)**8 - 2025*a**3*c**5*f*tan(e/2 + f*x/2)**6 + 900*a**3*c**5*f*tan(e/2 + f*x/2)**5 + 855*a**3*c**5*f*tan(e/2 + f*x/2)**4 - 720*a**3*c**5*f*tan(e/2 + f*x/2)**3 - 45*a**3*c**5*f*tan(e/2 + f*x/2)**2 + 180*a**3*c**5*f*tan(e/2 + f*x/2) - 45*a**3*c**5*f) - 60*tan(e/2 + f*x/2)**11/(45*a**3*c**5*f*tan(e/2 + f*x/2)**14 - 180*a**3*c**5*f*tan(e/2 + f*x/2)**13 + 45*a**3*c**5*f*tan(e/2 + f*x/2)**12 + 720*a**3*c**5*f*tan(e/2 + f*x/2)**11 - 855*a**3*c**5*f*tan(e/2 + f*x/2)**10 - 900*a**3*c**5*f*tan(e/2 + f*x/2)**9 + 2025*a**3*c**5*f*tan(e/2 + f*x/2)**8 - 2025*a**3*c**5*f*tan(e/2 + f*x/2)**6 + 900*a**3*c**5*f*tan(e/2 + f*x/2)**5 + 855*a**3*c**5*f*tan(e/2 + f*x/2)**4 - 720*a**3*c**5*f*tan(e/2 + f*x/2)**3 - 45*a**3*c**5*f*tan(e/2 + f*x/2)**2 + 180*a**3*c**5*f*tan(e/2 + f*x/2) - 45*a**3*c**5*f) - 480*tan(e/2 + f*x/2)**10/(45*a**3*c**5*f*tan(e/2 + f*x/2)**14 - 180*a**3*c**5*f*tan(e/2 + f*x/2)**13 + 45*a**3*c**5*f*tan(e/2 + f*x/2)**12 + 720*a**3*c**5*f*tan(e/2 + f*x/2)**11 - 855*a**3*c**5*f*tan(e/2 + f*x/2)**10 - 900*a**3*c**5*f*tan(e/2 + f*x/2)**9 + 2025*a**3*c**5*f*tan(e/2 + f*x/2)**8 - 2025*a**3*c**5*f*tan(e/2 + f*x/2)**6 + 900*a**3*c**5*f*tan(e/2 + f*x/2)**5 + 855*a**3*c**5*f*tan(e/2 + f*x/2)**4 - 720*a**3*c**5*f*tan(e/2 + f*x/2)**3 - 45*a**3*c**5*f*tan(e/2 + f*x/2)**2 + 180*a**3*c**5*f*tan(e/2 + f*x/2) - 45*a**3*c**5*f) + 138*tan(e/2 + f*x/2)**9/(45*a**3*c**5*f*tan(e/2 + f*x/2)**14 - 180*a**3*c**5*f*tan(e/2 + f*x/2)**13 + 45*a**3*c**5*f*tan(e/2 + f*x/2)**12 + 720*a**3*c**5*f*tan(e/2 + f*x/2)**11 - 855*a**3*c**5*f*tan(e/2 + f*x/2)**10 - 900*a**3*c**5*f*tan(e/2 + f*x/2)**9 + 2025*a**3*c**5*f*tan(e/2 + f*x/2)**8 - 2025*a**3*c**5*f*tan(e/2 + f*x/2)**6 + 900*a**3*c**5*f*tan(e/2 + f*x/2)**5 + 855*a**3*c**5*f*tan(e/2 + f*x/2)**4 - 720*a**3*c**5*f*tan(e/2 + f*x/2)**3 - 45*a**3*c**5*f*tan(e/2 + f*x/2)**2 + 180*a**3*c**5*f*tan(e/2 + f*x/2) - 45*a**3*c**5*f) + 708*tan(e/2 + f*x/2)**8/(45*a**3*c**5*f*tan(e/2 + f*x/2)**14 - 180*a**3*c**5*f*tan(e/2 + f*x/2)**13 + 45*a**3*c**5*f*tan(e/2 + f*x/2)**12 + 720*a**3*c**5*f*tan(e/2 + f*x/2)**11 - 855*a**3*c**5*f*tan(e/2 + f*x/2)**10 - 900*a**3*c**5*f*tan(e/2 + f*x/2)**9 + 2025*a**3*c**5*f*tan(e/2 + f*x/2)**8 - 2025*a**3*c**5*f*tan(e/2 + f*x/2)**6 + 900*a**3*c**5*f*tan(e/2 + f*x/2)**5 + 855*a**3*c**5*f*tan(e/2 + f*x/2)**4 - 720*a**3*c**5*f*tan(e/2 + f*x/2)**3 - 45*a**3*c**5*f*tan(e/2 + f*x/2)**2 + 180*a**3*c**5*f*tan(e/2 + f*x/2) - 45*a**3*c**5*f) - 1032*tan(e/2 + f*x/2)**7/(45*a**3*c**5*f*tan(e/2 + f*x/2)**14 - 180*a**3*c**5*f*tan(e/2 + f*x/2)**13 + 45*a**3*c**5*f*tan(e/2 + f*x/2)**12 + 720*a**3*c**5*f*tan(e/2 + f*x/2)**11 - 855*a**3*c**5*f*tan(e/2 + f*x/2)**10 - 900*a**3*c**5*f*tan(e/2 + f*x/2)**9 + 2025*a**3*c**5*f*tan(e/2 + f*x/2)**8 - 2025*a**3*c**5*f*tan(e/2 + f*x/2)**6 + 900*a**3*c**5*f*tan(e/2 + f*x/2)**5 + 855*a**3*c**5*f*tan(e/2 + f*x/2)**4 - 720*a**3*c**5*f*tan(e/2 + f*x/2)**3 - 45*a**3*c**5*f*tan(e/2 + f*x/2)**2 + 180*a**3*c**5*f*tan(e/2 + f*x/2) - 45*a**3*c**5*f) - 192*tan(e/2 + f*x/2)**6/(45*a**3*c**5*f*tan(e/2 + f*x/2)**14 - 180*a**3*c**5*f*tan(e/2 + f*x/2)**13 + 45*a**3*c**5*f*tan(e/2 + f*x/2)**12 + 720*a**3*c**5*f*tan(e/2 + f*x/2)**11 - 855*a**3*c**5*f*tan(e/2 + f*x/2)**10 - 900*a**3*c**5*f*tan(e/2 + f*x/2)**9 + 2025*a**3*c**5*f*tan(e/2 + f*x/2)**8 - 2025*a**3*c**5*f*tan(e/2 + f*x/2)**6 + 900*a**3*c**5*f*tan(e/2 + f*x/2)**5 + 855*a**3*c**5*f*tan(e/2 + f*x/2)**4 - 720*a**3*c**5*f*tan(e/2 + f*x/2)**3 - 45*a**3*c**5*f*tan(e/2 + f*x/2)**2 + 180*a**3*c**5*f*tan(e/2 + f*x/2) - 45*a**3*c**5*f) + 538*tan(e/2 + f*x/2)**5/(45*a**3*c**5*f*tan(e/2 + f*x/2)**14 - 180*a**3*c**5*f*tan(e/2 + f*x/2)**13 + 45*a**3*c**5*f*tan(e/2 + f*x/2)**12 + 720*a**3*c**5*f*tan(e/2 + f*x/2)**11 - 855*a**3*c**5*f*tan(e/2 + f*x/2)**10 - 900*a**3*c**5*f*tan(e/2 + f*x/2)**9 + 2025*a**3*c**5*f*tan(e/2 + f*x/2)**8 - 2025*a**3*c**5*f*tan(e/2 + f*x/2)**6 + 900*a**3*c**5*f*tan(e/2 + f*x/2)**5 + 855*a**3*c**5*f*tan(e/2 + f*x/2)**4 - 720*a**3*c**5*f*tan(e/2 + f*x/2)**3 - 45*a**3*c**5*f*tan(e/2 + f*x/2)**2 + 180*a**3*c**5*f*tan(e/2 + f*x/2) - 45*a**3*c**5*f) - 100*tan(e/2 + f*x/2)**4/(45*a**3*c**5*f*tan(e/2 + f*x/2)**14 - 180*a**3*c**5*f*tan(e/2 + f*x/2)**13 + 45*a**3*c**5*f*tan(e/2 + f*x/2)**12 + 720*a**3*c**5*f*tan(e/2 + f*x/2)**11 - 855*a**3*c**5*f*tan(e/2 + f*x/2)**10 - 900*a**3*c**5*f*tan(e/2 + f*x/2)**9 + 2025*a**3*c**5*f*tan(e/2 + f*x/2)**8 - 2025*a**3*c**5*f*tan(e/2 + f*x/2)**6 + 900*a**3*c**5*f*tan(e/2 + f*x/2)**5 + 855*a**3*c**5*f*tan(e/2 + f*x/2)**4 - 720*a**3*c**5*f*tan(e/2 + f*x/2)**3 - 45*a**3*c**5*f*tan(e/2 + f*x/2)**2 + 180*a**3*c**5*f*tan(e/2 + f*x/2) - 45*a**3*c**5*f) - 380*tan(e/2 + f*x/2)**3/(45*a**3*c**5*f*tan(e/2 + f*x/2)**14 - 180*a**3*c**5*f*tan(e/2 + f*x/2)**13 + 45*a**3*c**5*f*tan(e/2 + f*x/2)**12 + 720*a**3*c**5*f*tan(e/2 + f*x/2)**11 - 855*a**3*c**5*f*tan(e/2 + f*x/2)**10 - 900*a**3*c**5*f*tan(e/2 + f*x/2)**9 + 2025*a**3*c**5*f*tan(e/2 + f*x/2)**8 - 2025*a**3*c**5*f*tan(e/2 + f*x/2)**6 + 900*a**3*c**5*f*tan(e/2 + f*x/2)**5 + 855*a**3*c**5*f*tan(e/2 + f*x/2)**4 - 720*a**3*c**5*f*tan(e/2 + f*x/2)**3 - 45*a**3*c**5*f*tan(e/2 + f*x/2)**2 + 180*a**3*c**5*f*tan(e/2 + f*x/2) - 45*a**3*c**5*f) + 160*tan(e/2 + f*x/2)**2/(45*a**3*c**5*f*tan(e/2 + f*x/2)**14 - 180*a**3*c**5*f*tan(e/2 + f*x/2)**13 + 45*a**3*c**5*f*tan(e/2 + f*x/2)**12 + 720*a**3*c**5*f*tan(e/2 + f*x/2)**11 - 855*a**3*c**5*f*tan(e/2 + f*x/2)**10 - 900*a**3*c**5*f*tan(e/2 + f*x/2)**9 + 2025*a**3*c**5*f*tan(e/2 + f*x/2)**8 - 2025*a**3*c**5*f*tan(e/2 + f*x/2)**6 + 900*a**3*c**5*f*tan(e/2 + f*x/2)**5 + 855*a**3*c**5*f*tan(e/2 + f*x/2)**4 - 720*a**3*c**5*f*tan(e/2 + f*x/2)**3 - 45*a**3*c**5*f*tan(e/2 + f*x/2)**2 + 180*a**3*c**5*f*tan(e/2 + f*x/2) - 45*a**3*c**5*f) - 10*tan(e/2 + f*x/2)/(45*a**3*c**5*f*tan(e/2 + f*x/2)**14 - 180*a**3*c**5*f*tan(e/2 + f*x/2)**13 + 45*a**3*c**5*f*tan(e/2 + f*x/2)**12 + 720*a**3*c**5*f*tan(e/2 + f*x/2)**11 - 855*a**3*c**5*f*tan(e/2 + f*x/2)**10 - 900*a**3*c**5*f*tan(e/2 + f*x/2)**9 + 2025*a**3*c**5*f*tan(e/2 + f*x/2)**8 - 2025*a**3*c**5*f*tan(e/2 + f*x/2)**6 + 900*a**3*c**5*f*tan(e/2 + f*x/2)**5 + 855*a**3*c**5*f*tan(e/2 + f*x/2)**4 - 720*a**3*c**5*f*tan(e/2 + f*x/2)**3 - 45*a**3*c**5*f*tan(e/2 + f*x/2)**2 + 180*a**3*c**5*f*tan(e/2 + f*x/2) - 45*a**3*c**5*f) - 20/(45*a**3*c**5*f*tan(e/2 + f*x/2)**14 - 180*a**3*c**5*f*tan(e/2 + f*x/2)**13 + 45*a**3*c**5*f*tan(e/2 + f*x/2)**12 + 720*a**3*c**5*f*tan(e/2 + f*x/2)**11 - 855*a**3*c**5*f*tan(e/2 + f*x/2)**10 - 900*a**3*c**5*f*tan(e/2 + f*x/2)**9 + 2025*a**3*c**5*f*tan(e/2 + f*x/2)**8 - 2025*a**3*c**5*f*tan(e/2 + f*x/2)**6 + 900*a**3*c**5*f*tan(e/2 + f*x/2)**5 + 855*a**3*c**5*f*tan(e/2 + f*x/2)**4 - 720*a**3*c**5*f*tan(e/2 + f*x/2)**3 - 45*a**3*c**5*f*tan(e/2 + f*x/2)**2 + 180*a**3*c**5*f*tan(e/2 + f*x/2) - 45*a**3*c**5*f), Ne(f, 0)), (x/((a*sin(e) + a)**3*(-c*sin(e) + c)**5), True))","A",0
289,1,5661,0,160.147916," ","integrate(1/(a+a*sin(f*x+e))**3/(c-c*sin(f*x+e))**6,x)","\begin{cases} - \frac{990 \tan^{15}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{495 a^{3} c^{6} f \tan^{16}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2970 a^{3} c^{6} f \tan^{15}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4950 a^{3} c^{6} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4950 a^{3} c^{6} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 24750 a^{3} c^{6} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 16830 a^{3} c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 32670 a^{3} c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 54450 a^{3} c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 54450 a^{3} c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 32670 a^{3} c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 16830 a^{3} c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24750 a^{3} c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4950 a^{3} c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4950 a^{3} c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2970 a^{3} c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 495 a^{3} c^{6} f} + \frac{2970 \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{495 a^{3} c^{6} f \tan^{16}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2970 a^{3} c^{6} f \tan^{15}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4950 a^{3} c^{6} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4950 a^{3} c^{6} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 24750 a^{3} c^{6} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 16830 a^{3} c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 32670 a^{3} c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 54450 a^{3} c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 54450 a^{3} c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 32670 a^{3} c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 16830 a^{3} c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24750 a^{3} c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4950 a^{3} c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4950 a^{3} c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2970 a^{3} c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 495 a^{3} c^{6} f} - \frac{3630 \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{495 a^{3} c^{6} f \tan^{16}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2970 a^{3} c^{6} f \tan^{15}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4950 a^{3} c^{6} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4950 a^{3} c^{6} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 24750 a^{3} c^{6} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 16830 a^{3} c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 32670 a^{3} c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 54450 a^{3} c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 54450 a^{3} c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 32670 a^{3} c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 16830 a^{3} c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24750 a^{3} c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4950 a^{3} c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4950 a^{3} c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2970 a^{3} c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 495 a^{3} c^{6} f} - \frac{4950 \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{495 a^{3} c^{6} f \tan^{16}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2970 a^{3} c^{6} f \tan^{15}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4950 a^{3} c^{6} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4950 a^{3} c^{6} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 24750 a^{3} c^{6} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 16830 a^{3} c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 32670 a^{3} c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 54450 a^{3} c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 54450 a^{3} c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 32670 a^{3} c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 16830 a^{3} c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24750 a^{3} c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4950 a^{3} c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4950 a^{3} c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2970 a^{3} c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 495 a^{3} c^{6} f} + \frac{9834 \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{495 a^{3} c^{6} f \tan^{16}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2970 a^{3} c^{6} f \tan^{15}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4950 a^{3} c^{6} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4950 a^{3} c^{6} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 24750 a^{3} c^{6} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 16830 a^{3} c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 32670 a^{3} c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 54450 a^{3} c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 54450 a^{3} c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 32670 a^{3} c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 16830 a^{3} c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24750 a^{3} c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4950 a^{3} c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4950 a^{3} c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2970 a^{3} c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 495 a^{3} c^{6} f} + \frac{66 \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{495 a^{3} c^{6} f \tan^{16}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2970 a^{3} c^{6} f \tan^{15}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4950 a^{3} c^{6} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4950 a^{3} c^{6} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 24750 a^{3} c^{6} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 16830 a^{3} c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 32670 a^{3} c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 54450 a^{3} c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 54450 a^{3} c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 32670 a^{3} c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 16830 a^{3} c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24750 a^{3} c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4950 a^{3} c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4950 a^{3} c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2970 a^{3} c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 495 a^{3} c^{6} f} - \frac{23430 \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{495 a^{3} c^{6} f \tan^{16}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2970 a^{3} c^{6} f \tan^{15}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4950 a^{3} c^{6} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4950 a^{3} c^{6} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 24750 a^{3} c^{6} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 16830 a^{3} c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 32670 a^{3} c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 54450 a^{3} c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 54450 a^{3} c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 32670 a^{3} c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 16830 a^{3} c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24750 a^{3} c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4950 a^{3} c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4950 a^{3} c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2970 a^{3} c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 495 a^{3} c^{6} f} + \frac{17490 \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{495 a^{3} c^{6} f \tan^{16}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2970 a^{3} c^{6} f \tan^{15}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4950 a^{3} c^{6} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4950 a^{3} c^{6} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 24750 a^{3} c^{6} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 16830 a^{3} c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 32670 a^{3} c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 54450 a^{3} c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 54450 a^{3} c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 32670 a^{3} c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 16830 a^{3} c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24750 a^{3} c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4950 a^{3} c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4950 a^{3} c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2970 a^{3} c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 495 a^{3} c^{6} f} + \frac{4070 \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{495 a^{3} c^{6} f \tan^{16}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2970 a^{3} c^{6} f \tan^{15}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4950 a^{3} c^{6} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4950 a^{3} c^{6} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 24750 a^{3} c^{6} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 16830 a^{3} c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 32670 a^{3} c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 54450 a^{3} c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 54450 a^{3} c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 32670 a^{3} c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 16830 a^{3} c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24750 a^{3} c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4950 a^{3} c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4950 a^{3} c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2970 a^{3} c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 495 a^{3} c^{6} f} - \frac{16434 \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{495 a^{3} c^{6} f \tan^{16}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2970 a^{3} c^{6} f \tan^{15}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4950 a^{3} c^{6} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4950 a^{3} c^{6} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 24750 a^{3} c^{6} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 16830 a^{3} c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 32670 a^{3} c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 54450 a^{3} c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 54450 a^{3} c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 32670 a^{3} c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 16830 a^{3} c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24750 a^{3} c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4950 a^{3} c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4950 a^{3} c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2970 a^{3} c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 495 a^{3} c^{6} f} + \frac{1334 \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{495 a^{3} c^{6} f \tan^{16}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2970 a^{3} c^{6} f \tan^{15}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4950 a^{3} c^{6} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4950 a^{3} c^{6} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 24750 a^{3} c^{6} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 16830 a^{3} c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 32670 a^{3} c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 54450 a^{3} c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 54450 a^{3} c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 32670 a^{3} c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 16830 a^{3} c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24750 a^{3} c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4950 a^{3} c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4950 a^{3} c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2970 a^{3} c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 495 a^{3} c^{6} f} + \frac{7550 \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{495 a^{3} c^{6} f \tan^{16}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2970 a^{3} c^{6} f \tan^{15}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4950 a^{3} c^{6} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4950 a^{3} c^{6} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 24750 a^{3} c^{6} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 16830 a^{3} c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 32670 a^{3} c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 54450 a^{3} c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 54450 a^{3} c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 32670 a^{3} c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 16830 a^{3} c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24750 a^{3} c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4950 a^{3} c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4950 a^{3} c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2970 a^{3} c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 495 a^{3} c^{6} f} - \frac{6130 \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{495 a^{3} c^{6} f \tan^{16}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2970 a^{3} c^{6} f \tan^{15}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4950 a^{3} c^{6} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4950 a^{3} c^{6} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 24750 a^{3} c^{6} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 16830 a^{3} c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 32670 a^{3} c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 54450 a^{3} c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 54450 a^{3} c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 32670 a^{3} c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 16830 a^{3} c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24750 a^{3} c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4950 a^{3} c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4950 a^{3} c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2970 a^{3} c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 495 a^{3} c^{6} f} + \frac{470 \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{495 a^{3} c^{6} f \tan^{16}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2970 a^{3} c^{6} f \tan^{15}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4950 a^{3} c^{6} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4950 a^{3} c^{6} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 24750 a^{3} c^{6} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 16830 a^{3} c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 32670 a^{3} c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 54450 a^{3} c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 54450 a^{3} c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 32670 a^{3} c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 16830 a^{3} c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24750 a^{3} c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4950 a^{3} c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4950 a^{3} c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2970 a^{3} c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 495 a^{3} c^{6} f} + \frac{510 \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{495 a^{3} c^{6} f \tan^{16}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2970 a^{3} c^{6} f \tan^{15}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4950 a^{3} c^{6} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4950 a^{3} c^{6} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 24750 a^{3} c^{6} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 16830 a^{3} c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 32670 a^{3} c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 54450 a^{3} c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 54450 a^{3} c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 32670 a^{3} c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 16830 a^{3} c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24750 a^{3} c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4950 a^{3} c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4950 a^{3} c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2970 a^{3} c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 495 a^{3} c^{6} f} - \frac{250}{495 a^{3} c^{6} f \tan^{16}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 2970 a^{3} c^{6} f \tan^{15}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4950 a^{3} c^{6} f \tan^{14}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 4950 a^{3} c^{6} f \tan^{13}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 24750 a^{3} c^{6} f \tan^{12}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 16830 a^{3} c^{6} f \tan^{11}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 32670 a^{3} c^{6} f \tan^{10}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 54450 a^{3} c^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 54450 a^{3} c^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 32670 a^{3} c^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 16830 a^{3} c^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 24750 a^{3} c^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4950 a^{3} c^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 4950 a^{3} c^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2970 a^{3} c^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - 495 a^{3} c^{6} f} & \text{for}\: f \neq 0 \\\frac{x}{\left(a \sin{\left(e \right)} + a\right)^{3} \left(- c \sin{\left(e \right)} + c\right)^{6}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-990*tan(e/2 + f*x/2)**15/(495*a**3*c**6*f*tan(e/2 + f*x/2)**16 - 2970*a**3*c**6*f*tan(e/2 + f*x/2)**15 + 4950*a**3*c**6*f*tan(e/2 + f*x/2)**14 + 4950*a**3*c**6*f*tan(e/2 + f*x/2)**13 - 24750*a**3*c**6*f*tan(e/2 + f*x/2)**12 + 16830*a**3*c**6*f*tan(e/2 + f*x/2)**11 + 32670*a**3*c**6*f*tan(e/2 + f*x/2)**10 - 54450*a**3*c**6*f*tan(e/2 + f*x/2)**9 + 54450*a**3*c**6*f*tan(e/2 + f*x/2)**7 - 32670*a**3*c**6*f*tan(e/2 + f*x/2)**6 - 16830*a**3*c**6*f*tan(e/2 + f*x/2)**5 + 24750*a**3*c**6*f*tan(e/2 + f*x/2)**4 - 4950*a**3*c**6*f*tan(e/2 + f*x/2)**3 - 4950*a**3*c**6*f*tan(e/2 + f*x/2)**2 + 2970*a**3*c**6*f*tan(e/2 + f*x/2) - 495*a**3*c**6*f) + 2970*tan(e/2 + f*x/2)**14/(495*a**3*c**6*f*tan(e/2 + f*x/2)**16 - 2970*a**3*c**6*f*tan(e/2 + f*x/2)**15 + 4950*a**3*c**6*f*tan(e/2 + f*x/2)**14 + 4950*a**3*c**6*f*tan(e/2 + f*x/2)**13 - 24750*a**3*c**6*f*tan(e/2 + f*x/2)**12 + 16830*a**3*c**6*f*tan(e/2 + f*x/2)**11 + 32670*a**3*c**6*f*tan(e/2 + f*x/2)**10 - 54450*a**3*c**6*f*tan(e/2 + f*x/2)**9 + 54450*a**3*c**6*f*tan(e/2 + f*x/2)**7 - 32670*a**3*c**6*f*tan(e/2 + f*x/2)**6 - 16830*a**3*c**6*f*tan(e/2 + f*x/2)**5 + 24750*a**3*c**6*f*tan(e/2 + f*x/2)**4 - 4950*a**3*c**6*f*tan(e/2 + f*x/2)**3 - 4950*a**3*c**6*f*tan(e/2 + f*x/2)**2 + 2970*a**3*c**6*f*tan(e/2 + f*x/2) - 495*a**3*c**6*f) - 3630*tan(e/2 + f*x/2)**13/(495*a**3*c**6*f*tan(e/2 + f*x/2)**16 - 2970*a**3*c**6*f*tan(e/2 + f*x/2)**15 + 4950*a**3*c**6*f*tan(e/2 + f*x/2)**14 + 4950*a**3*c**6*f*tan(e/2 + f*x/2)**13 - 24750*a**3*c**6*f*tan(e/2 + f*x/2)**12 + 16830*a**3*c**6*f*tan(e/2 + f*x/2)**11 + 32670*a**3*c**6*f*tan(e/2 + f*x/2)**10 - 54450*a**3*c**6*f*tan(e/2 + f*x/2)**9 + 54450*a**3*c**6*f*tan(e/2 + f*x/2)**7 - 32670*a**3*c**6*f*tan(e/2 + f*x/2)**6 - 16830*a**3*c**6*f*tan(e/2 + f*x/2)**5 + 24750*a**3*c**6*f*tan(e/2 + f*x/2)**4 - 4950*a**3*c**6*f*tan(e/2 + f*x/2)**3 - 4950*a**3*c**6*f*tan(e/2 + f*x/2)**2 + 2970*a**3*c**6*f*tan(e/2 + f*x/2) - 495*a**3*c**6*f) - 4950*tan(e/2 + f*x/2)**12/(495*a**3*c**6*f*tan(e/2 + f*x/2)**16 - 2970*a**3*c**6*f*tan(e/2 + f*x/2)**15 + 4950*a**3*c**6*f*tan(e/2 + f*x/2)**14 + 4950*a**3*c**6*f*tan(e/2 + f*x/2)**13 - 24750*a**3*c**6*f*tan(e/2 + f*x/2)**12 + 16830*a**3*c**6*f*tan(e/2 + f*x/2)**11 + 32670*a**3*c**6*f*tan(e/2 + f*x/2)**10 - 54450*a**3*c**6*f*tan(e/2 + f*x/2)**9 + 54450*a**3*c**6*f*tan(e/2 + f*x/2)**7 - 32670*a**3*c**6*f*tan(e/2 + f*x/2)**6 - 16830*a**3*c**6*f*tan(e/2 + f*x/2)**5 + 24750*a**3*c**6*f*tan(e/2 + f*x/2)**4 - 4950*a**3*c**6*f*tan(e/2 + f*x/2)**3 - 4950*a**3*c**6*f*tan(e/2 + f*x/2)**2 + 2970*a**3*c**6*f*tan(e/2 + f*x/2) - 495*a**3*c**6*f) + 9834*tan(e/2 + f*x/2)**11/(495*a**3*c**6*f*tan(e/2 + f*x/2)**16 - 2970*a**3*c**6*f*tan(e/2 + f*x/2)**15 + 4950*a**3*c**6*f*tan(e/2 + f*x/2)**14 + 4950*a**3*c**6*f*tan(e/2 + f*x/2)**13 - 24750*a**3*c**6*f*tan(e/2 + f*x/2)**12 + 16830*a**3*c**6*f*tan(e/2 + f*x/2)**11 + 32670*a**3*c**6*f*tan(e/2 + f*x/2)**10 - 54450*a**3*c**6*f*tan(e/2 + f*x/2)**9 + 54450*a**3*c**6*f*tan(e/2 + f*x/2)**7 - 32670*a**3*c**6*f*tan(e/2 + f*x/2)**6 - 16830*a**3*c**6*f*tan(e/2 + f*x/2)**5 + 24750*a**3*c**6*f*tan(e/2 + f*x/2)**4 - 4950*a**3*c**6*f*tan(e/2 + f*x/2)**3 - 4950*a**3*c**6*f*tan(e/2 + f*x/2)**2 + 2970*a**3*c**6*f*tan(e/2 + f*x/2) - 495*a**3*c**6*f) + 66*tan(e/2 + f*x/2)**10/(495*a**3*c**6*f*tan(e/2 + f*x/2)**16 - 2970*a**3*c**6*f*tan(e/2 + f*x/2)**15 + 4950*a**3*c**6*f*tan(e/2 + f*x/2)**14 + 4950*a**3*c**6*f*tan(e/2 + f*x/2)**13 - 24750*a**3*c**6*f*tan(e/2 + f*x/2)**12 + 16830*a**3*c**6*f*tan(e/2 + f*x/2)**11 + 32670*a**3*c**6*f*tan(e/2 + f*x/2)**10 - 54450*a**3*c**6*f*tan(e/2 + f*x/2)**9 + 54450*a**3*c**6*f*tan(e/2 + f*x/2)**7 - 32670*a**3*c**6*f*tan(e/2 + f*x/2)**6 - 16830*a**3*c**6*f*tan(e/2 + f*x/2)**5 + 24750*a**3*c**6*f*tan(e/2 + f*x/2)**4 - 4950*a**3*c**6*f*tan(e/2 + f*x/2)**3 - 4950*a**3*c**6*f*tan(e/2 + f*x/2)**2 + 2970*a**3*c**6*f*tan(e/2 + f*x/2) - 495*a**3*c**6*f) - 23430*tan(e/2 + f*x/2)**9/(495*a**3*c**6*f*tan(e/2 + f*x/2)**16 - 2970*a**3*c**6*f*tan(e/2 + f*x/2)**15 + 4950*a**3*c**6*f*tan(e/2 + f*x/2)**14 + 4950*a**3*c**6*f*tan(e/2 + f*x/2)**13 - 24750*a**3*c**6*f*tan(e/2 + f*x/2)**12 + 16830*a**3*c**6*f*tan(e/2 + f*x/2)**11 + 32670*a**3*c**6*f*tan(e/2 + f*x/2)**10 - 54450*a**3*c**6*f*tan(e/2 + f*x/2)**9 + 54450*a**3*c**6*f*tan(e/2 + f*x/2)**7 - 32670*a**3*c**6*f*tan(e/2 + f*x/2)**6 - 16830*a**3*c**6*f*tan(e/2 + f*x/2)**5 + 24750*a**3*c**6*f*tan(e/2 + f*x/2)**4 - 4950*a**3*c**6*f*tan(e/2 + f*x/2)**3 - 4950*a**3*c**6*f*tan(e/2 + f*x/2)**2 + 2970*a**3*c**6*f*tan(e/2 + f*x/2) - 495*a**3*c**6*f) + 17490*tan(e/2 + f*x/2)**8/(495*a**3*c**6*f*tan(e/2 + f*x/2)**16 - 2970*a**3*c**6*f*tan(e/2 + f*x/2)**15 + 4950*a**3*c**6*f*tan(e/2 + f*x/2)**14 + 4950*a**3*c**6*f*tan(e/2 + f*x/2)**13 - 24750*a**3*c**6*f*tan(e/2 + f*x/2)**12 + 16830*a**3*c**6*f*tan(e/2 + f*x/2)**11 + 32670*a**3*c**6*f*tan(e/2 + f*x/2)**10 - 54450*a**3*c**6*f*tan(e/2 + f*x/2)**9 + 54450*a**3*c**6*f*tan(e/2 + f*x/2)**7 - 32670*a**3*c**6*f*tan(e/2 + f*x/2)**6 - 16830*a**3*c**6*f*tan(e/2 + f*x/2)**5 + 24750*a**3*c**6*f*tan(e/2 + f*x/2)**4 - 4950*a**3*c**6*f*tan(e/2 + f*x/2)**3 - 4950*a**3*c**6*f*tan(e/2 + f*x/2)**2 + 2970*a**3*c**6*f*tan(e/2 + f*x/2) - 495*a**3*c**6*f) + 4070*tan(e/2 + f*x/2)**7/(495*a**3*c**6*f*tan(e/2 + f*x/2)**16 - 2970*a**3*c**6*f*tan(e/2 + f*x/2)**15 + 4950*a**3*c**6*f*tan(e/2 + f*x/2)**14 + 4950*a**3*c**6*f*tan(e/2 + f*x/2)**13 - 24750*a**3*c**6*f*tan(e/2 + f*x/2)**12 + 16830*a**3*c**6*f*tan(e/2 + f*x/2)**11 + 32670*a**3*c**6*f*tan(e/2 + f*x/2)**10 - 54450*a**3*c**6*f*tan(e/2 + f*x/2)**9 + 54450*a**3*c**6*f*tan(e/2 + f*x/2)**7 - 32670*a**3*c**6*f*tan(e/2 + f*x/2)**6 - 16830*a**3*c**6*f*tan(e/2 + f*x/2)**5 + 24750*a**3*c**6*f*tan(e/2 + f*x/2)**4 - 4950*a**3*c**6*f*tan(e/2 + f*x/2)**3 - 4950*a**3*c**6*f*tan(e/2 + f*x/2)**2 + 2970*a**3*c**6*f*tan(e/2 + f*x/2) - 495*a**3*c**6*f) - 16434*tan(e/2 + f*x/2)**6/(495*a**3*c**6*f*tan(e/2 + f*x/2)**16 - 2970*a**3*c**6*f*tan(e/2 + f*x/2)**15 + 4950*a**3*c**6*f*tan(e/2 + f*x/2)**14 + 4950*a**3*c**6*f*tan(e/2 + f*x/2)**13 - 24750*a**3*c**6*f*tan(e/2 + f*x/2)**12 + 16830*a**3*c**6*f*tan(e/2 + f*x/2)**11 + 32670*a**3*c**6*f*tan(e/2 + f*x/2)**10 - 54450*a**3*c**6*f*tan(e/2 + f*x/2)**9 + 54450*a**3*c**6*f*tan(e/2 + f*x/2)**7 - 32670*a**3*c**6*f*tan(e/2 + f*x/2)**6 - 16830*a**3*c**6*f*tan(e/2 + f*x/2)**5 + 24750*a**3*c**6*f*tan(e/2 + f*x/2)**4 - 4950*a**3*c**6*f*tan(e/2 + f*x/2)**3 - 4950*a**3*c**6*f*tan(e/2 + f*x/2)**2 + 2970*a**3*c**6*f*tan(e/2 + f*x/2) - 495*a**3*c**6*f) + 1334*tan(e/2 + f*x/2)**5/(495*a**3*c**6*f*tan(e/2 + f*x/2)**16 - 2970*a**3*c**6*f*tan(e/2 + f*x/2)**15 + 4950*a**3*c**6*f*tan(e/2 + f*x/2)**14 + 4950*a**3*c**6*f*tan(e/2 + f*x/2)**13 - 24750*a**3*c**6*f*tan(e/2 + f*x/2)**12 + 16830*a**3*c**6*f*tan(e/2 + f*x/2)**11 + 32670*a**3*c**6*f*tan(e/2 + f*x/2)**10 - 54450*a**3*c**6*f*tan(e/2 + f*x/2)**9 + 54450*a**3*c**6*f*tan(e/2 + f*x/2)**7 - 32670*a**3*c**6*f*tan(e/2 + f*x/2)**6 - 16830*a**3*c**6*f*tan(e/2 + f*x/2)**5 + 24750*a**3*c**6*f*tan(e/2 + f*x/2)**4 - 4950*a**3*c**6*f*tan(e/2 + f*x/2)**3 - 4950*a**3*c**6*f*tan(e/2 + f*x/2)**2 + 2970*a**3*c**6*f*tan(e/2 + f*x/2) - 495*a**3*c**6*f) + 7550*tan(e/2 + f*x/2)**4/(495*a**3*c**6*f*tan(e/2 + f*x/2)**16 - 2970*a**3*c**6*f*tan(e/2 + f*x/2)**15 + 4950*a**3*c**6*f*tan(e/2 + f*x/2)**14 + 4950*a**3*c**6*f*tan(e/2 + f*x/2)**13 - 24750*a**3*c**6*f*tan(e/2 + f*x/2)**12 + 16830*a**3*c**6*f*tan(e/2 + f*x/2)**11 + 32670*a**3*c**6*f*tan(e/2 + f*x/2)**10 - 54450*a**3*c**6*f*tan(e/2 + f*x/2)**9 + 54450*a**3*c**6*f*tan(e/2 + f*x/2)**7 - 32670*a**3*c**6*f*tan(e/2 + f*x/2)**6 - 16830*a**3*c**6*f*tan(e/2 + f*x/2)**5 + 24750*a**3*c**6*f*tan(e/2 + f*x/2)**4 - 4950*a**3*c**6*f*tan(e/2 + f*x/2)**3 - 4950*a**3*c**6*f*tan(e/2 + f*x/2)**2 + 2970*a**3*c**6*f*tan(e/2 + f*x/2) - 495*a**3*c**6*f) - 6130*tan(e/2 + f*x/2)**3/(495*a**3*c**6*f*tan(e/2 + f*x/2)**16 - 2970*a**3*c**6*f*tan(e/2 + f*x/2)**15 + 4950*a**3*c**6*f*tan(e/2 + f*x/2)**14 + 4950*a**3*c**6*f*tan(e/2 + f*x/2)**13 - 24750*a**3*c**6*f*tan(e/2 + f*x/2)**12 + 16830*a**3*c**6*f*tan(e/2 + f*x/2)**11 + 32670*a**3*c**6*f*tan(e/2 + f*x/2)**10 - 54450*a**3*c**6*f*tan(e/2 + f*x/2)**9 + 54450*a**3*c**6*f*tan(e/2 + f*x/2)**7 - 32670*a**3*c**6*f*tan(e/2 + f*x/2)**6 - 16830*a**3*c**6*f*tan(e/2 + f*x/2)**5 + 24750*a**3*c**6*f*tan(e/2 + f*x/2)**4 - 4950*a**3*c**6*f*tan(e/2 + f*x/2)**3 - 4950*a**3*c**6*f*tan(e/2 + f*x/2)**2 + 2970*a**3*c**6*f*tan(e/2 + f*x/2) - 495*a**3*c**6*f) + 470*tan(e/2 + f*x/2)**2/(495*a**3*c**6*f*tan(e/2 + f*x/2)**16 - 2970*a**3*c**6*f*tan(e/2 + f*x/2)**15 + 4950*a**3*c**6*f*tan(e/2 + f*x/2)**14 + 4950*a**3*c**6*f*tan(e/2 + f*x/2)**13 - 24750*a**3*c**6*f*tan(e/2 + f*x/2)**12 + 16830*a**3*c**6*f*tan(e/2 + f*x/2)**11 + 32670*a**3*c**6*f*tan(e/2 + f*x/2)**10 - 54450*a**3*c**6*f*tan(e/2 + f*x/2)**9 + 54450*a**3*c**6*f*tan(e/2 + f*x/2)**7 - 32670*a**3*c**6*f*tan(e/2 + f*x/2)**6 - 16830*a**3*c**6*f*tan(e/2 + f*x/2)**5 + 24750*a**3*c**6*f*tan(e/2 + f*x/2)**4 - 4950*a**3*c**6*f*tan(e/2 + f*x/2)**3 - 4950*a**3*c**6*f*tan(e/2 + f*x/2)**2 + 2970*a**3*c**6*f*tan(e/2 + f*x/2) - 495*a**3*c**6*f) + 510*tan(e/2 + f*x/2)/(495*a**3*c**6*f*tan(e/2 + f*x/2)**16 - 2970*a**3*c**6*f*tan(e/2 + f*x/2)**15 + 4950*a**3*c**6*f*tan(e/2 + f*x/2)**14 + 4950*a**3*c**6*f*tan(e/2 + f*x/2)**13 - 24750*a**3*c**6*f*tan(e/2 + f*x/2)**12 + 16830*a**3*c**6*f*tan(e/2 + f*x/2)**11 + 32670*a**3*c**6*f*tan(e/2 + f*x/2)**10 - 54450*a**3*c**6*f*tan(e/2 + f*x/2)**9 + 54450*a**3*c**6*f*tan(e/2 + f*x/2)**7 - 32670*a**3*c**6*f*tan(e/2 + f*x/2)**6 - 16830*a**3*c**6*f*tan(e/2 + f*x/2)**5 + 24750*a**3*c**6*f*tan(e/2 + f*x/2)**4 - 4950*a**3*c**6*f*tan(e/2 + f*x/2)**3 - 4950*a**3*c**6*f*tan(e/2 + f*x/2)**2 + 2970*a**3*c**6*f*tan(e/2 + f*x/2) - 495*a**3*c**6*f) - 250/(495*a**3*c**6*f*tan(e/2 + f*x/2)**16 - 2970*a**3*c**6*f*tan(e/2 + f*x/2)**15 + 4950*a**3*c**6*f*tan(e/2 + f*x/2)**14 + 4950*a**3*c**6*f*tan(e/2 + f*x/2)**13 - 24750*a**3*c**6*f*tan(e/2 + f*x/2)**12 + 16830*a**3*c**6*f*tan(e/2 + f*x/2)**11 + 32670*a**3*c**6*f*tan(e/2 + f*x/2)**10 - 54450*a**3*c**6*f*tan(e/2 + f*x/2)**9 + 54450*a**3*c**6*f*tan(e/2 + f*x/2)**7 - 32670*a**3*c**6*f*tan(e/2 + f*x/2)**6 - 16830*a**3*c**6*f*tan(e/2 + f*x/2)**5 + 24750*a**3*c**6*f*tan(e/2 + f*x/2)**4 - 4950*a**3*c**6*f*tan(e/2 + f*x/2)**3 - 4950*a**3*c**6*f*tan(e/2 + f*x/2)**2 + 2970*a**3*c**6*f*tan(e/2 + f*x/2) - 495*a**3*c**6*f), Ne(f, 0)), (x/((a*sin(e) + a)**3*(-c*sin(e) + c)**6), True))","A",0
290,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(c-c*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
291,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(c-c*sin(f*x+e))**(5/2),x)","a \left(\int c^{2} \sqrt{- c \sin{\left(e + f x \right)} + c}\, dx + \int \left(- c^{2} \sqrt{- c \sin{\left(e + f x \right)} + c} \sin{\left(e + f x \right)}\right)\, dx + \int \left(- c^{2} \sqrt{- c \sin{\left(e + f x \right)} + c} \sin^{2}{\left(e + f x \right)}\right)\, dx + \int c^{2} \sqrt{- c \sin{\left(e + f x \right)} + c} \sin^{3}{\left(e + f x \right)}\, dx\right)"," ",0,"a*(Integral(c**2*sqrt(-c*sin(e + f*x) + c), x) + Integral(-c**2*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x), x) + Integral(-c**2*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x)**2, x) + Integral(c**2*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x)**3, x))","F",0
292,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(c-c*sin(f*x+e))**(3/2),x)","a \left(\int c \sqrt{- c \sin{\left(e + f x \right)} + c}\, dx + \int \left(- c \sqrt{- c \sin{\left(e + f x \right)} + c} \sin^{2}{\left(e + f x \right)}\right)\, dx\right)"," ",0,"a*(Integral(c*sqrt(-c*sin(e + f*x) + c), x) + Integral(-c*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x)**2, x))","F",0
293,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(c-c*sin(f*x+e))**(1/2),x)","a \left(\int \sqrt{- c \sin{\left(e + f x \right)} + c} \sin{\left(e + f x \right)}\, dx + \int \sqrt{- c \sin{\left(e + f x \right)} + c}\, dx\right)"," ",0,"a*(Integral(sqrt(-c*sin(e + f*x) + c)*sin(e + f*x), x) + Integral(sqrt(-c*sin(e + f*x) + c), x))","F",0
294,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))/(c-c*sin(f*x+e))**(1/2),x)","a \left(\int \frac{\sin{\left(e + f x \right)}}{\sqrt{- c \sin{\left(e + f x \right)} + c}}\, dx + \int \frac{1}{\sqrt{- c \sin{\left(e + f x \right)} + c}}\, dx\right)"," ",0,"a*(Integral(sin(e + f*x)/sqrt(-c*sin(e + f*x) + c), x) + Integral(1/sqrt(-c*sin(e + f*x) + c), x))","F",0
295,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))/(c-c*sin(f*x+e))**(3/2),x)","a \left(\int \frac{\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{1}{- 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(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(1/(-c*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x) + c*sqrt(-c*sin(e + f*x) + c)), x))","F",0
296,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))/(c-c*sin(f*x+e))**(5/2),x)","a \left(\int \frac{\sin{\left(e + f x \right)}}{c^{2} \sqrt{- c \sin{\left(e + f x \right)} + c} \sin^{2}{\left(e + f x \right)} - 2 c^{2} \sqrt{- c \sin{\left(e + f x \right)} + c} \sin{\left(e + f x \right)} + c^{2} \sqrt{- c \sin{\left(e + f x \right)} + c}}\, dx + \int \frac{1}{c^{2} \sqrt{- c \sin{\left(e + f x \right)} + c} \sin^{2}{\left(e + f x \right)} - 2 c^{2} \sqrt{- c \sin{\left(e + f x \right)} + c} \sin{\left(e + f x \right)} + c^{2} \sqrt{- c \sin{\left(e + f x \right)} + c}}\, dx\right)"," ",0,"a*(Integral(sin(e + f*x)/(c**2*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x)**2 - 2*c**2*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x) + c**2*sqrt(-c*sin(e + f*x) + c)), x) + Integral(1/(c**2*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x)**2 - 2*c**2*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x) + c**2*sqrt(-c*sin(e + f*x) + c)), x))","F",0
297,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))/(c-c*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
298,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**2*(c-c*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
299,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**2*(c-c*sin(f*x+e))**(5/2),x)","a^{2} \left(\int c^{2} \sqrt{- c \sin{\left(e + f x \right)} + c}\, dx + \int \left(- 2 c^{2} \sqrt{- c \sin{\left(e + f x \right)} + c} \sin^{2}{\left(e + f x \right)}\right)\, dx + \int c^{2} \sqrt{- c \sin{\left(e + f x \right)} + c} \sin^{4}{\left(e + f x \right)}\, dx\right)"," ",0,"a**2*(Integral(c**2*sqrt(-c*sin(e + f*x) + c), x) + Integral(-2*c**2*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x)**2, x) + Integral(c**2*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x)**4, x))","F",0
300,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**2*(c-c*sin(f*x+e))**(3/2),x)","a^{2} \left(\int c \sqrt{- c \sin{\left(e + f x \right)} + c}\, dx + \int c \sqrt{- c \sin{\left(e + f x \right)} + c} \sin{\left(e + f x \right)}\, dx + \int \left(- c \sqrt{- c \sin{\left(e + f x \right)} + c} \sin^{2}{\left(e + f x \right)}\right)\, dx + \int \left(- c \sqrt{- c \sin{\left(e + f x \right)} + c} \sin^{3}{\left(e + f x \right)}\right)\, dx\right)"," ",0,"a**2*(Integral(c*sqrt(-c*sin(e + f*x) + c), x) + Integral(c*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x), x) + Integral(-c*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x)**2, x) + Integral(-c*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x)**3, x))","F",0
301,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**2*(c-c*sin(f*x+e))**(1/2),x)","a^{2} \left(\int 2 \sqrt{- c \sin{\left(e + f x \right)} + c} \sin{\left(e + f x \right)}\, dx + \int \sqrt{- c \sin{\left(e + f x \right)} + c} \sin^{2}{\left(e + f x \right)}\, dx + \int \sqrt{- c \sin{\left(e + f x \right)} + c}\, dx\right)"," ",0,"a**2*(Integral(2*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x), x) + Integral(sqrt(-c*sin(e + f*x) + c)*sin(e + f*x)**2, x) + Integral(sqrt(-c*sin(e + f*x) + c), x))","F",0
302,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**2/(c-c*sin(f*x+e))**(1/2),x)","a^{2} \left(\int \frac{2 \sin{\left(e + f x \right)}}{\sqrt{- c \sin{\left(e + f x \right)} + c}}\, dx + \int \frac{\sin^{2}{\left(e + f x \right)}}{\sqrt{- c \sin{\left(e + f x \right)} + c}}\, dx + \int \frac{1}{\sqrt{- c \sin{\left(e + f x \right)} + c}}\, dx\right)"," ",0,"a**2*(Integral(2*sin(e + f*x)/sqrt(-c*sin(e + f*x) + c), x) + Integral(sin(e + f*x)**2/sqrt(-c*sin(e + f*x) + c), x) + Integral(1/sqrt(-c*sin(e + f*x) + c), x))","F",0
303,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**2/(c-c*sin(f*x+e))**(3/2),x)","a^{2} \left(\int \frac{2 \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{\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 + \int \frac{1}{- 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**2*(Integral(2*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(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) + Integral(1/(-c*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x) + c*sqrt(-c*sin(e + f*x) + c)), x))","F",0
304,-1,0,0,0.000000," ","integrate((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
305,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**2/(c-c*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
306,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**2/(c-c*sin(f*x+e))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
307,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**3*(c-c*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
308,-1,0,0,0.000000," ","integrate((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
309,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**3*(c-c*sin(f*x+e))**(3/2),x)","a^{3} \left(\int c \sqrt{- c \sin{\left(e + f x \right)} + c}\, dx + \int 2 c \sqrt{- c \sin{\left(e + f x \right)} + c} \sin{\left(e + f x \right)}\, dx + \int \left(- 2 c \sqrt{- c \sin{\left(e + f x \right)} + c} \sin^{3}{\left(e + f x \right)}\right)\, dx + \int \left(- c \sqrt{- c \sin{\left(e + f x \right)} + c} \sin^{4}{\left(e + f x \right)}\right)\, dx\right)"," ",0,"a**3*(Integral(c*sqrt(-c*sin(e + f*x) + c), x) + Integral(2*c*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x), x) + Integral(-2*c*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x)**3, x) + Integral(-c*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x)**4, x))","F",0
310,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**3*(c-c*sin(f*x+e))**(1/2),x)","a^{3} \left(\int 3 \sqrt{- c \sin{\left(e + f x \right)} + c} \sin{\left(e + f x \right)}\, dx + \int 3 \sqrt{- c \sin{\left(e + f x \right)} + c} \sin^{2}{\left(e + f x \right)}\, dx + \int \sqrt{- c \sin{\left(e + f x \right)} + c} \sin^{3}{\left(e + f x \right)}\, dx + \int \sqrt{- c \sin{\left(e + f x \right)} + c}\, dx\right)"," ",0,"a**3*(Integral(3*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x), x) + Integral(3*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x)**2, x) + Integral(sqrt(-c*sin(e + f*x) + c)*sin(e + f*x)**3, x) + Integral(sqrt(-c*sin(e + f*x) + c), x))","F",0
311,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**3/(c-c*sin(f*x+e))**(1/2),x)","a^{3} \left(\int \frac{3 \sin{\left(e + f x \right)}}{\sqrt{- c \sin{\left(e + f x \right)} + c}}\, dx + \int \frac{3 \sin^{2}{\left(e + f x \right)}}{\sqrt{- c \sin{\left(e + f x \right)} + c}}\, dx + \int \frac{\sin^{3}{\left(e + f x \right)}}{\sqrt{- c \sin{\left(e + f x \right)} + c}}\, dx + \int \frac{1}{\sqrt{- c \sin{\left(e + f x \right)} + c}}\, dx\right)"," ",0,"a**3*(Integral(3*sin(e + f*x)/sqrt(-c*sin(e + f*x) + c), x) + Integral(3*sin(e + f*x)**2/sqrt(-c*sin(e + f*x) + c), x) + Integral(sin(e + f*x)**3/sqrt(-c*sin(e + f*x) + c), x) + Integral(1/sqrt(-c*sin(e + f*x) + c), x))","F",0
312,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**3/(c-c*sin(f*x+e))**(3/2),x)","a^{3} \left(\int \frac{3 \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{3 \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 + \int \frac{\sin^{3}{\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{1}{- 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**3*(Integral(3*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(3*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) + Integral(sin(e + f*x)**3/(-c*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x) + c*sqrt(-c*sin(e + f*x) + c)), x) + Integral(1/(-c*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x) + c*sqrt(-c*sin(e + f*x) + c)), x))","F",0
313,-1,0,0,0.000000," ","integrate((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
314,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**3/(c-c*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
315,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**3/(c-c*sin(f*x+e))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
316,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**3/(c-c*sin(f*x+e))**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
317,-1,0,0,0.000000," ","integrate((c-c*sin(f*x+e))**(7/2)/(a+a*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
318,-1,0,0,0.000000," ","integrate((c-c*sin(f*x+e))**(5/2)/(a+a*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
319,0,0,0,0.000000," ","integrate((c-c*sin(f*x+e))**(3/2)/(a+a*sin(f*x+e)),x)","\frac{\int \frac{c \sqrt{- c \sin{\left(e + f x \right)} + c}}{\sin{\left(e + f x \right)} + 1}\, dx + \int \left(- \frac{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}{a}"," ",0,"(Integral(c*sqrt(-c*sin(e + f*x) + c)/(sin(e + f*x) + 1), x) + Integral(-c*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x)/(sin(e + f*x) + 1), x))/a","F",0
320,0,0,0,0.000000," ","integrate((c-c*sin(f*x+e))**(1/2)/(a+a*sin(f*x+e)),x)","\frac{\int \frac{\sqrt{- c \sin{\left(e + f x \right)} + c}}{\sin{\left(e + f x \right)} + 1}\, dx}{a}"," ",0,"Integral(sqrt(-c*sin(e + f*x) + c)/(sin(e + f*x) + 1), x)/a","F",0
321,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))**(1/2),x)","\frac{\int \frac{1}{\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(1/(sqrt(-c*sin(e + f*x) + c)*sin(e + f*x) + sqrt(-c*sin(e + f*x) + c)), x)/a","F",0
322,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))**(3/2),x)","\frac{\int \frac{1}{- 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(1/(-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
323,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))**(5/2),x)","\frac{\int \frac{1}{c^{2} \sqrt{- c \sin{\left(e + f x \right)} + c} \sin^{3}{\left(e + f x \right)} - c^{2} \sqrt{- c \sin{\left(e + f x \right)} + c} \sin^{2}{\left(e + f x \right)} - c^{2} \sqrt{- c \sin{\left(e + f x \right)} + c} \sin{\left(e + f x \right)} + c^{2} \sqrt{- c \sin{\left(e + f x \right)} + c}}\, dx}{a}"," ",0,"Integral(1/(c**2*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x)**3 - c**2*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x)**2 - c**2*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x) + c**2*sqrt(-c*sin(e + f*x) + c)), x)/a","F",0
324,-1,0,0,0.000000," ","integrate((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
325,-1,0,0,0.000000," ","integrate((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
326,-1,0,0,0.000000," ","integrate((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
327,0,0,0,0.000000," ","integrate((c-c*sin(f*x+e))**(3/2)/(a+a*sin(f*x+e))**2,x)","\frac{\int \frac{c \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 \left(- \frac{c \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}\right)\, dx}{a^{2}}"," ",0,"(Integral(c*sqrt(-c*sin(e + f*x) + c)/(sin(e + f*x)**2 + 2*sin(e + f*x) + 1), x) + Integral(-c*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
328,0,0,0,0.000000," ","integrate((c-c*sin(f*x+e))**(1/2)/(a+a*sin(f*x+e))**2,x)","\frac{\int \frac{\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}{a^{2}}"," ",0,"Integral(sqrt(-c*sin(e + f*x) + c)/(sin(e + f*x)**2 + 2*sin(e + f*x) + 1), x)/a**2","F",0
329,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))**2/(c-c*sin(f*x+e))**(1/2),x)","\frac{\int \frac{1}{\sqrt{- c \sin{\left(e + f x \right)} + c} \sin^{2}{\left(e + f x \right)} + 2 \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^{2}}"," ",0,"Integral(1/(sqrt(-c*sin(e + f*x) + c)*sin(e + f*x)**2 + 2*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x) + sqrt(-c*sin(e + f*x) + c)), x)/a**2","F",0
330,-1,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))**2/(c-c*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
331,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))**2/(c-c*sin(f*x+e))**(5/2),x)","\frac{\int \frac{1}{c^{2} \sqrt{- c \sin{\left(e + f x \right)} + c} \sin^{4}{\left(e + f x \right)} - 2 c^{2} \sqrt{- c \sin{\left(e + f x \right)} + c} \sin^{2}{\left(e + f x \right)} + c^{2} \sqrt{- c \sin{\left(e + f x \right)} + c}}\, dx}{a^{2}}"," ",0,"Integral(1/(c**2*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x)**4 - 2*c**2*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x)**2 + c**2*sqrt(-c*sin(e + f*x) + c)), x)/a**2","F",0
332,-1,0,0,0.000000," ","integrate((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
333,-1,0,0,0.000000," ","integrate((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
334,-1,0,0,0.000000," ","integrate((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
335,-1,0,0,0.000000," ","integrate((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
336,0,0,0,0.000000," ","integrate((c-c*sin(f*x+e))**(1/2)/(a+a*sin(f*x+e))**3,x)","\frac{\int \frac{\sqrt{- c \sin{\left(e + f x \right)} + c}}{\sin^{3}{\left(e + f x \right)} + 3 \sin^{2}{\left(e + f x \right)} + 3 \sin{\left(e + f x \right)} + 1}\, dx}{a^{3}}"," ",0,"Integral(sqrt(-c*sin(e + f*x) + c)/(sin(e + f*x)**3 + 3*sin(e + f*x)**2 + 3*sin(e + f*x) + 1), x)/a**3","F",0
337,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))**3/(c-c*sin(f*x+e))**(1/2),x)","\frac{\int \frac{1}{\sqrt{- c \sin{\left(e + f x \right)} + c} \sin^{3}{\left(e + f x \right)} + 3 \sqrt{- c \sin{\left(e + f x \right)} + c} \sin^{2}{\left(e + f x \right)} + 3 \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^{3}}"," ",0,"Integral(1/(sqrt(-c*sin(e + f*x) + c)*sin(e + f*x)**3 + 3*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x)**2 + 3*sqrt(-c*sin(e + f*x) + c)*sin(e + f*x) + sqrt(-c*sin(e + f*x) + c)), x)/a**3","F",0
338,-1,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))**3/(c-c*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
339,-1,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))**3/(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
340,-1,0,0,0.000000," ","integrate((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
341,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(1/2)*(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
342,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(1/2)*(c-c*sin(f*x+e))**(3/2),x)","\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}}\, dx"," ",0,"Integral(sqrt(a*(sin(e + f*x) + 1))*(-c*(sin(e + f*x) - 1))**(3/2), x)","F",0
343,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(1/2)*(c-c*sin(f*x+e))**(1/2),x)","\int \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(sqrt(a*(sin(e + f*x) + 1))*sqrt(-c*(sin(e + f*x) - 1)), x)","F",0
344,0,0,0,0.000000," ","integrate((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)}}{\sqrt{- c \left(\sin{\left(e + f x \right)} - 1\right)}}\, dx"," ",0,"Integral(sqrt(a*(sin(e + f*x) + 1))/sqrt(-c*(sin(e + f*x) - 1)), x)","F",0
345,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(1/2)/(c-c*sin(f*x+e))**(3/2),x)","\int \frac{\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(sqrt(a*(sin(e + f*x) + 1))/(-c*(sin(e + f*x) - 1))**(3/2), x)","F",0
346,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(1/2)/(c-c*sin(f*x+e))**(5/2),x)","\int \frac{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\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))/(-c*(sin(e + f*x) - 1))**(5/2), x)","F",0
347,-1,0,0,0.000000," ","integrate((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
348,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(3/2)*(c-c*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
349,-1,0,0,0.000000," ","integrate((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
350,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(3/2)*(c-c*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
351,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(3/2)*(c-c*sin(f*x+e))**(1/2),x)","\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)}\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**(3/2)*sqrt(-c*(sin(e + f*x) - 1)), x)","F",0
352,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(3/2)/(c-c*sin(f*x+e))**(1/2),x)","\int \frac{\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*(sin(e + f*x) + 1))**(3/2)/sqrt(-c*(sin(e + f*x) - 1)), x)","F",0
353,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(3/2)/(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(- 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)/(-c*(sin(e + f*x) - 1))**(3/2), x)","F",0
354,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(3/2)/(c-c*sin(f*x+e))**(5/2),x)","\int \frac{\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{5}{2}}}\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**(3/2)/(-c*(sin(e + f*x) - 1))**(5/2), x)","F",0
355,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(3/2)/(c-c*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
356,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(3/2)/(c-c*sin(f*x+e))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
357,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(3/2)/(c-c*sin(f*x+e))**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
358,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(5/2)*(c-c*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
359,-1,0,0,0.000000," ","integrate((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
360,-1,0,0,0.000000," ","integrate((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
361,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(5/2)*(c-c*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
362,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(5/2)/(c-c*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
363,-1,0,0,0.000000," ","integrate((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
364,-1,0,0,0.000000," ","integrate((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
365,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(5/2)/(c-c*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
366,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(5/2)/(c-c*sin(f*x+e))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
367,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(5/2)/(c-c*sin(f*x+e))**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
368,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(5/2)/(c-c*sin(f*x+e))**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
369,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(7/2)*(c-c*sin(f*x+e))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
370,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(7/2)*(c-c*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
371,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(7/2)*(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
372,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(7/2)*(c-c*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
373,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(7/2)*(c-c*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
374,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(7/2)/(c-c*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
375,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(7/2)/(c-c*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
376,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(7/2)/(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
377,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(7/2)/(c-c*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
378,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(7/2)/(c-c*sin(f*x+e))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
379,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(7/2)/(c-c*sin(f*x+e))**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
380,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(7/2)/(c-c*sin(f*x+e))**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
381,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(7/2)/(c-c*sin(f*x+e))**(15/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
382,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(7/2)/(c-c*sin(f*x+e))**(17/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
383,-1,0,0,0.000000," ","integrate((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
384,0,0,0,0.000000," ","integrate((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}}}{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)}}\, dx"," ",0,"Integral((-c*(sin(e + f*x) - 1))**(3/2)/sqrt(a*(sin(e + f*x) + 1)), x)","F",0
385,0,0,0,0.000000," ","integrate((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)}}{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)}}\, dx"," ",0,"Integral(sqrt(-c*(sin(e + f*x) - 1))/sqrt(a*(sin(e + f*x) + 1)), x)","F",0
386,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))**(1/2)/(c-c*sin(f*x+e))**(1/2),x)","\int \frac{1}{\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(1/(sqrt(a*(sin(e + f*x) + 1))*sqrt(-c*(sin(e + f*x) - 1))), x)","F",0
387,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))**(1/2)/(c-c*sin(f*x+e))**(3/2),x)","\int \frac{1}{\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(1/(sqrt(a*(sin(e + f*x) + 1))*(-c*(sin(e + f*x) - 1))**(3/2)), x)","F",0
388,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))**(1/2)/(c-c*sin(f*x+e))**(5/2),x)","\int \frac{1}{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)} \left(- c \left(\sin{\left(e + f x \right)} - 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(sqrt(a*(sin(e + f*x) + 1))*(-c*(sin(e + f*x) - 1))**(5/2)), x)","F",0
389,-1,0,0,0.000000," ","integrate((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
390,-1,0,0,0.000000," ","integrate((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
391,0,0,0,0.000000," ","integrate((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 \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*(sin(e + f*x) + 1))**(3/2), x)","F",0
392,0,0,0,0.000000," ","integrate((c-c*sin(f*x+e))**(1/2)/(a+a*sin(f*x+e))**(3/2),x)","\int \frac{\sqrt{- c \left(\sin{\left(e + f x \right)} - 1\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*(sin(e + f*x) + 1))**(3/2), x)","F",0
393,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))**(3/2)/(c-c*sin(f*x+e))**(1/2),x)","\int \frac{1}{\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(1/((a*(sin(e + f*x) + 1))**(3/2)*sqrt(-c*(sin(e + f*x) - 1))), x)","F",0
394,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))**(3/2)/(c-c*sin(f*x+e))**(3/2),x)","\int \frac{1}{\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(1/((a*(sin(e + f*x) + 1))**(3/2)*(-c*(sin(e + f*x) - 1))**(3/2)), x)","F",0
395,-1,0,0,0.000000," ","integrate(1/(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
396,-1,0,0,0.000000," ","integrate((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
397,-1,0,0,0.000000," ","integrate((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
398,-1,0,0,0.000000," ","integrate((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
399,0,0,0,0.000000," ","integrate((c-c*sin(f*x+e))**(3/2)/(a+a*sin(f*x+e))**(5/2),x)","\int \frac{\left(- c \left(\sin{\left(e + f x \right)} - 1\right)\right)^{\frac{3}{2}}}{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((-c*(sin(e + f*x) - 1))**(3/2)/(a*(sin(e + f*x) + 1))**(5/2), x)","F",0
400,0,0,0,0.000000," ","integrate((c-c*sin(f*x+e))**(1/2)/(a+a*sin(f*x+e))**(5/2),x)","\int \frac{\sqrt{- c \left(\sin{\left(e + f x \right)} - 1\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*(sin(e + f*x) + 1))**(5/2), x)","F",0
401,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))**(5/2)/(c-c*sin(f*x+e))**(1/2),x)","\int \frac{1}{\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(1/((a*(sin(e + f*x) + 1))**(5/2)*sqrt(-c*(sin(e + f*x) - 1))), x)","F",0
402,-1,0,0,0.000000," ","integrate(1/(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
403,-1,0,0,0.000000," ","integrate(1/(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
404,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(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}\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**m*(-c*(sin(e + f*x) - 1))**n, x)","F",0
405,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**3,x)","- c^{3} \left(\int 3 \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}\, dx + \int \left(- 3 \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)}\right)\, dx + \int \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{3}{\left(e + f x \right)}\, dx + \int \left(- \left(a \sin{\left(e + f x \right)} + a\right)^{m}\right)\, dx\right)"," ",0,"-c**3*(Integral(3*(a*sin(e + f*x) + a)**m*sin(e + f*x), x) + Integral(-3*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2, x) + Integral((a*sin(e + f*x) + a)**m*sin(e + f*x)**3, x) + Integral(-(a*sin(e + f*x) + a)**m, x))","F",0
406,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**2,x)","c^{2} \left(\int \left(- 2 \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}\right)\, dx + \int \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)}\, dx + \int \left(a \sin{\left(e + f x \right)} + a\right)^{m}\, dx\right)"," ",0,"c**2*(Integral(-2*(a*sin(e + f*x) + a)**m*sin(e + f*x), x) + Integral((a*sin(e + f*x) + a)**m*sin(e + f*x)**2, x) + Integral((a*sin(e + f*x) + a)**m, x))","F",0
407,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(c-c*sin(f*x+e)),x)","- c \left(\int \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}\, dx + \int \left(- \left(a \sin{\left(e + f x \right)} + a\right)^{m}\right)\, dx\right)"," ",0,"-c*(Integral((a*sin(e + f*x) + a)**m*sin(e + f*x), x) + Integral(-(a*sin(e + f*x) + a)**m, x))","F",0
408,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m/(c-c*sin(f*x+e)),x)","- \frac{\int \frac{\left(a \sin{\left(e + f x \right)} + a\right)^{m}}{\sin{\left(e + f x \right)} - 1}\, dx}{c}"," ",0,"-Integral((a*sin(e + f*x) + a)**m/(sin(e + f*x) - 1), x)/c","F",0
409,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m/(c-c*sin(f*x+e))**2,x)","\frac{\int \frac{\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}{c^{2}}"," ",0,"Integral((a*sin(e + f*x) + a)**m/(sin(e + f*x)**2 - 2*sin(e + f*x) + 1), x)/c**2","F",0
410,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m/(c-c*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
411,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
412,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
413,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(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)}\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**m*sqrt(-c*(sin(e + f*x) - 1)), x)","F",0
414,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m/(c-c*sin(f*x+e))**(1/2),x)","\int \frac{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{m}}{\sqrt{- c \left(\sin{\left(e + f x \right)} - 1\right)}}\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**m/sqrt(-c*(sin(e + f*x) - 1)), x)","F",0
415,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m/(c-c*sin(f*x+e))**(3/2),x)","\int \frac{\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)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**m/(-c*(sin(e + f*x) - 1))**(3/2), x)","F",0
416,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m/(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
417,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m/(c-c*sin(f*x+e))**(1/2),x)","\int \frac{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{m}}{\sqrt{- c \left(\sin{\left(e + f x \right)} - 1\right)}}\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**m/sqrt(-c*(sin(e + f*x) - 1)), x)","F",0
418,0,0,0,0.000000," ","integrate((c+c*sin(f*x+e))**m/(a-a*sin(f*x+e))**(1/2),x)","\int \frac{\left(c \left(\sin{\left(e + f x \right)} + 1\right)\right)^{m}}{\sqrt{- a \left(\sin{\left(e + f x \right)} - 1\right)}}\, dx"," ",0,"Integral((c*(sin(e + f*x) + 1))**m/sqrt(-a*(sin(e + f*x) - 1)), x)","F",0
419,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**(-3-m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
420,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**(-2-m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
421,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**(-1-m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
422,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m/((c-c*sin(f*x+e))**m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
423,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**(1-m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
424,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**(2-m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
425,1,580,0,6.568931," ","integrate((a+a*sin(f*x+e))*(c+d*sin(f*x+e))**4,x)","\begin{cases} a c^{4} x - \frac{a c^{4} \cos{\left(e + f x \right)}}{f} + 2 a c^{3} d x \sin^{2}{\left(e + f x \right)} + 2 a c^{3} d x \cos^{2}{\left(e + f x \right)} - \frac{2 a c^{3} d \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{4 a c^{3} d \cos{\left(e + f x \right)}}{f} + 3 a c^{2} d^{2} x \sin^{2}{\left(e + f x \right)} + 3 a c^{2} d^{2} x \cos^{2}{\left(e + f x \right)} - \frac{6 a c^{2} d^{2} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{3 a c^{2} d^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{4 a c^{2} d^{2} \cos^{3}{\left(e + f x \right)}}{f} + \frac{3 a c d^{3} x \sin^{4}{\left(e + f x \right)}}{2} + 3 a c d^{3} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)} + \frac{3 a c d^{3} x \cos^{4}{\left(e + f x \right)}}{2} - \frac{5 a c d^{3} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{4 a c d^{3} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{3 a c d^{3} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{2 f} - \frac{8 a c d^{3} \cos^{3}{\left(e + f x \right)}}{3 f} + \frac{3 a d^{4} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{3 a d^{4} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{3 a d^{4} x \cos^{4}{\left(e + f x \right)}}{8} - \frac{a d^{4} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{5 a d^{4} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{4 a d^{4} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{3 a d^{4} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{8 a d^{4} \cos^{5}{\left(e + f x \right)}}{15 f} & \text{for}\: f \neq 0 \\x \left(c + d \sin{\left(e \right)}\right)^{4} \left(a \sin{\left(e \right)} + a\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**4*x - a*c**4*cos(e + f*x)/f + 2*a*c**3*d*x*sin(e + f*x)**2 + 2*a*c**3*d*x*cos(e + f*x)**2 - 2*a*c**3*d*sin(e + f*x)*cos(e + f*x)/f - 4*a*c**3*d*cos(e + f*x)/f + 3*a*c**2*d**2*x*sin(e + f*x)**2 + 3*a*c**2*d**2*x*cos(e + f*x)**2 - 6*a*c**2*d**2*sin(e + f*x)**2*cos(e + f*x)/f - 3*a*c**2*d**2*sin(e + f*x)*cos(e + f*x)/f - 4*a*c**2*d**2*cos(e + f*x)**3/f + 3*a*c*d**3*x*sin(e + f*x)**4/2 + 3*a*c*d**3*x*sin(e + f*x)**2*cos(e + f*x)**2 + 3*a*c*d**3*x*cos(e + f*x)**4/2 - 5*a*c*d**3*sin(e + f*x)**3*cos(e + f*x)/(2*f) - 4*a*c*d**3*sin(e + f*x)**2*cos(e + f*x)/f - 3*a*c*d**3*sin(e + f*x)*cos(e + f*x)**3/(2*f) - 8*a*c*d**3*cos(e + f*x)**3/(3*f) + 3*a*d**4*x*sin(e + f*x)**4/8 + 3*a*d**4*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + 3*a*d**4*x*cos(e + f*x)**4/8 - a*d**4*sin(e + f*x)**4*cos(e + f*x)/f - 5*a*d**4*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 4*a*d**4*sin(e + f*x)**2*cos(e + f*x)**3/(3*f) - 3*a*d**4*sin(e + f*x)*cos(e + f*x)**3/(8*f) - 8*a*d**4*cos(e + f*x)**5/(15*f), Ne(f, 0)), (x*(c + d*sin(e))**4*(a*sin(e) + a), True))","A",0
426,1,386,0,2.680288," ","integrate((a+a*sin(f*x+e))*(c+d*sin(f*x+e))**3,x)","\begin{cases} a c^{3} x - \frac{a c^{3} \cos{\left(e + f x \right)}}{f} + \frac{3 a c^{2} d x \sin^{2}{\left(e + f x \right)}}{2} + \frac{3 a c^{2} d x \cos^{2}{\left(e + f x \right)}}{2} - \frac{3 a c^{2} d \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{3 a c^{2} d \cos{\left(e + f x \right)}}{f} + \frac{3 a c d^{2} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{3 a c d^{2} x \cos^{2}{\left(e + f x \right)}}{2} - \frac{3 a c d^{2} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{3 a c d^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{2 a c d^{2} \cos^{3}{\left(e + f x \right)}}{f} + \frac{3 a d^{3} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{3 a d^{3} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{3 a d^{3} x \cos^{4}{\left(e + f x \right)}}{8} - \frac{5 a d^{3} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{a d^{3} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{3 a d^{3} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{2 a d^{3} \cos^{3}{\left(e + f x \right)}}{3 f} & \text{for}\: f \neq 0 \\x \left(c + d \sin{\left(e \right)}\right)^{3} \left(a \sin{\left(e \right)} + a\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**3*x - a*c**3*cos(e + f*x)/f + 3*a*c**2*d*x*sin(e + f*x)**2/2 + 3*a*c**2*d*x*cos(e + f*x)**2/2 - 3*a*c**2*d*sin(e + f*x)*cos(e + f*x)/(2*f) - 3*a*c**2*d*cos(e + f*x)/f + 3*a*c*d**2*x*sin(e + f*x)**2/2 + 3*a*c*d**2*x*cos(e + f*x)**2/2 - 3*a*c*d**2*sin(e + f*x)**2*cos(e + f*x)/f - 3*a*c*d**2*sin(e + f*x)*cos(e + f*x)/(2*f) - 2*a*c*d**2*cos(e + f*x)**3/f + 3*a*d**3*x*sin(e + f*x)**4/8 + 3*a*d**3*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + 3*a*d**3*x*cos(e + f*x)**4/8 - 5*a*d**3*sin(e + f*x)**3*cos(e + f*x)/(8*f) - a*d**3*sin(e + f*x)**2*cos(e + f*x)/f - 3*a*d**3*sin(e + f*x)*cos(e + f*x)**3/(8*f) - 2*a*d**3*cos(e + f*x)**3/(3*f), Ne(f, 0)), (x*(c + d*sin(e))**3*(a*sin(e) + a), True))","A",0
427,1,199,0,1.330911," ","integrate((a+a*sin(f*x+e))*(c+d*sin(f*x+e))**2,x)","\begin{cases} a c^{2} x - \frac{a c^{2} \cos{\left(e + f x \right)}}{f} + a c d x \sin^{2}{\left(e + f x \right)} + a c d x \cos^{2}{\left(e + f x \right)} - \frac{a c d \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{2 a c d \cos{\left(e + f x \right)}}{f} + \frac{a d^{2} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{a d^{2} x \cos^{2}{\left(e + f x \right)}}{2} - \frac{a d^{2} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{a d^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{2 a d^{2} \cos^{3}{\left(e + f x \right)}}{3 f} & \text{for}\: f \neq 0 \\x \left(c + d \sin{\left(e \right)}\right)^{2} \left(a \sin{\left(e \right)} + a\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**2*x - a*c**2*cos(e + f*x)/f + a*c*d*x*sin(e + f*x)**2 + a*c*d*x*cos(e + f*x)**2 - a*c*d*sin(e + f*x)*cos(e + f*x)/f - 2*a*c*d*cos(e + f*x)/f + a*d**2*x*sin(e + f*x)**2/2 + a*d**2*x*cos(e + f*x)**2/2 - a*d**2*sin(e + f*x)**2*cos(e + f*x)/f - a*d**2*sin(e + f*x)*cos(e + f*x)/(2*f) - 2*a*d**2*cos(e + f*x)**3/(3*f), Ne(f, 0)), (x*(c + d*sin(e))**2*(a*sin(e) + a), True))","A",0
428,1,94,0,0.720999," ","integrate((a+a*sin(f*x+e))*(c+d*sin(f*x+e)),x)","\begin{cases} a c x - \frac{a c \cos{\left(e + f x \right)}}{f} + \frac{a d x \sin^{2}{\left(e + f x \right)}}{2} + \frac{a d x \cos^{2}{\left(e + f x \right)}}{2} - \frac{a d \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{a d \cos{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \left(c + d \sin{\left(e \right)}\right) \left(a \sin{\left(e \right)} + a\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c*x - a*c*cos(e + f*x)/f + a*d*x*sin(e + f*x)**2/2 + a*d*x*cos(e + f*x)**2/2 - a*d*sin(e + f*x)*cos(e + f*x)/(2*f) - a*d*cos(e + f*x)/f, Ne(f, 0)), (x*(c + d*sin(e))*(a*sin(e) + a), True))","A",0
429,1,19,0,0.232653," ","integrate(a+a*sin(f*x+e),x)","a x + a \left(\begin{cases} - \frac{\cos{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \sin{\left(e \right)} & \text{otherwise} \end{cases}\right)"," ",0,"a*x + a*Piecewise((-cos(e + f*x)/f, Ne(f, 0)), (x*sin(e), True))","A",0
430,1,537,0,119.905646," ","integrate((a+a*sin(f*x+e))/(c+d*sin(f*x+e)),x)","\begin{cases} \frac{\tilde{\infty} x \left(a \sin{\left(e \right)} + a\right)}{\sin{\left(e \right)}} & \text{for}\: c = 0 \wedge d = 0 \wedge f = 0 \\\frac{a d^{2} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{d^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - f \left(d^{2}\right)^{\frac{3}{2}}} + \frac{2 a d^{2}}{d^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - f \left(d^{2}\right)^{\frac{3}{2}}} - \frac{a d f x \sqrt{d^{2}}}{d^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - f \left(d^{2}\right)^{\frac{3}{2}}} + \frac{2 a d \sqrt{d^{2}}}{d^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - f \left(d^{2}\right)^{\frac{3}{2}}} & \text{for}\: c = - \sqrt{d^{2}} \\\frac{a d^{2} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{d^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + f \left(d^{2}\right)^{\frac{3}{2}}} + \frac{2 a d^{2}}{d^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + f \left(d^{2}\right)^{\frac{3}{2}}} + \frac{a d f x \sqrt{d^{2}}}{d^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + f \left(d^{2}\right)^{\frac{3}{2}}} - \frac{2 a d \sqrt{d^{2}}}{d^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + f \left(d^{2}\right)^{\frac{3}{2}}} & \text{for}\: c = \sqrt{d^{2}} \\\frac{a x + \frac{a \log{\left(\tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} \right)}}{f}}{d} & \text{for}\: c = 0 \\\frac{a x - \frac{a \cos{\left(e + f x \right)}}{f}}{c} & \text{for}\: d = 0 \\\frac{x \left(a \sin{\left(e \right)} + a\right)}{c + d \sin{\left(e \right)}} & \text{for}\: f = 0 \\- \frac{a c \log{\left(\tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + \frac{d}{c} - \frac{\sqrt{- c^{2} + d^{2}}}{c} \right)}}{d f \sqrt{- c^{2} + d^{2}}} + \frac{a c \log{\left(\tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + \frac{d}{c} + \frac{\sqrt{- c^{2} + d^{2}}}{c} \right)}}{d f \sqrt{- c^{2} + d^{2}}} + \frac{a \log{\left(\tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + \frac{d}{c} - \frac{\sqrt{- c^{2} + d^{2}}}{c} \right)}}{f \sqrt{- c^{2} + d^{2}}} - \frac{a \log{\left(\tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + \frac{d}{c} + \frac{\sqrt{- c^{2} + d^{2}}}{c} \right)}}{f \sqrt{- c^{2} + d^{2}}} + \frac{a x}{d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(a*sin(e) + a)/sin(e), Eq(c, 0) & Eq(d, 0) & Eq(f, 0)), (a*d**2*f*x*tan(e/2 + f*x/2)/(d**3*f*tan(e/2 + f*x/2) - f*(d**2)**(3/2)) + 2*a*d**2/(d**3*f*tan(e/2 + f*x/2) - f*(d**2)**(3/2)) - a*d*f*x*sqrt(d**2)/(d**3*f*tan(e/2 + f*x/2) - f*(d**2)**(3/2)) + 2*a*d*sqrt(d**2)/(d**3*f*tan(e/2 + f*x/2) - f*(d**2)**(3/2)), Eq(c, -sqrt(d**2))), (a*d**2*f*x*tan(e/2 + f*x/2)/(d**3*f*tan(e/2 + f*x/2) + f*(d**2)**(3/2)) + 2*a*d**2/(d**3*f*tan(e/2 + f*x/2) + f*(d**2)**(3/2)) + a*d*f*x*sqrt(d**2)/(d**3*f*tan(e/2 + f*x/2) + f*(d**2)**(3/2)) - 2*a*d*sqrt(d**2)/(d**3*f*tan(e/2 + f*x/2) + f*(d**2)**(3/2)), Eq(c, sqrt(d**2))), ((a*x + a*log(tan(e/2 + f*x/2))/f)/d, Eq(c, 0)), ((a*x - a*cos(e + f*x)/f)/c, Eq(d, 0)), (x*(a*sin(e) + a)/(c + d*sin(e)), Eq(f, 0)), (-a*c*log(tan(e/2 + f*x/2) + d/c - sqrt(-c**2 + d**2)/c)/(d*f*sqrt(-c**2 + d**2)) + a*c*log(tan(e/2 + f*x/2) + d/c + sqrt(-c**2 + d**2)/c)/(d*f*sqrt(-c**2 + d**2)) + a*log(tan(e/2 + f*x/2) + d/c - sqrt(-c**2 + d**2)/c)/(f*sqrt(-c**2 + d**2)) - a*log(tan(e/2 + f*x/2) + d/c + sqrt(-c**2 + d**2)/c)/(f*sqrt(-c**2 + d**2)) + a*x/d, True))","A",0
431,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))/(c+d*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
432,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))/(c+d*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
433,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))/(c+d*sin(f*x+e))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
434,1,1136,0,9.415670," ","integrate((a+a*sin(f*x+e))**2*(c+d*sin(f*x+e))**4,x)","\begin{cases} \frac{a^{2} c^{4} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{a^{2} c^{4} x \cos^{2}{\left(e + f x \right)}}{2} + a^{2} c^{4} x - \frac{a^{2} c^{4} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{2 a^{2} c^{4} \cos{\left(e + f x \right)}}{f} + 4 a^{2} c^{3} d x \sin^{2}{\left(e + f x \right)} + 4 a^{2} c^{3} d x \cos^{2}{\left(e + f x \right)} - \frac{4 a^{2} c^{3} d \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{4 a^{2} c^{3} d \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{8 a^{2} c^{3} d \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{4 a^{2} c^{3} d \cos{\left(e + f x \right)}}{f} + \frac{9 a^{2} c^{2} d^{2} x \sin^{4}{\left(e + f x \right)}}{4} + \frac{9 a^{2} c^{2} d^{2} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{2} + 3 a^{2} c^{2} d^{2} x \sin^{2}{\left(e + f x \right)} + \frac{9 a^{2} c^{2} d^{2} x \cos^{4}{\left(e + f x \right)}}{4} + 3 a^{2} c^{2} d^{2} x \cos^{2}{\left(e + f x \right)} - \frac{15 a^{2} c^{2} d^{2} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{4 f} - \frac{12 a^{2} c^{2} d^{2} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{9 a^{2} c^{2} d^{2} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{4 f} - \frac{3 a^{2} c^{2} d^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{8 a^{2} c^{2} d^{2} \cos^{3}{\left(e + f x \right)}}{f} + 3 a^{2} c d^{3} x \sin^{4}{\left(e + f x \right)} + 6 a^{2} c d^{3} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)} + 3 a^{2} c d^{3} x \cos^{4}{\left(e + f x \right)} - \frac{4 a^{2} c d^{3} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{5 a^{2} c d^{3} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{16 a^{2} c d^{3} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{4 a^{2} c d^{3} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{3 a^{2} c d^{3} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{f} - \frac{32 a^{2} c d^{3} \cos^{5}{\left(e + f x \right)}}{15 f} - \frac{8 a^{2} c d^{3} \cos^{3}{\left(e + f x \right)}}{3 f} + \frac{5 a^{2} d^{4} x \sin^{6}{\left(e + f x \right)}}{16} + \frac{15 a^{2} d^{4} x \sin^{4}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{16} + \frac{3 a^{2} d^{4} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{15 a^{2} d^{4} x \sin^{2}{\left(e + f x \right)} \cos^{4}{\left(e + f x \right)}}{16} + \frac{3 a^{2} d^{4} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{5 a^{2} d^{4} x \cos^{6}{\left(e + f x \right)}}{16} + \frac{3 a^{2} d^{4} x \cos^{4}{\left(e + f x \right)}}{8} - \frac{11 a^{2} d^{4} \sin^{5}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{16 f} - \frac{2 a^{2} d^{4} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{5 a^{2} d^{4} \sin^{3}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{6 f} - \frac{5 a^{2} d^{4} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{8 a^{2} d^{4} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{5 a^{2} d^{4} \sin{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{16 f} - \frac{3 a^{2} d^{4} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{16 a^{2} d^{4} \cos^{5}{\left(e + f x \right)}}{15 f} & \text{for}\: f \neq 0 \\x \left(c + d \sin{\left(e \right)}\right)^{4} \left(a \sin{\left(e \right)} + a\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c**4*x*sin(e + f*x)**2/2 + a**2*c**4*x*cos(e + f*x)**2/2 + a**2*c**4*x - a**2*c**4*sin(e + f*x)*cos(e + f*x)/(2*f) - 2*a**2*c**4*cos(e + f*x)/f + 4*a**2*c**3*d*x*sin(e + f*x)**2 + 4*a**2*c**3*d*x*cos(e + f*x)**2 - 4*a**2*c**3*d*sin(e + f*x)**2*cos(e + f*x)/f - 4*a**2*c**3*d*sin(e + f*x)*cos(e + f*x)/f - 8*a**2*c**3*d*cos(e + f*x)**3/(3*f) - 4*a**2*c**3*d*cos(e + f*x)/f + 9*a**2*c**2*d**2*x*sin(e + f*x)**4/4 + 9*a**2*c**2*d**2*x*sin(e + f*x)**2*cos(e + f*x)**2/2 + 3*a**2*c**2*d**2*x*sin(e + f*x)**2 + 9*a**2*c**2*d**2*x*cos(e + f*x)**4/4 + 3*a**2*c**2*d**2*x*cos(e + f*x)**2 - 15*a**2*c**2*d**2*sin(e + f*x)**3*cos(e + f*x)/(4*f) - 12*a**2*c**2*d**2*sin(e + f*x)**2*cos(e + f*x)/f - 9*a**2*c**2*d**2*sin(e + f*x)*cos(e + f*x)**3/(4*f) - 3*a**2*c**2*d**2*sin(e + f*x)*cos(e + f*x)/f - 8*a**2*c**2*d**2*cos(e + f*x)**3/f + 3*a**2*c*d**3*x*sin(e + f*x)**4 + 6*a**2*c*d**3*x*sin(e + f*x)**2*cos(e + f*x)**2 + 3*a**2*c*d**3*x*cos(e + f*x)**4 - 4*a**2*c*d**3*sin(e + f*x)**4*cos(e + f*x)/f - 5*a**2*c*d**3*sin(e + f*x)**3*cos(e + f*x)/f - 16*a**2*c*d**3*sin(e + f*x)**2*cos(e + f*x)**3/(3*f) - 4*a**2*c*d**3*sin(e + f*x)**2*cos(e + f*x)/f - 3*a**2*c*d**3*sin(e + f*x)*cos(e + f*x)**3/f - 32*a**2*c*d**3*cos(e + f*x)**5/(15*f) - 8*a**2*c*d**3*cos(e + f*x)**3/(3*f) + 5*a**2*d**4*x*sin(e + f*x)**6/16 + 15*a**2*d**4*x*sin(e + f*x)**4*cos(e + f*x)**2/16 + 3*a**2*d**4*x*sin(e + f*x)**4/8 + 15*a**2*d**4*x*sin(e + f*x)**2*cos(e + f*x)**4/16 + 3*a**2*d**4*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + 5*a**2*d**4*x*cos(e + f*x)**6/16 + 3*a**2*d**4*x*cos(e + f*x)**4/8 - 11*a**2*d**4*sin(e + f*x)**5*cos(e + f*x)/(16*f) - 2*a**2*d**4*sin(e + f*x)**4*cos(e + f*x)/f - 5*a**2*d**4*sin(e + f*x)**3*cos(e + f*x)**3/(6*f) - 5*a**2*d**4*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 8*a**2*d**4*sin(e + f*x)**2*cos(e + f*x)**3/(3*f) - 5*a**2*d**4*sin(e + f*x)*cos(e + f*x)**5/(16*f) - 3*a**2*d**4*sin(e + f*x)*cos(e + f*x)**3/(8*f) - 16*a**2*d**4*cos(e + f*x)**5/(15*f), Ne(f, 0)), (x*(c + d*sin(e))**4*(a*sin(e) + a)**2, True))","A",0
435,1,729,0,4.893894," ","integrate((a+a*sin(f*x+e))**2*(c+d*sin(f*x+e))**3,x)","\begin{cases} \frac{a^{2} c^{3} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{a^{2} c^{3} x \cos^{2}{\left(e + f x \right)}}{2} + a^{2} c^{3} x - \frac{a^{2} c^{3} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{2 a^{2} c^{3} \cos{\left(e + f x \right)}}{f} + 3 a^{2} c^{2} d x \sin^{2}{\left(e + f x \right)} + 3 a^{2} c^{2} d x \cos^{2}{\left(e + f x \right)} - \frac{3 a^{2} c^{2} d \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{3 a^{2} c^{2} d \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{2 a^{2} c^{2} d \cos^{3}{\left(e + f x \right)}}{f} - \frac{3 a^{2} c^{2} d \cos{\left(e + f x \right)}}{f} + \frac{9 a^{2} c d^{2} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{9 a^{2} c d^{2} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{3 a^{2} c d^{2} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{9 a^{2} c d^{2} x \cos^{4}{\left(e + f x \right)}}{8} + \frac{3 a^{2} c d^{2} x \cos^{2}{\left(e + f x \right)}}{2} - \frac{15 a^{2} c d^{2} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{6 a^{2} c d^{2} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{9 a^{2} c d^{2} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{3 a^{2} c d^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{4 a^{2} c d^{2} \cos^{3}{\left(e + f x \right)}}{f} + \frac{3 a^{2} d^{3} x \sin^{4}{\left(e + f x \right)}}{4} + \frac{3 a^{2} d^{3} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{2} + \frac{3 a^{2} d^{3} x \cos^{4}{\left(e + f x \right)}}{4} - \frac{a^{2} d^{3} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{5 a^{2} d^{3} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{4 f} - \frac{4 a^{2} d^{3} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{a^{2} d^{3} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{3 a^{2} d^{3} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{4 f} - \frac{8 a^{2} d^{3} \cos^{5}{\left(e + f x \right)}}{15 f} - \frac{2 a^{2} d^{3} \cos^{3}{\left(e + f x \right)}}{3 f} & \text{for}\: f \neq 0 \\x \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**2*c**3*x*sin(e + f*x)**2/2 + a**2*c**3*x*cos(e + f*x)**2/2 + a**2*c**3*x - a**2*c**3*sin(e + f*x)*cos(e + f*x)/(2*f) - 2*a**2*c**3*cos(e + f*x)/f + 3*a**2*c**2*d*x*sin(e + f*x)**2 + 3*a**2*c**2*d*x*cos(e + f*x)**2 - 3*a**2*c**2*d*sin(e + f*x)**2*cos(e + f*x)/f - 3*a**2*c**2*d*sin(e + f*x)*cos(e + f*x)/f - 2*a**2*c**2*d*cos(e + f*x)**3/f - 3*a**2*c**2*d*cos(e + f*x)/f + 9*a**2*c*d**2*x*sin(e + f*x)**4/8 + 9*a**2*c*d**2*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + 3*a**2*c*d**2*x*sin(e + f*x)**2/2 + 9*a**2*c*d**2*x*cos(e + f*x)**4/8 + 3*a**2*c*d**2*x*cos(e + f*x)**2/2 - 15*a**2*c*d**2*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 6*a**2*c*d**2*sin(e + f*x)**2*cos(e + f*x)/f - 9*a**2*c*d**2*sin(e + f*x)*cos(e + f*x)**3/(8*f) - 3*a**2*c*d**2*sin(e + f*x)*cos(e + f*x)/(2*f) - 4*a**2*c*d**2*cos(e + f*x)**3/f + 3*a**2*d**3*x*sin(e + f*x)**4/4 + 3*a**2*d**3*x*sin(e + f*x)**2*cos(e + f*x)**2/2 + 3*a**2*d**3*x*cos(e + f*x)**4/4 - a**2*d**3*sin(e + f*x)**4*cos(e + f*x)/f - 5*a**2*d**3*sin(e + f*x)**3*cos(e + f*x)/(4*f) - 4*a**2*d**3*sin(e + f*x)**2*cos(e + f*x)**3/(3*f) - a**2*d**3*sin(e + f*x)**2*cos(e + f*x)/f - 3*a**2*d**3*sin(e + f*x)*cos(e + f*x)**3/(4*f) - 8*a**2*d**3*cos(e + f*x)**5/(15*f) - 2*a**2*d**3*cos(e + f*x)**3/(3*f), Ne(f, 0)), (x*(c + d*sin(e))**3*(a*sin(e) + a)**2, True))","A",0
436,1,459,0,2.359048," ","integrate((a+a*sin(f*x+e))**2*(c+d*sin(f*x+e))**2,x)","\begin{cases} \frac{a^{2} c^{2} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{a^{2} c^{2} x \cos^{2}{\left(e + f x \right)}}{2} + a^{2} c^{2} x - \frac{a^{2} c^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{2 a^{2} c^{2} \cos{\left(e + f x \right)}}{f} + 2 a^{2} c d x \sin^{2}{\left(e + f x \right)} + 2 a^{2} c d x \cos^{2}{\left(e + f x \right)} - \frac{2 a^{2} c d \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{2 a^{2} c d \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{4 a^{2} c d \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{2 a^{2} c d \cos{\left(e + f x \right)}}{f} + \frac{3 a^{2} d^{2} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{3 a^{2} d^{2} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{a^{2} d^{2} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{3 a^{2} d^{2} x \cos^{4}{\left(e + f x \right)}}{8} + \frac{a^{2} d^{2} x \cos^{2}{\left(e + f x \right)}}{2} - \frac{5 a^{2} d^{2} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{2 a^{2} d^{2} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{3 a^{2} d^{2} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{a^{2} d^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{4 a^{2} d^{2} \cos^{3}{\left(e + f x \right)}}{3 f} & \text{for}\: f \neq 0 \\x \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**2*c**2*x*sin(e + f*x)**2/2 + a**2*c**2*x*cos(e + f*x)**2/2 + a**2*c**2*x - a**2*c**2*sin(e + f*x)*cos(e + f*x)/(2*f) - 2*a**2*c**2*cos(e + f*x)/f + 2*a**2*c*d*x*sin(e + f*x)**2 + 2*a**2*c*d*x*cos(e + f*x)**2 - 2*a**2*c*d*sin(e + f*x)**2*cos(e + f*x)/f - 2*a**2*c*d*sin(e + f*x)*cos(e + f*x)/f - 4*a**2*c*d*cos(e + f*x)**3/(3*f) - 2*a**2*c*d*cos(e + f*x)/f + 3*a**2*d**2*x*sin(e + f*x)**4/8 + 3*a**2*d**2*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + a**2*d**2*x*sin(e + f*x)**2/2 + 3*a**2*d**2*x*cos(e + f*x)**4/8 + a**2*d**2*x*cos(e + f*x)**2/2 - 5*a**2*d**2*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 2*a**2*d**2*sin(e + f*x)**2*cos(e + f*x)/f - 3*a**2*d**2*sin(e + f*x)*cos(e + f*x)**3/(8*f) - a**2*d**2*sin(e + f*x)*cos(e + f*x)/(2*f) - 4*a**2*d**2*cos(e + f*x)**3/(3*f), Ne(f, 0)), (x*(c + d*sin(e))**2*(a*sin(e) + a)**2, True))","A",0
437,1,199,0,0.983377," ","integrate((a+a*sin(f*x+e))**2*(c+d*sin(f*x+e)),x)","\begin{cases} \frac{a^{2} c x \sin^{2}{\left(e + f x \right)}}{2} + \frac{a^{2} c x \cos^{2}{\left(e + f x \right)}}{2} + a^{2} c x - \frac{a^{2} c \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{2 a^{2} c \cos{\left(e + f x \right)}}{f} + a^{2} d x \sin^{2}{\left(e + f x \right)} + a^{2} d x \cos^{2}{\left(e + f x \right)} - \frac{a^{2} d \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{a^{2} d \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{2 a^{2} d \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{a^{2} d \cos{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \left(c + d \sin{\left(e \right)}\right) \left(a \sin{\left(e \right)} + a\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c*x*sin(e + f*x)**2/2 + a**2*c*x*cos(e + f*x)**2/2 + a**2*c*x - a**2*c*sin(e + f*x)*cos(e + f*x)/(2*f) - 2*a**2*c*cos(e + f*x)/f + a**2*d*x*sin(e + f*x)**2 + a**2*d*x*cos(e + f*x)**2 - a**2*d*sin(e + f*x)**2*cos(e + f*x)/f - a**2*d*sin(e + f*x)*cos(e + f*x)/f - 2*a**2*d*cos(e + f*x)**3/(3*f) - a**2*d*cos(e + f*x)/f, Ne(f, 0)), (x*(c + d*sin(e))*(a*sin(e) + a)**2, True))","A",0
438,1,78,0,0.367390," ","integrate((a+a*sin(f*x+e))**2,x)","\begin{cases} \frac{a^{2} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{a^{2} x \cos^{2}{\left(e + f x \right)}}{2} + a^{2} x - \frac{a^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{2 a^{2} \cos{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \left(a \sin{\left(e \right)} + a\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x*sin(e + f*x)**2/2 + a**2*x*cos(e + f*x)**2/2 + a**2*x - a**2*sin(e + f*x)*cos(e + f*x)/(2*f) - 2*a**2*cos(e + f*x)/f, Ne(f, 0)), (x*(a*sin(e) + a)**2, True))","A",0
439,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**2/(c+d*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
440,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**2/(c+d*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
441,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**2/(c+d*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
442,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**2/(c+d*sin(f*x+e))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
443,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**2/(c+d*sin(f*x+e))**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
444,1,1176,0,9.290804," ","integrate((a+a*sin(f*x+e))**3*(c+d*sin(f*x+e))**3,x)","\begin{cases} \frac{3 a^{3} c^{3} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{3 a^{3} c^{3} x \cos^{2}{\left(e + f x \right)}}{2} + a^{3} c^{3} x - \frac{a^{3} c^{3} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{3 a^{3} c^{3} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{2 a^{3} c^{3} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{3 a^{3} c^{3} \cos{\left(e + f x \right)}}{f} + \frac{9 a^{3} c^{2} d x \sin^{4}{\left(e + f x \right)}}{8} + \frac{9 a^{3} c^{2} d x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{9 a^{3} c^{2} d x \sin^{2}{\left(e + f x \right)}}{2} + \frac{9 a^{3} c^{2} d x \cos^{4}{\left(e + f x \right)}}{8} + \frac{9 a^{3} c^{2} d x \cos^{2}{\left(e + f x \right)}}{2} - \frac{15 a^{3} c^{2} d \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{9 a^{3} c^{2} d \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{9 a^{3} c^{2} d \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{9 a^{3} c^{2} d \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{6 a^{3} c^{2} d \cos^{3}{\left(e + f x \right)}}{f} - \frac{3 a^{3} c^{2} d \cos{\left(e + f x \right)}}{f} + \frac{27 a^{3} c d^{2} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{27 a^{3} c d^{2} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{3 a^{3} c d^{2} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{27 a^{3} c d^{2} x \cos^{4}{\left(e + f x \right)}}{8} + \frac{3 a^{3} c d^{2} x \cos^{2}{\left(e + f x \right)}}{2} - \frac{3 a^{3} c d^{2} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{45 a^{3} c d^{2} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{4 a^{3} c d^{2} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{f} - \frac{9 a^{3} c d^{2} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{27 a^{3} c d^{2} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{3 a^{3} c d^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{8 a^{3} c d^{2} \cos^{5}{\left(e + f x \right)}}{5 f} - \frac{6 a^{3} c d^{2} \cos^{3}{\left(e + f x \right)}}{f} + \frac{5 a^{3} d^{3} x \sin^{6}{\left(e + f x \right)}}{16} + \frac{15 a^{3} d^{3} x \sin^{4}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{16} + \frac{9 a^{3} d^{3} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{15 a^{3} d^{3} x \sin^{2}{\left(e + f x \right)} \cos^{4}{\left(e + f x \right)}}{16} + \frac{9 a^{3} d^{3} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{5 a^{3} d^{3} x \cos^{6}{\left(e + f x \right)}}{16} + \frac{9 a^{3} d^{3} x \cos^{4}{\left(e + f x \right)}}{8} - \frac{11 a^{3} d^{3} \sin^{5}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{16 f} - \frac{3 a^{3} d^{3} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{5 a^{3} d^{3} \sin^{3}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{6 f} - \frac{15 a^{3} d^{3} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{4 a^{3} d^{3} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{f} - \frac{a^{3} d^{3} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{5 a^{3} d^{3} \sin{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{16 f} - \frac{9 a^{3} d^{3} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{8 a^{3} d^{3} \cos^{5}{\left(e + f x \right)}}{5 f} - \frac{2 a^{3} d^{3} \cos^{3}{\left(e + f x \right)}}{3 f} & \text{for}\: f \neq 0 \\x \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**3*c**3*x*sin(e + f*x)**2/2 + 3*a**3*c**3*x*cos(e + f*x)**2/2 + a**3*c**3*x - a**3*c**3*sin(e + f*x)**2*cos(e + f*x)/f - 3*a**3*c**3*sin(e + f*x)*cos(e + f*x)/(2*f) - 2*a**3*c**3*cos(e + f*x)**3/(3*f) - 3*a**3*c**3*cos(e + f*x)/f + 9*a**3*c**2*d*x*sin(e + f*x)**4/8 + 9*a**3*c**2*d*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + 9*a**3*c**2*d*x*sin(e + f*x)**2/2 + 9*a**3*c**2*d*x*cos(e + f*x)**4/8 + 9*a**3*c**2*d*x*cos(e + f*x)**2/2 - 15*a**3*c**2*d*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 9*a**3*c**2*d*sin(e + f*x)**2*cos(e + f*x)/f - 9*a**3*c**2*d*sin(e + f*x)*cos(e + f*x)**3/(8*f) - 9*a**3*c**2*d*sin(e + f*x)*cos(e + f*x)/(2*f) - 6*a**3*c**2*d*cos(e + f*x)**3/f - 3*a**3*c**2*d*cos(e + f*x)/f + 27*a**3*c*d**2*x*sin(e + f*x)**4/8 + 27*a**3*c*d**2*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + 3*a**3*c*d**2*x*sin(e + f*x)**2/2 + 27*a**3*c*d**2*x*cos(e + f*x)**4/8 + 3*a**3*c*d**2*x*cos(e + f*x)**2/2 - 3*a**3*c*d**2*sin(e + f*x)**4*cos(e + f*x)/f - 45*a**3*c*d**2*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 4*a**3*c*d**2*sin(e + f*x)**2*cos(e + f*x)**3/f - 9*a**3*c*d**2*sin(e + f*x)**2*cos(e + f*x)/f - 27*a**3*c*d**2*sin(e + f*x)*cos(e + f*x)**3/(8*f) - 3*a**3*c*d**2*sin(e + f*x)*cos(e + f*x)/(2*f) - 8*a**3*c*d**2*cos(e + f*x)**5/(5*f) - 6*a**3*c*d**2*cos(e + f*x)**3/f + 5*a**3*d**3*x*sin(e + f*x)**6/16 + 15*a**3*d**3*x*sin(e + f*x)**4*cos(e + f*x)**2/16 + 9*a**3*d**3*x*sin(e + f*x)**4/8 + 15*a**3*d**3*x*sin(e + f*x)**2*cos(e + f*x)**4/16 + 9*a**3*d**3*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + 5*a**3*d**3*x*cos(e + f*x)**6/16 + 9*a**3*d**3*x*cos(e + f*x)**4/8 - 11*a**3*d**3*sin(e + f*x)**5*cos(e + f*x)/(16*f) - 3*a**3*d**3*sin(e + f*x)**4*cos(e + f*x)/f - 5*a**3*d**3*sin(e + f*x)**3*cos(e + f*x)**3/(6*f) - 15*a**3*d**3*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 4*a**3*d**3*sin(e + f*x)**2*cos(e + f*x)**3/f - a**3*d**3*sin(e + f*x)**2*cos(e + f*x)/f - 5*a**3*d**3*sin(e + f*x)*cos(e + f*x)**5/(16*f) - 9*a**3*d**3*sin(e + f*x)*cos(e + f*x)**3/(8*f) - 8*a**3*d**3*cos(e + f*x)**5/(5*f) - 2*a**3*d**3*cos(e + f*x)**3/(3*f), Ne(f, 0)), (x*(c + d*sin(e))**3*(a*sin(e) + a)**3, True))","A",0
445,1,702,0,4.706994," ","integrate((a+a*sin(f*x+e))**3*(c+d*sin(f*x+e))**2,x)","\begin{cases} \frac{3 a^{3} c^{2} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{3 a^{3} c^{2} x \cos^{2}{\left(e + f x \right)}}{2} + a^{3} c^{2} x - \frac{a^{3} c^{2} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{3 a^{3} c^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{2 a^{3} c^{2} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{3 a^{3} c^{2} \cos{\left(e + f x \right)}}{f} + \frac{3 a^{3} c d x \sin^{4}{\left(e + f x \right)}}{4} + \frac{3 a^{3} c d x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{2} + 3 a^{3} c d x \sin^{2}{\left(e + f x \right)} + \frac{3 a^{3} c d x \cos^{4}{\left(e + f x \right)}}{4} + 3 a^{3} c d x \cos^{2}{\left(e + f x \right)} - \frac{5 a^{3} c d \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{4 f} - \frac{6 a^{3} c d \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{3 a^{3} c d \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{4 f} - \frac{3 a^{3} c d \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{4 a^{3} c d \cos^{3}{\left(e + f x \right)}}{f} - \frac{2 a^{3} c d \cos{\left(e + f x \right)}}{f} + \frac{9 a^{3} d^{2} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{9 a^{3} d^{2} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{a^{3} d^{2} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{9 a^{3} d^{2} x \cos^{4}{\left(e + f x \right)}}{8} + \frac{a^{3} d^{2} x \cos^{2}{\left(e + f x \right)}}{2} - \frac{a^{3} d^{2} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{15 a^{3} d^{2} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{4 a^{3} d^{2} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{3 a^{3} d^{2} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{9 a^{3} d^{2} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{a^{3} d^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{8 a^{3} d^{2} \cos^{5}{\left(e + f x \right)}}{15 f} - \frac{2 a^{3} d^{2} \cos^{3}{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \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**3*c**2*x*sin(e + f*x)**2/2 + 3*a**3*c**2*x*cos(e + f*x)**2/2 + a**3*c**2*x - a**3*c**2*sin(e + f*x)**2*cos(e + f*x)/f - 3*a**3*c**2*sin(e + f*x)*cos(e + f*x)/(2*f) - 2*a**3*c**2*cos(e + f*x)**3/(3*f) - 3*a**3*c**2*cos(e + f*x)/f + 3*a**3*c*d*x*sin(e + f*x)**4/4 + 3*a**3*c*d*x*sin(e + f*x)**2*cos(e + f*x)**2/2 + 3*a**3*c*d*x*sin(e + f*x)**2 + 3*a**3*c*d*x*cos(e + f*x)**4/4 + 3*a**3*c*d*x*cos(e + f*x)**2 - 5*a**3*c*d*sin(e + f*x)**3*cos(e + f*x)/(4*f) - 6*a**3*c*d*sin(e + f*x)**2*cos(e + f*x)/f - 3*a**3*c*d*sin(e + f*x)*cos(e + f*x)**3/(4*f) - 3*a**3*c*d*sin(e + f*x)*cos(e + f*x)/f - 4*a**3*c*d*cos(e + f*x)**3/f - 2*a**3*c*d*cos(e + f*x)/f + 9*a**3*d**2*x*sin(e + f*x)**4/8 + 9*a**3*d**2*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + a**3*d**2*x*sin(e + f*x)**2/2 + 9*a**3*d**2*x*cos(e + f*x)**4/8 + a**3*d**2*x*cos(e + f*x)**2/2 - a**3*d**2*sin(e + f*x)**4*cos(e + f*x)/f - 15*a**3*d**2*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 4*a**3*d**2*sin(e + f*x)**2*cos(e + f*x)**3/(3*f) - 3*a**3*d**2*sin(e + f*x)**2*cos(e + f*x)/f - 9*a**3*d**2*sin(e + f*x)*cos(e + f*x)**3/(8*f) - a**3*d**2*sin(e + f*x)*cos(e + f*x)/(2*f) - 8*a**3*d**2*cos(e + f*x)**5/(15*f) - 2*a**3*d**2*cos(e + f*x)**3/f, Ne(f, 0)), (x*(c + d*sin(e))**2*(a*sin(e) + a)**3, True))","A",0
446,1,371,0,2.000628," ","integrate((a+a*sin(f*x+e))**3*(c+d*sin(f*x+e)),x)","\begin{cases} \frac{3 a^{3} c x \sin^{2}{\left(e + f x \right)}}{2} + \frac{3 a^{3} c x \cos^{2}{\left(e + f x \right)}}{2} + a^{3} c x - \frac{a^{3} c \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{3 a^{3} c \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{2 a^{3} c \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{3 a^{3} c \cos{\left(e + f x \right)}}{f} + \frac{3 a^{3} d x \sin^{4}{\left(e + f x \right)}}{8} + \frac{3 a^{3} d x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{3 a^{3} d x \sin^{2}{\left(e + f x \right)}}{2} + \frac{3 a^{3} d x \cos^{4}{\left(e + f x \right)}}{8} + \frac{3 a^{3} d x \cos^{2}{\left(e + f x \right)}}{2} - \frac{5 a^{3} d \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{3 a^{3} d \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{3 a^{3} d \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{3 a^{3} d \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{2 a^{3} d \cos^{3}{\left(e + f x \right)}}{f} - \frac{a^{3} d \cos{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \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**3*c*x*sin(e + f*x)**2/2 + 3*a**3*c*x*cos(e + f*x)**2/2 + a**3*c*x - a**3*c*sin(e + f*x)**2*cos(e + f*x)/f - 3*a**3*c*sin(e + f*x)*cos(e + f*x)/(2*f) - 2*a**3*c*cos(e + f*x)**3/(3*f) - 3*a**3*c*cos(e + f*x)/f + 3*a**3*d*x*sin(e + f*x)**4/8 + 3*a**3*d*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + 3*a**3*d*x*sin(e + f*x)**2/2 + 3*a**3*d*x*cos(e + f*x)**4/8 + 3*a**3*d*x*cos(e + f*x)**2/2 - 5*a**3*d*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 3*a**3*d*sin(e + f*x)**2*cos(e + f*x)/f - 3*a**3*d*sin(e + f*x)*cos(e + f*x)**3/(8*f) - 3*a**3*d*sin(e + f*x)*cos(e + f*x)/(2*f) - 2*a**3*d*cos(e + f*x)**3/f - a**3*d*cos(e + f*x)/f, Ne(f, 0)), (x*(c + d*sin(e))*(a*sin(e) + a)**3, True))","A",0
447,1,121,0,0.743611," ","integrate((a+a*sin(f*x+e))**3,x)","\begin{cases} \frac{3 a^{3} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{3 a^{3} x \cos^{2}{\left(e + f x \right)}}{2} + a^{3} x - \frac{a^{3} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{3 a^{3} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{2 a^{3} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{3 a^{3} \cos{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \left(a \sin{\left(e \right)} + a\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a**3*x*sin(e + f*x)**2/2 + 3*a**3*x*cos(e + f*x)**2/2 + a**3*x - a**3*sin(e + f*x)**2*cos(e + f*x)/f - 3*a**3*sin(e + f*x)*cos(e + f*x)/(2*f) - 2*a**3*cos(e + f*x)**3/(3*f) - 3*a**3*cos(e + f*x)/f, Ne(f, 0)), (x*(a*sin(e) + a)**3, True))","A",0
448,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**3/(c+d*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
449,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**3/(c+d*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
450,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**3/(c+d*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
451,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**3/(c+d*sin(f*x+e))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
452,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**3/(c+d*sin(f*x+e))**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
453,1,8605,0,15.637842," ","integrate((c+d*sin(f*x+e))**4/(a+a*sin(f*x+e)),x)","\begin{cases} - \frac{12 c^{4} \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{36 c^{4} \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{36 c^{4} \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{12 c^{4}}{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{24 c^{3} d 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{24 c^{3} d 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{72 c^{3} d 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{72 c^{3} d 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{72 c^{3} d 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{72 c^{3} d 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{24 c^{3} d 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{24 c^{3} d 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{48 c^{3} d \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{144 c^{3} d \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{144 c^{3} d \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{48 c^{3} d}{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{36 c^{2} d^{2} 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{36 c^{2} d^{2} 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{108 c^{2} d^{2} 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{108 c^{2} d^{2} 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{108 c^{2} d^{2} 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{108 c^{2} d^{2} 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{36 c^{2} d^{2} 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{36 c^{2} d^{2} 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{72 c^{2} d^{2} \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{72 c^{2} d^{2} \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{288 c^{2} d^{2} \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{144 c^{2} d^{2} \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{360 c^{2} d^{2} \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{72 c^{2} d^{2} \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 c^{2} d^{2}}{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{36 c d^{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{36 c d^{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{108 c d^{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{108 c d^{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{108 c d^{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{108 c d^{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{36 c d^{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{36 c d^{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{72 c d^{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{72 c d^{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{192 c d^{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 c d^{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{216 c d^{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{24 c d^{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{96 c d^{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{9 d^{4} 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{9 d^{4} 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{27 d^{4} 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{27 d^{4} 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{27 d^{4} 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{27 d^{4} 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{9 d^{4} 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{9 d^{4} 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{18 d^{4} \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{18 d^{4} \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{48 d^{4} \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{48 d^{4} \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{78 d^{4} \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{14 d^{4} \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{32 d^{4}}{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(c + d \sin{\left(e \right)}\right)^{4}}{a \sin{\left(e \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-12*c**4*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) - 36*c**4*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) - 36*c**4*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) - 12*c**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) + 24*c**3*d*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) + 24*c**3*d*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) + 72*c**3*d*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) + 72*c**3*d*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) + 72*c**3*d*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) + 72*c**3*d*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) + 24*c**3*d*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) + 24*c**3*d*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) + 48*c**3*d*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) + 144*c**3*d*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) + 144*c**3*d*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) + 48*c**3*d/(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) - 36*c**2*d**2*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) - 36*c**2*d**2*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) - 108*c**2*d**2*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) - 108*c**2*d**2*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) - 108*c**2*d**2*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) - 108*c**2*d**2*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) - 36*c**2*d**2*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) - 36*c**2*d**2*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) - 72*c**2*d**2*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) - 72*c**2*d**2*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) - 288*c**2*d**2*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) - 144*c**2*d**2*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) - 360*c**2*d**2*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) - 72*c**2*d**2*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*c**2*d**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) + 36*c*d**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) + 36*c*d**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) + 108*c*d**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) + 108*c*d**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) + 108*c*d**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) + 108*c*d**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) + 36*c*d**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) + 36*c*d**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) + 72*c*d**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) + 72*c*d**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) + 192*c*d**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*c*d**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) + 216*c*d**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) + 24*c*d**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) + 96*c*d**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) - 9*d**4*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) - 9*d**4*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) - 27*d**4*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) - 27*d**4*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) - 27*d**4*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) - 27*d**4*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) - 9*d**4*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) - 9*d**4*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) - 18*d**4*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) - 18*d**4*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) - 48*d**4*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) - 48*d**4*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) - 78*d**4*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) - 14*d**4*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) - 32*d**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), Ne(f, 0)), (x*(c + d*sin(e))**4/(a*sin(e) + a), True))","A",0
454,1,3602,0,8.349721," ","integrate((c+d*sin(f*x+e))**3/(a+a*sin(f*x+e)),x)","\begin{cases} - \frac{4 c^{3} \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 c^{3} \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 c^{3}}{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 c^{2} 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{6 c^{2} 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{12 c^{2} 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{12 c^{2} 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{6 c^{2} 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{6 c^{2} 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{12 c^{2} 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{24 c^{2} 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{12 c^{2} 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{6 c 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{6 c 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{12 c 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{12 c 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{6 c 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{6 c 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{12 c 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{12 c 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{36 c 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{12 c 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{24 c 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{3 d^{3} 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 d^{3} 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 d^{3} 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 d^{3} 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 d^{3} 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 d^{3} 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 d^{3} \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 d^{3} \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 d^{3} \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 d^{3} \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 d^{3}}{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(c + d \sin{\left(e \right)}\right)^{3}}{a \sin{\left(e \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-4*c**3*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*c**3*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*c**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*c**2*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) + 6*c**2*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) + 12*c**2*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) + 12*c**2*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) + 6*c**2*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) + 6*c**2*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) + 12*c**2*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) + 24*c**2*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) + 12*c**2*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) - 6*c*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) - 6*c*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) - 12*c*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) - 12*c*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) - 6*c*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) - 6*c*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) - 12*c*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) - 12*c*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) - 36*c*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) - 12*c*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) - 24*c*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) + 3*d**3*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*d**3*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*d**3*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*d**3*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*d**3*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*d**3*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*d**3*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*d**3*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*d**3*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*d**3*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*d**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), Ne(f, 0)), (x*(c + d*sin(e))**3/(a*sin(e) + a), True))","A",0
455,1,940,0,3.666585," ","integrate((c+d*sin(f*x+e))**2/(a+a*sin(f*x+e)),x)","\begin{cases} - \frac{2 c^{2} \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 c^{2}}{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 c 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{2 c 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{2 c 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{2 c 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{4 c 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{4 c 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{d^{2} 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{d^{2} 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{d^{2} 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{d^{2} 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 d^{2} \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 d^{2} \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 d^{2}}{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(c + d \sin{\left(e \right)}\right)^{2}}{a \sin{\left(e \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*c**2*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*c**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*c*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) + 2*c*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) + 2*c*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) + 2*c*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) + 4*c*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) + 4*c*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) - d**2*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) - d**2*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) - d**2*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) - d**2*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*d**2*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*d**2*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*d**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), Ne(f, 0)), (x*(c + d*sin(e))**2/(a*sin(e) + a), True))","A",0
456,1,109,0,1.824595," ","integrate((c+d*sin(f*x+e))/(a+a*sin(f*x+e)),x)","\begin{cases} - \frac{2 c}{a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f} + \frac{d 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{d f x}{a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f} + \frac{2 d}{a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f} & \text{for}\: f \neq 0 \\\frac{x \left(c + d \sin{\left(e \right)}\right)}{a \sin{\left(e \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*c/(a*f*tan(e/2 + f*x/2) + a*f) + d*f*x*tan(e/2 + f*x/2)/(a*f*tan(e/2 + f*x/2) + a*f) + d*f*x/(a*f*tan(e/2 + f*x/2) + a*f) + 2*d/(a*f*tan(e/2 + f*x/2) + a*f), Ne(f, 0)), (x*(c + d*sin(e))/(a*sin(e) + a), True))","A",0
457,1,27,0,0.930665," ","integrate(1/(a+a*sin(f*x+e)),x)","\begin{cases} - \frac{2}{a f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a f} & \text{for}\: f \neq 0 \\\frac{x}{a \sin{\left(e \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2/(a*f*tan(e/2 + f*x/2) + a*f), Ne(f, 0)), (x/(a*sin(e) + a), True))","A",0
458,-1,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))/(c+d*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
459,-1,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))/(c+d*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
460,-1,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))/(c+d*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
461,-1,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**5/(a+a*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
462,1,8950,0,28.137992," ","integrate((c+d*sin(f*x+e))**4/(a+a*sin(f*x+e))**2,x)","\begin{cases} - \frac{12 c^{4} \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{12 c^{4} \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{32 c^{4} \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{24 c^{4} \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{28 c^{4} \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{12 c^{4} \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{8 c^{4}}{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 c^{3} d \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{16 c^{3} d \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{96 c^{3} d \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{32 c^{3} d \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{48 c^{3} d \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{16 c^{3} d}{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{36 c^{2} d^{2} 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{108 c^{2} d^{2} 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{180 c^{2} d^{2} 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{252 c^{2} d^{2} 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{252 c^{2} d^{2} 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{180 c^{2} d^{2} 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{108 c^{2} d^{2} 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{36 c^{2} d^{2} 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{72 c^{2} d^{2} \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{216 c^{2} d^{2} \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{240 c^{2} d^{2} \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 c^{2} d^{2} \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{264 c^{2} d^{2} \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{216 c^{2} d^{2} \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{96 c^{2} d^{2}}{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 c d^{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{144 c d^{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{240 c d^{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{336 c d^{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{336 c d^{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{240 c d^{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{144 c d^{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{48 c d^{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{96 c d^{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{288 c d^{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{448 c d^{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{672 c d^{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{512 c d^{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{384 c d^{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{160 c d^{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{21 d^{4} 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{63 d^{4} 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{105 d^{4} 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{147 d^{4} 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{147 d^{4} 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{105 d^{4} 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{63 d^{4} 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{21 d^{4} 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{42 d^{4} \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{126 d^{4} \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{196 d^{4} \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{252 d^{4} \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{194 d^{4} \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{150 d^{4} \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{64 d^{4}}{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(c + d \sin{\left(e \right)}\right)^{4}}{\left(a \sin{\left(e \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-12*c**4*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) - 12*c**4*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) - 32*c**4*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) - 24*c**4*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) - 28*c**4*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) - 12*c**4*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) - 8*c**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) - 48*c**3*d*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) - 16*c**3*d*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) - 96*c**3*d*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) - 32*c**3*d*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) - 48*c**3*d*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) - 16*c**3*d/(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) + 36*c**2*d**2*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) + 108*c**2*d**2*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) + 180*c**2*d**2*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) + 252*c**2*d**2*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) + 252*c**2*d**2*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) + 180*c**2*d**2*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) + 108*c**2*d**2*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) + 36*c**2*d**2*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) + 72*c**2*d**2*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) + 216*c**2*d**2*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) + 240*c**2*d**2*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*c**2*d**2*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) + 264*c**2*d**2*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) + 216*c**2*d**2*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) + 96*c**2*d**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) - 48*c*d**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) - 144*c*d**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) - 240*c*d**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) - 336*c*d**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) - 336*c*d**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) - 240*c*d**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) - 144*c*d**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) - 48*c*d**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) - 96*c*d**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) - 288*c*d**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) - 448*c*d**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) - 672*c*d**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) - 512*c*d**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) - 384*c*d**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) - 160*c*d**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) + 21*d**4*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) + 63*d**4*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) + 105*d**4*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) + 147*d**4*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) + 147*d**4*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) + 105*d**4*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) + 63*d**4*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) + 21*d**4*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) + 42*d**4*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) + 126*d**4*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) + 196*d**4*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) + 252*d**4*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) + 194*d**4*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) + 150*d**4*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) + 64*d**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), Ne(f, 0)), (x*(c + d*sin(e))**4/(a*sin(e) + a)**2, True))","A",0
463,1,3585,0,14.916514," ","integrate((c+d*sin(f*x+e))**3/(a+a*sin(f*x+e))**2,x)","\begin{cases} - \frac{6 c^{3} \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 c^{3} \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 c^{3} \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 c^{3} \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 c^{3}}{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 c^{2} 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{6 c^{2} 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{18 c^{2} 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{6 c^{2} 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{9 c 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{27 c 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{36 c 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{36 c 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{27 c 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{9 c 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{18 c 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{54 c 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{42 c 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{54 c 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{24 c 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 d^{3} 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 d^{3} 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 d^{3} 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 d^{3} 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 d^{3} 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 d^{3} 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 d^{3} \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 d^{3} \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 d^{3} \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 d^{3} \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 d^{3}}{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(c + d \sin{\left(e \right)}\right)^{3}}{\left(a \sin{\left(e \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-6*c**3*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*c**3*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*c**3*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*c**3*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*c**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) - 18*c**2*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) - 6*c**2*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) - 18*c**2*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) - 6*c**2*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) + 9*c*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) + 27*c*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) + 36*c*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) + 36*c*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) + 27*c*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) + 9*c*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) + 18*c*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) + 54*c*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) + 42*c*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) + 54*c*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) + 24*c*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*d**3*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*d**3*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*d**3*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*d**3*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*d**3*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*d**3*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*d**3*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*d**3*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*d**3*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*d**3*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*d**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), Ne(f, 0)), (x*(c + d*sin(e))**3/(a*sin(e) + a)**2, True))","A",0
464,1,915,0,8.059733," ","integrate((c+d*sin(f*x+e))**2/(a+a*sin(f*x+e))**2,x)","\begin{cases} - \frac{6 c^{2} \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 c^{2} \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 c^{2}}{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{12 c 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{4 c 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{3 d^{2} 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 d^{2} 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 d^{2} 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 d^{2} 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 d^{2} \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 d^{2} \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 d^{2}}{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(c + d \sin{\left(e \right)}\right)^{2}}{\left(a \sin{\left(e \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-6*c**2*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*c**2*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*c**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) - 12*c*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) - 4*c*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) + 3*d**2*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*d**2*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*d**2*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*d**2*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*d**2*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*d**2*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*d**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), Ne(f, 0)), (x*(c + d*sin(e))**2/(a*sin(e) + a)**2, True))","A",0
465,1,372,0,3.649242," ","integrate((c+d*sin(f*x+e))/(a+a*sin(f*x+e))**2,x)","\begin{cases} - \frac{6 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 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 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 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 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(c + d \sin{\left(e \right)}\right)}{\left(a \sin{\left(e \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-6*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*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*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*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*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*(c + d*sin(e))/(a*sin(e) + a)**2, True))","A",0
466,1,221,0,1.795381," ","integrate(1/(a+a*sin(f*x+e))**2,x)","\begin{cases} - \frac{6 \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 \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}{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 \sin{\left(e \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-6*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*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/(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*sin(e) + a)**2, True))","A",0
467,-1,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))**2/(c+d*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
468,-1,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))**2/(c+d*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
469,-1,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))**2/(c+d*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
470,-1,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**6/(a+a*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
471,-1,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**5/(a+a*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
472,1,7373,0,48.331366," ","integrate((c+d*sin(f*x+e))**4/(a+a*sin(f*x+e))**3,x)","\begin{cases} - \frac{30 c^{4} \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 c^{4} \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 c^{4} \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 c^{4} \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 c^{4} \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 c^{4} \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 c^{4}}{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 c^{3} 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{120 c^{3} 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{240 c^{3} 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{144 c^{3} 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{120 c^{3} 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{24 c^{3} 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{240 c^{2} 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{120 c^{2} 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{264 c^{2} 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{120 c^{2} 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{24 c^{2} 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{60 c 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{300 c 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{660 c 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{900 c 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{900 c 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{660 c 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{300 c 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{60 c 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{120 c 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{600 c 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{1280 c 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{1360 c 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{1336 c 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{760 c 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{176 c 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{45 d^{4} 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 d^{4} 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 d^{4} 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 d^{4} 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 d^{4} 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 d^{4} 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 d^{4} 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 d^{4} 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 d^{4} \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 d^{4} \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 d^{4} \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 d^{4} \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 d^{4} \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 d^{4} \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 d^{4}}{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(c + d \sin{\left(e \right)}\right)^{4}}{\left(a \sin{\left(e \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-30*c**4*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*c**4*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*c**4*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*c**4*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*c**4*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*c**4*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*c**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) - 120*c**3*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) - 120*c**3*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) - 240*c**3*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) - 144*c**3*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) - 120*c**3*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) - 24*c**3*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) - 240*c**2*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) - 120*c**2*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) - 264*c**2*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) - 120*c**2*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) - 24*c**2*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) + 60*c*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) + 300*c*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) + 660*c*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) + 900*c*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) + 900*c*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) + 660*c*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) + 300*c*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) + 60*c*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) + 120*c*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) + 600*c*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) + 1280*c*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) + 1360*c*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) + 1336*c*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) + 760*c*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) + 176*c*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) - 45*d**4*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*d**4*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*d**4*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*d**4*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*d**4*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*d**4*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*d**4*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*d**4*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*d**4*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*d**4*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*d**4*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*d**4*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*d**4*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*d**4*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*d**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), Ne(f, 0)), (x*(c + d*sin(e))**4/(a*sin(e) + a)**3, True))","A",0
473,1,2640,0,25.969309," ","integrate((c+d*sin(f*x+e))**3/(a+a*sin(f*x+e))**3,x)","\begin{cases} - \frac{30 c^{3} \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 c^{3} \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 c^{3} \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 c^{3} \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 c^{3}}{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{90 c^{2} 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{90 c^{2} 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{90 c^{2} 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{18 c^{2} 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{120 c 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{60 c 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{12 c 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{15 d^{3} 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 d^{3} 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 d^{3} 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 d^{3} 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 d^{3} 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 d^{3} 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 d^{3} \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 d^{3} \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 d^{3} \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 d^{3} \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 d^{3}}{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(c + d \sin{\left(e \right)}\right)^{3}}{\left(a \sin{\left(e \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-30*c**3*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*c**3*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*c**3*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*c**3*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*c**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) - 90*c**2*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) - 90*c**2*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) - 90*c**2*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) - 18*c**2*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) - 120*c*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) - 60*c*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) - 12*c*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) + 15*d**3*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*d**3*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*d**3*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*d**3*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*d**3*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*d**3*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*d**3*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*d**3*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*d**3*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*d**3*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*d**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), Ne(f, 0)), (x*(c + d*sin(e))**3/(a*sin(e) + a)**3, True))","A",0
474,1,1365,0,15.740194," ","integrate((c+d*sin(f*x+e))**2/(a+a*sin(f*x+e))**3,x)","\begin{cases} - \frac{30 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 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 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 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 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 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 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 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 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 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 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 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(c + d \sin{\left(e \right)}\right)^{2}}{\left(a \sin{\left(e \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-30*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*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*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*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*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*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*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*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*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*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*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*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*(c + d*sin(e))**2/(a*sin(e) + a)**3, True))","A",0
475,1,1015,0,9.061023," ","integrate((c+d*sin(f*x+e))/(a+a*sin(f*x+e))**3,x)","\begin{cases} - \frac{30 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 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 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 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 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 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 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 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 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(c + d \sin{\left(e \right)}\right)}{\left(a \sin{\left(e \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-30*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*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*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*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*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*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*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*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*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*(c + d*sin(e))/(a*sin(e) + a)**3, True))","A",0
476,1,558,0,3.536834," ","integrate(1/(a+a*sin(f*x+e))**3,x)","\begin{cases} - \frac{30 \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 \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 \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 \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}{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 \sin{\left(e \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-30*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*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*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*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/(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*sin(e) + a)**3, True))","A",0
477,-1,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))**3/(c+d*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
478,-1,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))**3/(c+d*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
479,-1,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))**3/(c+d*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
480,1,889,0,7.701834," ","integrate((A+B*sin(x))/(1+sin(x))**4,x)","- \frac{210 A \tan^{6}{\left(\frac{x}{2} \right)}}{105 \tan^{7}{\left(\frac{x}{2} \right)} + 735 \tan^{6}{\left(\frac{x}{2} \right)} + 2205 \tan^{5}{\left(\frac{x}{2} \right)} + 3675 \tan^{4}{\left(\frac{x}{2} \right)} + 3675 \tan^{3}{\left(\frac{x}{2} \right)} + 2205 \tan^{2}{\left(\frac{x}{2} \right)} + 735 \tan{\left(\frac{x}{2} \right)} + 105} - \frac{630 A \tan^{5}{\left(\frac{x}{2} \right)}}{105 \tan^{7}{\left(\frac{x}{2} \right)} + 735 \tan^{6}{\left(\frac{x}{2} \right)} + 2205 \tan^{5}{\left(\frac{x}{2} \right)} + 3675 \tan^{4}{\left(\frac{x}{2} \right)} + 3675 \tan^{3}{\left(\frac{x}{2} \right)} + 2205 \tan^{2}{\left(\frac{x}{2} \right)} + 735 \tan{\left(\frac{x}{2} \right)} + 105} - \frac{1260 A \tan^{4}{\left(\frac{x}{2} \right)}}{105 \tan^{7}{\left(\frac{x}{2} \right)} + 735 \tan^{6}{\left(\frac{x}{2} \right)} + 2205 \tan^{5}{\left(\frac{x}{2} \right)} + 3675 \tan^{4}{\left(\frac{x}{2} \right)} + 3675 \tan^{3}{\left(\frac{x}{2} \right)} + 2205 \tan^{2}{\left(\frac{x}{2} \right)} + 735 \tan{\left(\frac{x}{2} \right)} + 105} - \frac{1260 A \tan^{3}{\left(\frac{x}{2} \right)}}{105 \tan^{7}{\left(\frac{x}{2} \right)} + 735 \tan^{6}{\left(\frac{x}{2} \right)} + 2205 \tan^{5}{\left(\frac{x}{2} \right)} + 3675 \tan^{4}{\left(\frac{x}{2} \right)} + 3675 \tan^{3}{\left(\frac{x}{2} \right)} + 2205 \tan^{2}{\left(\frac{x}{2} \right)} + 735 \tan{\left(\frac{x}{2} \right)} + 105} - \frac{882 A \tan^{2}{\left(\frac{x}{2} \right)}}{105 \tan^{7}{\left(\frac{x}{2} \right)} + 735 \tan^{6}{\left(\frac{x}{2} \right)} + 2205 \tan^{5}{\left(\frac{x}{2} \right)} + 3675 \tan^{4}{\left(\frac{x}{2} \right)} + 3675 \tan^{3}{\left(\frac{x}{2} \right)} + 2205 \tan^{2}{\left(\frac{x}{2} \right)} + 735 \tan{\left(\frac{x}{2} \right)} + 105} - \frac{294 A \tan{\left(\frac{x}{2} \right)}}{105 \tan^{7}{\left(\frac{x}{2} \right)} + 735 \tan^{6}{\left(\frac{x}{2} \right)} + 2205 \tan^{5}{\left(\frac{x}{2} \right)} + 3675 \tan^{4}{\left(\frac{x}{2} \right)} + 3675 \tan^{3}{\left(\frac{x}{2} \right)} + 2205 \tan^{2}{\left(\frac{x}{2} \right)} + 735 \tan{\left(\frac{x}{2} \right)} + 105} - \frac{72 A}{105 \tan^{7}{\left(\frac{x}{2} \right)} + 735 \tan^{6}{\left(\frac{x}{2} \right)} + 2205 \tan^{5}{\left(\frac{x}{2} \right)} + 3675 \tan^{4}{\left(\frac{x}{2} \right)} + 3675 \tan^{3}{\left(\frac{x}{2} \right)} + 2205 \tan^{2}{\left(\frac{x}{2} \right)} + 735 \tan{\left(\frac{x}{2} \right)} + 105} - \frac{210 B \tan^{5}{\left(\frac{x}{2} \right)}}{105 \tan^{7}{\left(\frac{x}{2} \right)} + 735 \tan^{6}{\left(\frac{x}{2} \right)} + 2205 \tan^{5}{\left(\frac{x}{2} \right)} + 3675 \tan^{4}{\left(\frac{x}{2} \right)} + 3675 \tan^{3}{\left(\frac{x}{2} \right)} + 2205 \tan^{2}{\left(\frac{x}{2} \right)} + 735 \tan{\left(\frac{x}{2} \right)} + 105} - \frac{350 B \tan^{4}{\left(\frac{x}{2} \right)}}{105 \tan^{7}{\left(\frac{x}{2} \right)} + 735 \tan^{6}{\left(\frac{x}{2} \right)} + 2205 \tan^{5}{\left(\frac{x}{2} \right)} + 3675 \tan^{4}{\left(\frac{x}{2} \right)} + 3675 \tan^{3}{\left(\frac{x}{2} \right)} + 2205 \tan^{2}{\left(\frac{x}{2} \right)} + 735 \tan{\left(\frac{x}{2} \right)} + 105} - \frac{560 B \tan^{3}{\left(\frac{x}{2} \right)}}{105 \tan^{7}{\left(\frac{x}{2} \right)} + 735 \tan^{6}{\left(\frac{x}{2} \right)} + 2205 \tan^{5}{\left(\frac{x}{2} \right)} + 3675 \tan^{4}{\left(\frac{x}{2} \right)} + 3675 \tan^{3}{\left(\frac{x}{2} \right)} + 2205 \tan^{2}{\left(\frac{x}{2} \right)} + 735 \tan{\left(\frac{x}{2} \right)} + 105} - \frac{336 B \tan^{2}{\left(\frac{x}{2} \right)}}{105 \tan^{7}{\left(\frac{x}{2} \right)} + 735 \tan^{6}{\left(\frac{x}{2} \right)} + 2205 \tan^{5}{\left(\frac{x}{2} \right)} + 3675 \tan^{4}{\left(\frac{x}{2} \right)} + 3675 \tan^{3}{\left(\frac{x}{2} \right)} + 2205 \tan^{2}{\left(\frac{x}{2} \right)} + 735 \tan{\left(\frac{x}{2} \right)} + 105} - \frac{182 B \tan{\left(\frac{x}{2} \right)}}{105 \tan^{7}{\left(\frac{x}{2} \right)} + 735 \tan^{6}{\left(\frac{x}{2} \right)} + 2205 \tan^{5}{\left(\frac{x}{2} \right)} + 3675 \tan^{4}{\left(\frac{x}{2} \right)} + 3675 \tan^{3}{\left(\frac{x}{2} \right)} + 2205 \tan^{2}{\left(\frac{x}{2} \right)} + 735 \tan{\left(\frac{x}{2} \right)} + 105} - \frac{26 B}{105 \tan^{7}{\left(\frac{x}{2} \right)} + 735 \tan^{6}{\left(\frac{x}{2} \right)} + 2205 \tan^{5}{\left(\frac{x}{2} \right)} + 3675 \tan^{4}{\left(\frac{x}{2} \right)} + 3675 \tan^{3}{\left(\frac{x}{2} \right)} + 2205 \tan^{2}{\left(\frac{x}{2} \right)} + 735 \tan{\left(\frac{x}{2} \right)} + 105}"," ",0,"-210*A*tan(x/2)**6/(105*tan(x/2)**7 + 735*tan(x/2)**6 + 2205*tan(x/2)**5 + 3675*tan(x/2)**4 + 3675*tan(x/2)**3 + 2205*tan(x/2)**2 + 735*tan(x/2) + 105) - 630*A*tan(x/2)**5/(105*tan(x/2)**7 + 735*tan(x/2)**6 + 2205*tan(x/2)**5 + 3675*tan(x/2)**4 + 3675*tan(x/2)**3 + 2205*tan(x/2)**2 + 735*tan(x/2) + 105) - 1260*A*tan(x/2)**4/(105*tan(x/2)**7 + 735*tan(x/2)**6 + 2205*tan(x/2)**5 + 3675*tan(x/2)**4 + 3675*tan(x/2)**3 + 2205*tan(x/2)**2 + 735*tan(x/2) + 105) - 1260*A*tan(x/2)**3/(105*tan(x/2)**7 + 735*tan(x/2)**6 + 2205*tan(x/2)**5 + 3675*tan(x/2)**4 + 3675*tan(x/2)**3 + 2205*tan(x/2)**2 + 735*tan(x/2) + 105) - 882*A*tan(x/2)**2/(105*tan(x/2)**7 + 735*tan(x/2)**6 + 2205*tan(x/2)**5 + 3675*tan(x/2)**4 + 3675*tan(x/2)**3 + 2205*tan(x/2)**2 + 735*tan(x/2) + 105) - 294*A*tan(x/2)/(105*tan(x/2)**7 + 735*tan(x/2)**6 + 2205*tan(x/2)**5 + 3675*tan(x/2)**4 + 3675*tan(x/2)**3 + 2205*tan(x/2)**2 + 735*tan(x/2) + 105) - 72*A/(105*tan(x/2)**7 + 735*tan(x/2)**6 + 2205*tan(x/2)**5 + 3675*tan(x/2)**4 + 3675*tan(x/2)**3 + 2205*tan(x/2)**2 + 735*tan(x/2) + 105) - 210*B*tan(x/2)**5/(105*tan(x/2)**7 + 735*tan(x/2)**6 + 2205*tan(x/2)**5 + 3675*tan(x/2)**4 + 3675*tan(x/2)**3 + 2205*tan(x/2)**2 + 735*tan(x/2) + 105) - 350*B*tan(x/2)**4/(105*tan(x/2)**7 + 735*tan(x/2)**6 + 2205*tan(x/2)**5 + 3675*tan(x/2)**4 + 3675*tan(x/2)**3 + 2205*tan(x/2)**2 + 735*tan(x/2) + 105) - 560*B*tan(x/2)**3/(105*tan(x/2)**7 + 735*tan(x/2)**6 + 2205*tan(x/2)**5 + 3675*tan(x/2)**4 + 3675*tan(x/2)**3 + 2205*tan(x/2)**2 + 735*tan(x/2) + 105) - 336*B*tan(x/2)**2/(105*tan(x/2)**7 + 735*tan(x/2)**6 + 2205*tan(x/2)**5 + 3675*tan(x/2)**4 + 3675*tan(x/2)**3 + 2205*tan(x/2)**2 + 735*tan(x/2) + 105) - 182*B*tan(x/2)/(105*tan(x/2)**7 + 735*tan(x/2)**6 + 2205*tan(x/2)**5 + 3675*tan(x/2)**4 + 3675*tan(x/2)**3 + 2205*tan(x/2)**2 + 735*tan(x/2) + 105) - 26*B/(105*tan(x/2)**7 + 735*tan(x/2)**6 + 2205*tan(x/2)**5 + 3675*tan(x/2)**4 + 3675*tan(x/2)**3 + 2205*tan(x/2)**2 + 735*tan(x/2) + 105)","B",0
481,1,887,0,7.869095," ","integrate((A+B*sin(x))/(1-sin(x))**4,x)","- \frac{210 A \tan^{6}{\left(\frac{x}{2} \right)}}{105 \tan^{7}{\left(\frac{x}{2} \right)} - 735 \tan^{6}{\left(\frac{x}{2} \right)} + 2205 \tan^{5}{\left(\frac{x}{2} \right)} - 3675 \tan^{4}{\left(\frac{x}{2} \right)} + 3675 \tan^{3}{\left(\frac{x}{2} \right)} - 2205 \tan^{2}{\left(\frac{x}{2} \right)} + 735 \tan{\left(\frac{x}{2} \right)} - 105} + \frac{630 A \tan^{5}{\left(\frac{x}{2} \right)}}{105 \tan^{7}{\left(\frac{x}{2} \right)} - 735 \tan^{6}{\left(\frac{x}{2} \right)} + 2205 \tan^{5}{\left(\frac{x}{2} \right)} - 3675 \tan^{4}{\left(\frac{x}{2} \right)} + 3675 \tan^{3}{\left(\frac{x}{2} \right)} - 2205 \tan^{2}{\left(\frac{x}{2} \right)} + 735 \tan{\left(\frac{x}{2} \right)} - 105} - \frac{1260 A \tan^{4}{\left(\frac{x}{2} \right)}}{105 \tan^{7}{\left(\frac{x}{2} \right)} - 735 \tan^{6}{\left(\frac{x}{2} \right)} + 2205 \tan^{5}{\left(\frac{x}{2} \right)} - 3675 \tan^{4}{\left(\frac{x}{2} \right)} + 3675 \tan^{3}{\left(\frac{x}{2} \right)} - 2205 \tan^{2}{\left(\frac{x}{2} \right)} + 735 \tan{\left(\frac{x}{2} \right)} - 105} + \frac{1260 A \tan^{3}{\left(\frac{x}{2} \right)}}{105 \tan^{7}{\left(\frac{x}{2} \right)} - 735 \tan^{6}{\left(\frac{x}{2} \right)} + 2205 \tan^{5}{\left(\frac{x}{2} \right)} - 3675 \tan^{4}{\left(\frac{x}{2} \right)} + 3675 \tan^{3}{\left(\frac{x}{2} \right)} - 2205 \tan^{2}{\left(\frac{x}{2} \right)} + 735 \tan{\left(\frac{x}{2} \right)} - 105} - \frac{882 A \tan^{2}{\left(\frac{x}{2} \right)}}{105 \tan^{7}{\left(\frac{x}{2} \right)} - 735 \tan^{6}{\left(\frac{x}{2} \right)} + 2205 \tan^{5}{\left(\frac{x}{2} \right)} - 3675 \tan^{4}{\left(\frac{x}{2} \right)} + 3675 \tan^{3}{\left(\frac{x}{2} \right)} - 2205 \tan^{2}{\left(\frac{x}{2} \right)} + 735 \tan{\left(\frac{x}{2} \right)} - 105} + \frac{294 A \tan{\left(\frac{x}{2} \right)}}{105 \tan^{7}{\left(\frac{x}{2} \right)} - 735 \tan^{6}{\left(\frac{x}{2} \right)} + 2205 \tan^{5}{\left(\frac{x}{2} \right)} - 3675 \tan^{4}{\left(\frac{x}{2} \right)} + 3675 \tan^{3}{\left(\frac{x}{2} \right)} - 2205 \tan^{2}{\left(\frac{x}{2} \right)} + 735 \tan{\left(\frac{x}{2} \right)} - 105} - \frac{72 A}{105 \tan^{7}{\left(\frac{x}{2} \right)} - 735 \tan^{6}{\left(\frac{x}{2} \right)} + 2205 \tan^{5}{\left(\frac{x}{2} \right)} - 3675 \tan^{4}{\left(\frac{x}{2} \right)} + 3675 \tan^{3}{\left(\frac{x}{2} \right)} - 2205 \tan^{2}{\left(\frac{x}{2} \right)} + 735 \tan{\left(\frac{x}{2} \right)} - 105} - \frac{210 B \tan^{5}{\left(\frac{x}{2} \right)}}{105 \tan^{7}{\left(\frac{x}{2} \right)} - 735 \tan^{6}{\left(\frac{x}{2} \right)} + 2205 \tan^{5}{\left(\frac{x}{2} \right)} - 3675 \tan^{4}{\left(\frac{x}{2} \right)} + 3675 \tan^{3}{\left(\frac{x}{2} \right)} - 2205 \tan^{2}{\left(\frac{x}{2} \right)} + 735 \tan{\left(\frac{x}{2} \right)} - 105} + \frac{350 B \tan^{4}{\left(\frac{x}{2} \right)}}{105 \tan^{7}{\left(\frac{x}{2} \right)} - 735 \tan^{6}{\left(\frac{x}{2} \right)} + 2205 \tan^{5}{\left(\frac{x}{2} \right)} - 3675 \tan^{4}{\left(\frac{x}{2} \right)} + 3675 \tan^{3}{\left(\frac{x}{2} \right)} - 2205 \tan^{2}{\left(\frac{x}{2} \right)} + 735 \tan{\left(\frac{x}{2} \right)} - 105} - \frac{560 B \tan^{3}{\left(\frac{x}{2} \right)}}{105 \tan^{7}{\left(\frac{x}{2} \right)} - 735 \tan^{6}{\left(\frac{x}{2} \right)} + 2205 \tan^{5}{\left(\frac{x}{2} \right)} - 3675 \tan^{4}{\left(\frac{x}{2} \right)} + 3675 \tan^{3}{\left(\frac{x}{2} \right)} - 2205 \tan^{2}{\left(\frac{x}{2} \right)} + 735 \tan{\left(\frac{x}{2} \right)} - 105} + \frac{336 B \tan^{2}{\left(\frac{x}{2} \right)}}{105 \tan^{7}{\left(\frac{x}{2} \right)} - 735 \tan^{6}{\left(\frac{x}{2} \right)} + 2205 \tan^{5}{\left(\frac{x}{2} \right)} - 3675 \tan^{4}{\left(\frac{x}{2} \right)} + 3675 \tan^{3}{\left(\frac{x}{2} \right)} - 2205 \tan^{2}{\left(\frac{x}{2} \right)} + 735 \tan{\left(\frac{x}{2} \right)} - 105} - \frac{182 B \tan{\left(\frac{x}{2} \right)}}{105 \tan^{7}{\left(\frac{x}{2} \right)} - 735 \tan^{6}{\left(\frac{x}{2} \right)} + 2205 \tan^{5}{\left(\frac{x}{2} \right)} - 3675 \tan^{4}{\left(\frac{x}{2} \right)} + 3675 \tan^{3}{\left(\frac{x}{2} \right)} - 2205 \tan^{2}{\left(\frac{x}{2} \right)} + 735 \tan{\left(\frac{x}{2} \right)} - 105} + \frac{26 B}{105 \tan^{7}{\left(\frac{x}{2} \right)} - 735 \tan^{6}{\left(\frac{x}{2} \right)} + 2205 \tan^{5}{\left(\frac{x}{2} \right)} - 3675 \tan^{4}{\left(\frac{x}{2} \right)} + 3675 \tan^{3}{\left(\frac{x}{2} \right)} - 2205 \tan^{2}{\left(\frac{x}{2} \right)} + 735 \tan{\left(\frac{x}{2} \right)} - 105}"," ",0,"-210*A*tan(x/2)**6/(105*tan(x/2)**7 - 735*tan(x/2)**6 + 2205*tan(x/2)**5 - 3675*tan(x/2)**4 + 3675*tan(x/2)**3 - 2205*tan(x/2)**2 + 735*tan(x/2) - 105) + 630*A*tan(x/2)**5/(105*tan(x/2)**7 - 735*tan(x/2)**6 + 2205*tan(x/2)**5 - 3675*tan(x/2)**4 + 3675*tan(x/2)**3 - 2205*tan(x/2)**2 + 735*tan(x/2) - 105) - 1260*A*tan(x/2)**4/(105*tan(x/2)**7 - 735*tan(x/2)**6 + 2205*tan(x/2)**5 - 3675*tan(x/2)**4 + 3675*tan(x/2)**3 - 2205*tan(x/2)**2 + 735*tan(x/2) - 105) + 1260*A*tan(x/2)**3/(105*tan(x/2)**7 - 735*tan(x/2)**6 + 2205*tan(x/2)**5 - 3675*tan(x/2)**4 + 3675*tan(x/2)**3 - 2205*tan(x/2)**2 + 735*tan(x/2) - 105) - 882*A*tan(x/2)**2/(105*tan(x/2)**7 - 735*tan(x/2)**6 + 2205*tan(x/2)**5 - 3675*tan(x/2)**4 + 3675*tan(x/2)**3 - 2205*tan(x/2)**2 + 735*tan(x/2) - 105) + 294*A*tan(x/2)/(105*tan(x/2)**7 - 735*tan(x/2)**6 + 2205*tan(x/2)**5 - 3675*tan(x/2)**4 + 3675*tan(x/2)**3 - 2205*tan(x/2)**2 + 735*tan(x/2) - 105) - 72*A/(105*tan(x/2)**7 - 735*tan(x/2)**6 + 2205*tan(x/2)**5 - 3675*tan(x/2)**4 + 3675*tan(x/2)**3 - 2205*tan(x/2)**2 + 735*tan(x/2) - 105) - 210*B*tan(x/2)**5/(105*tan(x/2)**7 - 735*tan(x/2)**6 + 2205*tan(x/2)**5 - 3675*tan(x/2)**4 + 3675*tan(x/2)**3 - 2205*tan(x/2)**2 + 735*tan(x/2) - 105) + 350*B*tan(x/2)**4/(105*tan(x/2)**7 - 735*tan(x/2)**6 + 2205*tan(x/2)**5 - 3675*tan(x/2)**4 + 3675*tan(x/2)**3 - 2205*tan(x/2)**2 + 735*tan(x/2) - 105) - 560*B*tan(x/2)**3/(105*tan(x/2)**7 - 735*tan(x/2)**6 + 2205*tan(x/2)**5 - 3675*tan(x/2)**4 + 3675*tan(x/2)**3 - 2205*tan(x/2)**2 + 735*tan(x/2) - 105) + 336*B*tan(x/2)**2/(105*tan(x/2)**7 - 735*tan(x/2)**6 + 2205*tan(x/2)**5 - 3675*tan(x/2)**4 + 3675*tan(x/2)**3 - 2205*tan(x/2)**2 + 735*tan(x/2) - 105) - 182*B*tan(x/2)/(105*tan(x/2)**7 - 735*tan(x/2)**6 + 2205*tan(x/2)**5 - 3675*tan(x/2)**4 + 3675*tan(x/2)**3 - 2205*tan(x/2)**2 + 735*tan(x/2) - 105) + 26*B/(105*tan(x/2)**7 - 735*tan(x/2)**6 + 2205*tan(x/2)**5 - 3675*tan(x/2)**4 + 3675*tan(x/2)**3 - 2205*tan(x/2)**2 + 735*tan(x/2) - 105)","B",0
482,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(c+d*sin(f*x+e))**(5/2),x)","a \left(\int c^{2} \sqrt{c + d \sin{\left(e + f x \right)}}\, dx + \int c^{2} \sqrt{c + d \sin{\left(e + f x \right)}} \sin{\left(e + f x \right)}\, dx + \int d^{2} \sqrt{c + d \sin{\left(e + f x \right)}} \sin^{2}{\left(e + f x \right)}\, dx + \int d^{2} \sqrt{c + d \sin{\left(e + f x \right)}} \sin^{3}{\left(e + f x \right)}\, dx + \int 2 c d \sqrt{c + d \sin{\left(e + f x \right)}} \sin{\left(e + f x \right)}\, dx + \int 2 c d \sqrt{c + d \sin{\left(e + f x \right)}} \sin^{2}{\left(e + f x \right)}\, dx\right)"," ",0,"a*(Integral(c**2*sqrt(c + d*sin(e + f*x)), x) + Integral(c**2*sqrt(c + d*sin(e + f*x))*sin(e + f*x), x) + Integral(d**2*sqrt(c + d*sin(e + f*x))*sin(e + f*x)**2, x) + Integral(d**2*sqrt(c + d*sin(e + f*x))*sin(e + f*x)**3, x) + Integral(2*c*d*sqrt(c + d*sin(e + f*x))*sin(e + f*x), x) + Integral(2*c*d*sqrt(c + d*sin(e + f*x))*sin(e + f*x)**2, x))","F",0
483,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(c+d*sin(f*x+e))**(3/2),x)","a \left(\int c \sqrt{c + d \sin{\left(e + f x \right)}}\, dx + \int c \sqrt{c + d \sin{\left(e + f x \right)}} \sin{\left(e + f x \right)}\, dx + \int d \sqrt{c + d \sin{\left(e + f x \right)}} \sin{\left(e + f x \right)}\, dx + \int d \sqrt{c + d \sin{\left(e + f x \right)}} \sin^{2}{\left(e + f x \right)}\, dx\right)"," ",0,"a*(Integral(c*sqrt(c + d*sin(e + f*x)), x) + Integral(c*sqrt(c + d*sin(e + f*x))*sin(e + f*x), x) + Integral(d*sqrt(c + d*sin(e + f*x))*sin(e + f*x), x) + Integral(d*sqrt(c + d*sin(e + f*x))*sin(e + f*x)**2, x))","F",0
484,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(c+d*sin(f*x+e))**(1/2),x)","a \left(\int \sqrt{c + d \sin{\left(e + f x \right)}} \sin{\left(e + f x \right)}\, dx + \int \sqrt{c + d \sin{\left(e + f x \right)}}\, dx\right)"," ",0,"a*(Integral(sqrt(c + d*sin(e + f*x))*sin(e + f*x), x) + Integral(sqrt(c + d*sin(e + f*x)), x))","F",0
485,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))/(c+d*sin(f*x+e))**(1/2),x)","a \left(\int \frac{\sin{\left(e + f x \right)}}{\sqrt{c + d \sin{\left(e + f x \right)}}}\, dx + \int \frac{1}{\sqrt{c + d \sin{\left(e + f x \right)}}}\, dx\right)"," ",0,"a*(Integral(sin(e + f*x)/sqrt(c + d*sin(e + f*x)), x) + Integral(1/sqrt(c + d*sin(e + f*x)), x))","F",0
486,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))/(c+d*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
487,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))/(c+d*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
488,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))/(c+d*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
489,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**2*(c+d*sin(f*x+e))**(5/2),x)","a^{2} \left(\int c^{2} \sqrt{c + d \sin{\left(e + f x \right)}}\, dx + \int 2 c^{2} \sqrt{c + d \sin{\left(e + f x \right)}} \sin{\left(e + f x \right)}\, dx + \int c^{2} \sqrt{c + d \sin{\left(e + f x \right)}} \sin^{2}{\left(e + f x \right)}\, dx + \int d^{2} \sqrt{c + d \sin{\left(e + f x \right)}} \sin^{2}{\left(e + f x \right)}\, dx + \int 2 d^{2} \sqrt{c + d \sin{\left(e + f x \right)}} \sin^{3}{\left(e + f x \right)}\, dx + \int d^{2} \sqrt{c + d \sin{\left(e + f x \right)}} \sin^{4}{\left(e + f x \right)}\, dx + \int 2 c d \sqrt{c + d \sin{\left(e + f x \right)}} \sin{\left(e + f x \right)}\, dx + \int 4 c d \sqrt{c + d \sin{\left(e + f x \right)}} \sin^{2}{\left(e + f x \right)}\, dx + \int 2 c d \sqrt{c + d \sin{\left(e + f x \right)}} \sin^{3}{\left(e + f x \right)}\, dx\right)"," ",0,"a**2*(Integral(c**2*sqrt(c + d*sin(e + f*x)), x) + Integral(2*c**2*sqrt(c + d*sin(e + f*x))*sin(e + f*x), x) + Integral(c**2*sqrt(c + d*sin(e + f*x))*sin(e + f*x)**2, x) + Integral(d**2*sqrt(c + d*sin(e + f*x))*sin(e + f*x)**2, x) + Integral(2*d**2*sqrt(c + d*sin(e + f*x))*sin(e + f*x)**3, x) + Integral(d**2*sqrt(c + d*sin(e + f*x))*sin(e + f*x)**4, x) + Integral(2*c*d*sqrt(c + d*sin(e + f*x))*sin(e + f*x), x) + Integral(4*c*d*sqrt(c + d*sin(e + f*x))*sin(e + f*x)**2, x) + Integral(2*c*d*sqrt(c + d*sin(e + f*x))*sin(e + f*x)**3, x))","F",0
490,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**2*(c+d*sin(f*x+e))**(3/2),x)","a^{2} \left(\int c \sqrt{c + d \sin{\left(e + f x \right)}}\, dx + \int 2 c \sqrt{c + d \sin{\left(e + f x \right)}} \sin{\left(e + f x \right)}\, dx + \int c \sqrt{c + d \sin{\left(e + f x \right)}} \sin^{2}{\left(e + f x \right)}\, dx + \int d \sqrt{c + d \sin{\left(e + f x \right)}} \sin{\left(e + f x \right)}\, dx + \int 2 d \sqrt{c + d \sin{\left(e + f x \right)}} \sin^{2}{\left(e + f x \right)}\, dx + \int d \sqrt{c + d \sin{\left(e + f x \right)}} \sin^{3}{\left(e + f x \right)}\, dx\right)"," ",0,"a**2*(Integral(c*sqrt(c + d*sin(e + f*x)), x) + Integral(2*c*sqrt(c + d*sin(e + f*x))*sin(e + f*x), x) + Integral(c*sqrt(c + d*sin(e + f*x))*sin(e + f*x)**2, x) + Integral(d*sqrt(c + d*sin(e + f*x))*sin(e + f*x), x) + Integral(2*d*sqrt(c + d*sin(e + f*x))*sin(e + f*x)**2, x) + Integral(d*sqrt(c + d*sin(e + f*x))*sin(e + f*x)**3, x))","F",0
491,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**2*(c+d*sin(f*x+e))**(1/2),x)","a^{2} \left(\int 2 \sqrt{c + d \sin{\left(e + f x \right)}} \sin{\left(e + f x \right)}\, dx + \int \sqrt{c + d \sin{\left(e + f x \right)}} \sin^{2}{\left(e + f x \right)}\, dx + \int \sqrt{c + d \sin{\left(e + f x \right)}}\, dx\right)"," ",0,"a**2*(Integral(2*sqrt(c + d*sin(e + f*x))*sin(e + f*x), x) + Integral(sqrt(c + d*sin(e + f*x))*sin(e + f*x)**2, x) + Integral(sqrt(c + d*sin(e + f*x)), x))","F",0
492,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**2/(c+d*sin(f*x+e))**(1/2),x)","a^{2} \left(\int \frac{2 \sin{\left(e + f x \right)}}{\sqrt{c + d \sin{\left(e + f x \right)}}}\, dx + \int \frac{\sin^{2}{\left(e + f x \right)}}{\sqrt{c + d \sin{\left(e + f x \right)}}}\, dx + \int \frac{1}{\sqrt{c + d \sin{\left(e + f x \right)}}}\, dx\right)"," ",0,"a**2*(Integral(2*sin(e + f*x)/sqrt(c + d*sin(e + f*x)), x) + Integral(sin(e + f*x)**2/sqrt(c + d*sin(e + f*x)), x) + Integral(1/sqrt(c + d*sin(e + f*x)), x))","F",0
493,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**2/(c+d*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
494,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**2/(c+d*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
495,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**2/(c+d*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
496,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**3*(c+d*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
497,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**3*(c+d*sin(f*x+e))**(3/2),x)","a^{3} \left(\int c \sqrt{c + d \sin{\left(e + f x \right)}}\, dx + \int 3 c \sqrt{c + d \sin{\left(e + f x \right)}} \sin{\left(e + f x \right)}\, dx + \int 3 c \sqrt{c + d \sin{\left(e + f x \right)}} \sin^{2}{\left(e + f x \right)}\, dx + \int c \sqrt{c + d \sin{\left(e + f x \right)}} \sin^{3}{\left(e + f x \right)}\, dx + \int d \sqrt{c + d \sin{\left(e + f x \right)}} \sin{\left(e + f x \right)}\, dx + \int 3 d \sqrt{c + d \sin{\left(e + f x \right)}} \sin^{2}{\left(e + f x \right)}\, dx + \int 3 d \sqrt{c + d \sin{\left(e + f x \right)}} \sin^{3}{\left(e + f x \right)}\, dx + \int d \sqrt{c + d \sin{\left(e + f x \right)}} \sin^{4}{\left(e + f x \right)}\, dx\right)"," ",0,"a**3*(Integral(c*sqrt(c + d*sin(e + f*x)), x) + Integral(3*c*sqrt(c + d*sin(e + f*x))*sin(e + f*x), x) + Integral(3*c*sqrt(c + d*sin(e + f*x))*sin(e + f*x)**2, x) + Integral(c*sqrt(c + d*sin(e + f*x))*sin(e + f*x)**3, x) + Integral(d*sqrt(c + d*sin(e + f*x))*sin(e + f*x), x) + Integral(3*d*sqrt(c + d*sin(e + f*x))*sin(e + f*x)**2, x) + Integral(3*d*sqrt(c + d*sin(e + f*x))*sin(e + f*x)**3, x) + Integral(d*sqrt(c + d*sin(e + f*x))*sin(e + f*x)**4, x))","F",0
498,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**3*(c+d*sin(f*x+e))**(1/2),x)","a^{3} \left(\int 3 \sqrt{c + d \sin{\left(e + f x \right)}} \sin{\left(e + f x \right)}\, dx + \int 3 \sqrt{c + d \sin{\left(e + f x \right)}} \sin^{2}{\left(e + f x \right)}\, dx + \int \sqrt{c + d \sin{\left(e + f x \right)}} \sin^{3}{\left(e + f x \right)}\, dx + \int \sqrt{c + d \sin{\left(e + f x \right)}}\, dx\right)"," ",0,"a**3*(Integral(3*sqrt(c + d*sin(e + f*x))*sin(e + f*x), x) + Integral(3*sqrt(c + d*sin(e + f*x))*sin(e + f*x)**2, x) + Integral(sqrt(c + d*sin(e + f*x))*sin(e + f*x)**3, x) + Integral(sqrt(c + d*sin(e + f*x)), x))","F",0
499,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**3/(c+d*sin(f*x+e))**(1/2),x)","a^{3} \left(\int \frac{3 \sin{\left(e + f x \right)}}{\sqrt{c + d \sin{\left(e + f x \right)}}}\, dx + \int \frac{3 \sin^{2}{\left(e + f x \right)}}{\sqrt{c + d \sin{\left(e + f x \right)}}}\, dx + \int \frac{\sin^{3}{\left(e + f x \right)}}{\sqrt{c + d \sin{\left(e + f x \right)}}}\, dx + \int \frac{1}{\sqrt{c + d \sin{\left(e + f x \right)}}}\, dx\right)"," ",0,"a**3*(Integral(3*sin(e + f*x)/sqrt(c + d*sin(e + f*x)), x) + Integral(3*sin(e + f*x)**2/sqrt(c + d*sin(e + f*x)), x) + Integral(sin(e + f*x)**3/sqrt(c + d*sin(e + f*x)), x) + Integral(1/sqrt(c + d*sin(e + f*x)), x))","F",0
500,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**3/(c+d*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
501,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**3/(c+d*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
502,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**3/(c+d*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
503,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**3/(c+d*sin(f*x+e))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
504,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**(5/2)/(a+a*sin(f*x+e)),x)","\frac{\int \frac{c^{2} \sqrt{c + d \sin{\left(e + f x \right)}}}{\sin{\left(e + f x \right)} + 1}\, dx + \int \frac{d^{2} \sqrt{c + d \sin{\left(e + f x \right)}} \sin^{2}{\left(e + f x \right)}}{\sin{\left(e + f x \right)} + 1}\, dx + \int \frac{2 c d \sqrt{c + d \sin{\left(e + f x \right)}} \sin{\left(e + f x \right)}}{\sin{\left(e + f x \right)} + 1}\, dx}{a}"," ",0,"(Integral(c**2*sqrt(c + d*sin(e + f*x))/(sin(e + f*x) + 1), x) + Integral(d**2*sqrt(c + d*sin(e + f*x))*sin(e + f*x)**2/(sin(e + f*x) + 1), x) + Integral(2*c*d*sqrt(c + d*sin(e + f*x))*sin(e + f*x)/(sin(e + f*x) + 1), x))/a","F",0
505,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**(3/2)/(a+a*sin(f*x+e)),x)","\frac{\int \frac{c \sqrt{c + d \sin{\left(e + f x \right)}}}{\sin{\left(e + f x \right)} + 1}\, dx + \int \frac{d \sqrt{c + d \sin{\left(e + f x \right)}} \sin{\left(e + f x \right)}}{\sin{\left(e + f x \right)} + 1}\, dx}{a}"," ",0,"(Integral(c*sqrt(c + d*sin(e + f*x))/(sin(e + f*x) + 1), x) + Integral(d*sqrt(c + d*sin(e + f*x))*sin(e + f*x)/(sin(e + f*x) + 1), x))/a","F",0
506,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**(1/2)/(a+a*sin(f*x+e)),x)","\frac{\int \frac{\sqrt{c + d \sin{\left(e + f x \right)}}}{\sin{\left(e + f x \right)} + 1}\, dx}{a}"," ",0,"Integral(sqrt(c + d*sin(e + f*x))/(sin(e + f*x) + 1), x)/a","F",0
507,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))/(c+d*sin(f*x+e))**(1/2),x)","\frac{\int \frac{1}{\sqrt{c + d \sin{\left(e + f x \right)}} \sin{\left(e + f x \right)} + \sqrt{c + d \sin{\left(e + f x \right)}}}\, dx}{a}"," ",0,"Integral(1/(sqrt(c + d*sin(e + f*x))*sin(e + f*x) + sqrt(c + d*sin(e + f*x))), x)/a","F",0
508,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))/(c+d*sin(f*x+e))**(3/2),x)","\frac{\int \frac{1}{c \sqrt{c + d \sin{\left(e + f x \right)}} \sin{\left(e + f x \right)} + c \sqrt{c + d \sin{\left(e + f x \right)}} + d \sqrt{c + d \sin{\left(e + f x \right)}} \sin^{2}{\left(e + f x \right)} + d \sqrt{c + d \sin{\left(e + f x \right)}} \sin{\left(e + f x \right)}}\, dx}{a}"," ",0,"Integral(1/(c*sqrt(c + d*sin(e + f*x))*sin(e + f*x) + c*sqrt(c + d*sin(e + f*x)) + d*sqrt(c + d*sin(e + f*x))*sin(e + f*x)**2 + d*sqrt(c + d*sin(e + f*x))*sin(e + f*x)), x)/a","F",0
509,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))/(c+d*sin(f*x+e))**(5/2),x)","\frac{\int \frac{1}{c^{2} \sqrt{c + d \sin{\left(e + f x \right)}} \sin{\left(e + f x \right)} + c^{2} \sqrt{c + d \sin{\left(e + f x \right)}} + 2 c d \sqrt{c + d \sin{\left(e + f x \right)}} \sin^{2}{\left(e + f x \right)} + 2 c d \sqrt{c + d \sin{\left(e + f x \right)}} \sin{\left(e + f x \right)} + d^{2} \sqrt{c + d \sin{\left(e + f x \right)}} \sin^{3}{\left(e + f x \right)} + d^{2} \sqrt{c + d \sin{\left(e + f x \right)}} \sin^{2}{\left(e + f x \right)}}\, dx}{a}"," ",0,"Integral(1/(c**2*sqrt(c + d*sin(e + f*x))*sin(e + f*x) + c**2*sqrt(c + d*sin(e + f*x)) + 2*c*d*sqrt(c + d*sin(e + f*x))*sin(e + f*x)**2 + 2*c*d*sqrt(c + d*sin(e + f*x))*sin(e + f*x) + d**2*sqrt(c + d*sin(e + f*x))*sin(e + f*x)**3 + d**2*sqrt(c + d*sin(e + f*x))*sin(e + f*x)**2), x)/a","F",0
510,-1,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**(5/2)/(a+a*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
511,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**(3/2)/(a+a*sin(f*x+e))**2,x)","\frac{\int \frac{c \sqrt{c + d \sin{\left(e + f x \right)}}}{\sin^{2}{\left(e + f x \right)} + 2 \sin{\left(e + f x \right)} + 1}\, dx + \int \frac{d \sqrt{c + d \sin{\left(e + f x \right)}} \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(c*sqrt(c + d*sin(e + f*x))/(sin(e + f*x)**2 + 2*sin(e + f*x) + 1), x) + Integral(d*sqrt(c + d*sin(e + f*x))*sin(e + f*x)/(sin(e + f*x)**2 + 2*sin(e + f*x) + 1), x))/a**2","F",0
512,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**(1/2)/(a+a*sin(f*x+e))**2,x)","\frac{\int \frac{\sqrt{c + d \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(sqrt(c + d*sin(e + f*x))/(sin(e + f*x)**2 + 2*sin(e + f*x) + 1), x)/a**2","F",0
513,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))**2/(c+d*sin(f*x+e))**(1/2),x)","\frac{\int \frac{1}{\sqrt{c + d \sin{\left(e + f x \right)}} \sin^{2}{\left(e + f x \right)} + 2 \sqrt{c + d \sin{\left(e + f x \right)}} \sin{\left(e + f x \right)} + \sqrt{c + d \sin{\left(e + f x \right)}}}\, dx}{a^{2}}"," ",0,"Integral(1/(sqrt(c + d*sin(e + f*x))*sin(e + f*x)**2 + 2*sqrt(c + d*sin(e + f*x))*sin(e + f*x) + sqrt(c + d*sin(e + f*x))), x)/a**2","F",0
514,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))**2/(c+d*sin(f*x+e))**(3/2),x)","\frac{\int \frac{1}{c \sqrt{c + d \sin{\left(e + f x \right)}} \sin^{2}{\left(e + f x \right)} + 2 c \sqrt{c + d \sin{\left(e + f x \right)}} \sin{\left(e + f x \right)} + c \sqrt{c + d \sin{\left(e + f x \right)}} + d \sqrt{c + d \sin{\left(e + f x \right)}} \sin^{3}{\left(e + f x \right)} + 2 d \sqrt{c + d \sin{\left(e + f x \right)}} \sin^{2}{\left(e + f x \right)} + d \sqrt{c + d \sin{\left(e + f x \right)}} \sin{\left(e + f x \right)}}\, dx}{a^{2}}"," ",0,"Integral(1/(c*sqrt(c + d*sin(e + f*x))*sin(e + f*x)**2 + 2*c*sqrt(c + d*sin(e + f*x))*sin(e + f*x) + c*sqrt(c + d*sin(e + f*x)) + d*sqrt(c + d*sin(e + f*x))*sin(e + f*x)**3 + 2*d*sqrt(c + d*sin(e + f*x))*sin(e + f*x)**2 + d*sqrt(c + d*sin(e + f*x))*sin(e + f*x)), x)/a**2","F",0
515,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))**2/(c+d*sin(f*x+e))**(5/2),x)","\frac{\int \frac{1}{c^{2} \sqrt{c + d \sin{\left(e + f x \right)}} \sin^{2}{\left(e + f x \right)} + 2 c^{2} \sqrt{c + d \sin{\left(e + f x \right)}} \sin{\left(e + f x \right)} + c^{2} \sqrt{c + d \sin{\left(e + f x \right)}} + 2 c d \sqrt{c + d \sin{\left(e + f x \right)}} \sin^{3}{\left(e + f x \right)} + 4 c d \sqrt{c + d \sin{\left(e + f x \right)}} \sin^{2}{\left(e + f x \right)} + 2 c d \sqrt{c + d \sin{\left(e + f x \right)}} \sin{\left(e + f x \right)} + d^{2} \sqrt{c + d \sin{\left(e + f x \right)}} \sin^{4}{\left(e + f x \right)} + 2 d^{2} \sqrt{c + d \sin{\left(e + f x \right)}} \sin^{3}{\left(e + f x \right)} + d^{2} \sqrt{c + d \sin{\left(e + f x \right)}} \sin^{2}{\left(e + f x \right)}}\, dx}{a^{2}}"," ",0,"Integral(1/(c**2*sqrt(c + d*sin(e + f*x))*sin(e + f*x)**2 + 2*c**2*sqrt(c + d*sin(e + f*x))*sin(e + f*x) + c**2*sqrt(c + d*sin(e + f*x)) + 2*c*d*sqrt(c + d*sin(e + f*x))*sin(e + f*x)**3 + 4*c*d*sqrt(c + d*sin(e + f*x))*sin(e + f*x)**2 + 2*c*d*sqrt(c + d*sin(e + f*x))*sin(e + f*x) + d**2*sqrt(c + d*sin(e + f*x))*sin(e + f*x)**4 + 2*d**2*sqrt(c + d*sin(e + f*x))*sin(e + f*x)**3 + d**2*sqrt(c + d*sin(e + f*x))*sin(e + f*x)**2), x)/a**2","F",0
516,-1,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**(5/2)/(a+a*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
517,-1,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**(3/2)/(a+a*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
518,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**(1/2)/(a+a*sin(f*x+e))**3,x)","\frac{\int \frac{\sqrt{c + d \sin{\left(e + f x \right)}}}{\sin^{3}{\left(e + f x \right)} + 3 \sin^{2}{\left(e + f x \right)} + 3 \sin{\left(e + f x \right)} + 1}\, dx}{a^{3}}"," ",0,"Integral(sqrt(c + d*sin(e + f*x))/(sin(e + f*x)**3 + 3*sin(e + f*x)**2 + 3*sin(e + f*x) + 1), x)/a**3","F",0
519,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))**3/(c+d*sin(f*x+e))**(1/2),x)","\frac{\int \frac{1}{\sqrt{c + d \sin{\left(e + f x \right)}} \sin^{3}{\left(e + f x \right)} + 3 \sqrt{c + d \sin{\left(e + f x \right)}} \sin^{2}{\left(e + f x \right)} + 3 \sqrt{c + d \sin{\left(e + f x \right)}} \sin{\left(e + f x \right)} + \sqrt{c + d \sin{\left(e + f x \right)}}}\, dx}{a^{3}}"," ",0,"Integral(1/(sqrt(c + d*sin(e + f*x))*sin(e + f*x)**3 + 3*sqrt(c + d*sin(e + f*x))*sin(e + f*x)**2 + 3*sqrt(c + d*sin(e + f*x))*sin(e + f*x) + sqrt(c + d*sin(e + f*x))), x)/a**3","F",0
520,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))**3/(c+d*sin(f*x+e))**(3/2),x)","\frac{\int \frac{1}{c \sqrt{c + d \sin{\left(e + f x \right)}} \sin^{3}{\left(e + f x \right)} + 3 c \sqrt{c + d \sin{\left(e + f x \right)}} \sin^{2}{\left(e + f x \right)} + 3 c \sqrt{c + d \sin{\left(e + f x \right)}} \sin{\left(e + f x \right)} + c \sqrt{c + d \sin{\left(e + f x \right)}} + d \sqrt{c + d \sin{\left(e + f x \right)}} \sin^{4}{\left(e + f x \right)} + 3 d \sqrt{c + d \sin{\left(e + f x \right)}} \sin^{3}{\left(e + f x \right)} + 3 d \sqrt{c + d \sin{\left(e + f x \right)}} \sin^{2}{\left(e + f x \right)} + d \sqrt{c + d \sin{\left(e + f x \right)}} \sin{\left(e + f x \right)}}\, dx}{a^{3}}"," ",0,"Integral(1/(c*sqrt(c + d*sin(e + f*x))*sin(e + f*x)**3 + 3*c*sqrt(c + d*sin(e + f*x))*sin(e + f*x)**2 + 3*c*sqrt(c + d*sin(e + f*x))*sin(e + f*x) + c*sqrt(c + d*sin(e + f*x)) + d*sqrt(c + d*sin(e + f*x))*sin(e + f*x)**4 + 3*d*sqrt(c + d*sin(e + f*x))*sin(e + f*x)**3 + 3*d*sqrt(c + d*sin(e + f*x))*sin(e + f*x)**2 + d*sqrt(c + d*sin(e + f*x))*sin(e + f*x)), x)/a**3","F",0
521,-1,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))**3/(c+d*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
522,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(1/2)*(c+d*sin(f*x+e))**3,x)","\int \sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)} \left(c + d \sin{\left(e + f x \right)}\right)^{3}\, dx"," ",0,"Integral(sqrt(a*(sin(e + f*x) + 1))*(c + d*sin(e + f*x))**3, x)","F",0
523,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(1/2)*(c+d*sin(f*x+e))**2,x)","\int \sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)} \left(c + d \sin{\left(e + f x \right)}\right)^{2}\, dx"," ",0,"Integral(sqrt(a*(sin(e + f*x) + 1))*(c + d*sin(e + f*x))**2, x)","F",0
524,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(1/2)*(c+d*sin(f*x+e)),x)","\int \sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)} \left(c + d \sin{\left(e + f x \right)}\right)\, dx"," ",0,"Integral(sqrt(a*(sin(e + f*x) + 1))*(c + d*sin(e + f*x)), x)","F",0
525,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(1/2),x)","\int \sqrt{a \sin{\left(e + f x \right)} + a}\, dx"," ",0,"Integral(sqrt(a*sin(e + f*x) + a), x)","F",0
526,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(1/2)/(c+d*sin(f*x+e)),x)","\int \frac{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)}}{c + d \sin{\left(e + f x \right)}}\, dx"," ",0,"Integral(sqrt(a*(sin(e + f*x) + 1))/(c + d*sin(e + f*x)), x)","F",0
527,-1,0,0,0.000000," ","integrate((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
528,-1,0,0,0.000000," ","integrate((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
529,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(3/2)*(c+d*sin(f*x+e))**3,x)","\int \left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}} \left(c + d \sin{\left(e + f x \right)}\right)^{3}\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**(3/2)*(c + d*sin(e + f*x))**3, x)","F",0
530,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(3/2)*(c+d*sin(f*x+e))**2,x)","\int \left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}} \left(c + d \sin{\left(e + f x \right)}\right)^{2}\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**(3/2)*(c + d*sin(e + f*x))**2, x)","F",0
531,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(3/2)*(c+d*sin(f*x+e)),x)","\int \left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}} \left(c + d \sin{\left(e + f x \right)}\right)\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**(3/2)*(c + d*sin(e + f*x)), x)","F",0
532,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(3/2),x)","\int \left(a \sin{\left(e + f x \right)} + a\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a*sin(e + f*x) + a)**(3/2), x)","F",0
533,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(3/2)/(c+d*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
534,-1,0,0,0.000000," ","integrate((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
535,-1,0,0,0.000000," ","integrate((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
536,-1,0,0,0.000000," ","integrate((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
537,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(5/2)*(c+d*sin(f*x+e))**2,x)","\int \left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{5}{2}} \left(c + d \sin{\left(e + f x \right)}\right)^{2}\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**(5/2)*(c + d*sin(e + f*x))**2, x)","F",0
538,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(5/2)*(c+d*sin(f*x+e)),x)","\int \left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{5}{2}} \left(c + d \sin{\left(e + f x \right)}\right)\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**(5/2)*(c + d*sin(e + f*x)), x)","F",0
539,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(5/2),x)","\int \left(a \sin{\left(e + f x \right)} + a\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a*sin(e + f*x) + a)**(5/2), x)","F",0
540,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(5/2)/(c+d*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
541,-1,0,0,0.000000," ","integrate((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
542,-1,0,0,0.000000," ","integrate((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
543,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**3/(a+a*sin(f*x+e))**(1/2),x)","\int \frac{\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((c + d*sin(e + f*x))**3/sqrt(a*(sin(e + f*x) + 1)), x)","F",0
544,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**2/(a+a*sin(f*x+e))**(1/2),x)","\int \frac{\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((c + d*sin(e + f*x))**2/sqrt(a*(sin(e + f*x) + 1)), x)","F",0
545,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))/(a+a*sin(f*x+e))**(1/2),x)","\int \frac{c + d \sin{\left(e + f x \right)}}{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)}}\, dx"," ",0,"Integral((c + d*sin(e + f*x))/sqrt(a*(sin(e + f*x) + 1)), x)","F",0
546,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))**(1/2),x)","\int \frac{1}{\sqrt{a \sin{\left(e + f x \right)} + a}}\, dx"," ",0,"Integral(1/sqrt(a*sin(e + f*x) + a), x)","F",0
547,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))**(1/2)/(c+d*sin(f*x+e)),x)","\int \frac{1}{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)} \left(c + d \sin{\left(e + f x \right)}\right)}\, dx"," ",0,"Integral(1/(sqrt(a*(sin(e + f*x) + 1))*(c + d*sin(e + f*x))), x)","F",0
548,-1,0,0,0.000000," ","integrate(1/(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
549,-1,0,0,0.000000," ","integrate(1/(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
550,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**3/(a+a*sin(f*x+e))**(3/2),x)","\int \frac{\left(c + d \sin{\left(e + f x \right)}\right)^{3}}{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((c + d*sin(e + f*x))**3/(a*(sin(e + f*x) + 1))**(3/2), x)","F",0
551,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**2/(a+a*sin(f*x+e))**(3/2),x)","\int \frac{\left(c + d \sin{\left(e + f x \right)}\right)^{2}}{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((c + d*sin(e + f*x))**2/(a*(sin(e + f*x) + 1))**(3/2), x)","F",0
552,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))/(a+a*sin(f*x+e))**(3/2),x)","\int \frac{c + d \sin{\left(e + f x \right)}}{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((c + d*sin(e + f*x))/(a*(sin(e + f*x) + 1))**(3/2), x)","F",0
553,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))**(3/2),x)","\int \frac{1}{\left(a \sin{\left(e + f x \right)} + a\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a*sin(e + f*x) + a)**(-3/2), x)","F",0
554,-1,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))**(3/2)/(c+d*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
555,-1,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))**(3/2)/(c+d*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
556,-1,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))**(3/2)/(c+d*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
557,-1,0,0,0.000000," ","integrate((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
558,-1,0,0,0.000000," ","integrate((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
559,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))/(a+a*sin(f*x+e))**(5/2),x)","\int \frac{c + d \sin{\left(e + f x \right)}}{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((c + d*sin(e + f*x))/(a*(sin(e + f*x) + 1))**(5/2), x)","F",0
560,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))**(5/2),x)","\int \frac{1}{\left(a \sin{\left(e + f x \right)} + a\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a*sin(e + f*x) + a)**(-5/2), x)","F",0
561,-1,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))**(5/2)/(c+d*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
562,-1,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))**(5/2)/(c+d*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
563,-1,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))**(5/2)/(c+d*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
564,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(1/2)*(c+d*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
565,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(1/2)*(c+d*sin(f*x+e))**(3/2),x)","\int \sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)} \left(c + d \sin{\left(e + f x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(sqrt(a*(sin(e + f*x) + 1))*(c + d*sin(e + f*x))**(3/2), x)","F",0
566,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(1/2)*(c+d*sin(f*x+e))**(1/2),x)","\int \sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)} \sqrt{c + d \sin{\left(e + f x \right)}}\, dx"," ",0,"Integral(sqrt(a*(sin(e + f*x) + 1))*sqrt(c + d*sin(e + f*x)), x)","F",0
567,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(1/2)/(c+d*sin(f*x+e))**(1/2),x)","\int \frac{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)}}{\sqrt{c + d \sin{\left(e + f x \right)}}}\, dx"," ",0,"Integral(sqrt(a*(sin(e + f*x) + 1))/sqrt(c + d*sin(e + f*x)), x)","F",0
568,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(1/2)/(c+d*sin(f*x+e))**(3/2),x)","\int \frac{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)}}{\left(c + d \sin{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(a*(sin(e + f*x) + 1))/(c + d*sin(e + f*x))**(3/2), x)","F",0
569,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(1/2)/(c+d*sin(f*x+e))**(5/2),x)","\int \frac{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)}}{\left(c + d \sin{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt(a*(sin(e + f*x) + 1))/(c + d*sin(e + f*x))**(5/2), x)","F",0
570,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(1/2)/(c+d*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
571,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(3/2)*(c+d*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
572,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(3/2)*(c+d*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
573,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(3/2)*(c+d*sin(f*x+e))**(1/2),x)","\int \left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}} \sqrt{c + d \sin{\left(e + f x \right)}}\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**(3/2)*sqrt(c + d*sin(e + f*x)), x)","F",0
574,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(3/2)/(c+d*sin(f*x+e))**(1/2),x)","\int \frac{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}}}{\sqrt{c + d \sin{\left(e + f x \right)}}}\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**(3/2)/sqrt(c + d*sin(e + f*x)), x)","F",0
575,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(3/2)/(c+d*sin(f*x+e))**(3/2),x)","\int \frac{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}}}{\left(c + d \sin{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**(3/2)/(c + d*sin(e + f*x))**(3/2), x)","F",0
576,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(3/2)/(c+d*sin(f*x+e))**(5/2),x)","\int \frac{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}}}{\left(c + d \sin{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**(3/2)/(c + d*sin(e + f*x))**(5/2), x)","F",0
577,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(3/2)/(c+d*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
578,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(3/2)/(c+d*sin(f*x+e))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
579,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(5/2)*(c+d*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
580,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(5/2)*(c+d*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
581,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(5/2)*(c+d*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
582,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(5/2)/(c+d*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
583,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(5/2)/(c+d*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
584,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(5/2)/(c+d*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
585,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(5/2)/(c+d*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
586,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(5/2)/(c+d*sin(f*x+e))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
587,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(5/2)/(c+d*sin(f*x+e))**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
588,-1,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**(5/2)/(a+a*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
589,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**(3/2)/(a+a*sin(f*x+e))**(1/2),x)","\int \frac{\left(c + d \sin{\left(e + f x \right)}\right)^{\frac{3}{2}}}{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)}}\, dx"," ",0,"Integral((c + d*sin(e + f*x))**(3/2)/sqrt(a*(sin(e + f*x) + 1)), x)","F",0
590,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**(1/2)/(a+a*sin(f*x+e))**(1/2),x)","\int \frac{\sqrt{c + d \sin{\left(e + f x \right)}}}{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)}}\, dx"," ",0,"Integral(sqrt(c + d*sin(e + f*x))/sqrt(a*(sin(e + f*x) + 1)), x)","F",0
591,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))**(1/2)/(c+d*sin(f*x+e))**(1/2),x)","\int \frac{1}{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)} \sqrt{c + d \sin{\left(e + f x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(a*(sin(e + f*x) + 1))*sqrt(c + d*sin(e + f*x))), x)","F",0
592,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))**(1/2)/(c+d*sin(f*x+e))**(3/2),x)","\int \frac{1}{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)} \left(c + d \sin{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(sqrt(a*(sin(e + f*x) + 1))*(c + d*sin(e + f*x))**(3/2)), x)","F",0
593,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))**(1/2)/(c+d*sin(f*x+e))**(5/2),x)","\int \frac{1}{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)} \left(c + d \sin{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(sqrt(a*(sin(e + f*x) + 1))*(c + d*sin(e + f*x))**(5/2)), x)","F",0
594,-1,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**(5/2)/(a+a*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
595,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**(3/2)/(a+a*sin(f*x+e))**(3/2),x)","\int \frac{\left(c + d \sin{\left(e + f x \right)}\right)^{\frac{3}{2}}}{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((c + d*sin(e + f*x))**(3/2)/(a*(sin(e + f*x) + 1))**(3/2), x)","F",0
596,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**(1/2)/(a+a*sin(f*x+e))**(3/2),x)","\int \frac{\sqrt{c + d \sin{\left(e + f x \right)}}}{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(c + d*sin(e + f*x))/(a*(sin(e + f*x) + 1))**(3/2), x)","F",0
597,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))**(3/2)/(c+d*sin(f*x+e))**(1/2),x)","\int \frac{1}{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}} \sqrt{c + d \sin{\left(e + f x \right)}}}\, dx"," ",0,"Integral(1/((a*(sin(e + f*x) + 1))**(3/2)*sqrt(c + d*sin(e + f*x))), x)","F",0
598,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))**(3/2)/(c+d*sin(f*x+e))**(3/2),x)","\int \frac{1}{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}} \left(c + d \sin{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((a*(sin(e + f*x) + 1))**(3/2)*(c + d*sin(e + f*x))**(3/2)), x)","F",0
599,-1,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))**(3/2)/(c+d*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
600,-1,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**(5/2)/(a+a*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
601,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**(3/2)/(a+a*sin(f*x+e))**(5/2),x)","\int \frac{\left(c + d \sin{\left(e + f x \right)}\right)^{\frac{3}{2}}}{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((c + d*sin(e + f*x))**(3/2)/(a*(sin(e + f*x) + 1))**(5/2), x)","F",0
602,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**(1/2)/(a+a*sin(f*x+e))**(5/2),x)","\int \frac{\sqrt{c + d \sin{\left(e + f x \right)}}}{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt(c + d*sin(e + f*x))/(a*(sin(e + f*x) + 1))**(5/2), x)","F",0
603,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))**(5/2)/(c+d*sin(f*x+e))**(1/2),x)","\int \frac{1}{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{5}{2}} \sqrt{c + d \sin{\left(e + f x \right)}}}\, dx"," ",0,"Integral(1/((a*(sin(e + f*x) + 1))**(5/2)*sqrt(c + d*sin(e + f*x))), x)","F",0
604,-1,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))**(5/2)/(c+d*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
605,-1,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))**(5/2)/(c+d*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
606,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(c+d*sin(f*x+e))**n,x)","\int \left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{m} \left(c + d \sin{\left(e + f x \right)}\right)^{n}\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**m*(c + d*sin(e + f*x))**n, x)","F",0
607,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(c+d*sin(f*x+e))**3,x)","\int \left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{m} \left(c + d \sin{\left(e + f x \right)}\right)^{3}\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**m*(c + d*sin(e + f*x))**3, x)","F",0
608,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(c+d*sin(f*x+e))**2,x)","\int \left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{m} \left(c + d \sin{\left(e + f x \right)}\right)^{2}\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**m*(c + d*sin(e + f*x))**2, x)","F",0
609,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(c+d*sin(f*x+e)),x)","\int \left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{m} \left(c + d \sin{\left(e + f x \right)}\right)\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**m*(c + d*sin(e + f*x)), x)","F",0
610,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m,x)","\int \left(a \sin{\left(e + f x \right)} + a\right)^{m}\, dx"," ",0,"Integral((a*sin(e + f*x) + a)**m, x)","F",0
611,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m/(c+d*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
612,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m/(c+d*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
613,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m/(c+d*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
614,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(c+d*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
615,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(c+d*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
616,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(c+d*sin(f*x+e))**(1/2),x)","\int \left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{m} \sqrt{c + d \sin{\left(e + f x \right)}}\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**m*sqrt(c + d*sin(e + f*x)), x)","F",0
617,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m/(c+d*sin(f*x+e))**(1/2),x)","\int \frac{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{m}}{\sqrt{c + d \sin{\left(e + f x \right)}}}\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**m/sqrt(c + d*sin(e + f*x)), x)","F",0
618,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m/(c+d*sin(f*x+e))**(3/2),x)","\int \frac{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{m}}{\left(c + d \sin{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**m/(c + d*sin(e + f*x))**(3/2), x)","F",0
619,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m/(c+d*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
620,-1,0,0,0.000000," ","integrate((1+sin(f*x+e))**m*(3+5*sin(f*x+e))**(-1-m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
621,-1,0,0,0.000000," ","integrate((1+sin(f*x+e))**m*(3+4*sin(f*x+e))**(-1-m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
622,-1,0,0,0.000000," ","integrate((1+sin(f*x+e))**m*(3+3*sin(f*x+e))**(-1-m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
623,-1,0,0,0.000000," ","integrate((1+sin(f*x+e))**m*(3+2*sin(f*x+e))**(-1-m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
624,-1,0,0,0.000000," ","integrate((1+sin(f*x+e))**m*(3+sin(f*x+e))**(-1-m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
625,0,0,0,0.000000," ","integrate(3**(-1-m)*(1+sin(f*x+e))**m,x)","3^{- m - 1} \int \left(\sin{\left(e + f x \right)} + 1\right)^{m}\, dx"," ",0,"3**(-m - 1)*Integral((sin(e + f*x) + 1)**m, x)","F",0
626,-1,0,0,0.000000," ","integrate((3-sin(f*x+e))**(-1-m)*(1+sin(f*x+e))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
627,-1,0,0,0.000000," ","integrate((3-2*sin(f*x+e))**(-1-m)*(1+sin(f*x+e))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
628,-1,0,0,0.000000," ","integrate((3-3*sin(f*x+e))**(-1-m)*(1+sin(f*x+e))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
629,-1,0,0,0.000000," ","integrate((3-4*sin(f*x+e))**(-1-m)*(1+sin(f*x+e))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
630,-2,0,0,0.000000," ","integrate((3-5*sin(f*x+e))**(-1-m)*(1+sin(f*x+e))**m,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
631,-1,0,0,0.000000," ","integrate((3+5*sin(f*x+e))**(-1-m)*(a+a*sin(f*x+e))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
632,-1,0,0,0.000000," ","integrate((3+4*sin(f*x+e))**(-1-m)*(a+a*sin(f*x+e))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
633,-1,0,0,0.000000," ","integrate((3+3*sin(f*x+e))**(-1-m)*(a+a*sin(f*x+e))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
634,-1,0,0,0.000000," ","integrate((3+2*sin(f*x+e))**(-1-m)*(a+a*sin(f*x+e))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
635,-1,0,0,0.000000," ","integrate((3+sin(f*x+e))**(-1-m)*(a+a*sin(f*x+e))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
636,0,0,0,0.000000," ","integrate(3**(-1-m)*(a+a*sin(f*x+e))**m,x)","3^{- m - 1} \int \left(a \sin{\left(e + f x \right)} + a\right)^{m}\, dx"," ",0,"3**(-m - 1)*Integral((a*sin(e + f*x) + a)**m, x)","F",0
637,-1,0,0,0.000000," ","integrate((3-sin(f*x+e))**(-1-m)*(a+a*sin(f*x+e))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
638,-1,0,0,0.000000," ","integrate((3-2*sin(f*x+e))**(-1-m)*(a+a*sin(f*x+e))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
639,-1,0,0,0.000000," ","integrate((3-3*sin(f*x+e))**(-1-m)*(a+a*sin(f*x+e))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
640,-1,0,0,0.000000," ","integrate((3-4*sin(f*x+e))**(-1-m)*(a+a*sin(f*x+e))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
641,-2,0,0,0.000000," ","integrate((3-5*sin(f*x+e))**(-1-m)*(a+a*sin(f*x+e))**m,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
642,-1,0,0,0.000000," ","integrate((-3+5*sin(f*x+e))**(-1-m)*(a+a*sin(f*x+e))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
643,-1,0,0,0.000000," ","integrate((-3+4*sin(f*x+e))**(-1-m)*(a+a*sin(f*x+e))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
644,-1,0,0,0.000000," ","integrate((-3+3*sin(f*x+e))**(-1-m)*(a+a*sin(f*x+e))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
645,-1,0,0,0.000000," ","integrate((-3+2*sin(f*x+e))**(-1-m)*(a+a*sin(f*x+e))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
646,-1,0,0,0.000000," ","integrate((-3+sin(f*x+e))**(-1-m)*(a+a*sin(f*x+e))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
647,0,0,0,0.000000," ","integrate((-3)**(-1-m)*(a+a*sin(f*x+e))**m,x)","\left(-3\right)^{- m - 1} \int \left(a \sin{\left(e + f x \right)} + a\right)^{m}\, dx"," ",0,"(-3)**(-m - 1)*Integral((a*sin(e + f*x) + a)**m, x)","F",0
648,-1,0,0,0.000000," ","integrate((-3-sin(f*x+e))**(-1-m)*(a+a*sin(f*x+e))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
649,-1,0,0,0.000000," ","integrate((-3-2*sin(f*x+e))**(-1-m)*(a+a*sin(f*x+e))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
650,-1,0,0,0.000000," ","integrate((-3-3*sin(f*x+e))**(-1-m)*(a+a*sin(f*x+e))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
651,-1,0,0,0.000000," ","integrate((-3-4*sin(f*x+e))**(-1-m)*(a+a*sin(f*x+e))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
652,-1,0,0,0.000000," ","integrate((-3-5*sin(f*x+e))**(-1-m)*(a+a*sin(f*x+e))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
653,-1,0,0,0.000000," ","integrate((d*sin(f*x+e))**(-1-m)*(a+a*sin(f*x+e))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
654,-1,0,0,0.000000," ","integrate((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
655,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**3*(c+d*sin(f*x+e))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
656,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**2*(c+d*sin(f*x+e))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
657,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(c+d*sin(f*x+e))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
658,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**n,x)","\int \left(c + d \sin{\left(e + f x \right)}\right)^{n}\, dx"," ",0,"Integral((c + d*sin(e + f*x))**n, x)","F",0
659,-1,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**n/(a+a*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
660,-1,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**n/(a+a*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
661,-1,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**n/(a+a*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
662,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(5/2)*(c+d*sin(f*x+e))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
663,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(3/2)*(c+d*sin(f*x+e))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
664,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(1/2)*(c+d*sin(f*x+e))**n,x)","\int \sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)} \left(c + d \sin{\left(e + f x \right)}\right)^{n}\, dx"," ",0,"Integral(sqrt(a*(sin(e + f*x) + 1))*(c + d*sin(e + f*x))**n, x)","F",0
665,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**n/(a+a*sin(f*x+e))**(1/2),x)","\int \frac{\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((c + d*sin(e + f*x))**n/sqrt(a*(sin(e + f*x) + 1)), x)","F",0
666,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**n/(a+a*sin(f*x+e))**(3/2),x)","\int \frac{\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((c + d*sin(e + f*x))**n/(a*(sin(e + f*x) + 1))**(3/2), x)","F",0
667,-1,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**n/(a+a*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
668,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(c+d*sin(f*x+e))**(1/3),x)","a \left(\int \sqrt[3]{c + d \sin{\left(e + f x \right)}} \sin{\left(e + f x \right)}\, dx + \int \sqrt[3]{c + d \sin{\left(e + f x \right)}}\, dx\right)"," ",0,"a*(Integral((c + d*sin(e + f*x))**(1/3)*sin(e + f*x), x) + Integral((c + d*sin(e + f*x))**(1/3), x))","F",0
669,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))/(c+d*sin(f*x+e))**(1/3),x)","a \left(\int \frac{\sin{\left(e + f x \right)}}{\sqrt[3]{c + d \sin{\left(e + f x \right)}}}\, dx + \int \frac{1}{\sqrt[3]{c + d \sin{\left(e + f x \right)}}}\, dx\right)"," ",0,"a*(Integral(sin(e + f*x)/(c + d*sin(e + f*x))**(1/3), x) + Integral((c + d*sin(e + f*x))**(-1/3), x))","F",0
670,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))/(c+d*sin(f*x+e))**(4/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
671,1,386,0,1.856799," ","integrate((a+b*sin(f*x+e))*(c+d*sin(f*x+e))**3,x)","\begin{cases} a c^{3} x - \frac{3 a c^{2} d \cos{\left(e + f x \right)}}{f} + \frac{3 a c d^{2} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{3 a c d^{2} x \cos^{2}{\left(e + f x \right)}}{2} - \frac{3 a c d^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{a d^{3} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{2 a d^{3} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{b c^{3} \cos{\left(e + f x \right)}}{f} + \frac{3 b c^{2} d x \sin^{2}{\left(e + f x \right)}}{2} + \frac{3 b c^{2} d x \cos^{2}{\left(e + f x \right)}}{2} - \frac{3 b c^{2} d \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{3 b c d^{2} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{2 b c d^{2} \cos^{3}{\left(e + f x \right)}}{f} + \frac{3 b d^{3} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{3 b d^{3} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{3 b d^{3} x \cos^{4}{\left(e + f x \right)}}{8} - \frac{5 b d^{3} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{3 b d^{3} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} & \text{for}\: f \neq 0 \\x \left(a + b \sin{\left(e \right)}\right) \left(c + d \sin{\left(e \right)}\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**3*x - 3*a*c**2*d*cos(e + f*x)/f + 3*a*c*d**2*x*sin(e + f*x)**2/2 + 3*a*c*d**2*x*cos(e + f*x)**2/2 - 3*a*c*d**2*sin(e + f*x)*cos(e + f*x)/(2*f) - a*d**3*sin(e + f*x)**2*cos(e + f*x)/f - 2*a*d**3*cos(e + f*x)**3/(3*f) - b*c**3*cos(e + f*x)/f + 3*b*c**2*d*x*sin(e + f*x)**2/2 + 3*b*c**2*d*x*cos(e + f*x)**2/2 - 3*b*c**2*d*sin(e + f*x)*cos(e + f*x)/(2*f) - 3*b*c*d**2*sin(e + f*x)**2*cos(e + f*x)/f - 2*b*c*d**2*cos(e + f*x)**3/f + 3*b*d**3*x*sin(e + f*x)**4/8 + 3*b*d**3*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + 3*b*d**3*x*cos(e + f*x)**4/8 - 5*b*d**3*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 3*b*d**3*sin(e + f*x)*cos(e + f*x)**3/(8*f), Ne(f, 0)), (x*(a + b*sin(e))*(c + d*sin(e))**3, True))","A",0
672,1,199,0,0.829623," ","integrate((a+b*sin(f*x+e))*(c+d*sin(f*x+e))**2,x)","\begin{cases} a c^{2} x - \frac{2 a c d \cos{\left(e + f x \right)}}{f} + \frac{a d^{2} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{a d^{2} x \cos^{2}{\left(e + f x \right)}}{2} - \frac{a d^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{b c^{2} \cos{\left(e + f x \right)}}{f} + b c d x \sin^{2}{\left(e + f x \right)} + b c d x \cos^{2}{\left(e + f x \right)} - \frac{b c d \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{b d^{2} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{2 b 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} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**2*x - 2*a*c*d*cos(e + f*x)/f + a*d**2*x*sin(e + f*x)**2/2 + a*d**2*x*cos(e + f*x)**2/2 - a*d**2*sin(e + f*x)*cos(e + f*x)/(2*f) - b*c**2*cos(e + f*x)/f + b*c*d*x*sin(e + f*x)**2 + b*c*d*x*cos(e + f*x)**2 - b*c*d*sin(e + f*x)*cos(e + f*x)/f - b*d**2*sin(e + f*x)**2*cos(e + f*x)/f - 2*b*d**2*cos(e + f*x)**3/(3*f), Ne(f, 0)), (x*(a + b*sin(e))*(c + d*sin(e))**2, True))","A",0
673,1,94,0,0.324172," ","integrate((a+b*sin(f*x+e))*(c+d*sin(f*x+e)),x)","\begin{cases} a c x - \frac{a d \cos{\left(e + f x \right)}}{f} - \frac{b c \cos{\left(e + f x \right)}}{f} + \frac{b d x \sin^{2}{\left(e + f x \right)}}{2} + \frac{b d x \cos^{2}{\left(e + f x \right)}}{2} - \frac{b d \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} & \text{for}\: f \neq 0 \\x \left(a + b \sin{\left(e \right)}\right) \left(c + d \sin{\left(e \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c*x - a*d*cos(e + f*x)/f - b*c*cos(e + f*x)/f + b*d*x*sin(e + f*x)**2/2 + b*d*x*cos(e + f*x)**2/2 - b*d*sin(e + f*x)*cos(e + f*x)/(2*f), Ne(f, 0)), (x*(a + b*sin(e))*(c + d*sin(e)), True))","A",0
674,1,19,0,0.141862," ","integrate(a+b*sin(f*x+e),x)","a x + b \left(\begin{cases} - \frac{\cos{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \sin{\left(e \right)} & \text{otherwise} \end{cases}\right)"," ",0,"a*x + b*Piecewise((-cos(e + f*x)/f, Ne(f, 0)), (x*sin(e), True))","A",0
675,1,537,0,85.453429," ","integrate((a+b*sin(f*x+e))/(c+d*sin(f*x+e)),x)","\begin{cases} \frac{\tilde{\infty} x \left(a + b \sin{\left(e \right)}\right)}{\sin{\left(e \right)}} & \text{for}\: c = 0 \wedge d = 0 \wedge f = 0 \\\frac{2 a d \sqrt{d^{2}}}{d^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - f \left(d^{2}\right)^{\frac{3}{2}}} + \frac{b d^{2} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{d^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - f \left(d^{2}\right)^{\frac{3}{2}}} + \frac{2 b d^{2}}{d^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - f \left(d^{2}\right)^{\frac{3}{2}}} - \frac{b d f x \sqrt{d^{2}}}{d^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - f \left(d^{2}\right)^{\frac{3}{2}}} & \text{for}\: c = - \sqrt{d^{2}} \\- \frac{2 a d \sqrt{d^{2}}}{d^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + f \left(d^{2}\right)^{\frac{3}{2}}} + \frac{b d^{2} f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{d^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + f \left(d^{2}\right)^{\frac{3}{2}}} + \frac{2 b d^{2}}{d^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + f \left(d^{2}\right)^{\frac{3}{2}}} + \frac{b d f x \sqrt{d^{2}}}{d^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + f \left(d^{2}\right)^{\frac{3}{2}}} & \text{for}\: c = \sqrt{d^{2}} \\\frac{\frac{a \log{\left(\tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} \right)}}{f} + b x}{d} & \text{for}\: c = 0 \\\frac{a x - \frac{b \cos{\left(e + f x \right)}}{f}}{c} & \text{for}\: d = 0 \\\frac{x \left(a + b \sin{\left(e \right)}\right)}{c + d \sin{\left(e \right)}} & \text{for}\: f = 0 \\\frac{a \log{\left(\tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + \frac{d}{c} - \frac{\sqrt{- c^{2} + d^{2}}}{c} \right)}}{f \sqrt{- c^{2} + d^{2}}} - \frac{a \log{\left(\tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + \frac{d}{c} + \frac{\sqrt{- c^{2} + d^{2}}}{c} \right)}}{f \sqrt{- c^{2} + d^{2}}} - \frac{b c \log{\left(\tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + \frac{d}{c} - \frac{\sqrt{- c^{2} + d^{2}}}{c} \right)}}{d f \sqrt{- c^{2} + d^{2}}} + \frac{b c \log{\left(\tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + \frac{d}{c} + \frac{\sqrt{- c^{2} + d^{2}}}{c} \right)}}{d f \sqrt{- c^{2} + d^{2}}} + \frac{b x}{d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(a + b*sin(e))/sin(e), Eq(c, 0) & Eq(d, 0) & Eq(f, 0)), (2*a*d*sqrt(d**2)/(d**3*f*tan(e/2 + f*x/2) - f*(d**2)**(3/2)) + b*d**2*f*x*tan(e/2 + f*x/2)/(d**3*f*tan(e/2 + f*x/2) - f*(d**2)**(3/2)) + 2*b*d**2/(d**3*f*tan(e/2 + f*x/2) - f*(d**2)**(3/2)) - b*d*f*x*sqrt(d**2)/(d**3*f*tan(e/2 + f*x/2) - f*(d**2)**(3/2)), Eq(c, -sqrt(d**2))), (-2*a*d*sqrt(d**2)/(d**3*f*tan(e/2 + f*x/2) + f*(d**2)**(3/2)) + b*d**2*f*x*tan(e/2 + f*x/2)/(d**3*f*tan(e/2 + f*x/2) + f*(d**2)**(3/2)) + 2*b*d**2/(d**3*f*tan(e/2 + f*x/2) + f*(d**2)**(3/2)) + b*d*f*x*sqrt(d**2)/(d**3*f*tan(e/2 + f*x/2) + f*(d**2)**(3/2)), Eq(c, sqrt(d**2))), ((a*log(tan(e/2 + f*x/2))/f + b*x)/d, Eq(c, 0)), ((a*x - b*cos(e + f*x)/f)/c, Eq(d, 0)), (x*(a + b*sin(e))/(c + d*sin(e)), Eq(f, 0)), (a*log(tan(e/2 + f*x/2) + d/c - sqrt(-c**2 + d**2)/c)/(f*sqrt(-c**2 + d**2)) - a*log(tan(e/2 + f*x/2) + d/c + sqrt(-c**2 + d**2)/c)/(f*sqrt(-c**2 + d**2)) - b*c*log(tan(e/2 + f*x/2) + d/c - sqrt(-c**2 + d**2)/c)/(d*f*sqrt(-c**2 + d**2)) + b*c*log(tan(e/2 + f*x/2) + d/c + sqrt(-c**2 + d**2)/c)/(d*f*sqrt(-c**2 + d**2)) + b*x/d, True))","A",0
676,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))/(c+d*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
677,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))/(c+d*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
678,1,729,0,4.329453," ","integrate((a+b*sin(f*x+e))**2*(c+d*sin(f*x+e))**3,x)","\begin{cases} a^{2} c^{3} x - \frac{3 a^{2} c^{2} d \cos{\left(e + f x \right)}}{f} + \frac{3 a^{2} c d^{2} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{3 a^{2} c d^{2} x \cos^{2}{\left(e + f x \right)}}{2} - \frac{3 a^{2} c d^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{a^{2} d^{3} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{2 a^{2} d^{3} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{2 a b c^{3} \cos{\left(e + f x \right)}}{f} + 3 a b c^{2} d x \sin^{2}{\left(e + f x \right)} + 3 a b c^{2} d x \cos^{2}{\left(e + f x \right)} - \frac{3 a b c^{2} d \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{6 a b c d^{2} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{4 a b c d^{2} \cos^{3}{\left(e + f x \right)}}{f} + \frac{3 a b d^{3} x \sin^{4}{\left(e + f x \right)}}{4} + \frac{3 a b d^{3} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{2} + \frac{3 a b d^{3} x \cos^{4}{\left(e + f x \right)}}{4} - \frac{5 a b d^{3} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{4 f} - \frac{3 a b d^{3} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{4 f} + \frac{b^{2} c^{3} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{b^{2} c^{3} x \cos^{2}{\left(e + f x \right)}}{2} - \frac{b^{2} c^{3} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{3 b^{2} c^{2} d \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{2 b^{2} c^{2} d \cos^{3}{\left(e + f x \right)}}{f} + \frac{9 b^{2} c d^{2} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{9 b^{2} c d^{2} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{9 b^{2} c d^{2} x \cos^{4}{\left(e + f x \right)}}{8} - \frac{15 b^{2} c d^{2} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{9 b^{2} c d^{2} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{b^{2} d^{3} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{4 b^{2} d^{3} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{8 b^{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)^{2} \left(c + d \sin{\left(e \right)}\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c**3*x - 3*a**2*c**2*d*cos(e + f*x)/f + 3*a**2*c*d**2*x*sin(e + f*x)**2/2 + 3*a**2*c*d**2*x*cos(e + f*x)**2/2 - 3*a**2*c*d**2*sin(e + f*x)*cos(e + f*x)/(2*f) - a**2*d**3*sin(e + f*x)**2*cos(e + f*x)/f - 2*a**2*d**3*cos(e + f*x)**3/(3*f) - 2*a*b*c**3*cos(e + f*x)/f + 3*a*b*c**2*d*x*sin(e + f*x)**2 + 3*a*b*c**2*d*x*cos(e + f*x)**2 - 3*a*b*c**2*d*sin(e + f*x)*cos(e + f*x)/f - 6*a*b*c*d**2*sin(e + f*x)**2*cos(e + f*x)/f - 4*a*b*c*d**2*cos(e + f*x)**3/f + 3*a*b*d**3*x*sin(e + f*x)**4/4 + 3*a*b*d**3*x*sin(e + f*x)**2*cos(e + f*x)**2/2 + 3*a*b*d**3*x*cos(e + f*x)**4/4 - 5*a*b*d**3*sin(e + f*x)**3*cos(e + f*x)/(4*f) - 3*a*b*d**3*sin(e + f*x)*cos(e + f*x)**3/(4*f) + b**2*c**3*x*sin(e + f*x)**2/2 + b**2*c**3*x*cos(e + f*x)**2/2 - b**2*c**3*sin(e + f*x)*cos(e + f*x)/(2*f) - 3*b**2*c**2*d*sin(e + f*x)**2*cos(e + f*x)/f - 2*b**2*c**2*d*cos(e + f*x)**3/f + 9*b**2*c*d**2*x*sin(e + f*x)**4/8 + 9*b**2*c*d**2*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + 9*b**2*c*d**2*x*cos(e + f*x)**4/8 - 15*b**2*c*d**2*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 9*b**2*c*d**2*sin(e + f*x)*cos(e + f*x)**3/(8*f) - b**2*d**3*sin(e + f*x)**4*cos(e + f*x)/f - 4*b**2*d**3*sin(e + f*x)**2*cos(e + f*x)**3/(3*f) - 8*b**2*d**3*cos(e + f*x)**5/(15*f), Ne(f, 0)), (x*(a + b*sin(e))**2*(c + d*sin(e))**3, True))","A",0
679,1,459,0,1.942729," ","integrate((a+b*sin(f*x+e))**2*(c+d*sin(f*x+e))**2,x)","\begin{cases} a^{2} c^{2} x - \frac{2 a^{2} c d \cos{\left(e + f x \right)}}{f} + \frac{a^{2} d^{2} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{a^{2} d^{2} x \cos^{2}{\left(e + f x \right)}}{2} - \frac{a^{2} d^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{2 a b c^{2} \cos{\left(e + f x \right)}}{f} + 2 a b c d x \sin^{2}{\left(e + f x \right)} + 2 a b c d x \cos^{2}{\left(e + f x \right)} - \frac{2 a b c d \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{2 a b d^{2} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{4 a b d^{2} \cos^{3}{\left(e + f x \right)}}{3 f} + \frac{b^{2} c^{2} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{b^{2} c^{2} x \cos^{2}{\left(e + f x \right)}}{2} - \frac{b^{2} c^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{2 b^{2} c d \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{4 b^{2} c d \cos^{3}{\left(e + f x \right)}}{3 f} + \frac{3 b^{2} d^{2} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{3 b^{2} d^{2} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{3 b^{2} d^{2} x \cos^{4}{\left(e + f x \right)}}{8} - \frac{5 b^{2} d^{2} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{3 b^{2} d^{2} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} & \text{for}\: f \neq 0 \\x \left(a + b \sin{\left(e \right)}\right)^{2} \left(c + d \sin{\left(e \right)}\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c**2*x - 2*a**2*c*d*cos(e + f*x)/f + a**2*d**2*x*sin(e + f*x)**2/2 + a**2*d**2*x*cos(e + f*x)**2/2 - a**2*d**2*sin(e + f*x)*cos(e + f*x)/(2*f) - 2*a*b*c**2*cos(e + f*x)/f + 2*a*b*c*d*x*sin(e + f*x)**2 + 2*a*b*c*d*x*cos(e + f*x)**2 - 2*a*b*c*d*sin(e + f*x)*cos(e + f*x)/f - 2*a*b*d**2*sin(e + f*x)**2*cos(e + f*x)/f - 4*a*b*d**2*cos(e + f*x)**3/(3*f) + b**2*c**2*x*sin(e + f*x)**2/2 + b**2*c**2*x*cos(e + f*x)**2/2 - b**2*c**2*sin(e + f*x)*cos(e + f*x)/(2*f) - 2*b**2*c*d*sin(e + f*x)**2*cos(e + f*x)/f - 4*b**2*c*d*cos(e + f*x)**3/(3*f) + 3*b**2*d**2*x*sin(e + f*x)**4/8 + 3*b**2*d**2*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + 3*b**2*d**2*x*cos(e + f*x)**4/8 - 5*b**2*d**2*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 3*b**2*d**2*sin(e + f*x)*cos(e + f*x)**3/(8*f), Ne(f, 0)), (x*(a + b*sin(e))**2*(c + d*sin(e))**2, True))","A",0
680,1,199,0,0.831264," ","integrate((a+b*sin(f*x+e))**2*(c+d*sin(f*x+e)),x)","\begin{cases} a^{2} c x - \frac{a^{2} d \cos{\left(e + f x \right)}}{f} - \frac{2 a b c \cos{\left(e + f x \right)}}{f} + a b d x \sin^{2}{\left(e + f x \right)} + a b d x \cos^{2}{\left(e + f x \right)} - \frac{a b d \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{b^{2} c x \sin^{2}{\left(e + f x \right)}}{2} + \frac{b^{2} c x \cos^{2}{\left(e + f x \right)}}{2} - \frac{b^{2} c \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{b^{2} d \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{2 b^{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)^{2} \left(c + d \sin{\left(e \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c*x - a**2*d*cos(e + f*x)/f - 2*a*b*c*cos(e + f*x)/f + a*b*d*x*sin(e + f*x)**2 + a*b*d*x*cos(e + f*x)**2 - a*b*d*sin(e + f*x)*cos(e + f*x)/f + b**2*c*x*sin(e + f*x)**2/2 + b**2*c*x*cos(e + f*x)**2/2 - b**2*c*sin(e + f*x)*cos(e + f*x)/(2*f) - b**2*d*sin(e + f*x)**2*cos(e + f*x)/f - 2*b**2*d*cos(e + f*x)**3/(3*f), Ne(f, 0)), (x*(a + b*sin(e))**2*(c + d*sin(e)), True))","A",0
681,1,78,0,0.313087," ","integrate((a+b*sin(f*x+e))**2,x)","\begin{cases} a^{2} x - \frac{2 a b \cos{\left(e + f x \right)}}{f} + \frac{b^{2} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{b^{2} x \cos^{2}{\left(e + f x \right)}}{2} - \frac{b^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} & \text{for}\: f \neq 0 \\x \left(a + b \sin{\left(e \right)}\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x - 2*a*b*cos(e + f*x)/f + b**2*x*sin(e + f*x)**2/2 + b**2*x*cos(e + f*x)**2/2 - b**2*sin(e + f*x)*cos(e + f*x)/(2*f), Ne(f, 0)), (x*(a + b*sin(e))**2, True))","A",0
682,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**2/(c+d*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
683,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**2/(c+d*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
684,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**2/(c+d*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
685,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**2/(c+d*sin(f*x+e))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
686,1,1217,0,8.027092," ","integrate((a+b*sin(f*x+e))**3*(c+d*sin(f*x+e))**3,x)","\begin{cases} a^{3} c^{3} x - \frac{3 a^{3} c^{2} d \cos{\left(e + f x \right)}}{f} + \frac{3 a^{3} c d^{2} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{3 a^{3} c d^{2} x \cos^{2}{\left(e + f x \right)}}{2} - \frac{3 a^{3} c d^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{a^{3} d^{3} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{2 a^{3} d^{3} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{3 a^{2} b c^{3} \cos{\left(e + f x \right)}}{f} + \frac{9 a^{2} b c^{2} d x \sin^{2}{\left(e + f x \right)}}{2} + \frac{9 a^{2} b c^{2} d x \cos^{2}{\left(e + f x \right)}}{2} - \frac{9 a^{2} b c^{2} d \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{9 a^{2} b c d^{2} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{6 a^{2} b c d^{2} \cos^{3}{\left(e + f x \right)}}{f} + \frac{9 a^{2} b d^{3} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{9 a^{2} b d^{3} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{9 a^{2} b d^{3} x \cos^{4}{\left(e + f x \right)}}{8} - \frac{15 a^{2} b d^{3} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{9 a^{2} b d^{3} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} + \frac{3 a b^{2} c^{3} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{3 a b^{2} c^{3} x \cos^{2}{\left(e + f x \right)}}{2} - \frac{3 a b^{2} c^{3} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{9 a b^{2} c^{2} d \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{6 a b^{2} c^{2} d \cos^{3}{\left(e + f x \right)}}{f} + \frac{27 a b^{2} c d^{2} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{27 a b^{2} c d^{2} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{27 a b^{2} c d^{2} x \cos^{4}{\left(e + f x \right)}}{8} - \frac{45 a b^{2} c d^{2} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{27 a b^{2} c d^{2} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{3 a b^{2} d^{3} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{4 a b^{2} d^{3} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{f} - \frac{8 a b^{2} d^{3} \cos^{5}{\left(e + f x \right)}}{5 f} - \frac{b^{3} c^{3} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{2 b^{3} c^{3} \cos^{3}{\left(e + f x \right)}}{3 f} + \frac{9 b^{3} c^{2} d x \sin^{4}{\left(e + f x \right)}}{8} + \frac{9 b^{3} c^{2} d x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{9 b^{3} c^{2} d x \cos^{4}{\left(e + f x \right)}}{8} - \frac{15 b^{3} c^{2} d \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{9 b^{3} c^{2} d \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{3 b^{3} c d^{2} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{4 b^{3} c d^{2} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{f} - \frac{8 b^{3} c d^{2} \cos^{5}{\left(e + f x \right)}}{5 f} + \frac{5 b^{3} d^{3} x \sin^{6}{\left(e + f x \right)}}{16} + \frac{15 b^{3} d^{3} x \sin^{4}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{16} + \frac{15 b^{3} d^{3} x \sin^{2}{\left(e + f x \right)} \cos^{4}{\left(e + f x \right)}}{16} + \frac{5 b^{3} d^{3} x \cos^{6}{\left(e + f x \right)}}{16} - \frac{11 b^{3} d^{3} \sin^{5}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{16 f} - \frac{5 b^{3} d^{3} \sin^{3}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{6 f} - \frac{5 b^{3} d^{3} \sin{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{16 f} & \text{for}\: f \neq 0 \\x \left(a + b \sin{\left(e \right)}\right)^{3} \left(c + d \sin{\left(e \right)}\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*c**3*x - 3*a**3*c**2*d*cos(e + f*x)/f + 3*a**3*c*d**2*x*sin(e + f*x)**2/2 + 3*a**3*c*d**2*x*cos(e + f*x)**2/2 - 3*a**3*c*d**2*sin(e + f*x)*cos(e + f*x)/(2*f) - a**3*d**3*sin(e + f*x)**2*cos(e + f*x)/f - 2*a**3*d**3*cos(e + f*x)**3/(3*f) - 3*a**2*b*c**3*cos(e + f*x)/f + 9*a**2*b*c**2*d*x*sin(e + f*x)**2/2 + 9*a**2*b*c**2*d*x*cos(e + f*x)**2/2 - 9*a**2*b*c**2*d*sin(e + f*x)*cos(e + f*x)/(2*f) - 9*a**2*b*c*d**2*sin(e + f*x)**2*cos(e + f*x)/f - 6*a**2*b*c*d**2*cos(e + f*x)**3/f + 9*a**2*b*d**3*x*sin(e + f*x)**4/8 + 9*a**2*b*d**3*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + 9*a**2*b*d**3*x*cos(e + f*x)**4/8 - 15*a**2*b*d**3*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 9*a**2*b*d**3*sin(e + f*x)*cos(e + f*x)**3/(8*f) + 3*a*b**2*c**3*x*sin(e + f*x)**2/2 + 3*a*b**2*c**3*x*cos(e + f*x)**2/2 - 3*a*b**2*c**3*sin(e + f*x)*cos(e + f*x)/(2*f) - 9*a*b**2*c**2*d*sin(e + f*x)**2*cos(e + f*x)/f - 6*a*b**2*c**2*d*cos(e + f*x)**3/f + 27*a*b**2*c*d**2*x*sin(e + f*x)**4/8 + 27*a*b**2*c*d**2*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + 27*a*b**2*c*d**2*x*cos(e + f*x)**4/8 - 45*a*b**2*c*d**2*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 27*a*b**2*c*d**2*sin(e + f*x)*cos(e + f*x)**3/(8*f) - 3*a*b**2*d**3*sin(e + f*x)**4*cos(e + f*x)/f - 4*a*b**2*d**3*sin(e + f*x)**2*cos(e + f*x)**3/f - 8*a*b**2*d**3*cos(e + f*x)**5/(5*f) - b**3*c**3*sin(e + f*x)**2*cos(e + f*x)/f - 2*b**3*c**3*cos(e + f*x)**3/(3*f) + 9*b**3*c**2*d*x*sin(e + f*x)**4/8 + 9*b**3*c**2*d*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + 9*b**3*c**2*d*x*cos(e + f*x)**4/8 - 15*b**3*c**2*d*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 9*b**3*c**2*d*sin(e + f*x)*cos(e + f*x)**3/(8*f) - 3*b**3*c*d**2*sin(e + f*x)**4*cos(e + f*x)/f - 4*b**3*c*d**2*sin(e + f*x)**2*cos(e + f*x)**3/f - 8*b**3*c*d**2*cos(e + f*x)**5/(5*f) + 5*b**3*d**3*x*sin(e + f*x)**6/16 + 15*b**3*d**3*x*sin(e + f*x)**4*cos(e + f*x)**2/16 + 15*b**3*d**3*x*sin(e + f*x)**2*cos(e + f*x)**4/16 + 5*b**3*d**3*x*cos(e + f*x)**6/16 - 11*b**3*d**3*sin(e + f*x)**5*cos(e + f*x)/(16*f) - 5*b**3*d**3*sin(e + f*x)**3*cos(e + f*x)**3/(6*f) - 5*b**3*d**3*sin(e + f*x)*cos(e + f*x)**5/(16*f), Ne(f, 0)), (x*(a + b*sin(e))**3*(c + d*sin(e))**3, True))","A",0
687,1,729,0,4.292029," ","integrate((a+b*sin(f*x+e))**3*(c+d*sin(f*x+e))**2,x)","\begin{cases} a^{3} c^{2} x - \frac{2 a^{3} c d \cos{\left(e + f x \right)}}{f} + \frac{a^{3} d^{2} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{a^{3} d^{2} x \cos^{2}{\left(e + f x \right)}}{2} - \frac{a^{3} d^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{3 a^{2} b c^{2} \cos{\left(e + f x \right)}}{f} + 3 a^{2} b c d x \sin^{2}{\left(e + f x \right)} + 3 a^{2} b c d x \cos^{2}{\left(e + f x \right)} - \frac{3 a^{2} b c d \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{3 a^{2} b d^{2} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{2 a^{2} b d^{2} \cos^{3}{\left(e + f x \right)}}{f} + \frac{3 a b^{2} c^{2} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{3 a b^{2} c^{2} x \cos^{2}{\left(e + f x \right)}}{2} - \frac{3 a b^{2} c^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{6 a b^{2} c d \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{4 a b^{2} c d \cos^{3}{\left(e + f x \right)}}{f} + \frac{9 a b^{2} d^{2} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{9 a b^{2} d^{2} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{9 a b^{2} d^{2} x \cos^{4}{\left(e + f x \right)}}{8} - \frac{15 a b^{2} d^{2} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{9 a b^{2} d^{2} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{b^{3} c^{2} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{2 b^{3} c^{2} \cos^{3}{\left(e + f x \right)}}{3 f} + \frac{3 b^{3} c d x \sin^{4}{\left(e + f x \right)}}{4} + \frac{3 b^{3} c d x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{2} + \frac{3 b^{3} c d x \cos^{4}{\left(e + f x \right)}}{4} - \frac{5 b^{3} c d \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{4 f} - \frac{3 b^{3} c d \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{4 f} - \frac{b^{3} d^{2} \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{4 b^{3} d^{2} \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{8 b^{3} d^{2} \cos^{5}{\left(e + f x \right)}}{15 f} & \text{for}\: f \neq 0 \\x \left(a + b \sin{\left(e \right)}\right)^{3} \left(c + d \sin{\left(e \right)}\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*c**2*x - 2*a**3*c*d*cos(e + f*x)/f + a**3*d**2*x*sin(e + f*x)**2/2 + a**3*d**2*x*cos(e + f*x)**2/2 - a**3*d**2*sin(e + f*x)*cos(e + f*x)/(2*f) - 3*a**2*b*c**2*cos(e + f*x)/f + 3*a**2*b*c*d*x*sin(e + f*x)**2 + 3*a**2*b*c*d*x*cos(e + f*x)**2 - 3*a**2*b*c*d*sin(e + f*x)*cos(e + f*x)/f - 3*a**2*b*d**2*sin(e + f*x)**2*cos(e + f*x)/f - 2*a**2*b*d**2*cos(e + f*x)**3/f + 3*a*b**2*c**2*x*sin(e + f*x)**2/2 + 3*a*b**2*c**2*x*cos(e + f*x)**2/2 - 3*a*b**2*c**2*sin(e + f*x)*cos(e + f*x)/(2*f) - 6*a*b**2*c*d*sin(e + f*x)**2*cos(e + f*x)/f - 4*a*b**2*c*d*cos(e + f*x)**3/f + 9*a*b**2*d**2*x*sin(e + f*x)**4/8 + 9*a*b**2*d**2*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + 9*a*b**2*d**2*x*cos(e + f*x)**4/8 - 15*a*b**2*d**2*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 9*a*b**2*d**2*sin(e + f*x)*cos(e + f*x)**3/(8*f) - b**3*c**2*sin(e + f*x)**2*cos(e + f*x)/f - 2*b**3*c**2*cos(e + f*x)**3/(3*f) + 3*b**3*c*d*x*sin(e + f*x)**4/4 + 3*b**3*c*d*x*sin(e + f*x)**2*cos(e + f*x)**2/2 + 3*b**3*c*d*x*cos(e + f*x)**4/4 - 5*b**3*c*d*sin(e + f*x)**3*cos(e + f*x)/(4*f) - 3*b**3*c*d*sin(e + f*x)*cos(e + f*x)**3/(4*f) - b**3*d**2*sin(e + f*x)**4*cos(e + f*x)/f - 4*b**3*d**2*sin(e + f*x)**2*cos(e + f*x)**3/(3*f) - 8*b**3*d**2*cos(e + f*x)**5/(15*f), Ne(f, 0)), (x*(a + b*sin(e))**3*(c + d*sin(e))**2, True))","A",0
688,1,386,0,1.872319," ","integrate((a+b*sin(f*x+e))**3*(c+d*sin(f*x+e)),x)","\begin{cases} a^{3} c x - \frac{a^{3} d \cos{\left(e + f x \right)}}{f} - \frac{3 a^{2} b c \cos{\left(e + f x \right)}}{f} + \frac{3 a^{2} b d x \sin^{2}{\left(e + f x \right)}}{2} + \frac{3 a^{2} b d x \cos^{2}{\left(e + f x \right)}}{2} - \frac{3 a^{2} b d \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} + \frac{3 a b^{2} c x \sin^{2}{\left(e + f x \right)}}{2} + \frac{3 a b^{2} c x \cos^{2}{\left(e + f x \right)}}{2} - \frac{3 a b^{2} c \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{3 a b^{2} d \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{2 a b^{2} d \cos^{3}{\left(e + f x \right)}}{f} - \frac{b^{3} c \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{2 b^{3} c \cos^{3}{\left(e + f x \right)}}{3 f} + \frac{3 b^{3} d x \sin^{4}{\left(e + f x \right)}}{8} + \frac{3 b^{3} d x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{3 b^{3} d x \cos^{4}{\left(e + f x \right)}}{8} - \frac{5 b^{3} d \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{3 b^{3} d \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} & \text{for}\: f \neq 0 \\x \left(a + b \sin{\left(e \right)}\right)^{3} \left(c + d \sin{\left(e \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*c*x - a**3*d*cos(e + f*x)/f - 3*a**2*b*c*cos(e + f*x)/f + 3*a**2*b*d*x*sin(e + f*x)**2/2 + 3*a**2*b*d*x*cos(e + f*x)**2/2 - 3*a**2*b*d*sin(e + f*x)*cos(e + f*x)/(2*f) + 3*a*b**2*c*x*sin(e + f*x)**2/2 + 3*a*b**2*c*x*cos(e + f*x)**2/2 - 3*a*b**2*c*sin(e + f*x)*cos(e + f*x)/(2*f) - 3*a*b**2*d*sin(e + f*x)**2*cos(e + f*x)/f - 2*a*b**2*d*cos(e + f*x)**3/f - b**3*c*sin(e + f*x)**2*cos(e + f*x)/f - 2*b**3*c*cos(e + f*x)**3/(3*f) + 3*b**3*d*x*sin(e + f*x)**4/8 + 3*b**3*d*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + 3*b**3*d*x*cos(e + f*x)**4/8 - 5*b**3*d*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 3*b**3*d*sin(e + f*x)*cos(e + f*x)**3/(8*f), Ne(f, 0)), (x*(a + b*sin(e))**3*(c + d*sin(e)), True))","A",0
689,1,128,0,0.673146," ","integrate((a+b*sin(f*x+e))**3,x)","\begin{cases} a^{3} x - \frac{3 a^{2} b \cos{\left(e + f x \right)}}{f} + \frac{3 a b^{2} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{3 a b^{2} x \cos^{2}{\left(e + f x \right)}}{2} - \frac{3 a b^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{b^{3} \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} - \frac{2 b^{3} \cos^{3}{\left(e + f x \right)}}{3 f} & \text{for}\: f \neq 0 \\x \left(a + b \sin{\left(e \right)}\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*x - 3*a**2*b*cos(e + f*x)/f + 3*a*b**2*x*sin(e + f*x)**2/2 + 3*a*b**2*x*cos(e + f*x)**2/2 - 3*a*b**2*sin(e + f*x)*cos(e + f*x)/(2*f) - b**3*sin(e + f*x)**2*cos(e + f*x)/f - 2*b**3*cos(e + f*x)**3/(3*f), Ne(f, 0)), (x*(a + b*sin(e))**3, True))","A",0
690,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**3/(c+d*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
691,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**3/(c+d*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
692,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**3/(c+d*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
693,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**3/(c+d*sin(f*x+e))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
694,1,87,0,50.124440," ","integrate((b*B/a+B*sin(x))/(a+b*sin(x)),x)","\begin{cases} \frac{B x}{b} + \frac{B \sqrt{- a^{2} + b^{2}} \log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{b}{a} - \frac{\sqrt{- a^{2} + b^{2}}}{a} \right)}}{a b} - \frac{B \sqrt{- a^{2} + b^{2}} \log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{b}{a} + \frac{\sqrt{- a^{2} + b^{2}}}{a} \right)}}{a b} & \text{for}\: b \neq 0 \\- \frac{B \cos{\left(x \right)}}{a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((B*x/b + B*sqrt(-a**2 + b**2)*log(tan(x/2) + b/a - sqrt(-a**2 + b**2)/a)/(a*b) - B*sqrt(-a**2 + b**2)*log(tan(x/2) + b/a + sqrt(-a**2 + b**2)/a)/(a*b), Ne(b, 0)), (-B*cos(x)/a, True))","A",0
695,1,3,0,0.332328," ","integrate((a*B/b+B*sin(x))/(a+b*sin(x)),x)","\frac{B x}{b}"," ",0,"B*x/b","A",0
696,-1,0,0,0.000000," ","integrate((a+b*sin(x))/(b+a*sin(x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
697,1,42,0,0.878652," ","integrate((2-sin(x))/(2+sin(x)),x)","- x + \frac{8 \sqrt{3} \left(\operatorname{atan}{\left(\frac{2 \sqrt{3} \tan{\left(\frac{x}{2} \right)}}{3} + \frac{\sqrt{3}}{3} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{3}"," ",0,"-x + 8*sqrt(3)*(atan(2*sqrt(3)*tan(x/2)/3 + sqrt(3)/3) + pi*floor((x/2 - pi/2)/pi))/3","A",0
698,-1,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**4/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
699,-1,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**3/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
700,-1,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**2/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
701,1,537,0,84.853170," ","integrate((c+d*sin(f*x+e))/(a+b*sin(f*x+e)),x)","\begin{cases} \frac{\tilde{\infty} x \left(c + d \sin{\left(e \right)}\right)}{\sin{\left(e \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge f = 0 \\\frac{c x - \frac{d \cos{\left(e + f x \right)}}{f}}{a} & \text{for}\: b = 0 \\\frac{b^{2} d f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{b^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - f \left(b^{2}\right)^{\frac{3}{2}}} + \frac{2 b^{2} d}{b^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - f \left(b^{2}\right)^{\frac{3}{2}}} + \frac{2 b c \sqrt{b^{2}}}{b^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - f \left(b^{2}\right)^{\frac{3}{2}}} - \frac{b d f x \sqrt{b^{2}}}{b^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - f \left(b^{2}\right)^{\frac{3}{2}}} & \text{for}\: a = - \sqrt{b^{2}} \\\frac{b^{2} d f x \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{b^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + f \left(b^{2}\right)^{\frac{3}{2}}} + \frac{2 b^{2} d}{b^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + f \left(b^{2}\right)^{\frac{3}{2}}} - \frac{2 b c \sqrt{b^{2}}}{b^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + f \left(b^{2}\right)^{\frac{3}{2}}} + \frac{b d f x \sqrt{b^{2}}}{b^{3} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + f \left(b^{2}\right)^{\frac{3}{2}}} & \text{for}\: a = \sqrt{b^{2}} \\\frac{\frac{c \log{\left(\tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} \right)}}{f} + d x}{b} & \text{for}\: a = 0 \\\frac{x \left(c + d \sin{\left(e \right)}\right)}{a + b \sin{\left(e \right)}} & \text{for}\: f = 0 \\- \frac{a d \log{\left(\tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + \frac{b}{a} - \frac{\sqrt{- a^{2} + b^{2}}}{a} \right)}}{b f \sqrt{- a^{2} + b^{2}}} + \frac{a d \log{\left(\tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + \frac{b}{a} + \frac{\sqrt{- a^{2} + b^{2}}}{a} \right)}}{b f \sqrt{- a^{2} + b^{2}}} + \frac{c \log{\left(\tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + \frac{b}{a} - \frac{\sqrt{- a^{2} + b^{2}}}{a} \right)}}{f \sqrt{- a^{2} + b^{2}}} - \frac{c \log{\left(\tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + \frac{b}{a} + \frac{\sqrt{- a^{2} + b^{2}}}{a} \right)}}{f \sqrt{- a^{2} + b^{2}}} + \frac{d x}{b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(c + d*sin(e))/sin(e), Eq(a, 0) & Eq(b, 0) & Eq(f, 0)), ((c*x - d*cos(e + f*x)/f)/a, Eq(b, 0)), (b**2*d*f*x*tan(e/2 + f*x/2)/(b**3*f*tan(e/2 + f*x/2) - f*(b**2)**(3/2)) + 2*b**2*d/(b**3*f*tan(e/2 + f*x/2) - f*(b**2)**(3/2)) + 2*b*c*sqrt(b**2)/(b**3*f*tan(e/2 + f*x/2) - f*(b**2)**(3/2)) - b*d*f*x*sqrt(b**2)/(b**3*f*tan(e/2 + f*x/2) - f*(b**2)**(3/2)), Eq(a, -sqrt(b**2))), (b**2*d*f*x*tan(e/2 + f*x/2)/(b**3*f*tan(e/2 + f*x/2) + f*(b**2)**(3/2)) + 2*b**2*d/(b**3*f*tan(e/2 + f*x/2) + f*(b**2)**(3/2)) - 2*b*c*sqrt(b**2)/(b**3*f*tan(e/2 + f*x/2) + f*(b**2)**(3/2)) + b*d*f*x*sqrt(b**2)/(b**3*f*tan(e/2 + f*x/2) + f*(b**2)**(3/2)), Eq(a, sqrt(b**2))), ((c*log(tan(e/2 + f*x/2))/f + d*x)/b, Eq(a, 0)), (x*(c + d*sin(e))/(a + b*sin(e)), Eq(f, 0)), (-a*d*log(tan(e/2 + f*x/2) + b/a - sqrt(-a**2 + b**2)/a)/(b*f*sqrt(-a**2 + b**2)) + a*d*log(tan(e/2 + f*x/2) + b/a + sqrt(-a**2 + b**2)/a)/(b*f*sqrt(-a**2 + b**2)) + c*log(tan(e/2 + f*x/2) + b/a - sqrt(-a**2 + b**2)/a)/(f*sqrt(-a**2 + b**2)) - c*log(tan(e/2 + f*x/2) + b/a + sqrt(-a**2 + b**2)/a)/(f*sqrt(-a**2 + b**2)) + d*x/b, True))","A",0
702,1,177,0,10.630561," ","integrate(1/(a+b*sin(f*x+e)),x)","\begin{cases} \frac{2 \sqrt{b^{2}}}{b^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} - b f \sqrt{b^{2}}} & \text{for}\: a = - \sqrt{b^{2}} \\- \frac{2 \sqrt{b^{2}}}{b^{2} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + b f \sqrt{b^{2}}} & \text{for}\: a = \sqrt{b^{2}} \\\frac{\log{\left(\tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} \right)}}{b f} & \text{for}\: a = 0 \\\frac{x}{a + b \sin{\left(e \right)}} & \text{for}\: f = 0 \\\frac{\log{\left(\tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + \frac{b}{a} - \frac{\sqrt{- a^{2} + b^{2}}}{a} \right)}}{f \sqrt{- a^{2} + b^{2}}} - \frac{\log{\left(\tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + \frac{b}{a} + \frac{\sqrt{- a^{2} + b^{2}}}{a} \right)}}{f \sqrt{- a^{2} + b^{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*sqrt(b**2)/(b**2*f*tan(e/2 + f*x/2) - b*f*sqrt(b**2)), Eq(a, -sqrt(b**2))), (-2*sqrt(b**2)/(b**2*f*tan(e/2 + f*x/2) + b*f*sqrt(b**2)), Eq(a, sqrt(b**2))), (log(tan(e/2 + f*x/2))/(b*f), Eq(a, 0)), (x/(a + b*sin(e)), Eq(f, 0)), (log(tan(e/2 + f*x/2) + b/a - sqrt(-a**2 + b**2)/a)/(f*sqrt(-a**2 + b**2)) - log(tan(e/2 + f*x/2) + b/a + sqrt(-a**2 + b**2)/a)/(f*sqrt(-a**2 + b**2)), True))","A",0
703,-1,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))/(c+d*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
704,-1,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))/(c+d*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
705,-1,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))/(c+d*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
706,-1,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**4/(a+b*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
707,-1,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**3/(a+b*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
708,-1,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**2/(a+b*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
709,-1,0,0,0.000000," ","integrate((c+d*sin(f*x+e))/(a+b*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
710,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))**2,x)","\int \frac{1}{\left(a + b \sin{\left(e + f x \right)}\right)^{2}}\, dx"," ",0,"Integral((a + b*sin(e + f*x))**(-2), x)","F",0
711,-1,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))**2/(c+d*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
712,-1,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))**2/(c+d*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
713,-1,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))**2/(c+d*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
714,-1,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**5/(a+b*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
715,-1,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**4/(a+b*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
716,-1,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**3/(a+b*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
717,-1,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**2/(a+b*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
718,-1,0,0,0.000000," ","integrate((c+d*sin(f*x+e))/(a+b*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
719,-1,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
720,-1,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))**3/(c+d*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
721,-1,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))**3/(c+d*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
722,-1,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))**3/(c+d*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
723,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))*(c+d*sin(f*x+e))**(5/2),x)","\int \left(a + b \sin{\left(e + f x \right)}\right) \left(c + d \sin{\left(e + f x \right)}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a + b*sin(e + f*x))*(c + d*sin(e + f*x))**(5/2), x)","F",0
724,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))*(c+d*sin(f*x+e))**(3/2),x)","\int \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 + b*sin(e + f*x))*(c + d*sin(e + f*x))**(3/2), x)","F",0
725,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))*(c+d*sin(f*x+e))**(1/2),x)","\int \left(a + b \sin{\left(e + f x \right)}\right) \sqrt{c + d \sin{\left(e + f x \right)}}\, dx"," ",0,"Integral((a + b*sin(e + f*x))*sqrt(c + d*sin(e + f*x)), x)","F",0
726,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))/(c+d*sin(f*x+e))**(1/2),x)","\int \frac{a + b \sin{\left(e + f x \right)}}{\sqrt{c + d \sin{\left(e + f x \right)}}}\, dx"," ",0,"Integral((a + b*sin(e + f*x))/sqrt(c + d*sin(e + f*x)), x)","F",0
727,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))/(c+d*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
728,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))/(c+d*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
729,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))/(c+d*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
730,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**2*(c+d*sin(f*x+e))**(5/2),x)","\int \left(a + b \sin{\left(e + f x \right)}\right)^{2} \left(c + d \sin{\left(e + f x \right)}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a + b*sin(e + f*x))**2*(c + d*sin(e + f*x))**(5/2), x)","F",0
731,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**2*(c+d*sin(f*x+e))**(3/2),x)","\int \left(a + b \sin{\left(e + f x \right)}\right)^{2} \left(c + d \sin{\left(e + f x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*sin(e + f*x))**2*(c + d*sin(e + f*x))**(3/2), x)","F",0
732,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**2*(c+d*sin(f*x+e))**(1/2),x)","\int \left(a + b \sin{\left(e + f x \right)}\right)^{2} \sqrt{c + d \sin{\left(e + f x \right)}}\, dx"," ",0,"Integral((a + b*sin(e + f*x))**2*sqrt(c + d*sin(e + f*x)), x)","F",0
733,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**2/(c+d*sin(f*x+e))**(1/2),x)","\int \frac{\left(a + b \sin{\left(e + f x \right)}\right)^{2}}{\sqrt{c + d \sin{\left(e + f x \right)}}}\, dx"," ",0,"Integral((a + b*sin(e + f*x))**2/sqrt(c + d*sin(e + f*x)), x)","F",0
734,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**2/(c+d*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
735,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**2/(c+d*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
736,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**2/(c+d*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
737,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**3*(c+d*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
738,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**3*(c+d*sin(f*x+e))**(3/2),x)","\int \left(a + b \sin{\left(e + f x \right)}\right)^{3} \left(c + d \sin{\left(e + f x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*sin(e + f*x))**3*(c + d*sin(e + f*x))**(3/2), x)","F",0
739,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**3*(c+d*sin(f*x+e))**(1/2),x)","\int \left(a + b \sin{\left(e + f x \right)}\right)^{3} \sqrt{c + d \sin{\left(e + f x \right)}}\, dx"," ",0,"Integral((a + b*sin(e + f*x))**3*sqrt(c + d*sin(e + f*x)), x)","F",0
740,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**3/(c+d*sin(f*x+e))**(1/2),x)","\int \frac{\left(a + b \sin{\left(e + f x \right)}\right)^{3}}{\sqrt{c + d \sin{\left(e + f x \right)}}}\, dx"," ",0,"Integral((a + b*sin(e + f*x))**3/sqrt(c + d*sin(e + f*x)), x)","F",0
741,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**3/(c+d*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
742,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**3/(c+d*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
743,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**3/(c+d*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
744,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**3/(c+d*sin(f*x+e))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
745,-1,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**(5/2)/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
746,-1,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**(3/2)/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
747,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**(1/2)/(a+b*sin(f*x+e)),x)","\int \frac{\sqrt{c + d \sin{\left(e + f x \right)}}}{a + b \sin{\left(e + f x \right)}}\, dx"," ",0,"Integral(sqrt(c + d*sin(e + f*x))/(a + b*sin(e + f*x)), x)","F",0
748,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))/(c+d*sin(f*x+e))**(1/2),x)","\int \frac{1}{\left(a + b \sin{\left(e + f x \right)}\right) \sqrt{c + d \sin{\left(e + f x \right)}}}\, dx"," ",0,"Integral(1/((a + b*sin(e + f*x))*sqrt(c + d*sin(e + f*x))), x)","F",0
749,-1,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))/(c+d*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
750,-1,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))/(c+d*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
751,-1,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**(7/2)/(a+b*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
752,-1,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**(5/2)/(a+b*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
753,-1,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**(3/2)/(a+b*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
754,-1,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**(1/2)/(a+b*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
755,-1,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))**2/(c+d*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
756,-1,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))**2/(c+d*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
757,-1,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))**2/(c+d*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
758,-1,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**(9/2)/(a+b*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
759,-1,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**(7/2)/(a+b*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
760,-1,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**(5/2)/(a+b*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
761,-1,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**(3/2)/(a+b*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
762,-1,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**(1/2)/(a+b*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
763,-1,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))**3/(c+d*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
764,-1,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))**3/(c+d*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
765,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**(1/2)*(c+d*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
766,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**(1/2)*(c+d*sin(f*x+e))**(3/2),x)","\int \sqrt{a + b \sin{\left(e + f x \right)}} \left(c + d \sin{\left(e + f x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(sqrt(a + b*sin(e + f*x))*(c + d*sin(e + f*x))**(3/2), x)","F",0
767,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**(1/2)*(c+d*sin(f*x+e))**(1/2),x)","\int \sqrt{a + b \sin{\left(e + f x \right)}} \sqrt{c + d \sin{\left(e + f x \right)}}\, dx"," ",0,"Integral(sqrt(a + b*sin(e + f*x))*sqrt(c + d*sin(e + f*x)), x)","F",0
768,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**(1/2)/(c+d*sin(f*x+e))**(1/2),x)","\int \frac{\sqrt{a + b \sin{\left(e + f x \right)}}}{\sqrt{c + d \sin{\left(e + f x \right)}}}\, dx"," ",0,"Integral(sqrt(a + b*sin(e + f*x))/sqrt(c + d*sin(e + f*x)), x)","F",0
769,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**(1/2)/(c+d*sin(f*x+e))**(3/2),x)","\int \frac{\sqrt{a + b \sin{\left(e + f x \right)}}}{\left(c + d \sin{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(a + b*sin(e + f*x))/(c + d*sin(e + f*x))**(3/2), x)","F",0
770,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**(1/2)/(c+d*sin(f*x+e))**(5/2),x)","\int \frac{\sqrt{a + b \sin{\left(e + f x \right)}}}{\left(c + d \sin{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt(a + b*sin(e + f*x))/(c + d*sin(e + f*x))**(5/2), x)","F",0
771,-1,0,0,0.000000," ","integrate((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
772,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**(3/2)*(c+d*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
773,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**(3/2)*(c+d*sin(f*x+e))**(1/2),x)","\int \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))**(3/2)*sqrt(c + d*sin(e + f*x)), x)","F",0
774,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**(3/2)/(c+d*sin(f*x+e))**(1/2),x)","\int \frac{\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))**(3/2)/sqrt(c + d*sin(e + f*x)), x)","F",0
775,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**(3/2)/(c+d*sin(f*x+e))**(3/2),x)","\int \frac{\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))**(3/2)/(c + d*sin(e + f*x))**(3/2), x)","F",0
776,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**(3/2)/(c+d*sin(f*x+e))**(5/2),x)","\int \frac{\left(a + b \sin{\left(e + f x \right)}\right)^{\frac{3}{2}}}{\left(c + d \sin{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*sin(e + f*x))**(3/2)/(c + d*sin(e + f*x))**(5/2), x)","F",0
777,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**(5/2)*(c+d*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
778,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**(5/2)*(c+d*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
779,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**(5/2)*(c+d*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
780,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**(5/2)/(c+d*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
781,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**(5/2)/(c+d*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
782,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**(5/2)/(c+d*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
783,-1,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**(5/2)/(a+b*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
784,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**(3/2)/(a+b*sin(f*x+e))**(1/2),x)","\int \frac{\left(c + d \sin{\left(e + f x \right)}\right)^{\frac{3}{2}}}{\sqrt{a + b \sin{\left(e + f x \right)}}}\, dx"," ",0,"Integral((c + d*sin(e + f*x))**(3/2)/sqrt(a + b*sin(e + f*x)), x)","F",0
785,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**(1/2)/(a+b*sin(f*x+e))**(1/2),x)","\int \frac{\sqrt{c + d \sin{\left(e + f x \right)}}}{\sqrt{a + b \sin{\left(e + f x \right)}}}\, dx"," ",0,"Integral(sqrt(c + d*sin(e + f*x))/sqrt(a + b*sin(e + f*x)), x)","F",0
786,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))**(1/2)/(c+d*sin(f*x+e))**(1/2),x)","\int \frac{1}{\sqrt{a + b \sin{\left(e + f x \right)}} \sqrt{c + d \sin{\left(e + f x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(a + b*sin(e + f*x))*sqrt(c + d*sin(e + f*x))), x)","F",0
787,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))**(1/2)/(c+d*sin(f*x+e))**(3/2),x)","\int \frac{1}{\sqrt{a + b \sin{\left(e + f x \right)}} \left(c + d \sin{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(sqrt(a + b*sin(e + f*x))*(c + d*sin(e + f*x))**(3/2)), x)","F",0
788,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))**(1/2)/(c+d*sin(f*x+e))**(5/2),x)","\int \frac{1}{\sqrt{a + b \sin{\left(e + f x \right)}} \left(c + d \sin{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(sqrt(a + b*sin(e + f*x))*(c + d*sin(e + f*x))**(5/2)), x)","F",0
789,-1,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**(5/2)/(a+b*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
790,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**(3/2)/(a+b*sin(f*x+e))**(3/2),x)","\int \frac{\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((c + d*sin(e + f*x))**(3/2)/(a + b*sin(e + f*x))**(3/2), x)","F",0
791,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**(1/2)/(a+b*sin(f*x+e))**(3/2),x)","\int \frac{\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(sqrt(c + d*sin(e + f*x))/(a + b*sin(e + f*x))**(3/2), x)","F",0
792,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))**(3/2)/(c+d*sin(f*x+e))**(1/2),x)","\int \frac{1}{\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(1/((a + b*sin(e + f*x))**(3/2)*sqrt(c + d*sin(e + f*x))), x)","F",0
793,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))**(3/2)/(c+d*sin(f*x+e))**(3/2),x)","\int \frac{1}{\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(1/((a + b*sin(e + f*x))**(3/2)*(c + d*sin(e + f*x))**(3/2)), x)","F",0
794,-1,0,0,0.000000," ","integrate(1/(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
795,-1,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**(5/2)/(a+b*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
796,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**(3/2)/(a+b*sin(f*x+e))**(5/2),x)","\int \frac{\left(c + d \sin{\left(e + f x \right)}\right)^{\frac{3}{2}}}{\left(a + b \sin{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((c + d*sin(e + f*x))**(3/2)/(a + b*sin(e + f*x))**(5/2), x)","F",0
797,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**(1/2)/(a+b*sin(f*x+e))**(5/2),x)","\int \frac{\sqrt{c + d \sin{\left(e + f x \right)}}}{\left(a + b \sin{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt(c + d*sin(e + f*x))/(a + b*sin(e + f*x))**(5/2), x)","F",0
798,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))**(5/2)/(c+d*sin(f*x+e))**(1/2),x)","\int \frac{1}{\left(a + b \sin{\left(e + f x \right)}\right)^{\frac{5}{2}} \sqrt{c + d \sin{\left(e + f x \right)}}}\, dx"," ",0,"Integral(1/((a + b*sin(e + f*x))**(5/2)*sqrt(c + d*sin(e + f*x))), x)","F",0
799,-1,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))**(5/2)/(c+d*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
800,-1,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))**(5/2)/(c+d*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
801,-2,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**m*(c+d*sin(f*x+e))**n,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
802,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**m*(c+d*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
803,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**m*(c+d*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
804,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**m,x)","\int \left(a + b \sin{\left(e + f x \right)}\right)^{m}\, dx"," ",0,"Integral((a + b*sin(e + f*x))**m, x)","F",0
805,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**m/(c+d*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
806,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**m/(c+d*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
807,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**m/(c+d*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
808,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**m*(c+d*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
809,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**m*(c+d*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
810,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**m*(c+d*sin(f*x+e))**(1/2),x)","\int \left(a + b \sin{\left(e + f x \right)}\right)^{m} \sqrt{c + d \sin{\left(e + f x \right)}}\, dx"," ",0,"Integral((a + b*sin(e + f*x))**m*sqrt(c + d*sin(e + f*x)), x)","F",0
811,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**m/(c+d*sin(f*x+e))**(1/2),x)","\int \frac{\left(a + b \sin{\left(e + f x \right)}\right)^{m}}{\sqrt{c + d \sin{\left(e + f x \right)}}}\, dx"," ",0,"Integral((a + b*sin(e + f*x))**m/sqrt(c + d*sin(e + f*x)), x)","F",0
812,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**m/(c+d*sin(f*x+e))**(3/2),x)","\int \frac{\left(a + b \sin{\left(e + f x \right)}\right)^{m}}{\left(c + d \sin{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*sin(e + f*x))**m/(c + d*sin(e + f*x))**(3/2), x)","F",0
813,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**m/(c+d*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
814,0,0,0,0.000000," ","integrate((d*csc(f*x+e))**n*(a+a*sin(f*x+e))**3,x)","a^{3} \left(\int \left(d \csc{\left(e + f x \right)}\right)^{n}\, dx + \int 3 \left(d \csc{\left(e + f x \right)}\right)^{n} \sin{\left(e + f x \right)}\, dx + \int 3 \left(d \csc{\left(e + f x \right)}\right)^{n} \sin^{2}{\left(e + f x \right)}\, dx + \int \left(d \csc{\left(e + f x \right)}\right)^{n} \sin^{3}{\left(e + f x \right)}\, dx\right)"," ",0,"a**3*(Integral((d*csc(e + f*x))**n, x) + Integral(3*(d*csc(e + f*x))**n*sin(e + f*x), x) + Integral(3*(d*csc(e + f*x))**n*sin(e + f*x)**2, x) + Integral((d*csc(e + f*x))**n*sin(e + f*x)**3, x))","F",0
815,0,0,0,0.000000," ","integrate((d*csc(f*x+e))**n*(a+a*sin(f*x+e))**2,x)","a^{2} \left(\int \left(d \csc{\left(e + f x \right)}\right)^{n}\, dx + \int 2 \left(d \csc{\left(e + f x \right)}\right)^{n} \sin{\left(e + f x \right)}\, dx + \int \left(d \csc{\left(e + f x \right)}\right)^{n} \sin^{2}{\left(e + f x \right)}\, dx\right)"," ",0,"a**2*(Integral((d*csc(e + f*x))**n, x) + Integral(2*(d*csc(e + f*x))**n*sin(e + f*x), x) + Integral((d*csc(e + f*x))**n*sin(e + f*x)**2, x))","F",0
816,0,0,0,0.000000," ","integrate((d*csc(f*x+e))**n*(a+a*sin(f*x+e)),x)","a \left(\int \left(d \csc{\left(e + f x \right)}\right)^{n}\, dx + \int \left(d \csc{\left(e + f x \right)}\right)^{n} \sin{\left(e + f x \right)}\, dx\right)"," ",0,"a*(Integral((d*csc(e + f*x))**n, x) + Integral((d*csc(e + f*x))**n*sin(e + f*x), x))","F",0
817,0,0,0,0.000000," ","integrate((d*csc(f*x+e))**n/(a+a*sin(f*x+e)),x)","\frac{\int \frac{\left(d \csc{\left(e + f x \right)}\right)^{n}}{\sin{\left(e + f x \right)} + 1}\, dx}{a}"," ",0,"Integral((d*csc(e + f*x))**n/(sin(e + f*x) + 1), x)/a","F",0
818,0,0,0,0.000000," ","integrate((d*csc(f*x+e))**n/(a+a*sin(f*x+e))**2,x)","\frac{\int \frac{\left(d \csc{\left(e + f x \right)}\right)^{n}}{\sin^{2}{\left(e + f x \right)} + 2 \sin{\left(e + f x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral((d*csc(e + f*x))**n/(sin(e + f*x)**2 + 2*sin(e + f*x) + 1), x)/a**2","F",0
819,0,0,0,0.000000," ","integrate((c*(d*sin(f*x+e))**p)**n*(a+a*sin(f*x+e))**m,x)","\int \left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{m} \left(c \left(d \sin{\left(e + f x \right)}\right)^{p}\right)^{n}\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**m*(c*(d*sin(e + f*x))**p)**n, x)","F",0
820,0,0,0,0.000000," ","integrate((c*(d*sin(f*x+e))**p)**n*(a+a*sin(f*x+e))**3,x)","a^{3} \left(\int \left(c \left(d \sin{\left(e + f x \right)}\right)^{p}\right)^{n}\, dx + \int 3 \left(c \left(d \sin{\left(e + f x \right)}\right)^{p}\right)^{n} \sin{\left(e + f x \right)}\, dx + \int 3 \left(c \left(d \sin{\left(e + f x \right)}\right)^{p}\right)^{n} \sin^{2}{\left(e + f x \right)}\, dx + \int \left(c \left(d \sin{\left(e + f x \right)}\right)^{p}\right)^{n} \sin^{3}{\left(e + f x \right)}\, dx\right)"," ",0,"a**3*(Integral((c*(d*sin(e + f*x))**p)**n, x) + Integral(3*(c*(d*sin(e + f*x))**p)**n*sin(e + f*x), x) + Integral(3*(c*(d*sin(e + f*x))**p)**n*sin(e + f*x)**2, x) + Integral((c*(d*sin(e + f*x))**p)**n*sin(e + f*x)**3, x))","F",0
821,0,0,0,0.000000," ","integrate((c*(d*sin(f*x+e))**p)**n*(a+a*sin(f*x+e))**2,x)","a^{2} \left(\int \left(c \left(d \sin{\left(e + f x \right)}\right)^{p}\right)^{n}\, dx + \int 2 \left(c \left(d \sin{\left(e + f x \right)}\right)^{p}\right)^{n} \sin{\left(e + f x \right)}\, dx + \int \left(c \left(d \sin{\left(e + f x \right)}\right)^{p}\right)^{n} \sin^{2}{\left(e + f x \right)}\, dx\right)"," ",0,"a**2*(Integral((c*(d*sin(e + f*x))**p)**n, x) + Integral(2*(c*(d*sin(e + f*x))**p)**n*sin(e + f*x), x) + Integral((c*(d*sin(e + f*x))**p)**n*sin(e + f*x)**2, x))","F",0
822,0,0,0,0.000000," ","integrate((c*(d*sin(f*x+e))**p)**n*(a+a*sin(f*x+e)),x)","a \left(\int \left(c \left(d \sin{\left(e + f x \right)}\right)^{p}\right)^{n}\, dx + \int \left(c \left(d \sin{\left(e + f x \right)}\right)^{p}\right)^{n} \sin{\left(e + f x \right)}\, dx\right)"," ",0,"a*(Integral((c*(d*sin(e + f*x))**p)**n, x) + Integral((c*(d*sin(e + f*x))**p)**n*sin(e + f*x), x))","F",0
823,0,0,0,0.000000," ","integrate((c*(d*sin(f*x+e))**p)**n/(a+a*sin(f*x+e)),x)","\frac{\int \frac{\left(c \left(d \sin{\left(e + f x \right)}\right)^{p}\right)^{n}}{\sin{\left(e + f x \right)} + 1}\, dx}{a}"," ",0,"Integral((c*(d*sin(e + f*x))**p)**n/(sin(e + f*x) + 1), x)/a","F",0
824,0,0,0,0.000000," ","integrate((c*(d*sin(f*x+e))**p)**n/(a+a*sin(f*x+e))**2,x)","\frac{\int \frac{\left(c \left(d \sin{\left(e + f x \right)}\right)^{p}\right)^{n}}{\sin^{2}{\left(e + f x \right)} + 2 \sin{\left(e + f x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral((c*(d*sin(e + f*x))**p)**n/(sin(e + f*x)**2 + 2*sin(e + f*x) + 1), x)/a**2","F",0
825,0,0,0,0.000000," ","integrate((d*csc(f*x+e))**n*(a+b*sin(f*x+e))**3,x)","\int \left(d \csc{\left(e + f x \right)}\right)^{n} \left(a + b \sin{\left(e + f x \right)}\right)^{3}\, dx"," ",0,"Integral((d*csc(e + f*x))**n*(a + b*sin(e + f*x))**3, x)","F",0
826,0,0,0,0.000000," ","integrate((d*csc(f*x+e))**n*(a+b*sin(f*x+e))**2,x)","\int \left(d \csc{\left(e + f x \right)}\right)^{n} \left(a + b \sin{\left(e + f x \right)}\right)^{2}\, dx"," ",0,"Integral((d*csc(e + f*x))**n*(a + b*sin(e + f*x))**2, x)","F",0
827,0,0,0,0.000000," ","integrate((d*csc(f*x+e))**n*(a+b*sin(f*x+e)),x)","\int \left(d \csc{\left(e + f x \right)}\right)^{n} \left(a + b \sin{\left(e + f x \right)}\right)\, dx"," ",0,"Integral((d*csc(e + f*x))**n*(a + b*sin(e + f*x)), x)","F",0
828,0,0,0,0.000000," ","integrate((d*csc(f*x+e))**n/(a+b*sin(f*x+e)),x)","\int \frac{\left(d \csc{\left(e + f x \right)}\right)^{n}}{a + b \sin{\left(e + f x \right)}}\, dx"," ",0,"Integral((d*csc(e + f*x))**n/(a + b*sin(e + f*x)), x)","F",0
829,0,0,0,0.000000," ","integrate((d*csc(f*x+e))**n/(a+b*sin(f*x+e))**2,x)","\int \frac{\left(d \csc{\left(e + f x \right)}\right)^{n}}{\left(a + b \sin{\left(e + f x \right)}\right)^{2}}\, dx"," ",0,"Integral((d*csc(e + f*x))**n/(a + b*sin(e + f*x))**2, x)","F",0
830,0,0,0,0.000000," ","integrate((d*csc(f*x+e))**n/(a+b*sin(f*x+e))**3,x)","\int \frac{\left(d \csc{\left(e + f x \right)}\right)^{n}}{\left(a + b \sin{\left(e + f x \right)}\right)^{3}}\, dx"," ",0,"Integral((d*csc(e + f*x))**n/(a + b*sin(e + f*x))**3, x)","F",0
831,0,0,0,0.000000," ","integrate((c*(d*sin(f*x+e))**p)**n*(a+b*sin(f*x+e))**m,x)","\int \left(c \left(d \sin{\left(e + f x \right)}\right)^{p}\right)^{n} \left(a + b \sin{\left(e + f x \right)}\right)^{m}\, dx"," ",0,"Integral((c*(d*sin(e + f*x))**p)**n*(a + b*sin(e + f*x))**m, x)","F",0
832,0,0,0,0.000000," ","integrate((c*(d*sin(f*x+e))**p)**n*(a+b*sin(f*x+e))**3,x)","\int \left(c \left(d \sin{\left(e + f x \right)}\right)^{p}\right)^{n} \left(a + b \sin{\left(e + f x \right)}\right)^{3}\, dx"," ",0,"Integral((c*(d*sin(e + f*x))**p)**n*(a + b*sin(e + f*x))**3, x)","F",0
833,0,0,0,0.000000," ","integrate((c*(d*sin(f*x+e))**p)**n*(a+b*sin(f*x+e))**2,x)","\int \left(c \left(d \sin{\left(e + f x \right)}\right)^{p}\right)^{n} \left(a + b \sin{\left(e + f x \right)}\right)^{2}\, dx"," ",0,"Integral((c*(d*sin(e + f*x))**p)**n*(a + b*sin(e + f*x))**2, x)","F",0
834,0,0,0,0.000000," ","integrate((c*(d*sin(f*x+e))**p)**n*(a+b*sin(f*x+e)),x)","\int \left(c \left(d \sin{\left(e + f x \right)}\right)^{p}\right)^{n} \left(a + b \sin{\left(e + f x \right)}\right)\, dx"," ",0,"Integral((c*(d*sin(e + f*x))**p)**n*(a + b*sin(e + f*x)), x)","F",0
835,0,0,0,0.000000," ","integrate((c*(d*sin(f*x+e))**p)**n/(a+b*sin(f*x+e)),x)","\int \frac{\left(c \left(d \sin{\left(e + f x \right)}\right)^{p}\right)^{n}}{a + b \sin{\left(e + f x \right)}}\, dx"," ",0,"Integral((c*(d*sin(e + f*x))**p)**n/(a + b*sin(e + f*x)), x)","F",0
836,0,0,0,0.000000," ","integrate((c*(d*sin(f*x+e))**p)**n/(a+b*sin(f*x+e))**2,x)","\int \frac{\left(c \left(d \sin{\left(e + f x \right)}\right)^{p}\right)^{n}}{\left(a + b \sin{\left(e + f x \right)}\right)^{2}}\, dx"," ",0,"Integral((c*(d*sin(e + f*x))**p)**n/(a + b*sin(e + f*x))**2, x)","F",0
837,0,0,0,0.000000," ","integrate((c*(d*sin(f*x+e))**p)**n/(a+b*sin(f*x+e))**3,x)","\int \frac{\left(c \left(d \sin{\left(e + f x \right)}\right)^{p}\right)^{n}}{\left(a + b \sin{\left(e + f x \right)}\right)^{3}}\, dx"," ",0,"Integral((c*(d*sin(e + f*x))**p)**n/(a + b*sin(e + f*x))**3, x)","F",0
